Chapter 1 CHAIN, COMPASS AND PLANE TABLE SURVEYING Structure of this unit CHAIN, COMPASS, PLANE TABLE SURVEYING Learning Objectives 1. CHAIN 2. field and office work 3.
Ranging and Chaining
4. Reciprocal ranging 5. Well-conditioned triangles. 6. COMPASS 7. Prismatic compass 8. Surveyor’s compass 9. Bearing systems and conversions 10. Local attraction – Magnetic declination dip 11. Traversing – Plotting – Adjustment of error. 12. PLANE TABLE SURVEYING : Plane table instruments and accessories – merits and demerits – methods – Radiation- Intersection – Resection – Traversing.
1.1 Surveying Surveying techniques have existed throughout much of recorded history. Under the Romans, land surveyors were established as a profession, and they established the basic measurements under which the Roman Empire was divided, such as a tax register of conquered
In the 18th century in Europe triangulation was used to build a hierarchy of networks to allow point positioning within a country. Highest in the hierarchy were triangulation networks. These were densified into networks of traverses (polygons), into which local mapping surveying measurements, usually with measuring tape, corner prism and the familiar red and white poles, are tied. Surveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them, commonly practiced by licensed surveyors, and members of various building professions. These points are usually on the surface of the Earth, and they are often used to establish land maps and boundaries for ownership, locations (building corners, surface location of subsurface features) or other governmentally required or civil law purposes (property sales). To accomplish their objective, surveyors use of mathematics (geometry and trigonometry), physics, engineering and law.
An alternative definition, from the American Congress on Surveying and Mapping (ACSM), is the science and art of making all essential measurements to determine the relative position of points or physical and cultural details above, on, or beneath the surface of the Earth, and to depict them in a usable form, or to establish the position of points or details. Furthermore, as alluded to above, a particular type of surveying known as "land surveying" (also per ACSM) is the detailed study or inspection, as by gathering information through observations, measurements in the field, questionnaires, or research of legal instruments, and data analysis in the support of planning, designing, and establishing of property boundaries. It involves the reestablishment ofcadastral surveys and land boundaries based on documents of record and historical evidence, as well as certifying surveys (as required by statute or local ordinance) of subdivision plats or maps, registered land surveys, judicial surveys, and space delineation. Land surveying can include associated services such as mapping and related data accumulation, construction layout surveys, precision measurements of length, angle, elevation, area, and volume, as well as horizontal and vertical control surveys, and the analysis and utilization of land survey data. Surveyors use various tools to do their work successfully and accurately, such as total stations, robotic total stations, GPS receivers, prisms, 3D scanners, radio communicators, handheld tablets, digital levels, and surveying software. Surveying has been an essential element in the development of the human environment since the beginning of recorded history (about 6,000 years ago). It is required in the planning and execution of nearly every form of construction. Its most familiar modern uses are in the fields
of transport, building and construction, communications, mapping, and the definition of legal boundaries for land ownership. History of surveying Surveying techniques have existed throughout much of recorded history. In ancient Egypt, when the Nile River overflowed its banks and washed outfarm boundaries, boundaries were reestablished by a rope stretcher, or surveyor, through the application of simple geometry. The nearly perfect squareness and north-south orientation of the Great Pyramid of Giza, built c. 2700 BC, affirm the Egyptians' command of surveying. A brief history of surveying: • • •
The Egyptian land register (3000 BC). A recent reassessment of Stonehenge (c. 2500 BC) suggests that the monument was set out by prehistoric surveyors using peg and rope geometry. The Groma surveying instrument originated in Mesopotamia (early 1st millennium BC). •
Under the Romans, land surveyors were established as a profession, and they established the basic measurements under which the Roman Empire was divided, such as a tax register of conquered lands (300 AD).
The rise of the Caliphate led to extensive surveying throughout the Arab Empire. Arabic surveyors invented a variety of specialized instruments for surveying, including
Instruments for accurate leveling: A wooden board with a plumb line and two hooks, an equilateral triangle with a plumb line and two hooks, and a reed level.
A rotating alhidade, used for accurate alignment.
A surveying astrolabe, used for alignment, measuring angles, triangulation, finding the width of a river, and the distance between two points separated by an impassable obstruction. In England, The Domesday Book by William the Conqueror (1086) •
Covered all England
Contained names of the land owners, area, land quality, and specific information of the area's content and inhabitants.
Did not include maps showing exact locations.
In the 18th century in Europe triangulation was used to build a hierarchy of networks to allow point positioning within a country. Highest in the hierarchy were triangulation networks. These were densified into networks of traverses (polygons), into which local mapping surveying measurements, usually with measuring tape, corner prism and the familiar red and white poles, are tied. For example, in the late 1780s, a team from the Ordnance Survey of Great Britain, originally under General William Roy began the Principal Triangulation of Britain using the specially built Ramsden theodolite. Large scale surveys are known as geodetic surveys.
Continental Europe's cadastre was created in 1808 •
Founded by Napoleon I (Bonaparte)
Contained numbers of the parcels of land (or just land), land usage, names etc., and value of the land
100 million parcels of land, triangle survey, measurable survey, map scale: 1:2500 and 1:1250
spread fast around Europe, but faced problems especially in Mediterranean countries, Balkan, and Eastern Europe due to cadastre upkeep costs and troubles.
A cadastre loses its value if register and maps are not constantly updated. Because of the fundamental value of land and real estate to the local and global economy, land surveying was one of the first professions to require Professional Licensure. In many jurisdictions, the land surveyors license was the first Professional Licensure issued by the state, province, or federal government.
1.1.1 Surveying techniques Historically, distances were measured using a variety of means, such as with chains having links of a known length, for instance a Gunter's chain, or measuring tapes made of steel or invar. To measure horizontal distances, these chains or tapes were pulled taut according to temperature, to reduce sagging and slack. Additionally, attempts to hold the measuring instrument level would be made. In instances of measuring up a slope, the surveyor might have to "break" (break chain) the measurement- use an increment less than the total length of the chain. Historically, horizontal angles were measured using a compass, which would provide a magnetic bearing, from which deflections could be measured. This type of instrument was later improved, with more carefully scribed discs providing better angular resolution, as well as through mounting telescopes with reticles for more-precise sighting atop the disc (see theodolite). Additionally, levels and calibrated circles allowing measurement of vertical angles were added, along with verniers for measurement to a fraction of a degree—such as with a turn-of-thecentury transit. The simplest method for measuring height is with an altimeter – basically a barometer – using air pressure as an indication of height. But surveying requires greater precision. A variety of means, such as precise levels (also known as differential leveling), have been developed to do this. With precise leveling, a series of measurements between two points are taken using an instrument and a measuring rod. Differentials in height between the measurements are added and subtracted in a series to derive the net difference in elevation between the two endpoints of the series. With the advent of the Global Positioning System (GPS), elevation can also be derived with sophisticated satellite receivers, but usually with somewhat less accuracy than with traditional precise leveling. However, the accuracies may be similar if the traditional leveling would have to be run over a long distance. Triangulation is another method of horizontal location made almost obsolete by GPS. With the triangulation method, distances, elevations and directions between objects at great distance from one another can be determined. Since the early days of surveying, this was the primary method
of determining accurate positions of objects for topographic maps of large areas. A surveyor first needs to know the horizontal distance between two of the objects. Then the height, distances and angular position of other objects can be derived, as long as they are visible from one of the original objects. High-accuracy transits or theodolites were used for this work, and angles between objects were measured repeatedly for increased accuracy. See alsoTriangulation in three dimensions. Turning is a term used when referring to moving the level to take an elevation shot in a different location. When land surveying, there may be trees or other obstructions blocking the view from the level gun to the level rod. In order to "turn" the level gun, one must first take a shot on the rod from the current location and record the elevation. Keeping the level rod in exactly the same location and elevation, one may move the level gun to a different location where the level rod is still visible. Record the new elevation seen from the new location of the level rod and use the difference in elevations to find the new elevation of the level gun. Turning is not only used when there are obstructions in the way, but also when drastically changing elevations. You can turn up or down in elevation but the gun must always be at a higher elevation than the base of the rod. A level rod can usually be raised up to 25 feet high, which enables the gun to be set much higher. However, if the gun is lower than the base of the rod, you will not be able to take a shot because the rod cannot be lowered beyond the ground elevation. Surveying equipment As late as the 1990s, the basic tools used in planar surveying were a tape measure for determining shorter distances, a level to determine height or elevation differences, and a theodolite, set on a tripod, to measure angles (horizontal and vertical), combined with the process of triangulation. Starting from a position with known location and elevation, the distance and angles to the unknown point are measured. A more modern instrument is a total station, which is a theodolite with an electronic distance measurement device (EDM). A total station can also be used for leveling when set to the horizontal plane. Since their introduction, total stations have made the technological shift from being optical-mechanical devices to being fully electronic. Modern top-of-the-line total stations no longer require a reflector or prism (used to return the light pulses used for distancing) to return distance measurements, are fully robotic, and can even e-mail point data to the office computer and connect to satellite positioning systems, such as a Global Positioning System. Though Real Time Kinematic GPS systems have increased the speed and precision of surveying, they are still horizontally accurate to only about 20 mm and vertically accurate to about 30–40 mm. Total stations are still used widely, along with other types of surveying instruments, however, because GPS systems do not work well in areas with dense tree cover or constructions. Oneperson robotic-guided total stations allow surveyors to gather precise measurements without extra workers to look through and turn the telescope or record data. A faster but expensive way to measure large areas (not details, and no obstacles) is with a helicopter, equipped with a laser scanner, combined with a GPS to determine the position and elevation of the helicopter. To increase precision, surveyors place beacons on the ground (about 20 km (12 mi) apart). This method reaches precisions between 5–40 cm (depending on flight height).
1.1.2 Types of surveys and applicability ALTA/ACSM Land Title Survey: a surveying standard jointly proposed by the American Land Title Association and the American Congress on Surveying and Mapping that incorporates elements of the boundary survey, mortgage survey, and topographic survey. • •
• • •
Archaeological survey: used to accurately assess the relationship of archaeological sites in a landscape or to accurately record finds on an archaeological site. As-built survey: a survey carried out during or immediately after a construction project for record, completion evaluation and payment purposes. An as-built survey also known as a 'works as executed survey' documents the location of the recently constructed elements that are subject to completion evaluation. As built surveys are typically presented in red or redline and overlayed over existing design plans for direct comparison with design information. Bathymetric survey: a survey carried out to map the topography and features of the bed of an ocean, lake, river or other body of water. Boundary survey: a survey that establishes boundaries of a parcel using its legal description, which typically involves the setting or restoration of monuments or markers at the corners or along the lines of the parcel, often in the form of iron rods, pipes, or concrete monuments in the ground, or nails set in concrete or asphalt. Deformation survey: a survey to determine if a structure or object is changing shape or moving. The three-dimensional positions of specific points on an object are determined, a period of time is allowed to pass, these positions are then re-measured and calculated, and a comparison between the two sets of positions is made. Engineering surveys: those surveys associated with the engineering design (topographic, layout and as-built) often requiring geodetic computations beyond normal civil engineering practice. Foundation survey: a survey done to collect the positional data on a foundation that has been poured and is cured. This is done to ensure that the foundation was constructed in the location, and at the elevation, authorized in the plot plan, site plan, or subdivision plan. Geological survey: generic term for a survey conducted for the purpose of recording the geologically significant features of the area under investigation. . Hydrographic survey: a survey conducted with the purpose of mapping the coastline and seabed for navigation, engineering, or resource management purposes. Measured survey : a building survey to produce plans of the building. such a survey may be conducted before renovation works, for commercial purpose, or at end of the construction process "as built survey" Mortgage survey or physical survey: a simple survey that delineates land boundaries and building locations. In many places a mortgage survey is required by lending institutions as a precondition for a mortgage loan. Soil survey, or soil mapping, is the process of determining the soil types or other properties of the soil cover over a landscape, and mapping them for others to understand and use.
Structural survey: a detailed inspection to report upon the physical condition and structural stability of a building or other structure and to highlight any work needed to maintain it in good repair. • Tape survey: this type of survey is the most basic and inexpensive type of land survey. Popular in the middle part of the 20th century, tape surveys while being accurate for distance lack substantially in their accuracy of measuring angle and bearing standards that are practiced by professional land surveyors. • Topographic survey: a survey that measures the elevation of points on a particular piece of land, and presents them as contour lines on a plot. Surveying as a career •
The basic principles of surveying have changed little over the ages, but the tools used by surveyors have evolved tremendously. Engineering, especiallycivil engineering, depends heavily on surveyors. Whenever there are roads, railways, reservoir, dams, pipeline transports retaining walls, bridges or residential areas to be built, surveyors are involved. They establish the boundaries of legal descriptions and the boundaries of various lines of political divisions. They also provide advice and data forgeographical information systems (GIS), computer databases that contain data on land features and boundaries. Surveyors must have a thorough knowledge of algebra, basic calculus, geometry, and trigonometry. They must also know the laws that deal with surveys, property, and contracts. In addition, they must be able to use delicate instruments with accuracy and precision. In the United States, surveyors and civil engineers use units of feet wherein a survey foot is broken down into 10ths and 100ths. Many deed descriptions requiring distance calls are often expressed using these units (125.25 ft). On the subject of accuracy, surveyors are often held to a standard of one one-hundredth of a foot; about 1/8 inch. Calculation and mapping tolerances are much smaller wherein achieving near-perfect closures are desired. Though tolerances such as this will vary from project to project, in the field and day to day usage beyond a 100th of a foot is often impractical. Licensing In most of the United States, surveying is recognized as a distinct profession apart from engineering. Licensing requirements vary by state, but they generally have components of education, experience and examinations. In the past, experience gained through an apprenticeship, together with passing a series of state-administered examinations, was required to attain licensure. Now, most states insist upon basic qualification of a degree in surveying, plus experience and examination requirements. The licensing process typically follows two phases. First, upon graduation, the candidate may be eligible to take the Fundamentals of Surveying (FS) exam, to be certified upon passing and meeting all other requirements as a surveying intern (SI),(formerly surveyor in training (SIT)). Upon being certified as an SI, the candidate then needs to gain additional experience to become eligible for the second phase. That typically consists of the Principles and Practice of Land Surveying (PS) exam along with a state-specific examination.
Licensed surveyors usually denote themselves with the letters P.L.S. (professional land surveyor), P.S. (professional surveyor), L.S. (land surveyor), R.L.S. (registered land surveyor), R.P.L.S. (Registered Professional Land Surveyor), or P.S.M. (professional surveyor and mapper) following their names, depending upon the dictates of their particular jurisdiction of registration. In Canada, land Surveyors are registered to work in their respective province. The designation for a land surveyor breaks down by province, but follows the rule whereby the first letter indicates the province, followed by L.S. There is also a designation as a C.L.S. or Canada lands surveyor, who has the authority to work on Canada Lands, which include Indian Reserves, National Parks, the three territories and offshore lands. In many Commonwealth countries, the term Chartered Land Surveyor is used for someone holding a professional license to conduct surveys. A licensed land surveyor is typically required to sign and seal all plans, the format of which is dictated by their state jurisdiction, which shows their name and registration number. In many states, when setting boundary corners land surveyors are also required to place survey monuments bearing their registration numbers, typically in the form of capped iron rods, concrete monuments, or nails with washers. Building surveying Building surveying emerged in the 1970s as a profession in the United Kingdom by a group of technically minded general practice surveyors. Building surveying is a recognised profession in Britain, Ireland, Australia and Hong Kong. In Australia in particular, due to risk mitigation and limitation factors, the employment of surveyors at all levels of the construction industry is widespread. There are still many countries where it is not widely recognized as a profession. Building Surveyors are trained to some extent in all aspects of property but with specific training in Building Pathology, as such they have a wide understanding of the end implications of decisions taken by more specific professions and trades during the realisation process, thus making them suitable for employment as Project and Property Managers on the client side (i.e. managing external contractors). Services that building surveyors undertake are broad but can include: • • • • • • • • • •
Construction design and building works Project management and monitoring Property Legislation advice Insurance assessment and claims assistance Defect investigation and maintenance advice Building surveys and measured surveys Handling planning applications Building inspection to ensure compliance with building regulations Pre-acquisition surveys Negotiating dilapidations claims
Building surveyors also advise on many aspects of construction including:
• • • • • • •
design cost maintenance sustainability repair refurbishment restoration and preservation of buildings and monuments.
Clients of a building surveyor can be the government agencies, businesses and individuals. Surveyors work closely with architects, planners, quantity surveyors, engineers, homeowners and tenants groups. A building surveyor may be called to act as an expert witness. It is usual for building surveyors to earn a university degree before undertaking structured training to become a member of a professional organisation. With the enlargement of the European community, the profession of the building surveyor is becoming more widely known in other European states, particularly France, where many English-speaking people buy second homes. Lidar Surveying – Three-dimensional laser scanning provides high definition surveying for architectural, as-built, and engineering surveys. Recent technological advances make it the most cost-effective and time-sensitive solution for providing the highest level of detail available for interior and exterior building work. Land surveyor One of the primary roles of the land surveyor is to determine the boundary of real property on the ground. That boundary has already been established and described in legal documents and official plans and maps prepared by attorneys, engineers, and other land surveyors. The corners of the property will either have been monumented by a prior surveyor, or monumented by the surveyor hired to perform a survey of a new boundary which has been agreed upon by adjoining land owners. Monuments are categorized into two groups which are known as natural and artificial. Natural monuments are things such as trees, large stones and other substantial, naturally occurring objects that were in place before the survey was made. An artificial monument is anything within the regulations that are usually placed at corner points by landowners, surveyors, engineers and others. They may be referred to as iron pins or pipes, stakes, trees, concrete monuments or whatever the surveyor decides to use at the time, within the regulations for the area. The courts have held that natural monuments control over artificial monuments because they are more certain in identification and less likely to be disturbed. Over time, construction and maintenance of roads and many other acts of man, along with acts of nature such as earthquakes, movement of water, and tectonic shift can obliterate or damage the monumented locations of land boundaries. The land surveyor is often compelled to consider other evidence such as fence locations, wood lines, monuments on neighboring properties and recollections of people. This other evidence is known as Extrinsic Evidence and is a fairly common principle. Extrinsic evidence is defined as evidence outside the writings, in this case the deed. Extrinsic evidence is held to be synonymous with evidence from another source.
Today's land surveyor sets monumentation at actual physical points on the ground that define angle points of boundary lines that divide neighboring parcels. These monuments are most often 1/2" or 5/8" iron rebar rods or pipes placed at 18" minimum depth, but varies state by state. The more recent rods or pipes may have an affixed plastic cap over the top bearing the responsible surveyors' name and license number. Older monuments may exist such as old pipes, gun barrels, axles, mounds of stone, whiskey bottles, or even wooden stakes. In addition to rods and pipes, surveyors might use 4x4" concrete posts at corners of large parcels or anywhere that would require more stability (e.g. beach sand). They place them three feet deep. In places where there is asphalt or concrete, it is common to place nails or aluminum alloy caps to re-establish boundary corners. Marks are meant to be durable, stable, and as "permanent" as possible. The aim is to provide sufficient marks so some marks will remain for future re-establishment of boundaries. The material and marking used on monuments placed to mark boundary corners are often subject to state laws. Many states have laws that protect existing monuments and can have civil penalties if disturbed or destroyed. Cadastral land surveyors are licensed by governments. In the United States, cadastral surveys are typically conducted by the federal government, specifically through the Cadastral Surveys branch of the Bureau of Land Management (BLM), formerly the General Land Office(GLO). They consult with USFS, Park Service, Corps of Engineers, BIA, Fish and Wildlife Service, Bureau of Reclamation, etc. In states that have been organized per the Public Land Survey System (PLSS), surveyors carry out BLM Cadastral Surveys in accordance with that system. A common use of a survey is to determine a legal property boundary. The first stage in such a survey, known as a resurvey, is to obtain copies of the deed description and all other available documents from the owner. The deed description is that of the deed and not a tax statement or other incomplete document. The surveyor should then obtain copies of deed descriptions and maps of the adjoining properties, any records from the municipality or county, utility maps and any records of surveys. Depending on which region the survey is located in some or most of this information may not be available or even exist. Whether the information exists or not a thorough search should be conducted so that no records are neglected. Copies of deeds usually can be located in the county recorder's office and maps or plats can usually be found at the county recorder or surveyor's office. These arrangements will vary state to state and survey system to survey system so some familiarity maybe needed. When all the records are assembled, the surveyor examines the documents for errors, such as closure errors. When a metes and bounds description is involved, the seniority of the deeds must be determined. The title abstract usually gives the order of seniority for the deeds related to the tract being surveyed and should be used if available. After this data is gathered and analyzed the field survey may commence. The initial survey operations should be concentrated on locating monuments. In urban regions or a city, monuments should be sought initially but in the absence of monuments property corners marked by iron pins, metal survey markers, iron pipes and other features that may establish a line of possession should be located. When the approximate positions for the boundaries of the property have been located a traverse is run around the property. While the control traverse is being run, ties should be measured and all details relevant to the boundaries should be acquired. This includes but is not limited to locating the property corners, monuments, fences, hedge rows, walls, walks and all buildings on the lot. The Surveyor then takes this data collected and
compares it to the records that were received. When a solution is reached the property corners that are chosen as those that best fit all the data are coordinated and ties by direction and distance are computed from the nearest traverse point. Once this has been established the features on the lot can be drawn, dimensions can be shown from these features to the boundary line and a map or plat is prepared for the client. The art of surveying Many properties have considerable problems with regards to improper bounding, miscalculations in past surveys, titles, easements, and wildlife crossings. Also many properties are created from multiple divisions of a larger piece over the course of years, and with every additional division the risk of miscalculation increases. The result can be abutting properties not coinciding with adjacent parcels, resulting in hiatuses (gaps) and overlaps. Many times a surveyor must solve a puzzle using pieces that do not exactly fit together. In these cases, the solution is based upon the surveyor's research and interpretation, along with established procedures for resolving discrepancies. This essentially is a process of continual error correction and update, where official recordation documents countermand the previous and sometime erroneous survey documents recorded by older monuments and older survey methods.
1.2 Establishing the framework Most surveying frameworks are erected by measuring the angles and the lengths of the sides of a chain of triangles connecting the points fixed by global positioning. The locations of ground features are then determined in relation to these triangles by less accurate and therefore cheaper methods. Establishing the framework ensures that detail surveys conducted at different times or by different surveyors fit together without overlaps or gaps. For centuries the corners of these triangles have been located on hilltops, each visible from at least two others, at which the angles between the lines joining them are measured; this process is called triangulation. The lengths of one or two of these lines, called bases, are measured with great care; all the other lengths are derived by trigonometric calculations from them and the angles. Rapid checks on the accuracy are provided by measuring all three angles of each triangle, which must add up to 180 degrees. In small flat areas, working at large scales, it may be easier to measure the lengths of all the sides, using a tape or a chain, rather than the angles between them; this procedure, called trilateration, was impractical over large or hilly areas until the invention of electromagnetic distance measurement (EDM) in the mid-20th century. This procedure has made it possible to measure distances as accurately and easily as angles, by electronically timing the passage of radiation over the distance to be measured; microwaves, which penetrate atmospheric haze, are used for long distances and light or infrared radiation for short ones. In the devices used for EDM, the radiation is either light (generated by a laser or an electric lamp) or an ultrahighfrequency radio beam. The light beam requires a clear line of sight; the radio beam can penetrate fog, haze, heavy rain, dust, sandstorms, and some foliage. Both types have a transmitter-receiver
at one survey station. At the remote station the light type contains a set of corner mirrors; the high-frequency type incorporates a retransmitter (requiring an operator) identical to the transmitter-receiver at the original station. A corner mirror has the shape of the inside of a corner of a cube; it returns light toward the source from whatever angle it is received, within reasonable limits. A retransmitter must be aimed at the transmitter-receiver. In both types of instrument, the distance is determined by the length of time it takes the radio or light beam to travel to the target and back. The elapsed time is determined by the shift in phase of a modulating signal superimposed on the carrier beam. Electronic circuitry detects this phase shift and converts it to units of time; the use of more than one modulating frequency eliminates ambiguities that could arise if only a single frequency had been employed. EDM has greatly simplified an alternative technique, called traversing, for establishing a framework. In traversing, the surveyor measures a succession of distances and the angles between them, usually along a traveled route or a stream. Before EDM was available, traversing was used only in flat or forested areas where triangulation was impossible. Measuring all the distances by tape or chain was tedious and slow, particularly if great accuracy was required, and no check was obtainable until the traverse closed, either on itself or between two points already fixed by triangulation or by astronomical observations.
surveying, a means of making relatively large-scale, accurate measurements of the Earth’s surfaces. It includes the determination of the measurement data, the reduction and interpretation of the data to usable form, and, conversely, the establishment of relative position and size according to given measurement requirements. Thus, surveying has two similar but opposite functions: (1) the determination of existing relative horizontal and vertical position, such as that used for the process of mapping, and (2) the establishment of marks to control construction or to indicate land boundaries. Surveying has been an essential element in the development of the human environment for so many centuries that its importance is often forgotten. It is an imperative requirement in the planning and execution of nearly every form of construction. Surveying was essential at the dawn of history, and some of the most significant scientific discoveries could never have been implemented were it not for the contribution of surveying. Its principal modern uses are in the fields of transportation, building, apportionment of land, and communications. Except for minor details of technique and the use of one or two minor hand-held instruments, surveying is much the same throughout the world. The methods are a reflection of the instruments, manufactured chiefly in Switzerland, Austria, Great Britain, the United States, Japan, and Germany. Instruments made in Japan are similar to those made in the West.
History It is quite probable that surveying had its origin in ancient Egypt. The Great Pyramid of Khufu at Gizawas built about 2700 BCE, 755 feet (230 metres) long and 481 feet (147 metres) high. Its nearly perfect squareness and north–south orientation affirm the ancient Egyptians’ command of surveying. Evidence of some form of boundary surveying as early as 1400 BCE has been found in the fertile valleys and plains of the Tigris, Euphrates, and Nile rivers. Clay tablets of the Sumerians show records of land measurement and plans of cities and nearby agricultural areas. Boundary stones marking land plots have been preserved. There is a representation of land measurement on the wall of a tomb at Thebes(1400 BCE) showing head and rear chainmen measuring a grainfield with what appears to be a rope with knots or marks at uniform intervals. Other persons are shown. Two are of high estate, according to their clothing, probably a land overseer and an inspector of boundary stones. There is some evidence that, in addition to a marked cord, wooden rods were used by the Egyptians for distance measurement. There is no record of any angle-measuring instruments of that time, but there was a level consisting of a vertical wooden A-frame with a plumb bob supported at the peak of the A so that its cord hung past an indicator, or index, on the horizontal bar. The index could be properly placed by standing the device on two supports at approximately the same elevation, marking the position of the cord, reversing the A, and making a similar mark. Halfway between the two marks would be the correct place for the index. Thus, with their simple devices, the ancient Egyptians were able to measure land areas, replace property corners lost when the Nile covered the markers with silt during floods, and build the huge pyramids to exact dimensions. The Greeks used a form of log line for recording the distances run from point to point along the coast while making their slow voyages from the Indus to the Persian Gulf about 325 BCE. The magneticcompass was brought to the West by Arab traders in the 12th century CE. The astrolabe was introduced by the Greeks in the 2nd century BCE. An instrument for measuring the altitudes of stars, or their angle of elevation above the horizon, took the form of a graduated arc suspended from a hand-held cord. A pivoted pointer that moved over the graduations was pointed at the star. The instrument was not used for nautical surveying for several centuries, remaining a scientific aid only. The Greeks also possibly originated the use of the groma, a device used to establish right angles, butRoman surveyors made it a standard tool. It was made of a horizontal wooden cross pivoted at the middle and supported from above. From the end of each of the four arms hung a plumb bob. By sighting along each pair of plumb bob cords in turn, the right angle could be established. The device could be adjusted to a precise right angle by observing the same angle after turning the device approximately 90°. By shifting one of the cords to take up half the error, a perfect right angle would result.
About 15 BCE the Roman architect and engineer Vitruvius mounted a large wheel of known circumference in a small frame, in much the same fashion as the wheel is mounted on a wheelbarrow; when it was pushed along the ground by hand it automatically dropped a pebble into a container at each revolution, giving a measure of the distance traveled. It was, in effect, the first odometer. The water level consisted of either a trough or a tube turned upward at the ends and filled with water. At each end there was a sight made of crossed horizontal and vertical slits. When these were lined up just above the water level, the sights determined a level line accurate enough to establish the grades of the Roman aqueducts. In laying out their great road system, the Romans are said to have used theplane table. It consists of a drawing board mounted on a tripod or other stable support and of a straightedge—usually with sights for accurate aim (the alidade) to the objects to be mapped—along which lines are drawn. It was the first device capable of recording or establishing angles. Later adaptations of the plane table had magnetic compasses attached. Plane tables were in use in Europe in the 16th century, and the principle of graphic triangulation and intersection was practiced by surveyors. In 1615 Willebrord Snell, a Dutch mathematician, measured an arc of meridian by instrumental triangulation. In 1620 the English mathematician Edmund Gunterdeveloped a surveying chain, which was superseded only by the steel tape beginning in the late 19th century. The study of astronomy resulted in the development of angle-reading devices that were based on arcs of large radii, making such instruments too large for field use. With the publication of logarithmic tables in 1620, portable angle-measuring instruments came into use. They were called topographic instruments, or theodolites. They included pivoted arms for sighting and could be used for measuring both horizontal and vertical angles. Magnetic compasses may have been included on some. The vernier, an auxiliary scale permitting more accurate readings (1631), the micrometer microscope (1638), telescopic sights (1669), and spirit levels (about 1700) were all incorporated in theodolites by about 1720. Stadia hairs were first applied by James Watt in 1771. The development of the circle-dividing engine about 1775, a device for dividing a circle into degrees with great accuracy, brought one of the greatest advances in surveying methods, as it enabled angle measurements to be made with portable instruments far more accurately than had previously been possible. Modern surveying can be said to have begun by the late 18th century. One of the most notable early feats of surveyors was the measurement in the 1790s of the meridian from Barcelona, Spain, to Dunkirk, France, by two French engineers, Jean Delambre and Pierre Méchain, to establish the basic unit for the metric system of measurement.
Many improvements and refinements have been incorporated in all the basic surveying instruments. These have resulted in increased accuracy and speed of operations and opened up possibilities for improved methods in the field. In addition to modification of existing instruments, two revolutionary mapping and surveying changes were introduced: photogrammetry, or mapping from aerial photographs (about 1920), and electronic distance measurement, including the adoption of the laser for this purpose as well as for alignment (in the 1960s). Important technological developments starting in the late 20th century include the use of satellites as reference points for geodetic surveys and electronic computers to speed the processing and recording of survey data. The planning and design of all Civil Engineering projects such as construction of highways, bridges, tunnels, dams etc are based upon surveying measurements. Moreover, during execution, project of any magnitude is constructed along the lines and points established by surveying. Thus, surveying is a basic requirement for all Civil Engineering projects. Other principal works in which surveying is primarily utilised are • to fix the national and state boundaries; • to chart coastlines, navigable streams and lakes; • to establish control points; • to execute hydrographic and oceanographic charting and mapping; and • to prepare topographic map of land surface of the earth.
1.3 Basic Principle Of Surveying........ The following two basic principles should be considered while determining relative position of points on the surface of earth:1. determining suitable method for locating a point:- it is always practicableto select two points in the field to measure the distance between them. These can be represented on paper by two points placed in a convenient positions. 2.working from whole to the part:- in surveying an area, it is essential to establish first of all a system of control points with great precision. Minor control points can then be established by less precise method and the details can be located afterwards by method of triangulation or traversing between control points.
levelling................ IT is a branch of survey which helps in determination of elevation of a given point or object with espect to some specified point or object. . Common levelling instruments include the spirit level, the dumpy level, the digital level, and the laser level. The dumpy level is an older style of optical instrument. It is commonly believed that dumpy levelling is less accurate than other types of levelling, but such is not the case. Dumpy levelling requires shorter and therefore more numerous sights, but this fault is compensated by the practice of making foresights and backsights equal. survey......... surveying is the art of determining the relative positions of objects on the surface of earth.Surveying or land surveying is the technique, profession and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them.Surveying has been an essential element in the development of the human environment since the beginning of recorded history (about 5,000 years ago). It is required in the planning and execution of nearly every form of construction..
1.3.1 Classification of survey Based on the purpose (for which surveying is being conducted), Surveying has been classified into: • Control surveying : To establish horizontal and vertical positions of control points. • Land surveying : To determine the boundaries and areas of parcels of land, also known as property survey, boundary survey or cadastral survey. • Topographic survey : To prepare a plan/ map of a region which includes natural as well as and man-made features including elevation. • Engineering survey : To collect requisite data for planning, design and execution of engineering projects. Three broad steps are 1) Reconnaissance survey : To explore site conditions and availability of infrastructures. 2) Preliminary survey : To collect adequate data to prepare plan / map of area to be used for planning and design. 3) Location survey : To set out work on the ground for actual construction / execution of the project. • Route survey : To plan, design, and laying out of route such as highways, railways, canals, pipelines, and other linear projects.
• Construction surveys : Surveys which are required for establishment of points, lines, grades, and for staking out engineering works (after the plans have been prepared and the structural design has been done). • Astronomic surveys : To determine the latitude, longitude (of the observation station) and azimuth (of a line through observation station) from astronomical observation. • Mine surveys : To carry out surveying specific for opencast and underground mining purposes.
Surveying is the process by which a surveyor measures certain dimensions that generally occur on the surface of the Earth. Surveying equipment, such as levels and theodolites, are used for accurate measurement of angular deviation, horizontal, vertical and slope distances. With computerisation, electronic distance measurement (EDM), total stations, GPS surveying and laser scanning have supplemented (and to a large extent supplanted) the traditional optical instruments. This information is crucial to convert the data into a graphical representation of the Earth's surface, in the form of a map. This information is then used by civil engineers, contractors and even realtors to design from, build on, and trade, respectively. Elements of a building or structure must be correctly sized and positioned in relation to each other and to site boundaries and adjacent structures. Although surveying is a distinct profession with separate qualifications and licensing arrangements, civil engineers are trained in the basics of surveying and mapping, as well as geographic information systems. Surveyors may also lay out the routes of railways, tramway tracks, highways, roads, pipelines and streets as well as position other infrastructures, such as harbors, before construction. Land surveying In the United States, Canada, the United Kingdom and most Commonwealth countries land surveying is considered to be a distinct profession. Land surveyors are not considered to be engineers, and have their own professional associations and licencing requirements. The services of a licenced land surveyor are generally required for boundary surveys (to establish the boundaries of a parcel using its legal description) and subdivision plans (a plot or map based on a survey of a parcel of land, with boundary lines drawn inside the larger parcel to indicate the creation of new boundary lines and roads), both of which are generally referred to as cadastral surveying. Construction surveying Construction surveying is generally performed by specialised technicians. Unlike land surveyors, the resulting plan does not have legal status. Construction surveyors perform the following tasks: •
Survey existing conditions of the future work site, including topography, existing buildings and infrastructure, and even including underground infrastructure whenever possible;
Construction surveying (otherwise "lay-out" or "setting-out"): to stake out reference points and markers that will guide the construction of new structures such as roads or buildings for subsequent construction; • Verify the location of structures during construction; • As-Built surveying: a survey conducted at the end of the construction project to verify that the work authorized was completed to the specifications set on plans. Transportation engineering •
Transportation engineering is concerned with moving people and goods efficiently, safely, and in a manner conducive to a vibrant community. This involves specifying, designing, constructing, and maintaining transportation infrastructure which includes streets, canals, highways, rail systems, airports, ports, and mass transit. It includes areas such as transportation design, transportation planning, traffic engineering, some aspects of urban engineering, queueing theory, pavement engineering, Intelligent Transportation System (ITS), and infrastructure management. Municipal or urban engineering Municipal engineering is concerned with municipal infrastructure. This involves specifying, designing, constructing, and maintaining streets, sidewalks, water supply networks, sewers, street lighting, municipal solid waste management and disposal, storage depots for various bulk materials used for maintenance and public works (salt, sand, etc.), public parks and bicycle paths. In the case of underground utility networks, it may also include the civil portion (conduits and access chambers) of the local distribution networks of electrical and telecommunications services. It can also include the optimizing of waste collection and bus service networks. Some of these disciplines overlap with other civil engineering specialties, however municipal engineering focuses on the coordination of these infrastructure networks and services, as they are often built simultaneously, and managed by the same municipal authority. Forensic engineering Forensic engineering is the investigation of materials, products, structures or components that fail or do not operate or function as intended, causing personal injury or damage to property. The consequences of failure are dealt with by the law of product liability. The field also deals with retracing processes and procedures leading to accidents in operation of vehicles or machinery. The subject is applied most commonly in civil law cases, although it may be of use in criminal law cases. Generally the purpose of a Forensic engineering investigation is to locate cause or causes of failure with a view to improve performance or life of a component, or to assist a court in determining the facts of an accident. It can also involve investigation of intellectual property claims, especially patents. Control engineering Control engineering or control systems engineering is the branch of Civil Engineering discipline that applies control theory to design systems with desired behaviors. The practice uses sensors to measure the output performance of the device being controlled (often a vehicle) and those measurements can be used to give feedback to the input actuators that can make corrections toward desired performance. When a device is designed to perform without the need of human inputs for correction it is called automatic control (such as cruise control for regulating a car's
speed). Multi-disciplinary in nature, control systems engineering activities focus on implementation of control systems mainly derived by mathematical modeling of systems of a diverse range.
1.4 Chain survey Chain survey is the simplest method of surveying. In this survey only measurements are taken in the field, and the rest work, such as plotting calculation etc. are done in the office. This is most suitable adapted to small plane areas with very few details. If carefully done, it gives quite accurate results. The necessary requirements for field work are chain, tape, ranging rod, arrows and some time cross staff. Procedure in chain survey Reconnaissance: The preliminary inspection of the area to be surveyed is calledreconnaissance. The surveyor inspects the area to be surveyed, survey or prepares index sketch or key plan. Marking Station: Surveyor fixes up the required no stations at places from where maximum possible stations are possible. Some of the methods used for marking are: Fixing ranging poles Driving pegs Marking a cross if ground is hard Digging and fixing a stone. Then he selects the way for passing the main line, which should be horizontal and clean as possible and should pass approximately through the center of work. Then ranging roads are fixed on the stations. After fixing the stations, chaining could be started. Make ranging wherever necessary. Measure the change and offset. Enter in the field the book.
Survey Station: Survey stations are of two kinds Main Stations Subsidiary or tie Main Stations: Main stations are the end of the lines, which command the boundaries of the survey, and the lines joining the main stations re called the main survey line or the chain lines. Subsidiary or the tie stations: Subsidiary or the tie stations are the point selected on the main survey lines, where it is necessary to locate the interior detail such as fences, hedges, building etc. Tie or subsidiary lines: A tie line joints two fixed points on the main survey lines. It helps to checking the accuracy of surveying and to locate the interior details. The position of each tie line should be close to some features, such as paths, building etc. Base Lines: It is main and longest line, which passes approximately through the centre of the field. All the other measurements to show the details of the work are taken with respect of this line. Check Line: A check line also termed as a proof line is a line joining the apex of a triangle to some fixed points on any two sides of a triangle. A check line is measured to check the accuracy of the framework. The length of a check line, as measured on the ground should agree with its length on the plan. Offsets: These are the lateral measurements from the base line to fix the positions of the different objects of the work with respect to base line. These are generally set at right angle offsets. It can also be
drawn with the help of a tape. There are two kinds of offsets: 1) Perpendicular offsets, and 2) Oblique offsets. The measurements are taken at right angle to the survey line called perpendicular or right angled offsets. The measurements which are not made at right angles to the survey line are called oblique offsets or tie line offsets. A chain is made up of steel or iron pieces of wire known as links which are joined together with circular or oval rings that make for flexibility. It has a brack handle at both ends which is part and parcel of the total length of the chain known as chain length. A typical chain is made up of 100 links and has a bran tag at every 10th link called a teller. This makes for operating of length as the letters are numbered and differentiated from the next one for easy identification. Different kinds of chains exist including Equnter’s chain, Engineers chain and metric chains. Generally, chains have been replaced with chains for linear surveys. Chains are now being studied to get the historical perspective of the development of survey equipments over the years. To surveyors and collectors alike, the link chain symbolizes a rugged era, when surveying tools and techniques were literally defining America. The chain was a precision part of a surveyor's equipment and, as such, had to be calibrated and adjusted frequently, yet was sturdy enough to be dragged through rough terrain for years. Owning a link chain now captures a bit of this glorious past; to heft it enhances the kinship one feels with the surveyor who toiled in the field long ago. As collectors, we need to identify the type of chain we own, in order to understand its history. Each chain bears the clues of its use, such as the wire gauge used, the materials and design used, the lengths of the whole and of each link, the manufacturer's stamps, the presence or absence of brazing, the tally-tags, and the presence or absence of linking rings. Noting these components will make it possible to approximate the date and purpose of your link chain with the aid of period manufacturer's catalogs. The following is a nicely detailed account from the 1910 Manual of the Principal Instruments used in American Engineering and Surveying, published by the W. & L. E. Gurley Company of Troy, New York. Sizes of Wire - The sizes and diameters of iron and steel wire commonly used in making surveyor's and engineer's chains are as follows: No. 8, .162 inch; No. 10, .135 inch; No. 12, .105 inch; No. 15, .072 inch; and No. 18, .047 inch. Land Surveyor's Chain - The ordinary Gunter's or surveyor's chain is sixty-six feet or four poles long, and is composed of one hundred links, connected each to each by two rings, and furnished with a tally mark at the end of every ten links. A link in measurement includes a ring
at each end, and is seven and ninety two one hundredths inches long. In all the chains which we make the rings are oval and are sawed and well closed, the ends of the wore forming the hook being also filed and bent close to the link, to avoid kinking. The oval rings are about one third stronger than round ones. Handles - The handles are of brass and form part of the end links, to which they are connected by a short link and jam nuts, by which the length of the chain is adjusted. Tallies - The tallies are of brass, and have one, two, three or four notches, as they mark ten, twenty, thirty or forty links from either end. The fiftieth link is marked by a rounded tally to distinguish it from the others. Half Chains - In place of the four pole chain just described, many surveyors prefer a chain two rods or thirty three feet long, having only fifty links, which are counted by tallies from one end in a single direction. Iron and Steel Wire - Our surveyors' chains are made of Nos. 8 and 10 refined iron wire, and of Nos. 8, 10, 12 and 15 best steel wire. Steel chains are preferred on account of their greater strength, although they are more expensive than those of iron. Engineers' Chains - Engineers' chains differ from surveyors' chains, in that a link including a ring at each end is one foot long, and the wire is of steel Nos. 8, 10 and 12. They are either fifty or one hundred feet long, and are furnished with swivel handles and tallies like those just described. Brazed Steel Chains - A very light and strong chain is made of No. 12 steel wire, the links and rings of which are securely brazed. The wire is of a low spring temper, and the chain, though light, is almost incapable of being broken or stretched in careful use. Our brazed steel chains have been found exceedingly desirable for all kinds of measurement, and for the use of engineers upon railroads and canals have very generally superseded the heavier chains. Vara Chains - The meter is used as a standard measure of length in many countries, and chains of ten and twenty meters are often ordered. The chains are made of iron or steel wire, each meter being divided into five links. As a meter is 39.371 inches long, a link, including a ring at each end, measures 7.874 inches. A ten meter chain has fifty links and a twenty meter chain one hundred links. Each meter is marked with a round brass tally numbered from one to nine in the ten meter chain, and from one to nineteen in the twenty meter chain. Marking Pins - In chaining, eleven marking pins are needed, made either of iron, steel or brass wire, as preferred. They are about fourteen inches long, pointed at one end to enter the ground, and formed into a ring at the other end for convenience in handling.
Marking pins are sometimes loaded with a little mass of lead around the lower end, to serve as a plumb when the pin is dropped to the ground from the suspended end of the chain. Chain survey is suitable in the following cases: (i) Area to be surveyed is comparatively small (ii) Ground is fairly level (iii) Area is open and (iv) Details to be filled up are simple and less. In chain surveying only linear measurements are made i.e. no angular measurements are made. Since triangle is the only figure that can be plotted with measurement of sides only, in chain surveying the area to be surveyed should be covered with a network of triangles. Figure 12.11 shows a typical scheme of covering an area with a network of triangles. No angle of the network triangles should be less than 30º to precisely get plotted position of a station with respect to already plotted positions of other station. As far as possible angles should be close to 60º. However, the arrangements of triangles to be adopted depends on the shape, topography, natural and artificial obstacles in the field.
Figure 1.4 Technical Terms Various technical terms used in connection with the network of the triangles in surveying are explained below: Station: Station is a point of importance at the beginning or at the end of a survey line. Main station: These are the stations at the beginning or at the end of lines forming main skeleton. They are denoted as A, B, C etc. Subsidiary or tie stations: These are the stations
selected on main lines to run auxiliary/secondary lines for the purpose of locating interior details. These stations are denoted as a, b, c, …., etc., or as 1, 2, 3, … etc. Base line: It is the most important line and is the longest. Usually it is the line plotted first and then frame work of triangles are built on it. Detail lines: If the important objects are far away from the main lines, the offsets are too long, resulting into inaccuracies and taking more time for the measurements. In such cases the secondary lines are run by selecting secondary stations on main lines. Such lines are called detail lines. Check lines: These are the lines connecting main station and a substation on opposite side or the lines connecting to substations on the sides of main lines. The purpose of measuring such lines is to check the accuracy with which main stations are located. Selection of Stations The following points should be considered in selecting station points: (i) It should be visible from at least two or more stations. (ii) As far as possible main lines should run on level ground. (iii) All triangles should be well conditioned (No angle less than 30º). (iv) Main network should have as few lines as possible. (v) Each main triangle should have at least one check line. (vi) Obstacles to ranging and chaining should be avoided. (vii) Sides of the larger triangles should pass as close to boundary lines as possible. (viii) Tresspassing and frequent crossing of the roads should be avoided. Offsets Lateral measurements to chain lines for locating ground features are known as offsets. For this purpose perpendicular or oblique offsets may be taken. If the object to be located (say road) is curved more number of offsets should be taken. For measuring offsets tapes are commonly used.
For setting perpendicular offsets any one of the following methods are used: (i) Swinging (ii) Using cross staffs (iii) Using optical or prism square. Perpendicular Offset by Swinging
Chain is stretched along the survey line. An assistant holds the end of tape on the object. Surveyor swings the tape on chain line and selects the point on chain where offset distance is the least and notes chain reading as well as offset reading in a field book on a neat sketch of the object. Perpendicular Offsets Using Cross Staffs
Above Figure shows three different types of cross staffs used for setting perpendicular offsets. All cross staffs are having two perpendicular lines of sights. The cross staffs are mounted on stand. First line of sight is set along the chain line and without disturbing setting right angle line
of sight is checked to locate the object. With open cross staff it is possible to set perpendicular only, while with french cross staff, even 45º angle can be set. Adjustable cross staff can be used to set any angle also, since there are graduations and upper drum can be rotated over lower drum. Perpendicular Offsets Using Optical Square and Prism Square These instruments are based on the optical principle that if two mirrors are at angle ‘θ’ to each other, they reflect a ray at angle ‘2θ’. In below Figure shows a typical optical square.
Optical square consists of a metal box about 50 mm in diameter and 125 mm deep. In the rim of the box there are three openings: (i) a pin hole at E (ii) a small rectangular slot at G, and (iii) a large rectangular slot at F. A and B are the two mirrors placed at 45º to each other. Hence the image of an object at F which falls on A gets reflected and emerge at E which is at right angles to the line FA. The mirror A which is opposite to the opening at F is fully silvered. It is fitted to a frame which is attached to the bottom plate. If necessary this mirror can be adjusted by inserting a key on the top of the cover. The mirror B which is in the line with EG is silvered in the top half and plain in the bottom half. It is firmly attached to the bottom plate of the box. The ranging rod at Q is directly sighted by eye at E in the bottom half of the B which is a plain glass. At the same time in the top half of B, the reflected ray of the object at P is sighted. When the image of P is in the same vertical line as the object at Q, then the lines PA is at right angles to the line EB. This instrument can be used for finding foot of the perpendicular or to set a right angle. In prism square, instead of two mirrors at 45º to each other a prism which has two faces at 45º to each other is used. Its advantage is it will not go out of adjustment even after long usage.
Field Book All observations and measurements taken during chain surveying are to be recorded in a standard field book. It is a oblong book of size 200 mm × 120 mm, which can be carried in the pocket. There are two forms of the book (i) single line and (ii) double line. The pages of a single book are having a red line along the length of the paper in the middle of the width. It indicates the chain line. All chainages are written across it. The space on either side of the line is used for sketching the object and for noting offset distances. In double line book there are two blue lines with a space of 15 to 20 mm is the middle of each book. The space between the two lines is utilised for noting the chainages. in below Figure shows typical pages of a field books.
Field Work As soon as the survey party arrives in the field the following details are entered in the field book: (i) Title of the survey work (ii) The date of survey (iii) The names of the members of the party. The field work may be divided into the following: (i) Reconnaissance survey. (ii) Marking stations, drawing reference sketches. (iii) Line by line surveying. Reconnaissance survey consists in going round the field and identifying suitable stations for the network of triangles. Neat sketch of network is drawn and designated. The typical key plan drawn is similar to one shown in above figure. All main stations should be marked on the ground. Some of the methods used for marking are: (a) Fixing ranging poles (b) Driving pegs (c) Marking a cross if ground is hard (d) Digging and fixing a stone. Then reference sketches are drawn in the field book so as to identify stations when the development works are taken up. For this measurements with respect to three permanent points are noted. The permanent points may be (a) Corner of a building (b) Posts of gates (c) Corners of compound walls (d) Electric poles (e) A tree. After that, line by line surveying is conducted to locate various objects with respect to chain lines. Office Work It consists in preparing the plan of the area to a suitable scale making use of measurements and sketches noted in the field book.
1.5 COMPASS Compass surveying is a branch of surveying in which directions of surveying lines are determined with a compass and the length of lines are measured with a tape or chain. In practice the compass si generally used to run a traverse.
In surveying,"Traverse" consists of a series of straight lines connected together to form a open or a closed polygon. Methods of traversing: Depending on the type of instrument used for the measurement of angles the method of Traversing can be classified as under; 1.Chain Traverse 2.Compass Traverse. 3.Plane Table Traverse. 4.Stadia Traverse. 5.Theodolite Traverse. In Compass Traverse the direction of the traverse lines are determined with a magnetic compass. The magnetic Compass may be "SURVEYOR COMPASS" OR "PRISMATIC COMPASS" The types of compass that are used commonly are: (i) prismatic compass; and (ii) surveyor compass. The essential parts of both type are: (i) a magnetic needle, (ii) a graduated circle, (iii) a line of sight, and (iv) a box to house them. There are some differences in the essential parts of the two type of compass. The construction of the two types of compass is explained and the difference in them is pointed out in this article. Prismatic Compass in below Figure shows the cross-section of a typical prismatic compass. A magnetic needle of broad form (1) is balanced on a hard and pointed steel pivot (2). The top of the pointed pivot is protected with agate cap (3).
An aluminium graduated disk (4) is fixed to the top of the needle. The graduations are from zero to 360° in clockwise direction when read from top. The direction of north is treated as zero degrees, east as 90°, south as 180° and west as 270°. However, while taking the readings observations are at the other end of line of sight. Hence, the readings are shifted by 180° and graduations are marked as shown in below figure. The graduations are marked inverted because they are read through a prism.
The line of sight consists of object unit and the reading unit. Object unit consists of a slit metal frame hinged to the box. In the centre the slit is provided with a horse hair or a fine wire or thread The metal frame is provided with a hinged mirror , which can be placed upward or downward on the frame. It can be slided along the frame. The mirror can be adjusted to view objects too high or too low from the position of compass. Reading unit is provided at diametrically opposite edge. It consists of a prism with a sighting eye vane . The prism magnifies the readings on the graduation disk just below it. For focussing, the prism is lowered or raised on the frame carrying it and then fixed with the stud. Dark sunglasses provided near the line of sight can be interposed if the object to be
sighted is bright (e.g., sun). The bottom of the box which is about 85 mm to 110 mm supports the pivot of needle firmly at its centre. The object vane and the prism are supported on the sides of the box. The box is providedwith a glass lid which protects the graduation disc at the same time permit the direct reading from the top. When the object vane is folded on the glass top it presses a lifting pin which activates lifting lever lifts the needle off the pivot. Thus, it prevents undue wear of pivot point. While taking reading, if graduation disc vibrates, it can be dampened with a spring. For pressing spring a knob or brake pin is provided on the box. When not in use prism can be folded over the edge of the box. The box is provided with a lid to close it when the compass is not in use. The box is provided with a socket to fit it on the top of a tripod. Surveyors Compass In this type of compass graduation disc is fixed to the box and magnetic needle is free to rotate above it. There is no prism provided at viewing end, but has a narrow slit. After fixing the line of sight, the reading is directly taken from the top of the glass cover. Hence, graduations are written directly (not inverted). In this compass graduations are from zero to 90°, zero being to north or south and 90° being to east and west. An angle of 20° to north direction to the east is written as N 20° E, and an angle of 40° to east from south is written as S 40° E. Always first direction indicated is north or south and the last letter indicates east or west direction. In this system graduated circle rotates with line of sight and magnetic needle is always towards north. The reading is taken at the tip of needle. Hence, on the compass east and west are marked interchanged and marked shows the photograph of a surveyors compass.
Difference Between Prismatic Compass and Surveyors The difference between prismatic and surveyor’s compass are listed in below Table.
Bearing As stated earlier a bearing of a line is the angle made by the line with respect to a reference direction, the reference direction being known as meridian. The direction shown by a freely suspended and properly balanced magnetic needle is called magnetic meridian and the horizontal angle made by a line with this meridian is known as magnetic bearing. The points of intersection of earth’s axis with surface of the earth are known as geographic north and south pole. The line passing through geographic north, south and the point on earth is called true meridian at that point and the angle made by a line passing through that point is called truebearing. While traversing along lines A, B, C, D …, the bearing of lime AB is called fore bearing of AB and the bearing of BA is called back bearing. Fore bearing and back bearing differ by 180°.
1.6 PLANE TABLE SURVEYING In this method of surveying a table top, similar to drawing board fitted on to a tripod is the main instrument. A drawing sheet is fixed on to the table top, the observations are made to the objects, distances are scaled down and the objects are plotted in the field itself. Since the plotting is made in the field itself, there is no chance of omitting any necessary measurement in this surveying. However the accuracy achieved in this type of surveying is less. Hence this type of surveying is used for filling up details between the survey stations previously fixed by other methods. In this chapter, accessories required, working operations and methods of plane table surveying are explained. At the end advantages and limitations of this method are listed.
Plane Table and Its Accessories The most commonly used plane table is shown in below Fig. It consists of a well seasoned wooden table top mounted on a tripod. The table top can rotate about vertical axis freely. Whenever necessary table can be clamped in the desired orientation. The table can be levelled by adjusting tripod legs.
The following accessories are required to carry out plane table survey: 1. Alidade 2. Plumbing fork with plumb bob. 3. Spirit level 4. Trough compass 5. Drawing sheets and accessories for drawing.
Alidade It is a straight edge ruler having some form of sighting device. One edge of the ruler is bevelled and is graduated. Always this edge is used for drawing line of sight. Depending on the type of line of sight there are two types of alidade: (a) Plain alidade (b) Telescopic alidade Plain Alidade: in below Figure shows a typical plain adidate. A sight vane is provided at each end of the ruler. The vane with narrow slit serves as eye vane and the other with wide slit and having a thin wire at its centre serves as object vane. The two vanes are provided with hinges at the ends of ruler so that when not in use they can be folded on the ruler. Plain alidade is not suitable in surveying hilly areas as the inclination of line of sight in this case is limited.
Telescopic Alidade: It consists of a telescope mounted on a column fixed to the ruler. The line of sight through the telescope is kept parallel to the bevelled edge of the ruler. The telescope is provided with a level tube and vertical graduation arc. If horizontal sight is required bubble in the level tube is kept at the centre. If inclined sights are required vertical graduation helps in noting the inclination of the line of sight. By providing telescope the range and the accuracy of line of sight is increased.
Plumbing Fork and Plumb Bob Figure shows a typical plumbing fork with a plum bob. Plumbing fork is a U-shaped metal in frame with a upper horizontal arm and a lower inclined arm. The upper arm is provided with a pointer at the end while the lower arm is provided with a hook to suspend plumb bob. When the plumbing fork is kept on the plane table the vertical line (line of plumb bob) passes through the pointed edge of upper arm. The plumb bob helps in transferring the ground point to the drawing sheet and vice versa also.
SpiritLevel A flat based spirit level is used to level the plane table during surveying. To get perfect level, spirit level should show central position for bubble tube when checked with its positions in any two mutually perpendicular direction. TroughCompass It consists of a 80 to 150 mm long and 30 mm wide box carrying a freely suspended needle at its centre . At the ends of the needle graduations are marked on the box to indicate zero to five degrees on either side of the centre. The box is provided with glass top to prevent oscillation of the needle by wind. When needle is centred (reading 0–0), the line of needle is parallel to the edge of the box. Hence marking on the edges in this state indicates magnetic north–south direction.
Drawing Sheet and Accessories for Drawing A good quality, seasoned drawing sheet should be used for plane table surveying. The drawing sheet may be rolled when not in use, but should never is folded. For important works fibre glass sheets or paper backed with thin aluminium sheets are used. Clips clamps, adhesive tapes may be used for fixing drawing sheet to the plane table. Sharp hard pencil, good quality eraser, pencil cutter and sand paper to keep pencil point sharp are other accessories required for the drawing work. If necessary, plastic sheet should be carried to cover the drawing sheet from rain and dust.
1.6.1 Working Operation After fixing the table top to the stand and drawing sheet to the table, the following operations are to be carried out before map making: 1. Centering 2. Levelling 3. Orientation. 1 Centering Centering is the process of setting the plane table on the point so that its plotted position is exactly over the position on the ground. This is achieved by moving the legs of the tripod and checking the position of the point on the ground and on the paper with the help of plumbing fork and plumb bob. 2 Levelling The level of the plane table should be ensured in two positions of spirit level which are at right angles to each other. The legs of tripod are moved radially or along the circumference to adjust the plane table and get levelled surface. 3 Orientation Orientation is the process of setting plane table over a station such that all the lines already plotted are parallel to corresponding lines on the ground. Accuracy of plane table survey mainly depends upon the accuracy of orientation of plane table at each station point. It can be achieved by any one of the following methods: (a) using trough compass (b) by back sighting (c) by solving two point or three point problems. The first two methods are commonly used while the third method is used occationally. The third method is explained under the article methods of plane tabling by resection.
(a) Orientation Using Trough Compass: When the survey work starts, the plane table is set on first station and the table is oriented by rough judgement such that the plotted position of the area falls in the middle portion of the paper. Then the table is clamped and the north direction is marked on right hand side top corner of drawing sheet. Trough compass is used to identify north direction. This orientation is to be maintained at all subsequent stations. After centering and levelling the table trough compass is kept along the marked north direction and the table is rotated to get freely suspended magnetic needle centred. After achieving it the table is clamped. This method of orientation is considered rough, since the local attraction to magnetic needle affects the orientation. This method is used as preliminary orientation and finer tuning is made by observing the already plotted points. (b) Orientation by Back Sighting: It is the commonly used method in plane table surveying. After completing surveying from plane table set at A, if table is to be shifted to next station B, a line is drawn from the plotted position of station A towards station B. Then distance AB is measured, scaled down and plotted position of station B is obtained. Then table is shifted to station B, centred, levelled. Then keeping alidade along BA, station A is sighted and the table is clamped. Thus the orientation of the table is achieved by back sighting. Orientation may be checked by observing already plotted objects. Method of planning table The following four methods are available for carrying out plane table survey: 1. Radiation 2. Intersection 3. Traversing 4. Resection. The first two methods are employed for locating details while the other two methods are used for locating position of plane table station on drawing sheet. 1 Radiation After setting the plane table on a station, say O, it is required to find the plotted position of various objects A, B, C, D ….. . To get these positions, the rays OA, OB, OC ….. are drawn with soft pencil. Then the distances OA, OB, OC ….., are measured scaled down and the positions of A, B, C ….., are found on the drawing sheets. This method is suitable for surveying small areas and is convenient if the distances to be measured are small. For larger areas this method has wider scope, if telescopic alidade is used, in which the distances are measured technometrically.
Intersection In this method the plotted position of an object is obtained by plotting rays to the object from two stations. The intersection gives the plotted position. Thus it needs the linear measurements only between the station points and do not need the measurements to the objects. In below Figure shows the method for locating objects A and B from plane table positions O1 and O2.
This method is commonly employed for locating: (a) details (b) the distant and inaccessible points (c) the stations which may be used latter. Traversing This is the method used for locating plane table survey stations. In this method, ray is drawn to next station before shifting the table and distance between the stations measured. The distance is scaled down and next station is located. After setting the plane table at new station orientation is
achieved by back sighting. To ensure additional checks, rays are taken to other stations also, whenever it is possible. In below Figure shows a scheme of plane table survey of closed area. This method can be used for open traverses also.
Resection This method is just opposite to the method of intersection. In the method of intersection, the plotted position of stations are known and the plotted position of objects are obtained by intersection. In this method the plotted position of objects are known and the plotted position of station is obtained. If a, b and c are the plotted positions of objects A, B and C respectively, to locate instrument station P on the paper, the orientation of table is achieved with the help of a, b, c and then resectors Aa, Bb, Cc are drawn to get the ‘p’ , the plotted position of P. Hence in the resection method major work is to ensure suitable orientation by any one of the methods. The following methods are employed in the method of resection: (a) by compass (b) by back sighting (c) by solving two point problem (d) by solving three point problem. (a) Resection after Orientation by Compass: Let a and b be the plotted positions of A and B of two well defined points in the field. Keeping the through compass along north direction marked on the drawing sheet table is oriented on station P, the position of which is to be found on paper. The resectors Aa and Bb are drawn to locate ‘p’ the plotted position of station point P. This method gives satisfactory results, if the area is not influenced by local attractions. It is used for small scale mapping only.
(b) Resection after Orientation by Back Sighting: in below Figure shows the scheme of resection after orientation by back sighting. From station A, the position of B is plotted as ‘b’ and ray has been taken to station P as ap′. Then plane table is set at P and oriented by back sighting A, line AP is not measured but the position of P is obtained on the paper by taking resection Bb.
(c) Resection after Solving Two Point Problem: The problem of finding plotted position of the station point occupied by the plane table with the help of plotted positions of two well defined points is known as solving two point problem. In below Figure shows the scheme of solving this.
Let A and B be two well defined points like lightening conductor or spire of church, the plotted positions a and b already known. Now the problem is to orient the table at P so that by resection its plotted position p can be obtained. The following steps may be followed to solve this problems: (i) Select a suitable point Q near P such that the angles PAQ and PBQ are not accute. (ii) Roughly orient the table at Q and draw the resectors Aa and Bb to get the point ‘q’. (iii) Draw the ray qp and locate p1 with estimated distance QP. (iv) Shift the plane table to P and orient the table by back sighting to Q. (v) Draw the resector Aa to get ‘p’. (vi) Draw the ray pB. Let it intersect line bq at b1.
(vii) The points b and b1 are not coinciding due to the angular error in the orientation of table. The angle bab, is the angular error in orientation. To correct it, * Fix a ranging rod at R along ab, * Unclamp the table and rotate it till line ab sights ranging rod at R. Then clamp the table. This gives the correct orientation of the table which was used in plotting the points A and B. (viii) The resectors Aa and Bb are drawn to get the correct plotted position ‘p’ of the station P. (d) Resection after Solving Three Point Problem: Locating the plotted position of a station point using observations to three well defined points whose plotted positions are known, is called solving three point problem. Let A, B, C be three well defined objects on the field whose plotted positions a, b and c are known. Now the problem is to locate plotted position of the station point P. Any one of the following methods can be used. (i) Mechanical (Tracing paper) method, (ii) Graphical method, or (iii) Trial and error method (Lehman’s method). (i) Mechanical Method: This method is known as tracing paper method since it needs a tracing paper. The method involved the following steps
* Set the table over station P and by observation approximately orient the table. * Fix the tracing paper on the plane table and select P approximately, say as p′. From p′, draw p′ A, p′ B and p′ C. These lines may not pass through the plotted positions a, b and c since the orientation is not exact. * Loosen the tracing paper and rotate it so that the rays pass through respective points a, b and c. Now prick the point p′ to get the plotted position ‘p’ of the station P. * Keep the alidade along pa and sight A. Then clamp the table. This is correct orientation. Check the orientation by observing along pb and pc. (ii) Graphical Method: The following two graphical methods are available to solve three point problem: * Bessel’s solution * Method of perpendiculars. Bessels Solution: It involves the following steps: 1. Keep the bevelled edge of alidade along ba and sight object at A. Clamp the table and draw bc′ along the line bc. 2. Keep bevelled edge of alidade along ab, unclamp the table and sight B. Clamp the table. Draw line ac intersecting bc′ at d. 3. Keep the alidade along dc and bisect C. Clamp the table. This gives the
correct orientation. 4. Draw resectors to get ‘p’.
Method of Perpendiculars This is another graphical method. It involves the following steps. 1. Draw line ae perpendicular to ab. Keep alidade along ea and turn the table till A is sighted. Clamp the table and draw the ray Bb to intersect the ray Aac at e. 2. Draw cf perpendicular to bc and clamp the table when fcC are in a line. Draw Bb to intersect Ccf at F .
3. Join cf drop bp perpendicular to ef to get the plotted position ‘p’. 4. Orient the table such that pbB are in a line. Clamp the table to place it in correct orientation. Resections Aa and Cc may be used to check the orientation. Trial and Error Method This method is also known as ‘triangle of error method’ and ‘Lehman’s Method’. It involves the following steps: 1. Set the table over point P and orient the table approximately, just by observation. 2. Draw the rays aA, bB and cC. If the orientation was perfect, the three rays would have intersected at a single point, i.e. at point ‘p’. Otherwise a triangle of error is formed. 3. To eliminate the triangle of error an approximate position, ray p′, is selected near the triangle of error. Then keeping alidade along p′a object A is sighted and the table is clamped. Draw the
resectors cC and bB to check the orientation. 4. Above step is repeated till triangle of error is eliminated.
Lehman presented the following guidelines to select ‘p′’ so that triangle of error is eliminated quickly. Rule 1: The distance of point sought ‘p’ is in the same proportion from the corresponding rays as the distance of those from the plane table station. Rule 2: The point sought ‘p’ is on the same side of all the three resectors. Defining the triangle ABC on the field as great triangle and the circle passing through them as great circle, from the above two rules of Lehman, the following sub-rules may be drawn.
* If ‘P’ lies within the great triangle, the point ‘p’ is within the triangle of error * If the plane table station P lies outside the great triangle the point sought ‘p’ is outside the triangle of errors (p2). * If the ‘P’ is on the great circle, the correct solution is impossible (p3 and p4). * If ‘P’ is outside the great circle, ‘p’ is nearer to the intersection of rays to the nearest two points (P5). * If point P is outside the great circle and the two rays drawn are parallel to each other the point sought is outside the parallel lines and on the same side of the three rays (P6).
1.6.2 Error in Plane Table Serveying The errors may be grouped into the instrumental and personal errors. Instrumental Errors 1. The surface of plane table not perfectly plane. 2. Bevelled edge of alidade not straight. 3. Sight vanes of alidade not perfectly perpendicular to the base. 4. Plane table clamp being loose. 5. Magnetic compass being sluggish. 6. Drawing sheet being of poor quality. Personal Errors 1. Centering errors 2. Levelling errors 3. Orientation errors 4. Sighting errors 5. Errors in measurement 6. Plotting errors 7. Errors due to instability of tripod. Advantages are 1. Possibility of omitting measurement is eliminated. 2. The surveyor can compare the plotted work in the field then and there only. 3. Irregular objects are plotted more accurately, since they are seen while plotting. 4. Booking errors are eliminated. 5. Local attractions do not influence the plotting. 6. No great skill is required to produce satisfactory maps. 7. Method is fast. 8. No costly instruments are required. Limitations are 1. Survey cannot be conducted in wet weather and rainy days. 2. Plane table is cumbersome and heavy to carry. 3. It needs many accessories. 4. It is less accurate. 5. Reproduction of map to different scale is difficult.
Review Questions 1. Describe chain principle and classification with example? 2. What is surveying explain in detail? 3. Explain the chaining in reciprocal ? 4. What is the technique of compass in surveying ? 5. What is pessimistic compass explain with example? 6. What is adjustment of error explain? 7. Explain Local Attraction? 8. Explain the technique of Plain Table Serveying ? 9. What are the merit and demerit of plane table surveying? 10. What are the radiation intersection and radiation traversing explain?
Chapter 2 LEVELLING AND THEODOLITE SURVEYING Structure of this unit LEVELLING, THEODOLITE Learning Objectives 1. LEVELLING 2. Level line 3. Horizontal line 4. Levels and Staves 5. Spirit level 6. sensitiveness 7. Bench marks 8. Temporary and Permanent adjustments 9. Fly and check levelling – Booking 10. Reduction 11. Curvature and Refraction 12. Reciprocal levelling 13. Longitudinal and Cross sections – Plotting . 14. THEODOLITE 15. Theodolite 16. Vernier and Microptic 17. Description and uses 18. Temporary and Permanent adjustments of vernier transit 19. Horizontal angles – Heights and Distances 20. Traversing – Closing error and distribution.
2.1 LEVELLING Elevation measurements involve measurements in vertical plane. It is also known as levelling. It may be defined as the art of determining the elevations of given points above or below a datum line or establishing given points of required heights above or below the datum line. Levelling (or leveling in American spelling) is a branch of surveying, the object of which is to 1. Find the elevation of a given point with respect to the given or assumed Datum. 2. Establish a point at a given elevation with respect to the given or assumed Datum. Levelling is the measurement of geodetic height using an optical levelling instrument and a level staff or rod having a numbered scale. Common levelling instruments include the spirit level, thedumpy level, the digital level, and the laser level. Spirit (Optical) levelling Spirit levelling employs a spirit level, an instrument consisting of a telescope with a crosshair and a tube level like that used by carpenters, rigidly connected. When the bubble in the tube level is centered the telescope's line of sight is supposed to be horizontal (i.e. perpendicular to the local vertical). The spirit level is on a tripod midway between the two points whose height difference is to be determined. A leveling staff or rod is held vertical on each point; the rod is graduated in centimetres and fractions or tenths and hundredths of a foot. The observer focuses in turn on each rod and reads the value. Subtracting the "back" and "forward" value provides the height difference. We can't expect the instrument to be in perfect adjustment, but we can hope that when the bubble is centered the telescope's line of sight is always the same small angle off of horizontal. If it is, we can still level accurately by setting the instrument equidistant from the points to be measured, so the errors cancel. 2.1.1 Leveling Procedure A typical procedure is to set up the instrument within 100 metres (110 yards) of a point of known or assumed elevation. A rod or staff is held vertical on that point and the instrument is used manually or automatically to read the rod scale. This gives the height of the instrument above the starting (backsight) point and allows the height of the instrument (H.I.) above the datum to be computed. The rod is then held on an unknown point and a reading is taken in the same manner, allowing the elevation of the new (foresight) point to be computed. The procedure is repeated until the destination point is reached. It is usual practice to perform either a complete loop back to the starting point or else close the traverse on a second point whose elevation is already known. The closure check guards against blunders in the operation, and allows residual error to be distributed in the most likely manner among the stations.
Some insstruments prrovide three crosshairs which w allow stadia meassurement of the foresighht and backsighht distances. These T also allow a use of the average of the three readings (3--wire levelinng) as a check against a blun nders and forr averaging out the erroor of interpoolation betweeen marks on o the rod scalee. The two main types of levellingg are single--levelling as already desscribed, and double-leveelling (Double--rodding). In n double-levvelling, a surrveyor takess two foresigghts and two backsightss and makes suure the difference betweeen the foressights and thhe differencee between thhe backsightts are equal, thhereby reduccing the amoount of erroor. Double-levelling cossts twice as much as siinglelevelling. Refractiion and Currvature The curvvature of thee earth meanns that a linee of sight thaat is horizonntal at the innstrument will w be higher annd higher ab bove a spherroid at greateer distances. The effect may be signnificant for some work at distances d und der 100 meteers. The line of sight is horizontal h at the instrum ment, but is not n a straightt line becausse of refractiion in the air. The T change of air presssure with eleevation causses the line of sight to bend towarrd the earth. Thhe amount off refraction depends d slighhtly on air teemperature and a pressuree. The combbined correcction is approoximately: or For precise p work k these effeccts need to be b calculatedd and correcttions appliedd. For most work it is sufficient s to o keep the fooresight and backsight distances d appproximately equal so thaat the refracction and cu urvature effeccts cancel ouut. Levelingg loops and Gravity G Variaations If the Eaarth's gravity y field were completelyy regular andd gravity constant, levelling loops would w always cllose preciselly:
around a loop. In thee real gravitty field of thhe Earth, thiis happens only o approxiimately; on small loops typpical of engineering projjects, the looop closure iss negligible, but on largeer loops covvering regions or o continentss it is not. Instead of o height diffferences, geoopotential diifferences doo close arounnd loops:
where stands for gravity g at thhe leveling innterval i. Forr precise levveling netwoorks on a nattional scale, thee latter formu ula should always be useed.
should bee used in alll computatioons, producinng geopotenttial values network.
for the beenchmarks of o the
Levellingg Instrumentts Older In nstruments The wye level is the oldest and bulkiest of the older sttyle optical instruments.. A low-pow wered telescopee is placed in n a pair of cllamp mountss, and the insstrument theen leveled ussing a spirit level, l which is mounted paarallel to the main telescoope. The dum mpy level was developedd by English civil engineeer William Gravatt, whhile surveyinng the route of a proposed railway linee form Londdon to Doveer. More coompact and hence h both more robust annd easier to transport, t it is commonly believed that dumpy levelling l is less l accuratee than other typpes of levelliing, but suchh is not the case. c Dumpyy levelling requires r shorrter and therrefore more num merous sigh hts, but this fault is com mpensated by the practice of makinng foresightss and backsighhts equal. Precise Level L design ns were ofteen used for large levelinng projects where utmoost accuracyy was required. They differr from other levels in havving a very precise p spiritt level tube and a a microm meter adjustmeent to raise or o lower the line of sightt so that the crosshair can be made too coincide with w a line on thhe rod scale and no interrpolation is required. r Automattic level Automatic levels make use of a compensator c r that ensures that the linne of sight reemains horizzontal once thee operator has h roughly leveled thee instrumennt (to withinn maybe 0.05 degree). The surveyor sets the instrument upp quickly annd doesn't haave to relevvel it carefuully each tim me he sights onn a rod on an nother pointt. It also redduces the efffect of minorr settling off the tripod to t the actual am mount of mottion instead of leveraginng the tilt over the sight distance. d Suuch levels became standard in the laterr part of the twentieth century. Thhree level screws s are used u to leveel the instrumennt. Digital Level L Digital levels l electrronically reaad a bar-coded scale on o the staff. f. These insttruments ussually include data d recordin ng capabilityy. The autom mation remooves the reqquirement foor the operattor to read a sccale and writte down the value, and so reduces blunders. b It may m also coompute and apply a refractionn and curvatture correctioons. Laser levvel Laser levvels project a beam whiich is visible and/or dettectable by a sensor on the levelingg rod. This stylle is widely y used in construction work but not n for morre precise control workk. An advantagge is that on ne person can c perform m the levelliing independdently, wheereas other types require one o person att the instrum ment and one holding the rod. The sensor can be mo ounted on eaarth-moving machinery to t allow autoomated gradding.
2.1.2 Object and use of leveling As stated in the definition of levelling, the object is (i) to determine the elevations of given points with respect to a datum (ii) to establish the points of required height above or below the datum line. Uses of levelling are (i) to determine or to set the plinth level of a building. (ii) to decide or set the road, railway, canal or sewage line alignment. (iii) to determine or to set various levels of dams, towers, etc. (iv) to determine the capacity of a reservoir.
2.1.3 Term used in leveling Before studying the art of levelling, it is necessary to clearly understand the following terms used in levelling: 1. Level Surface: A surface parallel to the mean spheroid of the earth is called a level surface and the line drawn on the level surface is known as a level line. Hence all points lying on a level surface are equidistant from the centre of the earth. In below Figure shows a typical level surface.
2. Horizontal Surface: A surface tangential to level surface at a given point is called horizontal surface at that point. Hence a horizontal line is at right angles to the plumb line at that point
3. Vertical Line: A vertical line at a point is the line connecting the point to the centre of the earth. It is the plumb line at that point. Vertical and horizontal lines at a point are at right angles to each other. 4. Datum: The level of a point or the surface with respect to which levels of other points or planes are calculated, is called a datum or datum surface. 5. Mean Sea Level (MSL): MSL is the average height of the sea for all stages of the tides. At any particular place MSL is established by finding the mean sea level (free of tides) after averaging tide heights over a long period of at least 19 years. In India MSL used is that established at Karachi, presently, in Pakistan. In all important surveys this is used as datum. 6. Reduced Levels (RL): The level of a point taken as height above the datum surface is known as RL of that point. 7. Benchmarks: A benchmark is a relatively permanent reference point, the elevation of which is known (assumed or known w.r.t. MSL). It is used as a starting point for levelling or as a point upon which to close for a check. The following are the different types of benchmarks used in surveying: (a) GTS benchmarks (b) Permanent benchmarks (c) Arbitrary benchmarks and (d) Temporary benchmarks. (a) GTS Benchmark: The long form of GTS benchmark is Great Trigonometrical Survey benchmark. These benchmarks are established by national agency. In India, the department of Survey of India is entrusted with such works. GTS benchmarks are established all over the country with highest precision survey, the datum being mean sea level. A bronze plate provided on the top of a concrete pedastal with elevation engraved on it serves as benchmark. It is well protected with masonry structure built around it so that its position is not disturbed by animals or by any unauthorised person. The position of GTS benchmarks are shown in the topo sheets published. (b) Permanent Benchmark: These are the benchmarks established by state government agencies like PWD. They are established with reference to GTS benchmarks. They are usually on the corner of plinth of public buildings. (c) Arbitrary Benchmark: In many engineering projects the difference in elevations of neighbouring points is more important than their reduced level with respect to mean sea level. In such cases a relatively permanent point, like plinth of a building or corner of a culvert, are taken as benchmarks, their level assumed arbitrarily such as 100.0 m, 300.0 m, etc. (d) Temporary Benchmark: This type of benchmark is established at the end of the day’s work, so that the next day work may be continued from that point. Such point should be on a permanent object so that next day it is easily identified.
2.1.4 Levelling Instruments A level is an instrument giving horizontal line of sight and magnifying the reading at a far away distance. It consists of the following parts: (i) A telescope to provide a line of sight (ii) A level tube to make the line of sight horizontal and (iii) A levelling head to level the instrument. The following types of levels are available: (i) Dumpy level (ii) Wye (or, Y) level
(iii) Cooke’s reversible level (iv) Cushing’s level (v) Tilting level and (vi) Auto level. DumpyLevel It is a short and stout instrument with telescope tube rigidly connected to the vertical spindle. Hence the level tube cannot move in vertical plane. It cannot be removed from its support. Hence it is named as dumpy level. The telescope rotates in horizontal plane in the socket of the levelling head. A bubble tube is attached to the top of the telescope. Figure 15.3 shows a typical dumpy level. In below shows its photograph.
Telescope is a tube with object glass and eyepiece. Object glass can be adjusted using the focussing screw before sighting the graduated staff held on the object. Eyepiece can be adjusted by rotating it to see that parallel is removed and cross hairs appears distinctly. Eyepiece once adjusted needs no change as long as the same person takes the readings.
Level tube is a glass tube with slightly curved shape provided over the level tube. The tube is filled with ether or alcohol leaving a little air gap, which takes the shape of a bubble. The air bubble is always at the highest point. The level tube is fixed with its axis parallel to telescope tube, so that when bubble is centred, the telescope is horizontal. The tube is graduated on either side of its centre to estimate how much the bubble is out of centre. The glass tube is placed inside a brass tube which is open from top and on lower side it is fixed to telescope tube by means of capston headed nuts. The bubble tube is adjusted with these nuts, if it is out of order. Levelling head consists of two parallel plates with three foot screws. The upper plate is known as tribratch plate and the lower one as the trivet. The lower plate can be screwed on to the tripod stand. By adjusting the screws the instrument can be levelled to get perfect horizontal line of sight. Dumpy level is to be fitted to a tripod stand to use it in the field. The tripod stand consists of three legs connected to a head to which the lower plate of level can be fitted. The lower side of the legs are provided with metal shoes to get good grip with ground. In below Plate shows typical level stands.
Wye or Y-Level In this type of level, the telescope is supported in two Y-shaped supports and can be fixed with the help of curved clips. Clips can be opened and telescope can be reversed end to end and fitted. The advantage of this level is some of the errors eliminated, if the readings are taken in both the direction of telescope. Cooke’sReversibleLevel In this instrument the telescope is supported by two rigid sockets into which telescope can be introduced from either end and then screwed. For taking the readings in the reversed position of telescope, the screw is slackened and then the telescope is taken out and reversed end for end. Thus it combines the rigidity of dumpy level and reversibility of Y-level. CushingsLevel In this reversing of telescope end for end is achieved by interchanging the eyepiece and the objective piece since both collars are exactly the same.
TiltingLevel In this, telescope can be tilted through about four degrees with the help of a tilting screw. Hence bubble can be easily centered. But it needs centering of the bubble before taking every reading. Hence it is useful, if at every setting of the instrument number of readings to be taken are few. AutoLevel The auto-level or the automatic-level is a self aligning level. Within a certain range of tilt automatic levelling is achieved by an inclination compensating device. The operational comfort, high speed and precision are the advantages of this instrument.
Levelling Staff Along with a level, a levelling staff is also required for levelling. The levelling staff is a rectangular rod having graduations. The staff is provided with a metal shoes at its bottom to resist wear and tear. The foot of the shoe represents zero reading. Levelling staff may be divided into two groups: (i) Self reading staff (ii) Target staff. (i) Self reading staff: This staff reading is directly read by the instrument man through telescope. In a metric system staff, one metre length is divided into 200 subdivisions, each of uniform thickness of 5 mm. All divisions are marked with black in a white background. Metres and decimetres are written in red colour. The following three types of self reading staffs are available: (a) Solid staff: It is a single piece of 3 m. (b) Folding staff: A staff of two pieces each of 2 m which can be folded one over the other. (c) Telescopic staff: A staff of 3 pieces with upper one solid and lower two hollow. The upper part can slide into the central one and the central part can go into the lower part. Each length can be pulled up and held in position by means of brass spring. The total length may be 4 m or 5 m .
(ii) Target staff: If the sighting distance is more, instrument man finds it difficult to read self reading staff. In such case a target staff shown in may be used. Target staff is similar to self reading staff, but provided with a movable target. Target is a circular or oval shape, painted red and white in alternate quadrant. It is fitted with a vernier at the centre. The instrument man directs the person holding target staff to move the target, till its centre is in the horizontal line of sight. Then target man reads the target and is recorded.
2.1.5 Method of Levelling The following methods are used to determine the difference in elevation of various points: (i) Barometric levelling (ii) Hypsometric levelling (iii) Direct levelling and (iv) Indirect levelling. Barometric Levelling This method depends on the principle that atmospheric pressure depends upon the elevation of place. Barometer is used to measure the atmospheric pressure and hence elevation is computed. However it is not accurate method since the atmospheric pressure depends upon season and temperature also. It may be used in exploratory surveys. Hypsometric Levelling This is based on the principle that boiling point of water decreases with the elevation of the place. Hence the elevation difference between two points may be found by noting the difference in boiling point of water in the two places. This method is also useful only for exploratory survey. Direct Levelling It is common form of levelling in all engineering projects. In this method horizontal sight is taken on a graduated staff and the difference in the elevation of line of sight and ground at which staff is held are found. Knowing the height of line of sight from the instrument station the difference in the elevations of instrument station and the ground on which staff is held can be found. This method is thoroughly explained in next article. Indirect Methods In this method instruments are used to measure the vertical angles. Distance between the instrument and staff is measured by various methods. Then using trigonometric relations, the difference in elevation can be computed. This is considered beyond the scope of this book. One can find details of such methods in books on surveying and levelling.
2.1.6 Terms Used in Direct Levelling Methods The following terms are used in direct method of levelling: (i) Plane of Collimation: It is the reduced level of plane of sight with respect to the datum selected. It is also known as ‘height of instrument’. It should not be confused with the height of telescope from the ground where the instrument is set. (ii) Back Sight (BS): It is the sight taken on a level staff held on the point of known elevation with an intension of determining the plane of collimation. It is always the first reading after the instrument is set in a place. It is also known as plus sight, since this reading is to be added to RL of the point (Benchmark or change point) to get plane of collimation. (iii) Intermediate Sight (IS): Sights taken on staff after back sight (first sight) and before the last sight (fore sight) are known as intermediate sights. The intension of taking these readings is to find the reduced levels of the points where staff is held. These sights are known as ‘minus sights’ since the IS reading is to be subtracted from plane of collimation to get RL of the point where staff is held. (iv) Fore Sight (FS): This is the last reading taken from the instrument station before shifting it or just before ending the work. This is also a minus sight. (v) Change Point (CP): This is also known as turning point (TP). This is a point on which both fore sights and back sights are taken. After taking fore sight on this point instrument is set at some other convenient point and back sight is taken on the staff held at the same point. The two readings help in establishing the new plane of collimation with respect to the earlier datum. Since there is time gap between taking the two sights on the change point, it is advisable to select change point on a well defined point.
2.1.6 Temporary Adjustments of Level The adjustments to be made at every setting of the instrument are called temporary adjustments. The following three adjustments are required for the instrument whenever set over a new point before taking a reading: (i) Setting (ii) Levelling and (iii) Focussing. Setting Tripod stand is set on the ground firmly so that its top is at a convenient height. Then the level is fixed on its top. By turning tripod legs radially or circumferentially, the instrument is approximately levelled. Some instruments are provided with a less sensitive circular bubble on tribrach for this purpose. Levelling The procedure of accurate levelling with three levelling screw is as given below: (i) Loosen the clamp and turn the telescope until the bubble axis is parallel to the line joining any two screws.
(ii) Turn the two screws inward or outward equally and simultaneously till bubble is centred. (iii) Turn the telescope by 90° so that it lies over the third screw and level the instrument by operating the third screw. (iv) Turn back the telescope to its original position and check the bubble. Repeat steps (ii) to (iv) till bubble is centred for both positions of the telescope. (v) Rotate the instrument by 180°. Check the levelling. Focussing Focussing is necessary to eliminate parallax while taking reading on the staff. The following two stepsare required in focussing: (i) Focussing the eyepiece: For this, hold a sheet of white paper in front of telescope and rotate eyepiece in or out till the cross hairs are seen sharp and distinct. (ii) Focussing the objective: For this telescope is directed towards the staff and the focussing screw is turned till the reading appears clear and sharp.
2.1.7 Types of Direct Levelling The following are the different types of direct levelling: (i) Simple levelling (ii) Differential levelling (iii) Fly levelling (iv) Profile levelling (v) Cross sectioning and (vi) Reciprocal levelling. Simple Levelling It is the method used for finding difference between the levels of two nearby points. Figure 15.6 shows one such case in which level of A is assumed, say 200.00 m. RL of B is required.
RL of A = 200.00 m Back sight on A = 2.7 m. Plane of collimation for setting at station = 200 + 2.7 = 202.7 m Fore sight on B = 0.80 m RL of B = 202.7 – 0.80 = 201.9 m It may be noted that the instrument station L1 need not be along the line AB (in plan) and RL of L1 do not appear in the calculations. Differential Levelling If the distance between two points A and B is large, it may not be possible to take the readings on A and B from a single setting. In such situation differential levelling is used. In differential levelling the instrument is set at more than one position, each shifting facilitated by a change point. Figure 15.7 shows a scheme of such setting.
RL of A is 200.00 m. Instrument is set up at L1 and back sight on A is 1.35 m. The fore sight on change point CP1 is 1.65 m. Then instrument is shifted to L2 and back sight on CP1 is 1.40 m. Fore sight on CP2 is 1.70 m. After this instrument is shifted to L3 and back sight on CP2 is 1.3 m. The work ended with a fore sight of 1.85 m on B. The RL of B is to be found. RL of A = 200.00 m Back sight on A = 1.35 m Plane of collimation at L1 = 200 + 1.35 = 201.35 m Fore sight on CP1 = 1.65 m RL of CP1 = 201.35 – 1.65 = 199.70 m Back sight to CP1 from L2 = 1.40 Plane of collimation at L2 = 199.70 + 1.40 = 201.10 m Fore sight to CP2 = 1.70 m RL of CP2 = 201.10 – 1.70 = 199.40 m Back sight to CP2 from L3 = 1.30 m Plane of collimation at L3 = 199.40 + 1.30 = 200.70 m Fore sight to B = 1.85 m RL of B = 200.70 – 1.85 = 198.85 m Ans. If there are intermediate sight to the points E1 and E2, the RL of those points may be obtained by subtracting readings for E1 and E2 from the corresponding plane of collimations.
Booking and Reducing the Levels The booking of readings and reducing the levels can be carried out systematically in the tabular form. There are two such methods: (i) Plane of collimation method (ii) Rise and fall method. For the above problem, with intermediate sights to E1 = 0.80 m and E2 = 0.70 m is illustrated below by the both methods.
In this method note the following: 1. Plane of collimation for first setting = RL of BM + BS 2. Subtract IS from plane of collimation to get RL of intermediate station and subtract FS from plane of collimation to get RL of change point. 3. Add back sight to RL of change point to get new plane of collimation. 4. Check: Σ BS – Σ FS = RL of Last point – RL of first point. If it is –ve, it is fall and if +ve it is rise.
Note the following: 1. From A to E1, difference = 1.35 – 0.80 = 0.55, rise 2. From E1 to CP1, difference = 0.80 – 1.65 = – 0.85, fall 3. From CP1 to E2, difference = 1.40 – 0.70 = 0.70, rise 4. From E2 to CP2, difference = 0.70 – 1.70 = –1.00, fall 5. From CP2 to B, difference = 1.30 – 1.85 = – 0.55, fall. Fly Levelling If the work site is away from the benchmark, surveyor starts the work with a back sight on the benchmark by setting instrument at a convenient point. Then he proceeds towards the site by taking fore sights and back sights on a number of change points till he establishes a temporary benchmark in the site. Rest of the levelling work is carried out in the site. At the end of the work again levelling is carried out by taking a set of convenient change points till the bench work is reached. This type of levelling in which only back sight and fore sights are taken, is called fly levelling, the purpose being to connect a benchmark with a temporary benchmark or vice versa. Thus the difference between fly levelling and differential levelling is only in the purpose of levelling. Profile Levelling This type of levelling is known as longitudinal sectioning. In high way, railway, canal or sewage line projects profile of the ground along selected routes are required. In such cases, along the route, at regular interval readings are taken and RL of various points are found. Then the section of the route is drawn to get the profile. In below fig (a) shows the plan view of the scheme of levelling and in below fig (b) shows the profile of the route. For drawing profile of the route, vertical scale is usually larger compared to scale for horizontal distances. It gives clear picture of the profile of the route.
The typical page of field book for this work will be having an additional column to note distances as shown in above table
Cross-Sectioning In many engineering projects, not only longitudinal profile but also the profile of cross-sections at regular intervals are required. These profiles help in calculating the earth works involved in the projects. in below Figure shows the scheme of such work in which longitudinal profile is found by taking readings at 20 m interval along chain lines AB, BC and readings are taken at an interval of 3 m on either side. The distances on the cross-sections are treated as left or right of the lines as they are found while facing the forward station of survey. The cross-sectional length depends upon the nature of the project.
Reciprocal Levelling In levelling, it is better to keep distance of back sight and fore sight equal. By doing so the following errors are eliminated: (i) Error due to non-parallelism of line of collimation and axis of bubble tube. (ii) Errors due to curvature and refraction. But in levelling across obstacles like river and ravine, it is not possible to maintain equal
distances for fore sight and back sight. In such situations reciprocal levelling as described below is used:
2.2 THEODOLITE A theodolite /θiːˈɒdəlaɪt/ is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are used mainly forsurveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology. A modern theodolite consists of a movable telescope mounted within two perpendicular axes—the horizontal or trunnion axis, and the vertical axis. When the telescope is pointed at a target object, the angle of each of these axes can be measured with great precision, typically to seconds of arc. Theodolites, such as the Brunton Pocket Transit commonly employed for field measurements by geologists and archaeologists, have been in continuous use since 1894. Theodolites may be either transit or non-transit. Transit theodolites (or just 'Transits') are those in which the telescope can be inverted in the vertical plane, whereas the rotation in the same plane is restricted to a semi-circle for non-transit theodolites. Some types of transit theodolites do not allow the measurement of vertical angles. The builder's level is sometimes mistaken for a transit theodolite, but it measures neither horizontal nor vertical angles. It uses a spirit level to set atelescope level to define a line of sight along a level plane.
Concept of operation Diagram of an Optical Theodolite
The axess and circles of a theodollite A theoddolite is mounted m onn its tripod head by means of a forced centering plate or tribracch containing g four thum mbscrews, orr in modernn theodolitees, three forr rapid levelling. Before use, u a theodo olite must bee precisely placed p verticcal above thee point to bee measured using u a plumb bob, opticall plummet orr laser plum mmet. The instrument is then t set leveel using leveelling footscrew ws and circular and moree precise tubbular spirit buubbles. Both axees of a theeodolite aree equipped with graduated circless that can be b read thrrough magnifyiing lenses. (R R. Anders heelped M. Deenham discover this techhnology in 1864) The veertical circle whhich 'transits' about the horizontal h axxis should reead 90° (1000 grad) whenn the sight axis is horizontaal, or 270° (3 300 grad) whhen the instrrument is in its second position, p thatt is, "turned over" o or "plungged". Half off the differennce betweenn the two possitions is callled the "indeex error". Errors in n measurem ment The horizzontal and vertical v axess of a theodoolite must bee perpendicuular, if not thhen a "horizzontal axis erroor" exists. This T can be tested by aligning a the tubular spiirit bubble parallel p to a line between two footscrews and settting the bubbble central. A horizontaal axis errorr is present if i the bubble ruuns off central when thhe tubular spirit s bubblee is reversedd (turned thhrough 180°). To adjust, thhe operator removes r hallf the amounnt the bubblle has run offf using the adjusting sccrew, then re-leevel, test and d refine the adjustment. a The optical axis of the telescoppe, called thhe "sight axiis", defined by the optical center of o the objectivee lens and the center of the t crosshairrs in its focall plane, must also be perrpendicular to t the horizontaal axis. If no ot, then a "coollimation errror" exists. Index error, e horizzontal axis error annd collimation error are regulaarly determ mined by calibrration and arre removed by b mechaniccal adjustmeent. Their exxistence is taaken into acccount in the chhoice of meaasurement procedure p in order to eliiminate their effect on the t measureement results. History The term m diopter wass sometimes used in old texts as a syynonym for theodolite. This T derives from an older astronomicaal instrumentt called a diooptra. Prior to the theodoliite, instrumeents such as the geomettric square and a various graduated g ciircles (see circuumferentor) and semiciircles (see grraphometer)) were usedd to obtain either e verticcal or
horizontal angle measurements. It was only a matter of time before someone put two measuring devices into a single instrument that could measure both angles simultaneously. Gregorius Reisch showed such an instrument in the appendix of his book Margarita Philosophica, which he published in Strasburg in 1512. It was described in the appendix by Martin Waldseemüller, a Rhineland topographer andcartographer, who made the device in the same year. Waldseemüller called his instrument the polimetrum. The first occurrence of the word "theodolite" is found in the surveying textbook A geometric practice named Pantometria (1571) by Leonard Digges, which was published posthumously by his son, Thomas Digges. The etymology of the word is unknown. The first part of the New Latin theo-delitusmight stem from the Greek θεᾶσθαι, "to behold or look attentively upon" or θεῖν "to run", but the second part is more puzzling and is often attributed to an unscholarly variation of one of the following Greek words: δῆλος, meaning "evident" or "clear", or δολιχός "long", or δοῦλος "slave", or an unattested Neolatin compound combining ὁδός "way" and λιτός "plain"It has been also suggested that -delitus is a variation of the Latin supinedeletus, in the sense of "crossed out". There is some confusion about the instrument to which the name was originally applied. Some identify the early theodolite as an azimuth instrument only, while others specify it as an altazimuth instrument. In Digges's book, the name "theodolite" described an instrument for measuring horizontal angles only. He also described an instrument that measured both altitude and azimuth, which he called a topographicall instrument [sic]. Thus the name originally applied only to the azimuth instrument and only later became associated with the altazimuth instrument. The 1728 Cyclopaediacompares "graphometer" to "half-theodolite". Even as late as the 19th century, the instrument for measuring horizontal angles only was called asimple theodolite and the altazimuth instrument, the plain theodolite. The first instrument more like a true theodolite was likely the one built by Joshua Habermel (de:Erasmus Habermehl) in Germany in 1576, complete with compass and tripod. The earliest altazimuth instruments consisted of a base graduated with a full circle at the limb and a vertical angle measuring device, most often a semicircle. Analidade on the base was used to sight an object for horizontal angle measurement, and a second alidade was mounted on the vertical semicircle. Later instruments had a single alidade on the vertical semicircle and the entire semicircle was mounted so as to be used to indicate horizontal angles directly. Eventually, the simple, open-sight alidade was replaced with a sighting telescope. This was first done by Jonathan Sisson in 1725. The theodolite became a modern, accurate instrument in 1787 with the introduction of Jesse Ramsden's famous great theodolite, which he created using a very accurate dividing engine of his own design. The demand could not be met by foreign theodolites owing to their inadequate precision, hence all instruments meeting high precision requirements were made in England. Despite the many German instrument builders at the turn of the century, there were no usable German theodolites available. A transition was brought about by Breithaupt and the symbiosis of Utzschneider, Reichenbach and Fraunhofer. As technology progressed, in the 1840s, the vertical partial circle was replaced with a full circle, and both vertical and horizontal circles were finely graduated. This was thetransit theodolite. Theodolites were later adapted to a wider variety of mountings and uses. In the 1870s, an interesting waterborne version of the theodolite (using a pendulum device to counteract wave movement) was invented
by Edward Samuel Ritchie. It was used by the U.S. Navy to take the first precision surveys of American harbors on the Atlantic and Gulf coasts. In the early part of the 20th century, Heinrich Wild produced theodolites that became popular with surveyors. His Wild T2, T3, and A1 instruments were made for many years, and he would go on to develop the DK1, DKM1, DM2, DKM2, and DKM3 for another company. With continuing refinements instruments steadily evolved into the modern theodolite used by surveyors today. Operation in surveying Triangulation, as invented by Gemma Frisius around 1533, consists of making such direction plots of the surrounding landscape from two separate standpoints. The two graphing papers are superimposed, providing a scale model of the landscape, or rather the targets in it. The true scale can be obtained by measuring one distance both in the real terrain and in the graphical representation. Modern triangulation as, e.g., practised by Snellius, is the same procedure executed by numerical means. Photogrammetric block adjustment of stereo pairs of aerial photographs is a modern, three-dimensional variant. In the late 1780s Jesse Ramsden, a Yorkshireman from Halifax, England who had developed the dividing engine for dividing angular scales accurately to within a second of arc, was commissioned to build a new instrument for the British Ordnance Survey. The Ramsden theodolite was used over the next few years to map the whole of southern Britain by triangulation. In network measurement, the use of forced centering speeds up operations while maintaining the highest precision. The theodolite or the target can be rapidly removed from, or socketed into, the forced centering plate with sub-mm precision. Nowadays GPS antennas used for geodetic positioning use a similar mounting system. The height of the reference point of the theodolite— or the target—above the ground benchmark must be measured precisely. The American transit gained popularity during the 19th century with American railroad engineers pushing west. The transit replaced the railroad compass, sextantand octant and was distinguished by having a telescope shorter than the base arms, allowing the telescope to be vertically rotated past straight down. The transit had the ability to "flip" over on its vertical circle and easily show the exact 180 degree sight to the user. This facilitated the viewing of long straight lines, such as when surveying the American West. Previously the user rotated the telescope on its horizontal circle to 180 and had to carefully check the angle when turning 180 degree turns. Modern theodolites In today's theodolites, the reading out of the horizontal and vertical circles is usually done electronically. The readout is done by a rotary encoder, which can be absolute, e.g. using Gray codes, or incremental, using equidistant light and dark radial bands. In the latter case the circles spin rapidly, reducing angle measurement to electronic measurement of time differences. Additionally, lately CCD sensors have been added to the focal plane of the telescope allowing
both auto-targeting and the automated measurement of residual target offset. All this is implemented in embedded software. Also, many modern theodolites, costing up to $10,000 apiece, are equipped with integrated electro-optical distance measuring devices, generally infrared based, allowing the measurement in one go of complete three-dimensional vectors — albeit in instrument-defined polar coordinates, which can then be transformed to a pre-existing co-ordinate system in the area by means of a sufficient number of control points. This technique is called a resection solution or free station position surveying and is widely used in mapping surveying. The instruments, "intelligent" theodolites called self-registering tacheometers or "total stations", perform the necessary operations, saving data into internal registering units, or into external data storage devices. Typically, ruggedized laptops or PDAs are used as data collectors for this purpose. Gyrotheodolites A gyrotheodolite is used when the north-south reference bearing of the meridian is required in the absence of astronomical star sights. This occurs mainly in the underground mining industry and in tunnel engineering. For example, where a conduit must pass under a river, a vertical shaft on each side of the river might be connected by a horizontal tunnel. A gyrotheodolite can be operated at the surface and then again at the foot of the shafts to identify the directions needed to tunnel between the base of the two shafts. Unlike an artificial horizon or inertial navigation system, a gyrotheodolite cannot be relocated while it is operating. It must be restarted again at each site. The gyrotheodolite comprises a normal theodolite with an attachment that contains a gyroscope mounted so as to sense rotation of the Earth and from that the alignment of the meridian. The meridian is the plane that contains both the axis of the Earth’s rotation and the observer. The intersection of the meridian plane with the horizontal contains the true north-south geographic reference bearing required. The gyrotheodolite is usually referred to as being able to determine or find true north. A gyrotheodolite will function at the equator and in both the northern and southern hemispheres. The meridian is undefined at the geographic poles. A gyrotheodolite cannot be used at the poles where the Earth’s axis is precisely perpendicular to the horizontal axis of the spinner, indeed it is not normally used within about 15 degrees of the pole because the east-west component of the Earth’s rotation is insufficient to obtain reliable results. When available, astronomical star sights are able to give the meridian bearing to better than one hundred times the accuracy of the gyrotheodolite. Where this extra precision is not required, the gyrotheodolite is able to produce a result quickly without the need for night observations. Theodolite is an instrument which replaced compass and level. It can measure both horizontal and vertical angles. If telescope is kept at zero reading of vertical angle it serves as an ordinary level. In this modern era of electronics equipments have come up to measure the distances to relieve surveyor from chaining long lines. Total station is another modern survey equipment which combines the features of theodolite and electromagnetic distance measurement (EDM) instruments. Global positioning system is an instrument, which establishes global position of the station making use at least 4 satellite stations.
It is a commonly used instrument for measuring horizontal and vertical angles. It is used for prolonging a line, levelling and even for measuring the distances indirectly (techeometry). Using verniers angles can be read accurately up to 20″. Precise theodolites are available which can read angles up to even 1″ accuracy. They use optical principle for more accurate instruments. Now a days electronic theodolites are also available which display the angles. In this article construction and use of vernier theodolite is explained. Though for sketch maps the compass or graphic techniques are acceptable for measuring angles, only the theodolite can assure the accuracy required in the framework needed for precise mapping. The theodolite consists of a telescope pivoted around horizontal and vertical axes so that it can measure both horizontal and vertical angles. These angles are read from circles graduated in degrees and smaller intervals of 10 or 20 minutes. The exact position of the index mark (showing the direction of the line of sight) between two of these graduations is measured on both sides of the circle with the aid of a vernier or a micrometer. The accuracy in modern first-order or geodetic instruments, with five-inch glass circles, is approximately one second of arc, or 1/3,600 of a degree. With such an instrument a sideways movement of the target of one centimetre can be detected at a distance of two kilometres. By repeating the measurement as many as 16 times and averaging the results, horizontal angles can be measured more closely; in geodetic surveying, measurements of all three angles of a triangle are expected to give a sum of 180 degrees within one second of arc. In the most precise long-distance work, signaling lamps or heliographs reflecting the Sun are used as targets for the theodolite. For less demanding work and work over shorter distances, smaller theodolites with simpler reading systems can be used; targets are commonly striped poles or ranging rods held vertical by an assistant. An extensive set of these measurements establishes a network of points both on the map, where their positions are plotted by their coordinates, and on the ground, where they are marked by pillars,concrete ground marks, bolts let into the pavement, or wooden pegs of varying degrees of cost and permanence, depending on the importance and accuracy of the framework and the maps to be based on it. Once this framework has been established, the surveyor proceeds to the detail mapping, starting from these ground marks and knowing that their accuracy ensures that the data obtained will fit precisely with similar details obtained elsewhere in the framework.
2.2.1 PartsofaVernierTheodolite In below Figure shows a sectional view of a typical vernier theodolite and plate 16.1 shows photograph of such theodolite. Main parts of such a theodolite are: 1. Telescope: A telescope is mounted on a horizontal axis (trunnian axis) hence it can rotate in vertical plane. Its length varies from 100 mm 175 mm and its diameter is 38 mm at objective end. Its functions is to provide a line of sight.
Vertical Circle: A vertical circle graduated up to an accuracy of 20′ is rigidly connected to the telescope and hence moves with it when the telescope is rotated in vertical plane. The graduations are in quadrantal system, 0-0 line being horizontal.
Vernier Frame: It is a T-shaped frame consisting of a vertical arm and a horizontal arm. With the help of the climping screws the vertical frame and hence the telescope can be clamped at desired angle. Vertical frame is also known as T-frame or index frame.
The vernier arm is known as index arm. At the ends it carries verniers C and D so as to read graduations on vertical circle. They are provided with glass magnifiers. Altitude bubble tube is fitted over the horizontal arm. Standards or A-Frame: The frames supporting telescope are in the form of English letter ‘A’. This frame allows telescope to rotate on its trunnian axis in vertical frame. The T-frame and the clamps are also fixed to this frame. 5. Upper Plate : Upper plate supports standards on its top surface. On lower side it is attached to a inner spindle which rotates in the outer spindle of lower plate. Using upper clamp, upper plate can be clamped to lower plate. Using tangent screws, it is possible to give slight relative motion between the two plates, even after clamping. Two diametrically opposite verniers A and B fixed to upper plate help in reading horizontal circle graduations. They are provided with magnifying glasses.
Lower Plate: The lower plate, attached to the outer spindle carries a graduated circle at its bevelled edge. Graduations are up to an accuracy of 20′. It can be clamped at any desired position using lower clamps. If upper clamp is locked and the lower one is loosened the two plates rotate together. If the upper clamp is loosened and lower clamp locked, upper plate alone rotates. This mechanism is utilised in measuring horizontal angle. 7. Plate Level: One or two plate level tubes are mounted on the upper plate. If the two level tubes are provided they will be at right angles to each other one of them being parallel to trunnion axis. These levels help in making the vertical axis of the instrument truely vertical. 8. Levelling Head: It consists of two parallel triangular plates known as tribratch plates. The upper tribratch plate is provided with three levelling screws—each one carried by a arm of tribratch plate. By operating screws the levelling of upper plate and hence telescope can be ensured. The lower tribratch can be fitted into a tripod head. 9. Tripod: Theodolite is always used by mounting it on a tripod. The legs of tripod may be solid or framed. At the lower end the legs are provided with steel shoes to get good grip with the ground. The top of tripod is provided with external screw to which the lower tribratch plate can be screwed. When not in use tripod head may be protected with a steel cap, provided for this purpose.
10. Plumb Bob: A hook is provided at the middle of lower tribratch plate from which a plumb bob can be suspended. It facilitates exact centering of the theodolite on a station. 11. Shifting Head: It is provided below the lower plate. In this, one plate slides over another over a small area of about 10 mm radius. The two plates can be tightened in the desired position. It facilitates exact centering of the instruments. 12. Magnetic Compass: In some theodolites a magnetic compass is fixed on one of the strands. It is useful if readings are to be recorded with magnetic north as meridian. UseofTheodolite Theodolite is used for measuring horizontal and vertical angles. For this the theodolite should be centered on the desired station point, levelled and telescope is focussed. This process of centering, levelling and focussing is called temporary adjustment of the instrument. Measurement of Horizontal Angle The procedure is explained for measuring horizontal angle θ = PQR at station Q 1. Set the theodolite at Q with vertical circle to the left of the line of sight and complete all temporary adjustments. 2. Release both upper and lower clamps and turn upper plate to get 0° on the main scale. Then clamp main screw and using tangent screw get exactly zero reading. At this stage vernier A reads 0° and vernier B reads 180°. 3. Through telescope take line of sight to signal at P and lock the lower clamp. Use tangent screw for exact bisection. 4. Release the upper clamp and swing telescope to bisect signal at R. Lock upper clamp and use tangent screen to get exact bisection of R. 5. Read verniers A and B. The reading of vernier A gives desired angle PQR directly, while 180° is to be subtracted from the reading of vernier B to get the angle PQR. 6. Transit (move by 180° in vertical plane) the telescope to make vertical circle to the right of telescope. Repeat steps 2 to 5 to get two more values for the angle. 7. The average of 4 values found for θ, give the horizontal angle. Two values obtained with face left and two obtained with face right position of vertical circle are called one set of readings. 8. If more precision is required the angle may be measured repeatedly. i.e., after step 5, release lower clamp, sight signal at P, then lock lower clamp, release upper clamp and swing the telescope to signal at Q. The reading of vernier A doubles. The angle measured by vernier B is also doubled. Any number of repetitions may be made and average taken. Similar readings are then taken with face right also. Finally average angle is found and is taken as desired angle ‘Q’. This is called method of repetition.
9. There is another method of getting precise horizontal angles. It is called method of reiteration. If a number of angles are to be measured from a station this technique is used. With zero reading of vernier A signal at P is sighted exactly and lower clamp and its tangent screw are locked. Then θ1 is measured by sighting Q and noted. Then θ2, θ3 and θ4 are measured by unlocking upper clamp and bisecting signals at R, S and P. The angles are calculated and checked to see that sum is 360º. In each case both verniers are read and similar process is carried out by changing the face (face left and face right).
Measurement of Vertical Angle Horizontal sight is taken as zero vertical angle. Angle of elevations are noted as +ve angles and angle of depression as –ve angles. To measure vertical angle the following procedure may be followed: 1. Complete all temporary adjustment at the required station. 2. Take up levelling of the instrument with respect to altitude level provided on the A – frame. This levelling process is similar to that used for levelling dumpy level i.e., first altitude level is kept parallel to any two levelling screws and operating those two screws bubble is brought to centre. Then by rotating telescope, level tube is brought at right angles to the original position and is levelled with the third screw. The procedure is repeated till bubble is centred in both positions. 3. Then loosen the vertical circle clamp, bisect P and lock the clamp. Read verniers C and D to get vertical angle. Take the average as the actual vertical angle.
Review Questions 21. What is Levelling method? 22. Explain horizontal Line with all its levels? 23. What is Curvature and Refraction explain? 24. What is Reciprocal leveling? 25. Explain . Theodolite with diagram? 26. What is Vernier and Microptic in theodolite? 27. What is Temporary and Permanent adjustments of vernier transit? 28. Explain Horizontal angles in theolodoite? 29. What is Distances –Traversing? 30. Explain Closing error and distribution in detail?
Chapter 3 TACHEOMETRIC SURVEYING Structure of this unit Tacheometric Systems , Stadia systems Learning Objectives 1. Tacheometric Systems 2. Tangential, Stadia and substense methods 3. Stadia systems – horizontal and inclined sights 4. vertical and normal staff – fixed and movable hair 5. stadia constants, anallatic lens – subtense bar 6. Self reducing tacheometers.
3.1 Tacheometric Systems Tacheometry is a method of measuring both horizontal distance and vertical elevation of a point in the distance, without the use of sophisticated technology such as electronic distance measurement (EDM) or satellite transmissions. Traditional surveying techniques that involve taping, pacing, or odometers are also not used. It is considered less accurate than the most modern methods of surveying, but is still of practical value in topographic mapping for regions that don't have access to high technology. There are several different types of tacheometry system, including the stadia, subtense bar, and optical wedge systems. The stadia tacheometry method is the most commonly used, however, and incorporates a theodolite controlled by one operator, and a level staff with precise, measured markings on it held by another surveyor at a distance. The theodolite is essentially a custom telescope with horizontal and vertical cross hairs. The telescope is pointed at the staff, and vertical and horizontal angles are displayed in relation to markings on the staff, which determines distance and elevation. The two horizontal markings on the theodolite are known as stadia hairs, which are an equal distance above and below a horizontal line, and they cross a central vertical cross hair line. Theodolites used in the process of tacheometry have varying levels of sophistication. The first types made in the early 19th century had fixed stadia hairs and an ability to flip over and sight in the reverse direction, so that a point of reference could be established to reduce measurement errors. Some newer theodolites have movable horizontal stadia hairs, and their position can be measured with a micrometer for more accurate horizontal and vertical sighting. Early theodolites were referred to as transit instruments, and are still used for basic topographic mapping and quick measure uses such as in archeology and geology, where precise measurements of distance and height are not required. One of the advantages of tacheometry is that it is a rapid surveying method, and, if a basic theodolite is used, the equipment is fairly lightweight and easy to take into the field. It requires only two operators, one to hold the leveling rod with the stadia hair markings and one to measure it with the theodolite from a distance. The accuracy of the measured distances decreases in tacheometry as the distance between the leveling staff and theodolite increases. At a range of a quarter-mile (402 meters), the process is considered quite accurate, and, at a distance of a mile (1,609 meters), the error in horizontal distance is around 32 feet (9.75 meters) and 4 inches (10.16 centimeters) vertically The ordinary methods of surveying with a theodolite, chain, and levelling instrument are fairly satisfactory when the ground is pretty clear of obstructions and not very precipitous, but it becomes extremely cumbersome when the ground is covered with bush, or broken up by ravines. Chain measurements then become slow and liable to considerable error; the levelling, too, is carried on at great disadvantage in point of speed, though without serious loss of accuracy. Tacheometry is a branch of surveying in which horizontal and vertical distances are determined by angular observations with a tacheometer.There is no linear measurement.Tacheometry is not
as accurate as chaining,but it is more rapid in rough and difficult countries where levelling is tedious and chaining is inaccurate and slow. It is a method of surveying in which horizontal distances and (relative) vertical elevations are determined from subtended intervals and vertical angles observed with an instrument. Tacheometry is used for 1. preparation of topographic map where both horizontal and vertical distances are required to be measured; 2. survey work in difficult terrain where direct methods of measurements are inconvenient; 3. reconnaissance survey for highways and railways etc; 4. establishment of secondary control points. Instrument The instruments employed in tacheometry are the engineer's transit and the leveling rod or stadia rod, the theodolite and the subtense bar, the self-reducing theodolite and the leveling rod, the distance wedge and the horizontal distance rod, and the reduction tacheometer and the horizontal distance rod.
3.1.1 Systems or Techeometry measurement Depending on the type of instrument and methods/types of observations, tacheometric measurement systems can be divided into two basic types: (i) Stadia systems and (ii) Non-stadia systems Stadia Systems In there system's, staff intercepts at a pair of stadia hairs present at diaphragm, are considered. The stadia system consists of two methods: • •
Fixed-hair method and Movable-hair method
Non Stadia Syatems This method of surveying is primarily based on principles of trigonometry and thus telescopes without stadia diaphragm are used. This system comprises of two methods: (i) Tangential method and (ii) Subtense bar method.
Fixed air method or stadia method It is the most prevalent method for tacheometric surveying. In this method, the telescope of the theodolite is equipped with two additional cross hairs, one above and the other below the main horizontal hair at equal distance. These additional cross hairs are known as stadia hairs. This is also known as tacheometer. Principle of stadia method A tacheometer is temporarily adjusted on the station P with horizontal line of sight. Let a and b be the lower and the upper stadia hairs of the instrument and their actual vertical separation be designated as i. Let f be the focal length of the objective lens of the tacheometer and c be horizontal distance between the optical centre of the objective lens and the vertical axis of the instrument. Let the objective lens is focused to a staff held vertically at Q, say at horizontal distance D from the instrument station.
By the laws of optics, the images of readings at A and B of the staff will appear along the stadia hairs at a and b respectively. Let the staff interval i.e., the difference between the readings at A and B be designated by s. Similar triangle between the object and image will form with vertex at the focus of the objective lens (F). Let the horizontal distance of the staff from F be d. Then, from the similar ABF and a' b' F,
as a' b' = ab = i. The ratio (f / i) is a constant for a particular instrument and is known as stadia interval factor, also instrument constant. It is denoted by K and thus d = K.s --------------------- Equation (.1) The horizontal distance (D) between the center of the instrument and the station point (Q) at which the staff is held is d + f + c. If C is substituted for (f + c), then the horizontal distance D from the center of the instrument to the staff is given by the equation D = Ks + C ---------------------- Equation (2) The distance C is called the stadia constant. Equation (2) is known as the stadia equation for a line of sight perpendicular to the staff intercept. Determination of Tacheometric Constants The stadia interval factor (K) and the stadia constant (C) are known as tacheometric constants. Before using a tacheometer for surveying work, it is reqired to determine these constants. These can be computed from field observation by adopting following procedure. Step 1 : Set up the tacheometer at any station say P on a flat ground. Step 2 : Select another point say Q about 200 m away. Measure the distance between P and Q accurately with a precise tape. Then, drive pegs at a uniform interval, say 50 m, along PQ. Mark the peg points as 1, 2, 3 and last peg -4 at station Q. Step 3 : Keep the staff on the peg-1, and obtain the staff intercept say s1 . Step 4 : Likewise, obtain the staff intercepts say s2, when the staff is kept at the peg-2, Step 5 : Form the simultaneous equations, using Equation (2) D1 = K. s 1 + C --------------(i) and D 2 = K. s 2+ C -------------(ii)
Solving Equations (i) and (ii), determine the values of K and C say K1 and C1 . Step 6 : Form another set of observations to the pegs 3 & 4, Simultaneous equations can be obtained from the staff intercepts s3 and s4 at the peg-3 and point Q respectively. Solving those equations, determine the values of K and C again say K2 and C2. Step 7 : The average of the values obtained in steps (5) and (6), provide the tacheometric constants K and C of the instrument.
Anallactic Lens It is a special convex lens, fitted in between the object glass and eyepiece, at a fixed distance from the object glass, inside the telescope of a tacheometer. The function of the anallactic lens is to reduce the stadia constant to zero. Thus, when tacheometer is fitted with anallactic lens, the distance measured between instrument station and staff position (for line of sight perpendicular to the staff intercept) becomes directly proportional to the staff intercept. Anallactic lens is provided in external focusing type telescopes only.
Inclined Stadia Measurements It is usual that the line of sight of the tacheometer is inclined to the horizontal. Thus, it is frequently required to reduce the inclined observations into horizontal distance and difference in elevation.
Let us consider a tacheometer (having constants K and C) is temporarily adjusted on a station, say P. The instrument is sighted to a staff held vertically, say at Q. Thus, it is required to find the horizontal distance PP1 (= H) and the difference in elevation P1Q. Let A, R and B be the staff points whose images are formed respectively at the upper, middle and lower cross hairs of the tacheometer. The line of sight, corresponding to the middle cross hair, is inclined at an angle of elevation q and thus, the staff with a line perpendicular to the line of sight. Therefore A'B' = AB cos q = s cos q where s is the staff intercept AB. The distance D (= OR) is C + K. scos q . But the distance OO1 is the horizontal distance H, which equals OR cos q. Therefore the horizontal distance H is given by the equation. H = (Ks cos q + C) cos q Or H = Ks cos2 q + C cos q ----------------- Equation(.3) in which K is the stadia interval factor (f / i), s is the stadia interval, C is the stadia constant (f + c), and q is the vertical angle of the line of sight read on the vertical circle of the transit. The distance RO1, which equals OR sin q, is the vertical distance between the telescope axis and the middle cross-hair reading. Thus V is given by the equation V = (K s cos q + c) sin q V = Ks sin q cos q + C sin q ----------------- Equation (.4)
----------------- Equation (.5) Thus, the difference in elevation between P and Q is (h + V - r), where h is the height of the instrument at P and r is the staff reading corresponding to the middle hair. Examples Ex1 In order to carry out tacheometric surveying, following observations were taken through a tacheometer set up at station P at a height 1.235m. Staff held Vertical at Q R S
Horizontal distance from P Staff Reading Angle of (m) Elevation (m) 100 1.01 0° 200 2.03 0° 3.465, 2.275, ? 5° 24' 40" 1.280
Compute the horizontal distance of S from P and reduced level of station at S if R.L. of station P
Figure Solution : Since the staff station P and Q are at known distances and observations are taken at horizontal line of sight, from equation 2 i.e. from D = K.s + C, we get 100 = K. 1.01 + C --------------- Equation 1 200 = K. 2.03 + C --------------- Equation 2 where K and C are the stadia interval factor and stadia constant of the instrument.
Therefore Solving equation 1 and 2 , Substituting, value of K in Equation 1, we get C = 100 - 1.01 x 98.04 = 0.98
Now, for the observation at staff station S, the staff intercept s = 3.465 - 1.280 = 2.185 m; Given, the angle of elevation (of a observation at S), q = 5° 24' 40" Using equation 23.3 i.e., D = K s cos2 q + C.cos q, the horizontal distance of S from P is D = 98.04 x 2.185 x cos2 5° 24' 40" + 0.98 cos 5° 24' 40" = 212.312 + 0.9756 = 213.288 m
= (20.11 + 0.0924)m = 20.203 m Thus R.L. of station S = R.L. of P + h + V - r = 262.575 + 1.235 + 20.203 - 2.275 = 281.738 m Uses of Stadia Method The stadia method of surveying is particularly useful for following cases: 1. In differential leveling, the backsight and foresight distances are balanced conveniently if the level is equipped with stadia hairs. 2. In profile leveling and cross sectioning, stadia is a convenient means of finding distances from level to points on which rod readings are taken. 3. In rough trigonometric, or indirect, leveling with the transit, the stadia method is more rapid than any other method. 4. For traverse surveying of low relative accuracy, where only horizontal angles and distances are required, the stadia method is a useful rapid method. 5. On surveys of low relative accuracy - particularly topographic surveys-where both the relative location of points in a horizontal plane and the elevation of these points are desired, stadia is useful. The horizontal angles, vertical angles, and the stadia interval are observed, as each point is sighted; these three observations define the location of the point sighted.
Errors in Stadia Measurement Most of the errors associated with stadia measurement are those that occur during observations for horizontal angles (Lesson 22) and differences in elevation (Lesson 16). Specific sources of errors in horizontal and vertical distances computed from observed stadia intervals are as follows: 1. Error in Stadia Interval factor This produces a systematic error in distances proportional to the amount of error in the stadia interval factor. 2. Error in staff graduations If the spaces on the rod are uniformly too long or too short, a systematic error proportional to the stadia interval is produced in each distance. 3. Incorrect stadia Interval The stadia interval varies randomly owing to the inability of the instrument operator to observe the stadia interval exactly. In a series of connected observations (as a traverse) the error may be expected to vary as the square root of the number of sights. This is the principal error affecting the precision of distances. It can be kept to a minimum by proper focusing to eliminate parallax, by taking observations at favorable times, and by care in observing. 4. Error in verticality of staff This condition produces a perceptible error in measurement of large vertical angles than for small angles. It also produces an appreciable error in the observed stadia interval and hence in computed distances. It can be eliminated by using a staff level. 5. Error due to refraction This causes random error in staff reading. 6. Error in vertical angle Error in vertical angle is relatively unimportant in their effect upon horizontal distance if the angle is small but it is perceptible if the vertical angle is large.
Review Questions 1. What is is Tacheometric Surveying 2. What is Tangential explain with diagram? 3. Explain Stadia and substense methods with diagram? 4. What is horizontal and inclined sights in stadia method? 5. What is vertical and normal staff ? 6. What is fixed and movable hair – stadia constants? 7. Explain anallatic lens? 8. What is Self reducing tacheometers. 9. What are the application of Tacheometric Surveying 10. What are the merit and demerit of Tacheometric Surveying?
Chapter 4 TRIANGULATION SURVEYING Structure of this unit Horizontal and vertical control , Trigonometric leveling, Satellite station Learning Objectives 1. Horizontal and vertical control methods 2. triangulation –network- Signals. Base line 3.
instruments and accessories – extension of base lines - corrections
Satellite station – reduction to centre – Intervisibility of height and distances
5. Trigonometric levelling – Axis single corrections.
4.1 TRIANGULATION SURVEYING In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly (trilateration). The point can then be fixed as the third point of a triangle with one known side and two known angles. Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks. This followed from the work ofWillebrord Snell in 1615–17, who showed how a point could be located from the angles subtended from three known points, but measured at the new unknown point rather than the previously fixed points, a problem called resectioning. Surveying error is minimized if a mesh of triangles at the largest appropriate scale is established first. Points inside the triangles can all then be accurately located with reference to it. Such triangulation methods were used for accurate large-scale land surveying until the rise of global navigation satellite systems in the 1980s. A system of triangles usually affords superior horizontal control. All of the angles and at least one side (the base) of the triangulation system are measured. Though several arrangements can be used, one of the best is the quadrangle or a chain of quadrangles. Each quadrangle, with its four sides and two diagonals, provides eight angles that are measured. To be geometrically consistent, the angles must satisfy three so-called angle equations and one side equation. That is to say the three angles of each triangle, which add to 180°, must be of such sizes that computation through any set of adjacent triangles within the quadrangles will give the same values for any side. Ideally, the quadrangles should be parallelograms. If the system is connected with previously determined stations, the new system must fit the established measurements. When the survey encompasses an area large enough for the Earth’s curvature to be a factor, an imaginary mathematical representation of the Earth must be employed as a reference surface. A level surface at mean sea level is considered to represent the Earth’s size and shape, and this is called thegeoid. Because of gravity anomalies, the geoid is irregular; however, it is very nearly the surface generated by an ellipse rotating on its minor axis—i.e., an ellipsoid slightly flattened at the ends, or oblate. Such a figure is called a spheroid. Several have been computed by various authorities; the one usually used as a reference surface by English-speaking nations is (Alexander Ross) Clarke’s Spheroid of 1866. This oblate spheroid has a polar diameter about 27 miles (43 kilometres) less than its diameter at the Equator. Because the directions of gravity converge toward the geoid, a length of the Earth’s surface measured above the geoid must be reduced to its sea-level equivalent—i.e., to that of the geoid. These lengths are assumed to be the distances, measured on the spheroid, between the extended lines of gravity down to the spheroid from the ends of the measured lengths on the actual surface of the Earth. The positions of the survey stations on the Earth’s surface are given in
spherical coordinates. Bench marks, or marked points on the Earth’s surface, connected by precise leveling constitute the vertical controls of surveying. The elevations of bench marks are given in terms of their heights above a selected level surface called a datum. In large-level surveys the usual datum is the geoid. The elevation taken as zero for the reference datum is the height of mean sea level determined by a series of observations at various points along the seashore taken continuously for a period of 19 years or more. Because mean sea level is not quite the same as the geoid, probably because of ocean currents, in adjusting the level grid for the United States and Canada all heights determined for mean sea level have been held at zero elevation. Because the level surfaces, determined by leveling, are distorted slightly in the area toward the Earth’s poles (because of the reduction in centrifugal force and the increase in the force of gravity at higher latitudes), the distances between the surfaces and the geoid do not exactly represent the surfaces’ heights from the geoid. To correct these distortions, orthometric corrections must be applied to long lines of levels at high altitudes that have a north–south trend. Trigonometric leveling often is necessary where accurate elevations are not available or when the elevations of inaccessible points must be determined. From two points of known position and elevation, the horizontal position of the unknown point is found by triangulation, and the vertical angles from the known points are measured. The differences in elevation from each of the known points to the unknown point can be computed trigonometrically. The National Ocean Service in recent years has hoped to increase the density of horizontal control to the extent that no location in the United States will be farther than 50 miles (80 kilometres) from a primary point, and advances anticipated in analytic phototriangulation suggest that the envisioned density of control may soon suffice insofar as topographic mapping is concerned. Existing densities of control in Britain and much of western Europe are already adequate for mapping and cadastral surveys. Applications Optical 3d measuring systems use this principle as well in order to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object’s surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base b and must be known. By determining the angles between the projection rays of the sensors and the basis, the intersection point, and thus the 3d coordinate, is
calculateed from the triangular t relations. Distancee to a point by b measuringg two fixed angles a
Triangullation may be b used to calculate the coordinates anddistancee from the shhore to the ship. The obsserver at Am measures the angle α beetween the shore and the t ship, annd the obseerver at B does likewise fo or β . With the t length l or o thecoordinnates of A annd B knownn, then the laaw of sines cann be applied to find the coordinates c o the ship at of a C and the distanced. d
The coorrdinates and d distance to a point cann be found by b calculatinng the lengtth of one sidde of a triangle, given meaasurements of o angles annd sides of thhe triangle formed fo by thhat point andd two other known reference points. The folllowing form mulae apply in flat or Euclidean E g geometry. T They becom me inaccuratte if distancess become ap ppreciable coompared to thecurvaturee of the Earrth, but can be b replaced with more com mplicated reesults derivedd using spheerical trigonoometry. Calculation
Using thhe trigonomeetric identitiees tan α = sinn α / cos α and a sin(α + β) β = sin α coss β + cos α sin s β,
this is eqquivalent to:
From this, it is easy y to determiine the distaance of the unknown pooint from eiither observaation point, itts north/soutth and east//west offsetts from the observationn point, andd finally itss full coordinaates. History
Liu Hui (c. 263), Ho ow to measurre the heightt of a sea islaand. Illustrattion from ann edition of 1726 1
Gemma Frisius's 153 33 proposal to use trianggulation for mapmaking m
Nineteennth-century triangulation t n network foor the trianguulation of Rhhineland-Hessse Triangullation today is used for many purpooses, includingg surveying,, navigation,, metrology, astrometry, binocular vision, moddel rocketryy and gun direction ofweap pons. The use of triangless to estimate distances goes back to t antiquity.. In the 6th century BC C the Greek philosopher p Thales T is reecorded as using similaar triangles to estimatee the heighht of the pyram mids by meaasuring the length l of theeir shadows and a that of his h own at thhe same mom ment, and com mparing the ratios r to his height (inteercept theoreem); and to have h estimatted the distaances
to ships at sea as seen from a clifftop, by measuring the horizontal distance traversed by the line-of-sight for a known fall, and scaling up to the height of the whole cliff. Such techniques would have been familiar to the ancient Egyptians. Problem 57 of the Rhind papyrus, a thousand years earlier, defines the seqt or seked as the ratio of the run to the rise of a slope, i.e. the reciprocal of gradients as measured today. The slopes and angles were measured using a sighting rod that the Greeks called a dioptra, the forerunner of the Arabicalidade. A detailed contemporary collection of constructions for the determination of lengths from a distance using this instrument is known, the Dioptraof Hero of Alexandria (c. 10–70 AD), which survived in Arabic translation; but the knowledge became lost in Europe. In China, Pei Xiu (224–271) identified "measuring right angles and acute angles" as the fifth of his six principles for accurate map-making, necessary to accurately establish distances; while Liu Hui (c. 263) gives a version of the calculation above, for measuring perpendicular distances to inaccessible places. In the field, triangulation methods were apparently not used by the Roman specialist land surveyors, the agromensores; but were introduced into medieval Spain through Arabic treatises on the astrolabe, such as that by Ibn al-Saffar (d. 1035). Abu Rayhan Biruni (d. 1048) also introduced triangulation techniques to measure the size of the Earth and the distances between various places. Simplified Roman techniques then seem to have co-existed with more sophisticated techniques used by professional surveyors. But it was rare for such methods to be translated into Latin (a manual on Geometry, the eleventh century Geomatria incerti auctoris is a rare exception), and such techniques appear to have percolated only slowly into the rest of Europe. Increased awareness and use of such techniques in Spain may be attested by the medieval Jacob's staff, used specifically for measuring angles, which dates from about 1300; and the appearance of accurately surveyed coastlines in the Portolan charts, the earliest of which that survives is dated 1296. Gemma Frisius and triangulation for mapmaking On land, the Flemish cartographer Gemma Frisius proposed using triangulation to accurately position far-away places for map-making in his 1533 pamphlet Libellus de Locorum describendorum ratione (Booklet concerning a way of describing places), which he bound in as an appendix in a new edition of Peter Apian's best-selling 1524 Cosmographica. This became very influential, and the technique spread across Germany, Austria and the Netherlands. The astronomer Tycho Brahe applied the method in Scandinavia, completing a detailed triangulation in 1579 of the island of Hven, where his observatory was based, with reference to key landmarks on both sides of the Øresund, producing an estate plan of the island in 1584. In England Frisius's method was included in the growing number of books on surveying which appeared from the middle of the century onwards, including William Cuningham's Cosmographical Glasse (1559), Valentine Leigh's Treatise of Measuring All Kinds of Lands (1562), William Bourne's Rules of Navigation(1571), Thomas Digges's Geometrical Practise named Pantometria (1571), and John Norden's Surveyor's Dialogue (1607). It has been suggested thatChristopher Saxton may have used rough-and-ready triangulation to place features in his county maps of the 1570s; but others suppose that, having obtained rough bearings to features from key vantage points, he may have estimated the
distances to them simply by guesswork Willebrord Snell and modern triangulation networks The modern systematic use of triangulation networks stems from the work of the Dutch mathematician Willebrord Snell, who in 1615 surveyed the distance from Alkmaar to Bergen op Zoom, approximately 70 miles (110 kilometres), using a chain of quadrangles containing 33 triangles in all. The two towns were separated by one degree on the meridian, so from his measurement he was able to calculate a value for the circumference of the earth – a feat celebrated in the title of his book Eratosthenes Batavus (The Dutch Eratosthenes), published in 1617. Snell calculated how the planar formulae could be corrected to allow for the curvature of the earth. He also showed how to resection, or calculate, the position of a point inside a triangle using the angles cast between the vertices at the unknown point. These could be measured much more accurately than bearings of the vertices, which depended on a compass. This established the key idea of surveying a large-scale primary network of control points first, and then locating secondary subsidiary points later, within that primary network. Snell's methods were taken up by Jean Picard who in 1669–70 surveyed one degree of latitude along the Paris Meridian using a chain of thirteen triangles stretching north from Paris to the clocktower of Sourdon, near Amiens. Thanks to improvements in instruments and accuracy, Picard's is rated as the first reasonably accurate measurement of the radius of the earth. Over the next century this work was extended most notably by the Cassini family: between 1683 and 1718 Jean-Dominique Cassini and his son Jacques Cassini surveyed the whole of the Paris meridian from Dunkirk toPerpignan; and between 1733 and 1740 Jacques and his son César Cassini undertook the first triangulation of the whole country, including a re-surveying of the meridian arc, leading to the publication in 1745 of the first map of France constructed on rigorous principles. Triangulation methods were by now well established for local mapmaking, but it was only towards the end of the 18th century that other countries began to establish detailed triangulation network surveys to map whole countries. The Principal Triangulation of Great Britain was begun by the Ordnance Survey in 1783, though not completed until 1853; and the Great Trigonometric Survey of India, which ultimately named and mapped Mount Everest and the other Himalayan peaks, was begun in 1801. For the Napoleonic French state, the French triangulation was extended by Jean Joseph Tranchot into the German Rhineland from 1801, subsequently completed after 1815 by the Prussian general Karl von Müffling. Meanwhile, the famous mathematicianCarl Friedrich Gauss was entrusted from 1821 to 1825 with the triangulation of the kingdom of Hanover, for which he developed the method of least squares to find the best fit solution for problems of large systems of simultaneous equations given more real-world measurements than unknowns. Today, large-scale triangulation networks for positioning have largely been superseded by the Global navigation satellite systems established since the 1980s. But many of the control points for the earlier surveys still survive as valued historical features in the landscape, such as the concretetriangulation pillars set up for retriangulation of Great Britain (1936–1962), or the triangulation points set up for the Struve Geodetic Arc (1816–1855), now scheduled as a
UNESCO World Heritage Site.
4.2 Triangulation network The horizontal positions of points is a network developed to provide accurate control for topographic mapping, charting lakes, rivers and ocean coast lines, and for the surveys required for the design and construction of public and private works of large extent. The horizontal positions of the points can be obtained in a number of different ways in addition to traversing. These methods are triangulation, trilateration, intersection, resection, and satellite positioning. The method of surveying called triangulation is based on the trigonometric proposition that if one side and two angles of a triangle are known, the remaining sides can be computed. Furthermore, if the direction of one side is known, the directions of the remaining sides can be determined. A triangulation system consists of a series of joined or overlapping triangles in which an occasional side is measured and remaining sides are calculated from angles measured at the vertices of the triangles. The vertices of the triangles are known as triangulation stations. The side of the triangle whose length is predetermined, is called the base line. The lines of triangulation system form a network that ties together all the triangulation stations.
Triangulation network A trilateration system also consists of a series of joined or overlapping triangles. However, for trilateration the lengths of all the sides of the triangle are measured and few directions or angles are measured to establish azimuth. Trilateration has become feasible with the development of electronic distance measuring (EDM) equipment which has made possible the measurement of all lengths with high order of accuracy under almost all field conditions. A combined triangulation and trilateration system consists of a network of triangles in which all the angles and all the lengths are measured. Such a combined system represents the strongest network for creating horizontal control. Since a triangulation or trilateration system covers very large area, the curvature of the earth has
to be taken into account. These surveys are, therefore, invariably geodetic. Triangulation surveys were first carried out by Snell, a Dutchman, in 1615. Field procedures for the establishment of trilateration station are similar to the procedures used for triangulation, and therefore, henceforth in this chapter the term triangulation will only be used.
Principle of triangulation
4.2.1 OBJECTIVE OF TRIANGULATION SURVEYS The main objective of triangulation or trilateration surveys is to provide a number of stations whose relative and absolute positions, horizontal as well as vertical, are accurately established. More detailed location or engineering survey are then carried out from these stations. The triangulation surveys are carried out
(i) to establish accurate control for plane and geodetic surveys of large areas, by terrestrial methods, (ii) to establish accurate control for photogrammetric surveys of large areas, (iii) to assist in the determination of the size and shape of the earth by making observations for latitude, longitude and gravity, and (iv) to determine accurate locations of points in engineering works such as : (a) Fixing centre line and abutments of long bridges over large rivers. (b) Fixing centre line, terminal points, and shafts for long tunnels. (c) Transferring the control points across wide sea channels, large water bodies, etc. (d) Detection of crustal movements, etc. (e) Finding the direction of the movement of clouds.
4.2.2 CLASSIFICATION OF TRIANGULATION SYSTEM Based on the extent and purpose of the survey, and consequently on the degree of accuracy desired, triangulation surveys are classified as first-order or primary, second-order or secondary, and third-order or tertiary. First-order triangulation is used to determine the shape and size of the earth or to cover a vast area like a whole country with control points to which a second-order triangulation system can be connected. A second-order triangulation system consists of a network within a first-order triangulation. It is used to cover areas of the order of a region, small country, or province. A third-order triangulation is a framework fixed within and connected to a second-order triangulation system. It serves the purpose of furnishing the immediate control for detailed engineering and location surveys.
TRIANGULATION FIGURES AND LAYOUTS The basic figures used in triangulation networks are the triangle, braced or geodetic quadilateral, and the polygon with a central station
The triangles in a triangulation system can be arranged in a number of ways. Some of the commonly used arrangements, also called layouts, are as follows : 1. Single chain of triangles 2. Double chain of triangles 3. Braced quadrilaterals 4. Centered triangles and polygons 5. A combination of above systems.
4.2 Single chain of triangles When the control points are required to be established in a narrow strip of terrain such as a valley between ridges, a layout consisting of single chain of triangles is generally used as shown in. This system is rapid and economical due to its simplicity of sighting only four other stations, and does not involve observations of long diagonals. On the other hand, simple triangles of a triangulation system provide only one route through which distances can be computed, and hence, this system does not provide any check on the accuracy of observations. Check base lines and astronomical observations for azimuths have to be provided at frequent intervals to avoid excessive accumulation of errors in this layout.
Double chain of triangles A layout of double chain of triangles is shown in Fig. 1.5. This arrangement is used for covering the larger width of a belt. This system also has disadvantages of single chain of triangles system.
Braced quadrilaterals A triangulation system consisting of figures containing four corner stations and observed diagonals shown in below Fig. is known as a layout of braced quadrilaterals. In fact, braced quadrilateral consists of overlapping triangles. This system is treated to be the strongest and the best arrangement of triangles, and it provides a means of computing the lengths of the sides using different combinations of sides and angles. Most of the triangulation systems use this arrangement.
Centered triangles and polygons A triangulation system which consists of figures containing interior stations in triangle and polygon as shown in below Fig., is known as centered triangles and polygons.
This layout in a triangulation system is generally used when vast area in all directions is required to be covered. The centered figures generally are quadrilaterals, pentagons, or hexagons with central stations. Though this system provides checks on the accuracy of the work, generally it is not as strong as the braced quadrilateral arrangement. Moreover, the progress of work is quite slow due to the fact that more settings of the instrument are required. A combination of all above systems Sometimes a combination of above systems may be used which may be according to the shape of the area and the accuracy requirements. LAYOUT OF PRIMARY TRIANGULATION FOR LARGE COUNTRIES The following two types of frameworks of primary triangulation are provided for a large country to cover the entire area. 1. Grid iron system 2. Central system Grid iron system In this system, the primary triangulation is laid in series of chains of triangles, which usually runs roughly along meridians (northsouth) and along perpendiculars to the meridians (east-west), throughout the country. The distance between two such chains may vary from 150 to 250 km. The area between the parallel and perpendicular series of primary triangulation, are filled by the secondary and tertiary triangulation systems. Grid iron system has been adopted in India and other countries like Austria, Spain, France, etc.
Central system In this system, the whole area is covered by a network of primary triangulation extending in all directions from the initial triangulation figure ABC, which is generally laid at the centre of the country (Fig. 1.9). This system is generally used for the survey of an area of moderate extent. It has been adopted in United Kingdom and various other countries.
CRITERIA FOR SELECTION OF THE LAYOUT OF TRIANGLES The under mentioned points should be considered while deciding and selecting a suitable layout of triangles. 1. Simple triangles should be preferably equilateral. 2. Braced quadrilaterals should be preferably approximate squares. 3. Centered polygons should be regular. 4. The arrangement should be such that the computations can be done through two or more independent routes. 5. The arrangement should be such that at least one route and preferably two routes form wellconditioned triangles. 6. No angle of the figure, opposite a known side should be small, whichever end of the series is used for computation. 7. Angles of simple triangles should not be less than 45°, and in the case of quadrilaterals, no angle should be less than 30°. In the case of centered polygons, no angle should be less than 40°. 8. The sides of the figures should be of comparable lengths. Very long lines and very short lines should be avoided. 9. The layout should be such that it requires least work to achieve maximum progress. 10. As far as possible, complex figures should not involve more than 12 conditions. It may be noted that if a very small angle of a triangle does not fall opposite the known side it does not affect the accuracy of triangulation. 4.3 WELL-CONDITIONED TRIANGLES The accuracy of a triangulation system is greatly affected by the arrangement of triangles in the layout and the magnitude of the angles in individual triangles. The triangles of such a shape, in which any error in angular measurement has a minimum effect upon the computed lengths, is known as well-conditioned triangle. In any triangle of a triangulation system, the length of one side is generally obtained from computation of the adjacent triangle. The error in the other two sides if any, will affect the sides of the triangles whose computation is based upon their values. Due to accumulated errors, entire triangulation system is thus affected thereafter. To ensure that two sides of any triangle are equally affected, these should, therefore, be equal in length. This condition suggests that all the triangles must, therefore, be isoceles. Let us consider an isosceles triangle ABC whose one side AB is of known length. Let A, B, and C be the three angles of the triangle and a, b, and c are the three sides opposite to the angles, respectively.
As the triangle is isosceles, let the sides a and b be equal
4.4 STRENGTH OF FIGURE The strength of figure is a factor to be considered in establishing a triangulation system to maintain the computations within a desired degree of precision. It plays also an important role in deciding the layout of a triangulation system. The U.S. Coast and Geodetic Surveys has developed a convenient method of evaluating the strength of a triangulation figure. It is based on the fact that computations in triangulation involve use of angles of triangle and length of one known side. The other two sides are computed by sine law. For a given change in the angles, the sine of small angles change more rapidly than those of large angles. This suggests that smaller angles less than 30° should not be used in the computation of triangulation. If, due to unavoidable circumstances, angles less than 30° are used, then it must be ensured that this is not opposite the side whose length is required to be computed for carrying forward the triangulation series. The expression given by the U.S. Coast and Geodetic Surveys for evaluation of the strength of figure, is for the square of the probable error (L²) that would occur in the sixth place of the logarithm of any side, if the computations are carried from a known side through a single chain of triangles after the net has been adjusted for the side and angle conditions. The expression for L² is ………………..9 where d is the probable error of an observed direction in seconds of arc, and R is a term which represents the shape of figure. It is given by
Where D = the number of directions observed excluding the known side of the figure, A B C δ ,δ ,δ = the difference per second in the sixth place of logarithm of the sine of the distance angles A, B and C, respectively. (Distance angle is the angle in a triangle opposite to a side), and C = the number of geometric conditions for side and angle to be satisfied in each figure. It is given by
where n = the total number of lines including the known side in a figure, n' = the number of lines observed in both directions including the known side, S = the total number of stations, and
S' = the number of stations occupied For the computation of the quantity In any triangulation system more than one routes are possible for various stations. The strength of figure decided by the factor R alone determines the most appropriate route to adopt the best shaped triangulation net route. If the computed value of R is less, the strength of figure is more and vice versa.
4.5 ACCURACY OF TRIANGULATION Errors are inevitable and, therefore, inspite of all precautions the errors get accumulated. It is, therefore, essential to know the accuracy of the triangulation network achieved so that no appreciable error in plotting is introduced. The following formula for root mean square error may be used.
where m = the root mean square error of unadjusted horizontal angles in seconds of arc as obtained from the triangular errors, ΣE = the sum of the squares of all the triangular errors in the triangulation series, and n =the total number of triangles in the series. It may be noted that (i) all the triangles have been included in the computations, (ii) all the four triangles of a braced quadrilateral have been included in the computations, and (iii) if the average triangular error of the series is 8", probable error in latitudes and departures after a distance of 100 km, is approximately 8 m
Example 1.5Compute the strength of the figure ABCD for all the routes by which the length CD can be computed from the known side AB. Assume that all the stations were occupied.
4.6 ROUTINE OF TRIANGULATION SURVEY The routine of triangulation survey, broadly consists of (a) field work, and (b) computations. The field work of triangulation is divided into the following operations : (i) Reconnaissance (ii) Erection of signals and towers (iii) Measurement of base line (iv) Measurement of horizontal angles (v) Measurement of vertical angles (vi) Astronomical observations to determine the azimuth of the lines
4.7 RECONNAISSANCE Reconnaissance is the preliminary field inspection of the entire area to be covered by triangulation, and collection of relevant data. Since the basic principle of survey is working from whole to the part, reconnaissance is very important in all types of surveys. It requires great skill, experience and judgement. The accuracy and economy of triangulation greatly depends upon proper reconnaissance survey. It includes the following operations: 1. Examination of terrain to be surveyed. 2. Selection of suitable sites for measurement of base lines. 3. Selection of suitable positions for triangulation stations. 4. Determination of intervisibility of triangulation stations. 5. Selection of conspicuous well-defined natural points to be used as intersected points. 6. Collection of miscellaneous information regarding: (a) Access to various triangulation stations (b) Transport facilities
(c) Availability of food, water, etc. (d) Availability of labour (e) Camping ground. Reconnaissance may be effectively carried out if accurate topographical maps of the area are available. Help of aerial photographs and mosaics, if available, is also taken. If maps and aerial photographs are not available, a rapid preliminary reconnaissance is undertaken to ascertain the general location of possible schemes of triangulation suitable for the topography. Later on, main reconnaissance is done to examine these schemes. The main reconnaissance is a very rough triangulation. The plotting of the rough triangulation may be done by protracting the angles. The essential features of the topography are also sketched in. The final scheme is selected by studying the relative strengths and cost to various schemes. For reconnaissance the following instruments are generally employed: 1. Small theodolite and sextant for measurement of angles. 2. Prismatic compass for measurement of bearings. 3. Steel tape. 4. Aneroid barometer for ascertaining elevations. 5. Heliotropes for ascertaining intervisibility. 6. Binocular. 7. Drawing instruments and material 8. Guyed ladders, creepers, ropes, etc., for climbing trees.
4.8 Erection of signals and towers A signal is a device erected to define the exact position of a triangulation station so that it can be observed from other stations whereas a tower is a structure over a station to support the instrument and the observer, and is provided when the station or the signal, or both are to be elevated. Before deciding the type of signal to be used, the triangulation stations are selected. The selection of triangulation stations is based upon the following criteria.
Criteria for selection of triangulation stations 1. Triangulation stations should be intervisible. For this purpose the station points should be on the highest ground such as hill tops, house tops, etc. 2. Stations should be easily accessible with instruments. 3. Station should form well-conditioned triangles. 4. Stations should be so located that the lengths of sights are neither too small nor too long. Small sights cause errors of bisection and centering. Long sights too cause direction error as the signals become too indistinct for accurate bisection. 5. Stations should be at commanding positions so as to serve as control for subsidiary triangulation, and for possible extension of the main triangulation scheme. 6. Stations should be useful for providing intersected points and also for detail survey. 7. In wooded country, the stations should be selected such that the cost of clearing and cutting, and building towers, is minimum. 8. Grazing line of sights should be avoided, and no line of sight should pass over the industrial areas to avoid irregular atmospheric refraction. Determination of intervisibility of triangulation stations As stated above, triangulations stations should be chosen on high ground so that all relevant stations are intervisible. For small distances, intervisibility can be ascertained during reconnaissance by direct observation with the aid of binocular, contoured map of the area, plane mirrors or heliotropes using reflected sun rays from either station. However, if the distance between stations is large, the intervisibility is ascertained by knowing the horizontal distance between the stations as under. Case-I Invervisibility not obstructed by intervening ground If the intervening ground does not obstruct the intervisibility, the distance of visible horizon from the station of known elevation is calculated from the following formula:
Example 6 Two stations A and B, 80 km apart, have elevations 15 m and 270 m above mean sea level, respectively. Calculate the minimum height of the signal at B.
Example 7 There are two stations P and Q at elevations of 200 m and 995 m, respectively. The distance of Q from P is 105 km. If the elevation of a peak M at a distance of 38 km from P is 301 m, determine whether Q is visible from P or not. If not, what would be the height of scaffolding required at Q so that Q becomes visible from P ?
Example 9 In a triangulation survey, the altitudes of two proposed stations A and B, 100 km apart, are respectively 425 m and 750 m. The intervening ground situated at C, 60 km from A, has an elevation of 435 m. Ascertain if A and B are intervisible, and if necessary find by how much B should be raised so that the line of sight must nowhere be less than 3 m above the surface of the ground. Take R = 6400 km and m = 0.07.
4.9 Station Mark The triangulation stations should be permanently marked on the ground so that the theodolite and signal may be centered accurately over them. The following points should be considered while marking the exact position of a triangulation station : (i) The station should be marked on perfectly stable foundation or rock. The station mark on a large size rock is generally preferred so that the theodolite and observer can stand on it. Generally, a hole 10 to 15 cm deep is made in the rock and a copper or iron bolt is fixed with cement. (ii) If no rock is available, a large stone is embeded about 1 m deep into the ground with a circle, and dot cut on it. A second stone with a circle and dot is placed vertically above the first stone. (iii) A G.I. pipe of about 25 cm diameter driven vertically into ground up to a depth of one metre, also served as a good station mark. (iv) The mark may be set on a concrete monument. The station should be marked with a copper or bronze tablet. The name of the station and the date on which it was set, should be stamped on the tablet. (v) In earth, generally two marks are set, one about 75 cm below the surface of the ground, and the other extending a few centimeters above the surface of the ground. The underground mark may consist of a stone with a copper bolt in the centre, or a concrete monument with a tablet mark set on it (vi) The station mark with a vertical pole placed centrally, should be covered with a conical heap of stones placed symmetrically. This
4.10 SIGNALS Signals are centered vertically over the station mark, and the observations are made to these signals from other stations. The accuracy of triangulation is entirely dependent on the degree of accuracy of centering the signals. Therefore, it is very essential that the signals are truly vertical, and centered over the station mark. Greatest care of centering the transit over the station mark will be useless, unless some degree of care in centering the signal is impressed upon. A signal should fulfil the following requirements : (i) It should be conspicuous and clearly visible against any background. To make the signal conspicuous, it should be kept at least 75 cm above the station mark. (ii) It should be capable of being accurately centered over the station mark. (iii) It should be suitable for accurate bisection from other stations. (iv) It should be free from phase, or should exhibit little phase Classification of signals The signals may be classified as under : (i) Non-luminous, opaque or daylight signals (ii) Luminous signals.
(i) Non-luminous signals Non-luminous signals are used during day time and for short distances. These are of various types, and the most commonly used are of following types. (a) Pole signal: It consists of a round pole painted black and white in alternate strips, and is supported vertically over the station mark, generally on a tripod. Pole signals are suitable upto a distance of about 6 km. (b) Target signal: It consists of a pole carrying two squares or rectangular targets placed at right angles to each other. The targets are generally made of cloth stretched on wooden frames. Target signals are suitable upto a distance of 30 km.
(c) Pole and brush signal It consists of a straight pole about 2.5 m long with a bunch of long grass tied symmetrically round the top making a cross. The signal is erected vertically over the station mark by heaping a pile of stones, upto 1.7 m round the pole. A rough coat of white wash is given to make it more conspicuous to be seen against black background. These signals are very useful, and must be erected over every station of observation during reconnaissance. (d) Stone cairn: A pile of stone heaped in a conical shape about 3 m high with a cross shape signal erected over the stone heap, is stone cairn. This white washed opaque signal is very useful if the background is dark.
(e) Beacons: It consists of red and white cloth tied round the three straight poles. The beacon can easily be centered over the station mark. It is very useful for making simultaneous observations.
(ii) Luminous signals Luminous signals may be classified into two types : (i) Sun signals (ii) Night signals. (a) Sun signals: Sun signals reflect the rays of the sun towards the station of observation, and are also known as heliotropes. Such signals can be used only in day time in clear weather.
Heliotrope : It consists of a circular plane mirror with a small hole at its centre to reflect the sun rays, and a sight vane with an aperture carrying a cross-hairs. The circular mirror can be rotated horizontally as well as vertically through 360°. The heliotrope is centered over the station mark, and the line of sight is directed towards the station of observation. The sight vane is adjusted looking through the hole till the flashes given from the station of observation fall at the centre of the cross of the sight vane. Once this is achieved, the heliotrope is disturbed. Now the heliotrope frame carrying the mirror is rotated in such a way that the black shadow of the small central hole of the plane mirror falls exactly at the cross of the sight vane. By doing so, the reflected beam of rays will be seen at the station of observation. Due to motion of the sun, this small shadown also moves, and it should be constantly ensured that the shadow always remains at the cross till the observations are over.
The heliotropes do not give better results compared to signals. These are useful when the signal station is in flat plane, and the station of observation is on elevated ground. When the distance between the stations exceed 30 km, the heliotropes become very useful. (b) Night signals: When the observations are required to be made at night, the night signals of following types may be used. 1. Various forms of oil lamps with parabolic reflectors for sights less than 80 km. 2. Acetylene lamp designed by Capt. McCaw for sights more than 80 km. 3. Magnesium lamp with parabolic reflectors for long sights. 4. Drummond’s light consisting of a small ball of lime placed at the focus of the parabolic reflector, and raised to a very high temperature by impinging on it a stream of oxygen. 5. Electric lamps.
4.11 TOWERS A tower is erected at the triangulation station when the station or the signal or both are to be elevated to make the observations possible form other stations in case of problem of intervisibility. The height of tower depends upon the character of the terrain and the length of the sight. The towers generally have two independent structures. The outer structure is for supporting the observer and the signal whereas the inner one is for supporting the instrument only. The two structures are made entirely independent of each other so that the movement of the observer does not disturb the instrument setting. The two towers may be made of masonary, timber or steel. For small heights, masonary towers are most suitable. Timber scaffolds are most commonly used, and have been constructed to heights over 50 m. Steel towers made of light sections are very portable, and can be easily erected and dismantled. Bilby towers patented by J.S. Bilby of the U.S. Coast and Geodetic Survey, are popular for heights ranging from 30 to 40 m. This tower weighing about 3 tonnes, can be easily erected by five persons in just 5 hrs. A schematic of such a tower is shown in Fig. 1.30.
PHASE OF A SIGNAL When cylindrical opaque signals are used, they require a correction in the observed horizontal angles due an error known as the phase. The cylindrical signal is partly illuminated by the sun, and the other part remains in shadow, and becomes invisible to the observer. While making the observations, the observer may bisect the bright portion or the bright line. Thus the signal is not bisected at the centre, and an error due to wrong bisection is introduced. It is, thus, the apparent displacement of the signal. The phase correction is thus necessary so that the observed horizontal angles may be reduced to that corresponding to the centre of the signal. Depending upon the method of observation, phase correction is computed under the following two conditions. Windows Lamp Screen Outer tower (with bracings) Inner tower (without bracings
Applying the phase correction
to the measured horizontal angles correction, and the observed stations with respect to the line OP, must be noted carefully.
4.11.1 MEASUREMENT OF BASE LINE The accuracy of an entire triangulation system depends on that attained in the measurement of the base line and, therefore, the measurement of base line forms the most important part of the triangulation operations. As base line forms the basis for computations of triangulation system it is laid down with great accuracy in its measurement and alignment. The length of the base line depends upon the grade of the triangulation. The length of the base is also determined by the desirability of securing strong figures in the base net. Ordinarily the longer base, the easier it will be found to secure strong figures. The base is connected to the triangulation system through a base net. This connection may be made through a simple figure , or through a much more complicated figures discussed in the base line extension. Apart from main base line, several
other check bases are also measured at some suitable intervals. In India, ten bases were measured, the length of nine bases vary from 6.4 to 7.8 miles, and that of the tenth base is 1.7 miles.
Selection of site for base line Since the accuracy in the measurement of the base line depends upon the site conditions, the following points should be taken into consideration while selecting the site for a base line. 1. The site should be fairly level or gently undulating. If the ground is sloping, the slope should be uniform and gentle. 2. The site should be free from obstructions throughout the length of the base line. 3. The ground should be firm and smooth. 4. The two extremities of the base line should be intervisible. 5. The site should be such that well-conditioned triangles can be obtained while connecting extremities to the main triangulation stations. 6. The site should be such that a minimum length of the base line as specified, is available. Equipment for base line measurement Generally the following types of base measuring equipments are used : 1. Standardised tapes : These are used for measuring short bases in plain grounds. 2. Hunter’s short base: It is used for measuring 80 m long base line and its extension is made by
subtense method. 3. Tacheometric base measurements : It is used in undulating grounds for small. . 4. Electronic distance measurement: This is used for fairly long distances and has been discussed in Standardised tapes : For measuring short bases in plain areas standardised tapes are generally used. After having measured the length, the correct length of the base is calculated by applying the required corrections. For details of corrections,. If the triangulation system is of extensive nature, the corrected lengths of the base is reduced to the mean sea level. Hunter’s short base : Dr. Hunter who was a Director of Survey of India, designed an equipment to measure the base line, which was named as Hunter’s short base. It consists of four chains, each of 22 yards (20.117 m) linked together. There are 5 stands, three-intermediate two-legged stands, and two three-legged stands at . A 1 kg weight is suspended at the end of an arm, so that the chains remain straight during observations. The correct length of the individual chains is supplied by the manufacturer or is determined in the laboratory. The lengths of the joints between two chains at intermediate supports, are measured directly with the help of a graduated scale. To obtain correct length between the centres of the targets, usual corrections such as temperature, sag, slope, etc., are applied. To set up of the Hunter’s short base the stand at the end A (marked in red colour) is centered on the ground mark and the target is fitted with a clip. The target A is made truly vertical so that the notch on its tip side is centered on the ground mark. The end of the base is hooked with the plate A and is spread carefully till its other end is reached. In between, at every joint of the chains, two-legged supports are fixed to carry the base. The end B (marked in green colour) is fixed to the B stand and the 1 kg weight is attached at the end of the lever. While fixing the end supports A and B it should be ensured that their third leg should face each other under the base. Approximate alignment of the base is the done by eye judgement. For final alignment, a theodolite is set up exactly over the notch of the target A, levelled and centered accurately. The target at B is then bisected. All intermediate supports are set in line with the vertical cross-hair of the theodolite. At the end again ensure that all the intermediate supports and the target B are in one line. In case the base is spread along undulating ground, slope correction is applied. To measure the slope angles of individual supports, a target is fixed to a long iron rod of such a length that it is as high above the tape at A as the trunion axis of the theodolite. The rod is held vertically at each support and the vertical angles for each support are read.
4.11.2 Extension of base line Usually the length of the base lines is much shorter than the average length of the sides of the triangles. This is mainly due to the following reasons: (a) It is often not possible to get a suitable site for a longer base. (b) Measurement of a long base line is difficult and expensive. The extension of short base is done through forming a base net consisting of well-conditioned triangles.There are a great variety of the extension layouts but the following important points should be kept in mind in selecting the one. (i) Small angles opposite the known sides must be avoided. (ii) The length of the base line should be as long as possible. (iii) The length of the base line should be comparable with the mean side length of the triangulation net. (iv) A ratio of base length to the mean side length should be at least 0.5 so as to form wellconditioned triangles. (v) The net should have sufficient redundant lines to provide three or four side equations within the figure. (vi) Subject to the above, it should provide the quickest extension with the fewest stations. There are two ways of connecting the selected base to the triangulation stations. There are (a) extension by prolongation, and (b) extension by double sighting. (a) Extension by prolongation Let up suppose that AB is a short base line which is required to be extended by four times. The following steps are involved to extend AB.
(i) Select C and D two points on either side of AB such that the triangles BAC and BAD are wellconditioned. (ii) Set up the theodolite over the station A, and prolong the line AB accurately to a point E which is visible from points C and D, ensuring that triangles AEC and AED are well-conditioned. (iii) In triangle ABC, side AB is measured. The length of AC and AD are computed using the measured angles of the triangles ABC and ABD, respectively. (iv) The length of AE is calculated using the measured angles of triangles ACE and ADE, and taking mean value. (v) Length of BE is also computed in similar manner using the measured angles of the triangles BEC and BDE. The sum of lengths of AB and BE should agree with the length of AE obtained in step . (vi) If found necessary, the base can be extended to H in the similar way. (b) Extension by double sighting Let AB be the base line. To extend the base to the length of side EF, following steps are involved. (i) Chose intervisible points C, D, E, and F. (ii) Measure all the angles marked in triangles ABC and ABD. The most probable values of these angles are found by the theory of least-squares discussed in Chapter 2. (iii) Calculate the length of CD from these angles and the measured length AB, by applying the sine law to triangles ACB and ADB first, and then to triangles ADC and BDC
(iv) The new base line CD can be further extended to the length EF following the same procedure as above. The line EF may from a side of the triangulation system. If the base line AB is measured on a good site which is well located for extension and connection to the main triangulation system, the accuracy of the system is not much affected by the extension of the base line. In fact, in some cases, the accuracy may be higher than that of a longer base line measured over a poor terrain 4.11.3 MEASUREMENT OF HORIZONTAL ANGLES The horizontal angles of a triangulation system can be observed by the following methods: (i) Repetition method (ii) Reiteration method. The procedure of observation of the horizontal angles by the above methods has been discussed in (i) Repetition method For measuring an angle to the highest degree of precision, several sets of repetitions are usually taken. There are following two methods of taking a single set. (a) In the first method, the angle is measured clockwise by 6 repetitions keeping the telescope normal. The first value of the angle is obtained by dividing the final reading by 6. The telescope is inverted, and the angle is measured again in anticlockwise direction by 6 repetitions. The second
value of the angle is obtained by dividing the final reading by 6. The mean of the first and second values of the angle is the average value of the angle by first set. For first-order work, five or six sets are usually required. The final value of the angle is the mean of the values obtained by different sets. (b) In the second method, the angle is measured clockwise by six repetitions, the first three with telescope normal and the last three with telescope inverted. The first value of the angle is obtained by dividing the final reading by 6. Now without altering the reading obtained in the sixth repetition, the explement angle (i.e., 360°– the angle), is measured clockwise by six repetitions, the first three with telescope inverted and the last three with telescope normal. The final reading should theoretically be zero. If the final reading is not zero, the error is noted, and half of the error is distributed to the first value of the angle. The result is the corrected value of the angle by the first set. As many sets as desired are taken, and the mean of all the value of various sets, is the average value of the angle. For more accurate work and to eliminate the errors due to inaccurate graduations of the horizontal circle, the initial reading at the beginning of each set may not be set to zero but to different values. If n sets are required, the initial setting should be sucessively increased by 180°/n. For example, for 6 sets the initial readings would be 0°, 30°, 60°, 90°, 120° and 150°, respectively. (ii) Reiteration method or direction method In the reiteration method, the triangulation signals are bisected successively, and a value is obtained for each direction in each of several rounds of observations. One of the triangulation stations which is likely to be always clearly visible may be selected as the initial station or reference station. The theodolites used for the measurement of angles for triangulation surveys, have more than one micrometer. One of the micrometer is set to 0° and with telescope normal, the initial station is bisected, and all the micrometers are read. Each of the successive stations are then bisected, and all the micrometers are read. The stations are then again bisected in the reverse direction, and all the micrometers are read after each bisection. Thus, two values are obtained for each angle when the telescope is normal. The telescope is then inverted, and the observations are repeated. This constitutes one set in which four value of each angle are obtained. The micrometer originally at 0° is now brought to a new reading equal to 360°/mn (where m is the number of micrometers and n is the number of sets), and a second set is observed in the same manner. The number of sets depends on the accuracy required. For first-order triangulation, sixteen such sets are required with a 1" direction theodolite, while for second-order triangulation four, and for third-order triangulation two. With more refined instrument having finer graduations, however, six to eight sets are sufficient for the geodetic work.
4.12 MEASUREMENT OF VERTICAL ANGLES Measurement of vertical angles is required to compute the elevation of the triangulation stations. 4.12.1 ASTRONOMICAL OBSERVATIONS To determine the azimuth of the initial side, intermediate sides, and the last side of the triangulation net, astronomical observations are made. For detailed procedure and methods of observation 4.12.2 SOME EXTRA PRECAUTIONS IN TAKING OBSERVATIONS To satisfy first-second, and third-order specifications, care must be exercised. Observer must ensure the following: 1. The instrument and signals have been centred very carefully. 2. Phase in signals has been eliminated. 3. The instrument is protected form the heating effects of the sun and vibrations caused by wind. 4. The support for the instrument is adequately stable. 5. In case of adverse horizontal refraction, observations should be rescheduled to the time when the horizontal refraction is minimum. Horizontal angles should be measured when the air is the clearest, and the lateral refraction is minimum. If the observations are planned for day hours, the best time in clear weather is from 6 AM to 9 AM and from 4 PM till sunset. In densely clouded weather satisfactory work can be done all day. The best time for measuring vertical angles is form 10 AM to 2 PM when the vertical refraction is the least variable. First-order work is generally done at night, since observations at night using illuminated signals help in reducing bad atmospheric conditions, and optimum results can be obtained. Also working at night doubles the hours of working available during a day. Night operations are confined to period from sunset to midnight. 4.12.3 SATELLITE STATION AND REDUCTION TO CENTRE To secure well-conditioned triangles or to have good visibility, objects such as chimneys, church spires, flat poles, towers, lighthouse, etc., are selected as triangulation stations. Such stations can be sighted from other stations but it is not possible to occupy the station directly below suchexcellent targets for making the observations by setting up the instrument over the station point. Also, signals are frequently blown out of position, and angles read on them have to be corrected to the true position of the triangulation station. Thus, there are two types of problems: 1. When the instrument is not set up over the true station, and 2. When the target is out of position. In below Fig., A, B, and C are the three triangulation stations. It is not possible to place instrument at C. To solve this problem another station S, in the vicinity of C, is selected where the instrument can be set up, and
from where all the three stations are visible for making the angle observations. Such station is known as satellite station. As the observations from C are not possible, the observations form S are made on A, B, and, C from A and B on C. From the observations made, the required angle ACB is calculated. This is known as reduction to centre.
In the other case, S is treated as the true station point, and the signal is considered to be shifted to the position C. This case may also be looked upon as a case of eccentricity of signal. Thus, the observations from S are made to the triangulation stations A and B, but from A and B the observations are made on the signal at the shifted position C. This causes errors in the measured values of the angles BAC and ABC. Both the problems discussed above are solved by reduction to centre. Let the measured
4.13 ECCENTRICITY OF SIGNAL When the signal is found shifted from its true position, the distance between the shifted signal and the station point d is measured. The corrections α and β to the observed angles BAC and ABC, respectively, are computed and the corrected values of the angles are obtained as under
4.14 Trigonometrical Levelling Trigonometric Levelling is the branch of Surveying in which we find out the vertical distance between two points by taking the vertical angular observations and the known distances. The known distances are either assumed to be horizontal or the geodetic lengths at the mean sea level(MSL). The distances are measured directly(as in the plane surveying) or they are computed as in the geodetic surveying. The trigonometric Leveling can be done in two ways: (1) Observations taken for the height and distances (2) Geodetic Observations. In the first way, we can measure the horizontal distance between the given points if it is accessible.We take the observation of the vertical angles and then compute the distances using them. If the distances are large enough then we have to provide the correction for the curvature and refraction and that we provide to the linearly to the distances that we have computed. In the second way, i.e geodetic observations, the distances between the two points are geodetic distances and the principles of the plane surveying are not applicable here. The corrections for the curvature and refraction are applied directly to the angles directly. Now we will discuss the various cases to find out the difference in elevation between the two.
(1) The two points are at known distance: The base of the object is accessible. When the two points are at a known horizontal distance then we can find out the distance between them by taking the vertical angle observations. If the vertical angle of elevation from the point to be observed to the instrument axis is known we can calculate the vertical distance by taking the help of the trigonometry. Horizontal distance*Tan(verticle angle) = Vertical difference between the two. If the points are at small distance apart then there is no need to apply the correction for the curvature and refraction else you can apply the correction as given below: C= 0.06728D*D Where D is the horizontal distance between the given two points in Kilometers. but the Correction is in meters (m). (2) The base of the object is not accessible : (a)( When the instrument is shifted to the nearby place and the observations are taken from the same level of the line of sight: In such case we have to take the two angular observations of the vertical angles. The instrument is shifted to a nearby place of known distance, and then with the known distance between these two and the angular observations from these two stations, we can find the vertical difference in distance between the line of sight of the instrument and the top point of the object. (b) When the line of sights of the two instrument setting is different : Here again there are two cases: (i) When the line of sights are at a small vertical distance which can be measured through the vertical staff readings. (ii) When the difference is larger than the staff height. (i) In first case, It is advised to apply the formula for the difference in the height of the top of the object from these two lines of sights. The difference in lines of sights is same as the staff readings difference, when the staff is kept at a little distance from these two points. So we can get the solution for the vertical distance easily. (ii) In the second case, there is a need to put a vane staff at the first instrument station and the angle of elevation is measured from the second point of observation. This gives us the difference in the line of the sights between the two points of instrument station. Then again we do the same. (c) When the instrument station and the top of object are not in same vertical plane: In this case there is a need to measure at-least two horizontal angles of the horizontal triangle formed by the two instrument stations and the base of the object. Again we will take the vertical angular observations from the two instrument stations also and then we can apply the sine rule to solve the horizontal distances of the triangle. With the help of these angles and the distances we can get the vertical distance between any two point(Instrument station and the top of object). For rapid leveling or leveling in rolling ground or for inaccessible points, trigonometric method of leveling is being used. In this method, theodolite (an instrument which can measure angle) is being generally used as an instrument for taking different measurements.
Let us consider two stations T an by trigonometric method of leveling. At T, a theodolite instrument is set up. TT ' is the height of the instrument above the point T (to be recorded at the time of observation). A leveling staff is held at X. At the vertical angle of elevation of the actual line of sight a, let x1 is the observed staff reading. The difference in level between T and X is given by
where xt' xh is deviation of the horizontal line of sight due to curvature of the earth and refraction of light (given by 0.0675 T' x h2 ). xh x1 is T' x1 sina or T' x h tana , T' x1 is the inclined distance from the instrument to the staff and T' xh is the horizontal distance between the points, x1 X is the staff reading at X. Example In order to eliminate the uncertainty due to refraction, observations for vertical angle are made at both ends of the line as close in point of time as possible. The vertical angle at the lower of the two peaks to the upper peak is +3° 02' 05"?. The reciprocal vertical angle at the upper peak is 3° 12' 55"?. The height of instrument are kept to be same in all observation. The slope distance between two mountain peaks determined by EDM measurement is 21,345m. Compute the difference in elevations between the two peaks.
Solution : Average vertical angle a = (3° 02' 05" + 3° 12' 55") / 2 = 6° 15' 00 " Difference in elevation = 21.345 sin 3° 07' 30 " + 0.0675 (21.345 cos 3° 07' 30 ")2 = (1.163 + 30.662) m = 31.825 me Reciprocal leveling To find accurate relative elevations of two widely separated intervisible points (between which levels cannot be set), reciprocal leveling is being used. To find the difference in elevation between two points, say X and Y, a level is set up at L near X and readings (X1 and Y1) are observed with staff on both X and Y respectively. The level is then set up near Y and staff readings (Y2 and X2 ) are taken respectively to the near and distant points. If the differences in the set of observations are not same, then the observations are fraught with errors. The errors may arise out of the curvature of the earth or intervening atmosphere (associated with variation in temperature and refraction) or instrument (due to error in collimation) or any combination of these.
The true difference in elevation and errors associated with observation, if any, can be found as follows:
Let the true difference in elevation between the points be rh and the total error be e. Assuming, no error on observation of staff near the level (as the distance is very small) Then, rh = X1 ~ (Y1 - e) [From first set of observation] and rh = (X2 - e) ~ Y2 [From second set of observation]
Thus, the true difference in elevation between any two points can be obtained by taking the mean of the two differences in observation.
Thus, total error in observations can be obtained by taking the difference of the two differences in observation. The total error consist of error due to curvature of the earth, atmospheric errors (due to temperature and refraction) and instrumental errors (due to error in collimation) etc. Example In order to transfer reduced level across a canyon, a reciprocal leveling campaign was conducted. Simultaneous readings were observed using two levels one at each side of the canyon. Each of the levels are having same magnifying power and sensitiveness of level tube. With instruments interchanged during leveling operation yielded the following average readings:
Instrrument statioon X Y
L of X = 1011.345 m Av verage near Avverage distant, R.L reeadings, metter reaadings, meter Disstance, XY = 1.025Km 1.780 2.3345 e currvature = 0.07785 XY 2 2.435 1.8870
Find out the R.L. of unknown u pooint. Commeent on the errrors associatted with obseervations. Solution n: The diffeerence in elevation betweeen X and Y is
= 0.5665 m (Y loweer than X) R.L. of Y (unknown Point) = R.L L. of X - Dh = 101.345 - 0.565 = 1000.780 m Since tw wo leveling rods r are used and the ellapsed time between reaading in a set s observatiion is little, thee error due to change in atmosphheric conditiion can be neglected. Moreover, since readings were taken with instruuments intercchanged, insstrumental errors e get caancelled between t observattions are reppeated and averages of the t readings have different set of obserrvation. As the been connsidered for further calcculation, it is expected that t error asssociated wiith observatiion is minimizeed thus rem moved. Onlyy error present in the observation o is that associated withh the curvaturee of the earth h.
4.15 Trrilateration n
In above Figure . Thee plane z = 0, 0 showing thhe three spheere centers, P1, P P2, and P3; theirx,y-coordinattes; and the three spheree radii, r1, r22, and r3. Thhe two intersections of thhe three spheere surfaces are directly in front and directly behhind the poinnt designatedd intersectionns in the z = 0 plane. In geomeetry, trilaterration is the process of determining d absolute or relative r locaations of poinnts by measuurement of distances, d usiing the geom metry of circles, spheres or triangles.. In addition to its interesst as a geom metric problem m, trilateratiion does havve practical applications a in surveyying and nav vigation, inclluding globaal positioningg systems (G GPS). In conttrast to trianguulation it doees not involvve the measuurement of angles. a In two-diimensional geometry, g it is known that if a point lies on two circles c then the t circle ceenters and the tw wo radii pro ovide sufficieent informatiion to narrow w the possibble locations down to twoo. Additionnal informatio on may narrrow the possibilities dow wn to one uniique locationn. In three-ddimensional geometry, when w it is knnown that a point p lies on the surfacess of three sphheres then the centers c of th he three spheeres along wiith their radiii provide suufficient infoormation to narrow thhe possible locations l dow wn to no moore than two (unless the centres c lie onn a straight line). l This articcle describess a method for fo determiniing the interssections of thhree sphere surfaces givven the centeers and radii of the three spheres. Contentss • •
1 Derivation 2 Preliminary y and final coomputationss
Derivation The interrsections of the t surfaces of three sphheres is foundd by formulaating the equuations for thhe three sphhere surfacess and then soolving the thrree equationns for the threee unknownns, x, y, and z. z To simplify the calculatiions, the equuations are foormulated soo that the cennters of the spheres s are on o o other is on the z = 0 plane. Also the formulaation is such that one cennter is at the origin, and one ble to formuulate the equaations in thiss manner sinnce any threee non-colinear the x-axiss. It is possib points liee on a uniquee plane. Afteer finding the solution it can be transsformed backk to the origginal three dim mensional Caartesian coorrdinate systeem. We start with the equ uations for thhe three spheeres:
We needd to find a po oint located at a (x, y, z) thaat satisfies all a three equaations. s for x: First we subtract the second equaation from thhe first and solve
We assum me that the first f two spheres intersecct in more thhan one pointt, that is thatt
In this caase substitutiing the equattion for x baack into the equation e for the first sphhere produces the equation for a circle, the solutionn to the intersection of thhe first two spheres: s
into the formula for the third sphhere and solvving for y thhere
Now thatt we have the x- and y-cooordinates of the solution point, we can simply rearrange r thee formula for f the first sphere s to finnd the z-coorrdinate:
Now we have the sollution to all three t points x, y and z. Because B z is expressed e ass the positivee or negative square root,, it is possiblle for there to be zero, onne or two solutions to thhe problem. This last part can be visualized as taking the circle foundd from intersecting the fiirst and second sphere annd intersectin ng that with the third sphhere. If that circle falls entirely e outsiide or insidee of the spherre, z is equal to thesquaree root of a negative num mber: no real solution exiists. If that circle touches the t sphere on n exactly one point, z is equal to zeroo. If that circcle touches the t surface of o the sphere att two points, then z is equual to plus or o minus the square root of a positivee number.
Prelimin nary and fin nal computaations The Deriivation sectio on pointed out o that the coordinate c syystem in whiich the spherre centers arre designateed must be such that (1) all three cennters are in thhe plane z = 0, (2) the spphere center,, P1, is at the origin, o and (3) the spheree center, P2,, is on the x--axis. In geneeral the probblem will not be given in a form such that these reequirements are met. This probblem can be overcome as a described below b wheree the points, P1, P2, andd P3 are treatted as vectorrs from the origin o where indicated. P1, P P2, and P3 P are of couurse expresseed in the original coordinatte system.
m P1 to P2. is the unit vector in the dirrection from iis the signedd magnitude of the x com mponent, in the t figure 1 cooordinate sy ystem, of the vector from m P1 to P3.
is the unit vector in the y direction. Note that t the points P1, P2 2, and P3 aree all in the z = 0 plane off the figure 1 coordinate system. The thirdd basis unit vector v is
. Therefore, the distance d betw ween the cennters P1 andd P2 and
is the signedd magnitudee of the y com mponent, in the figure 1 cooordinate sy ystem, of the vector from m P1 to P3. Using Then
ass computed above, a solvee for x, y andd z as describbed in the Deerivation secction.
gives thee points in th he original cooordinate sysstem since are expreessed in the original o coorrdinate systeem. Resectionn method Resection is a method m foor determiining a a compasss and topog graphic map (or nautical chart)
, the basiss unit vectorrs,
Resection versus intersection Resection and its related method, intersection, are used in surveying as well as in general land navigation (including inshore marine navigation using shore-based landmarks). Both methods involve taking azimuths or bearings to two or more objects, then drawing lines of position along those recorded bearings or azimuths. When intersecting lines of position are used to fix the position of an unmapped feature or point by fixing its position relative to two (or more) mapped or known points, the method is known asintersection. At each known point (hill, lighthouse, etc.), the navigator measures the bearing to the same unmapped target, drawing a line on the map from each known position to the target. The target is located where the lines intersect on the map. In earlier times, the intersection method was used by forest agencies and others using specialized alidades to plot the (unknown) location of an observed forest fire from two or more mapped (known) locations, such as forest fire observer towers. The reverse of the intersection technique is appropriately termed resection. Resection simply reverses the intersection process by using crossed back bearings, where the navigator's position is the unknown. Two or more bearings to mapped, known points are taken; their resultant lines of position drawn from those points to where they intersect will reveal the navigator's location. Fixing a position When resecting or fixing a position, the geometric strength (angular disparity) of the mapped points affects the precision and accuracy of the outcome. Accuracy increases as the angle between the two position lines approaches 90 degrees. Magnetic bearings are observed on the ground from the point under location to two or more features shown on a map of the area. Lines of reverse bearings, or lines of position, are then drawn on the map from the known features; two and more lines provide the resection point (the navigator's location). When three or more lines of position are utilized, the method is often popularly (though erroneously) referred to as triangulation (in precise terms, using three or more lines of position is still correctly called resection, as angular law of tangents (cot) calculations are not performed). When using a map and compass to perform resection, it is important to allow for the difference between the magnetic bearings observed and grid north (or true north) bearings (magnetic declination) of the map or chart. Resection continues to be employed in land and inshore navigation today, as it is a simple and quick method requiring only an inexpensive magnetic compass and map/chart. Resection in surveying In surveying work, the most common methods of computing the coordinates of a point by resection are Cassini's Method and the Tienstra formula, though the first known solution was given byWillebrord Snellius (see Snellius–Pothenot problem). For the type of precision work involved in surveying, the unmapped point is located by measuring the angles subtended by lines of sight from it to a minimum of three mapped (coordinated) points. In geodetic operations the observations are adjusted for spherical excess and projection variations. Precise angular measurements between lines from the point under location using theodolites provides more
accurate results, with trig beacons erected on high points and hills to enable quick and unambiguous sights to known points. Caution: When planning to perform a resection, the surveyor must first plot the locations of the known points along with the approximate unknown point of observation. If all points, including the unknown point, lie close to a circle that can be placed on all four points, then there is no solution or the high risk of an erroneous solution. This is known as observing on the “danger circle”. The poor solution stems from the property of a chord subtending equal angles to any other point on the circle.
4.16 GPS The Global Positioning System (GPS) is a space-based satellite navigation system that provides location and time information in all weather conditions, anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. The system provides critical capabilities to military, civil and commercial users around the world. It is maintained by the United States government and is freely accessible to anyone with a GPS receiver. The GPS project was developed in 1973 to overcome the limitations of previous navigation systems, integrating ideas from several predecessors, including a number of classified engineering design studies from the 1960s. GPS was created and realized by the U.S. Department of Defense (DoD) and was originally run with 24 satellites. It became fully operational in 1994. Bradford Parkinson, Roger L. Easton, and Ivan A. Getting are credited with inventing it. Advances in technology and new demands on the existing system have now led to efforts to modernize the GPS system and implement the next generation of GPS III satellites and Next Generation Operational Control System (OCX). Announcements from Vice President Al Gore and the White House in 1998 initiated these changes. In 2000, the U.S. Congress authorized the modernization effort, GPS III. In addition to GPS, other systems are in use or under development. The Russian Global Navigation Satellite System (GLONASS) was developed contemporaneously with GPS, but suffered from incomplete coverage of the globe until the mid-2000s. There are also the planned European UnionGalileo positioning system, Chinese Compass navigation system, and Indian Regional Navigational Satellite System. History The design of GPS is based partly on similar ground-based radio-navigation systems, such as LORAN and the Decca Navigator, developed in the early 1940s and used during World War II. Predecessors In 1956, the German-American physicist Friedwardt Winterberg proposed a test of general relativity (for time slowing in a strong gravitational field) using accurate atomic clocks placed in orbit inside artificial satellites. Without the use of general relativity to correct for time running more quickly by 38 microseconds per day in orbit, GPS would suffer gross
malfunction. Additional inspiration for GPS came when the Soviet Union launched the first manmade satellite, Sputnik, in 1957. Two American physicists, William Guier and George Weiffenbach, at Johns Hopkins's Applied Physics Laboratory (APL), decided to monitor Sputnik's radio transmissions. Within hours they realized that, because of the Doppler effect, they could pinpoint where the satellite was along its orbit. The Director of the APL gave them access to their UNIVAC to do the heavy calculations required. The next spring, Frank McClure, the deputy director of the APL, asked Guier and Weiffenbach to investigate the inverse problem—pinpointing the user's location given that of the satellite. (The Navy was developing the submarine-launched Polaris missile, which required them to know the submarine's location.) This led them and APL to develop the Transit system. In 1959, ARPA (renamed DARPA in 1972) also played a role in Transit.\The first satellite navigation system, Transit, used by the United States Navy, was first successfully tested in 1960. It used a constellation of five satellites and could provide a navigational fix approximately once per hour. In 1967, the U.S. Navy developed the Timation satellite that proved the ability to place accurate clocks in space, a technology required by GPS. In the 1970s, the ground-based Omega Navigation System, based on phase comparison of signal transmission from pairs of stations, became the first worldwide radio navigation system. Limitations of these systems drove the need for a more universal navigation solution with greater accuracy. While there were wide needs for accurate navigation in military and civilian sectors, almost none of those was seen as justification for the billions of dollars it would cost in research, development, deployment, and operation for a constellation of navigation satellites. During the Cold War arms race, the nuclear threat to the existence of the United States was the one need that did justify this cost in the view of the United States Congress. This deterrent effect is why GPS was funded. It is also the reason for the ultra secrecy at that time. The nuclear triad consisted of the United States Navy's submarine-launched ballistic missiles (SLBMs) along with United States Air Force (USAF) strategic bombers and intercontinental ballistic missiles (ICBMs). Considered vital to the nuclear-deterrence posture, accurate determination of the SLBM launch position was a force multiplier. Precise navigation would enable United States submarines to get an accurate fix of their positions before they launched their SLBMs. The USAF, with two thirds of the nuclear triad, also had requirements for a more accurate and reliable navigation system. The Navy and Air Force were developing their own technologies in parallel to solve what was essentially the same problem. To increase the survivability of ICBMs, there was a proposal to use mobile launch platforms (such as Russian SS-24 and SS-25) and so the need to fix the launch position had similarity to the SLBM situation. In 1960, the Air Force proposed a radio-navigation system called MOSAIC (MObile System for Accurate ICBM Control) that was essentially a 3-D LORAN. A follow-on study, Project 57, was worked in 1963 and it was "in this study that the GPS concept was born". That same year, the concept was pursued as Project 621B, which had "many of the attributes that you now see in GPS" and promised increased accuracy for Air Force bombers as well as ICBMs. Updates from the Navy Transit system were too slow for the high speeds of Air Force operation. The Naval Research Laboratory continued advancements with their Timation (Time Navigation) satellites, first launched in 1967, and with the third one in 1974 carrying the first atomic clock into orbit.
Another important predecessor to GPS came from a different branch of the United States military. In 1964, the United States Army orbited its first Sequential Collation of Range (SECOR) satellite used for geodetic surveying. The SECOR system included three ground-based transmitters from known locations that would send signals to the satellite transponder in orbit. A fourth ground-based station, at an undetermined position, could then use those signals to fix its location precisely. The last SECOR satellite was launched in 1969. Decades later, during the early years of GPS, civilian surveying became one of the first fields to make use of the new technology, because surveyors could reap benefits of signals from the less-than-complete GPS constellation years before it was declared operational. GPS can be thought of as an evolution of the SECOR system where the ground-based transmitters have been migrated into orbit. Development With these parallel developments in the 1960s, it was realized that a superior system could be developed by synthesizing the best technologies from 621B, Transit, Timation, and SECOR in a multi-service program. During Labor Day weekend in 1973, a meeting of about 12 military officers at the Pentagon discussed the creation of a Defense Navigation Satellite System (DNSS). It was at this meeting that "the real synthesis that became GPS was created." Later that year, the DNSS program was named Navstar, or Navigation System Using Timing and Ranging. With the individual satellites being associated with the name Navstar (as with the predecessors Transit and Timation), a more fully encompassing name was used to identify the constellation of Navstar satellites, NavstarGPS, which was later shortened simply to GPS. After Korean Air Lines Flight 007, a Boeing 747 carrying 269 people, was shot down in 1983 after straying into the USSR's prohibited airspace, in the vicinity of Sakhalin and Moneron Islands, President Ronald Reagan issued a directive making GPS freely available for civilian use, once it was sufficiently developed, as a common good. The first satellite was launched in 1989, and the 24th satellite was launched in 1994. The GPS program cost at this point, not including the cost of the user equipment, but including the costs of the satellite launches, has been estimated to be about USD$5 billion (then-year dollars). Roger L. Easton is widely credited as the primary inventor of GPS. Initially, the highest quality signal was reserved for military use, and the signal available for civilian use was intentionally degraded (Selective Availability). This changed with President Bill Clintonordering Selective Availability to be turned off at midnight May 1, 2000, improving the precision of civilian GPS from 100 meters (330 ft) to 20 meters (66 ft). The executive order signed in 1996 to turn off Selective Availability in 2000 was proposed by the U.S. Secretary of Defense, William Perry, because of the widespread growth of differential GPS services to improve civilian accuracy and eliminate the U.S. military advantage. Moreover, the U.S. military was actively developing technologies to deny GPS service to potential adversaries on a regional basis. Over the last decade, the U.S. has implemented several improvements to the GPS service, including new signals for civil use and increased accuracy and integrity for all users, all while maintaining compatibility with existing GPS equipment.
GPS modernizationhas now become an ongoing initiative to upgrade the Global Positioning System with new capabilities to meet growing military, civil, and commercial needs. The program is being implemented through a series of satellite acquisitions, including GPS Block III and the Next Generation Operational Control System (OCX). The U.S. Government continues to improve the GPS space and ground segments to increase performance and accuracy. GPS is owned and operated by the United States Government as a national resource. Department of Defense (DoD) is the steward of GPS. Interagency GPS Executive Board (IGEB) oversaw GPS policy matters from 1996 to 2004. After that the National Space-Based Positioning, Navigation and Timing Executive Committee was established by presidential directive in 2004 to advise and coordinate federal departments and agencies on matters concerning the GPS and related systems. The executive committee is chaired jointly by the deputy secretaries of defense and transportation. Its membership includes equivalent-level officials from the departments of state, commerce, and homeland security, the joint chiefs of staff, and NASA. Components of the executive office of the president participate as observers to the executive committee, and the FCC chairman participates as a liaison. The DoD is required by law to "maintain a Standard Positioning Service (as defined in the federal radio navigation plan and the standard positioning service signal specification) that will be available on a continuous, worldwide basis," and "develop measures to prevent hostile use of GPS and its augmentations without unduly disrupting or degrading civilian uses." Basic concept of GPS A GPS receiver calculates its position by precisely timing the signals sent by GPS satellites high above the Earth. Each satellite continually transmits messages that include • •
the time the message was transmitted satellite position at time of message transmission
The receiver uses the messages it receives to determine the transit time of each message and computes the distance to each satellite using the speed of light. Each of these distances and satellites' locations define a sphere. The receiver is on the surface of each of these spheres when the distances and the satellites' locations are correct. These distances and satellites' locations are used to compute the location of the receiver using the navigation equations. This location is then displayed, perhaps with a moving map display or latitude and longitude; elevation or altitude information may be included, based on height above the geoid (e.g. EGM96). Many GPS units show derived information such as direction and speed, calculated from position changes. In typical GPS operation, four or more satellites must be visible to obtain an accurate result. Four sphere surfaces typically do not intersect. Because of this, it can be said with confidence that when the navigation equations are solved to find an intersection, this solution gives the position of the receiver along with the difference between the time kept by the receiver's on-board clock and the true time-of-day, thereby eliminating the need for a very large, expensive, and power hungry clock. The very accurately computed time is used only for display or not at all in many GPS applications, which use only the location. A number of applications for GPS do make use of
this cheap and highly accurate timing. These include time transfer, traffic signal timing, andsynchronization of cell phone base stations. Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known, a receiver can determine its position using only three satellites. For example, a ship or aircraft may have known elevation. Some GPS receivers may use additional clues or assumptions such as reusing the last known altitude, dead reckoning, inertial navigation, or including information from the vehicle computer, to give a (possibly degraded) position when fewer than four satellites are visible. Structure The current GPS consists of three major segments. These are the space segment (SS), a control segment (CS), and a user segment (US). The U.S. Air Force develops, maintains, and operates the space and control segments. GPS satellites broadcast signals from space, and each GPS receiver uses these signals to calculate its three-dimensional location (latitude, longitude, and altitude) and the current time. The space segment is composed of 24 to 32 satellites in medium Earth orbit and also includes the payload adapters to the boosters required to launch them into orbit. The control segment is composed of a master control station, an alternate master control station, and a host of dedicated and shared ground antennas and monitor stations. The user segment is composed of hundreds of thousands of U.S. and allied military users of the secure GPS Precise Positioning Service, and tens of millions of civil, commercial, and scientific users of the Standard Positioning Service (seeGPS navigation devices). Space segment The space segment (SS) is composed of the orbiting GPS satellites, or Space Vehicles (SV) in GPS parlance. The GPS design originally called for 24 SVs, eight each in three approximately circular orbits, but this was modified to six orbital planes with four satellites each. The six orbit planes have approximately 55° inclination (tilt relative to Earth's equator) and are separated by 60° right ascension of the ascending node (angle along the equator from a reference point to the orbit's intersection). The orbital period is one-half a sidereal day, i.e., 11 hours and 58 minutes so that the satellites pass over the same locations or almost the same locations every day. The orbits are arranged so that at least six satellites are always within line of sight from almost everywhere on Earth's surface. The result of this objective is that the four satellites are not evenly spaced (90 degrees) apart within each orbit. In general terms, the angular difference between satellites in each orbit is 30, 105, 120, and 105 degrees apart which sum to 360 degrees. Orbiting at an altitude of approximately 20,200 km (12,600 mi); orbital radius of approximately 26,600 km (16,500 mi), each SV makes two complete orbits each sidereal day, repeating the same ground track each day. This was very helpful during development because even with only four satellites, correct alignment means all four are visible from one spot for a few hours each day. For military operations, the ground track repeat can be used to ensure good coverage in combat zones. As of December 2012, there are 32 satellites in the GPS constellation. The additional satellites improve the precision of GPS receiver calculations by providing redundant measurements. With
the increased number of satellites, the constellation was changed to a nonuniform arrangement. Such an arrangement was shown to improve reliability and availability of the system, relative to a uniform system, when multiple satellites fail. About nine satellites are visible from any point on the ground at any one time (see animation at right), ensuring considerable redundancy over the minimum four satellites needed for a position. Control segment The control segment is composed of 1. 2. 3. 4.
a master control station (MCS), an alternate master control station, four dedicated ground antennas and six dedicated monitor stations
The MCS can also access U.S. Air Force Satellite Control Network (AFSCN) ground antennas (for additional command and control capability) and NGA (National Geospatial-Intelligence Agency) monitor stations. The flight paths of the satellites are tracked by dedicated U.S. Air Force monitoring stations in Hawaii, Kwajalein Atoll, Ascension Island, Diego Garcia, Colorado Springs, Colorado and Cape Canaveral, along with shared NGA monitor stations operated in England, Argentina, Ecuador, Bahrain, Australia and Washington DC. The tracking information is sent to the Air Force Space Command MCS at Schriever Air Force Base 25 km (16 mi) ESE of Colorado Springs, which is operated by the 2nd Space Operations Squadron(2 SOPS) of the U.S. Air Force. Then 2 SOPS contacts each GPS satellite regularly with a navigational update using dedicated or shared (AFSCN) ground antennas (GPS dedicated ground antennas are located at Kwajalein, Ascension Island, Diego Garcia, and Cape Canaveral). These updates synchronize the atomic clocks on board the satellites to within a few nanoseconds of each other, and adjust the ephemeris of each satellite's internal orbital model. The updates are created by a Kalman filter that uses inputs from the ground monitoring stations, space weather information, and various other inputs. Satellite maneuvers are not precise by GPS standards. So to change the orbit of a satellite, the satellite must be marked unhealthy, so receivers will not use it in their calculation. Then the maneuver can be carried out, and the resulting orbit tracked from the ground. Then the new ephemeris is uploaded and the satellite marked healthy again. The Operation Control Segment (OCS) currently serves as the control segment of record. It provides the operational capability that supports global GPS users and keeps the GPS system operational and performing within specification. OCS successfully replaced the legacy 1970s-era mainframe computer at Schriever Air Force Base in September 2007. After installation, the system helped enable upgrades and provide a foundation for a new security architecture that supported the U.S. armed forces. OCS will continue to be the ground control system of record until the new segment, Next Generation GPS Operation Control System (OCX), is fully developed and functional. The new capabilities provided by OCX will be the cornerstone for revolutionizing GPS's mission capabilities, and enabling Air Force Space Command to greatly enhance GPS operational services to U.S. combat forces, civil partners and myriad domestic and international users.
The GPS OCX program also will reduce cost, schedule and technical risk. It is designed to provide 50% sustainment cost savings through efficient software architecture and Performance-Based Logistics. In addition, GPS OCX expected to cost millions less than the cost to upgrade OCS while providing four times the capability. The GPS OCX program represents a critical part of GPS modernization and provides significant information assurance improvements over the current GPS OCS program. • •
• • •
OCX will have the ability to control and manage GPS legacy satellites as well as the next generation of GPS III satellites, while enabling the full array of military signals. Built on a flexible architecture that can rapidly adapt to the changing needs of today's and future GPS users allowing immediate access to GPS data and constellations status through secure, accurate and reliable information. Empowers the warfighter with more secure, actionable and predictive information to enhance situational awareness. Enables new modernized signals (L1C, L2C, and L5) and has M-code capability, which the legacy system is unable to do. Provides significant information assurance improvements over the current program including detecting and preventing cyber attacks, while isolating, containing and operating during such attacks. Supports higher volume near real-time command and control capabilities and abilities.
On September 14, 2011, the U.S. Air Force announced the completion of GPS OCX Preliminary Design Review and confirmed that the OCX program is ready for the next phase of development. The GPS OCX program has achieved major milestones and is on track to support the GPS IIIA launch in May 2014. User segment The user segment is composed of hundreds of thousands of U.S. and allied military users of the secure GPS Precise Positioning Service, and tens of millions of civil, commercial and scientific users of the Standard Positioning Service. In general, GPS receivers are composed of an antenna, tuned to the frequencies transmitted by the satellites, receiver-processors, and a highly stable clock (often a crystal oscillator). They may also include a display for providing location and speed information to the user. A receiver is often described by its number of channels: this signifies how many satellites it can monitor simultaneously. Originally limited to four or five, this has progressively increased over the years so that, as of 2007, receivers typically have between 12 and 20 channels. GPS receivers may include an input for differential corrections, using the RTCM SC-104 format. This is typically in the form of an RS-232 port at 4,800 bit/s speed. Data is actually sent at a much lower rate, which limits the accuracy of the signal sent using RTCMReceivers with internal DGPS receivers can outperform those using external RTCM data] As of 2006, even lowcost units commonly include Wide Area Augmentation System (WAAS) receivers. Many GPS receivers can relay position data to a PC or other device using the NMEA 0183 protocol. Although this protocol is officially defined by the National Marine Electronics
Association (NMEA), references to this protocol have been compiled from public records, allowing open source tools likegpsd to read the protocol without violating intellectual property laws. Other proprietary protocols exist as well, such as the SiRF andMTK protocols. Receivers can interface with other devices using methods including a serial connection, USB, or Bluetooth. Applications While originally a military project, GPS is considered a dual-use technology, meaning it has significant military and civilian applications. GPS has become a widely deployed and useful tool for commerce, scientific uses, tracking, and surveillance. GPS's accurate time facilitates everyday activities such as banking, mobile phone operations, and even the control of power grids by allowing well synchronized hand-off switching. Civilian Astronomy: Both positional and clock synchronization data is used in Astrometry and Celestial mechanics calculations. It is also used in amateur astronomy using small telescopes to professionals observatories, for example, while finding extrasolar planets. • • •
• • • •
Automated vehicle: Applying location and routes for cars and trucks to function without a human driver. Cartography: Both civilian and military cartographers use GPS extensively. Cellular telephony: Clock synchronization enables time transfer, which is critical for synchronizing its spreading codes with other base stations to facilitate inter-cell handoff and support hybrid GPS/cellular position detection for mobile emergency calls and other applications. The first handsets with integrated GPS launched in the late 1990s. The U.S. Federal Communications Commission (FCC) mandated the feature in either the handset or in the towers (for use in triangulation) in 2002 so emergency services could locate 911 callers. Third-party software developers later gained access to GPS APIs from Nextel upon launch, followed by Sprint in 2006, and Verizon soon thereafter. Clock synchronization: The accuracy of GPS time signals (±10 ns) is second only to the atomic clocks upon which they are based. Disaster relief/emergency services: Depend upon GPS for location and timing capabilities. Fleet Tracking: The use of GPS technology to identify, locate and maintain contact reports with one or more fleet vehicles in real-time. Geofencing: Vehicle tracking systems, person tracking systems, and pet tracking systems use GPS to locate a vehicle, person, or pet. These devices are attached to the vehicle, person, or the pet collar. The application provides continuous tracking and mobile or Internet updates should the target leave a designated area. Geotagging: Applying location coordinates to digital objects such as photographs (in exif data) and other documents for purposes such as creating map overlays with devices like Nikon GP-1 GPS Aircraft Tracking
GPS for Mining: The use of RTK GPS has significantly improved several mining operations such as drilling, shoveling, vehicle tracking, and surveying. RTK GPS provides centimeterlevel positioning accuracy. • GPS tours: Location determines what content to display; for instance, information about an approaching point of interest. • Navigation: Navigators value digitally precise velocity and orientation measurements. • Phasor measurements: GPS enables highly accurate timestamping of power system measurements, making it possible to compute phasors. • Recreation: For example, geocaching, geodashing, GPS drawing and waymarking. • Robotics: Self-navigating, autonomous robots using a GPS sensors, which calculate latitude, longitude, time, speed, and heading. • Surveying: Surveyors use absolute locations to make maps and determine property boundaries. • Tectonics: GPS enables direct fault motion measurement in earthquakes. • Telematics: GPS technology integrated with computers and mobile communications technology in automotive navigation systems Restrictions on civilian use •
The U.S. Government controls the export of some civilian receivers. All GPS receivers capable of functioning above 18 kilometres (11 mi) altitude and 515 metres per second (1,001 kn) or designed, modified for use with unmanned air vehicles like e.g. ballistic or cruise missile systems are classified as munitions (weapons) for which State Department export licenses are required. This rule applies even to otherwise purely civilian units that only receive the L1 frequency and the C/A (Coarse/Acquisition) code and cannot correct for Selective Availability (U.S. government discontinued SA on May 1, 2000, resulting in a much- improved autonomous GPS accuracy), etc. Disabling operation above these limits exempts the receiver from classification as a munition. Vendor interpretations differ. The rule refers to operation at both the target altitude and speed, but some receivers stop operating even when stationary. This has caused problems with some amateur radio balloon launches that regularly reach 30 kilometres (19 mi). These limits only apply to units exported from (or which have components exported from) the USA – there is a growing trade in various components, including GPS units, supplied by other countries, which are expressly sold as ITAR-free. Military As of 2009, military applications of GPS include: •
Navigation: GPS allows soldiers to find objectives, even in the dark or in unfamiliar territory, and to coordinate troop and supply movement. In the United States armed forces, commanders use the Commanders Digital Assistant and lower ranks use the Soldier Digital Assistant.
Target tracking: Various military weaponns systems use u GPS to track t potentiial ground annd air ] targeets before flagging f them as hostille. These weapon systeems pass taarget coordiinates to preecision-guid ded munitionns to allow them t to enggage targets accurately. Military airrcraft, particcularly in aiir-to-ground roles, use GPS G to find targets (forr example, gun g camera video v from m AH-1 Cobras in Iraq shhow GPS co-ordinates c s that can be b viewed with speciaalized softw ware). Missile and projectile guidannce: GPS allows accuraate targeting of various military m weaapons incluuding ICBMss, cruise m missiles, preecision-guideed munitiions and Arttillery projecctiles. Embeedded GPS S receiverss able to withstand acceleratioons of 122,000 g or about a 118 km/s k 2 have been b develooped for usee in 155 miillimetres (66.1 in) howitzzers. Searchh and Rescue: Downed d pilots can be b located faaster if their position p is known. k Recoonnaissance: Patrol moveement can bee managed more m closelyy. GPS satellites caarry a set of nuclear detoonation deteectors consissting of an optical o sensoor (Ysensoor), an X-raay sensor, a dosimeter, and an eleectromagnettic pulse (EM MP) sensorr (Wsensoor), that forrm a majorr portion off the Unitedd States Nuuclear Detonnation Deteection Systeem. General William Shhelton has stated s that thhis feature may m be droppped from future f satelllites in orderr to save money. Commuunicatio
Demodu ulation and decoding d
Demodulatin D ng and Decooding GPS Satellite S Siggnals using the Coarse/A Acquisition Gold c code. Because all of the saatellite signalls are modullated onto thhe same L1 carrier c frequuency, the signals must be separated after demoddulation. Thhis is donee by assigniing each saatellite a unnique binary seequence know wn as a Goold code. The T signals are decoded after dem modulation using u addition of the Gold codes corressponding to the satellitess monitored by the receivver. If the alm manac inform mation has previously p beeen acquiredd, the receiveer picks the satellites s to listen l for by theeir PRNs, un nique numbeers in the rannge 1 through 32. If the almanac a infoormation is not n in memory,, the receiveer enters a seearch mode until a lockk is obtainedd on one of the satellites. To obtain a lock, it is neecessary thaat there be ann unobstructted line of sight s from thhe receiver to t the satellite. The receiveer can then acquire a the almanac a andd determine the satellitees it should listen l for. As itt detects eacch satellite's signal, it ideentifies it byy its distinct C/A code pattern. p There can
be a delaay of up to 30 0 seconds beefore the firsst estimate of position beecause of thee need to reaad the ephemeriis data. Processinng of the nav vigation message enablees the determ mination of the time of transmissionn and the satelllite position n at this tiime. For more m informaation see Deemodulationn and Decooding, Advanced. Navigatioon equationss The receiver uses meessages receeived from satellites to determine d thhe satellite poositions andd time sent. Thee x, y, and z componentss of satellitee position annd the time sent s are desiignated as [xxi, yi, zi, ti] wheere the subsccript i denotees the satelliite and has thhe value 1, 2, 2 ..., n, wherre W When the time of message reception inndicated by the on-boarrd clock is where is
, the true reception tim me is
is receiver's clock bias b (i.e., cllock delay). The messaage's transit time
. Assuming the message m travveled at the speed of ligght, , the distance travveled
is . Knowing thhe distance from receiver to satellitte and the satellite's possition implies that t the recceiver is onn the surfacce of a sphhere centereed at the saatellite's possition with radiius equal to this distancee. Thus the receiver r is at a or near thee intersectioon of the surrfaces of the fouur or more spheres. In thhe ideal casee of no errorss, the receiver is at the inntersection of o the surfaces of the spherees. The clocck error or bias, b b, is thee amount thhat the receivver's clock is i off. The receiver r hass four unknownns, the three componentts of GPS reeceiver posittion and thee clock bias [x, y, z, b]. The equationss of the spheere surfaces are given byy:
or in term ms of pseudooranges,
, as .
These eqquations can be solved byy algebraic or o numericall methods. Least squares method When moore than fou ur satellites are a availablee, the calculation can usse the four best b or moree than four, coonsidering number n of channels, processing capability, and geomeetric dilutioon of precisionn(GDOP). Using U more than four iss an over-deetermined system of eqquations witth no unique solution, s wh hich must be b solved by a least-sqquares methood. Errors can c be estim mated through the t residualss. With eachh combinatioon of four or o more satelllites, a GDO OP factor caan be calculateed, based on the relative sky directioons of the sattellites used.. The locatioon is expresssed in a specificc coordinatee system or as a latitude annd longitudee, using the WGS W 84 geoodetic datum m or a country-sspecific systtem.
Bancroft's method involves an algebraic as opposed to numerical method and can be used for the case of four or more satellites. Bancroft's method provides one or two solutions for the four unknowns. However when there are two solutions, only one of these two solutions will be a near earth sensible solution. When there are four satellites, we use the inverse of the B matrix in section 2 of. If there are more than four satellites then we use the Generalized inverse (i.e. the pseudoinvers) of the B matrix since in this case the B matrix is no longer square. Error sources and analysis GPS error analysis examines the sources of errors in GPS results and the expected size of those errors. GPS makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected. Sources of error include signal arrival time measurements, numerical calculations, atmospheric effects, ephemeris and clock data, multipath signals, and natural and artificial interference. The magnitude of the residual errors resulting from these sources is dependent on geometric dilution of precision. Artificial errors may result from jamming devices and threaten ships and aircraft.
Review Questions 1. What is Triangulation Surveying In detail? 2. What is horizontal and vertical control method explain? 3. What is signals explain in detail? 4. Explain base line? 5. What are the instruments and accessories extension of base lines? 6. What is Satellite station explain with digram? 7. What is Intervisibility of height and distances in satellite explain? 8. What is Trigonometric leveling ? 9. What is Axis single corrections explain? 10. What are the application of satellite?
Chapter 5 ENGINEERING SURVEYS Structure of this unit Reconnaissance, CURVES, CONTOUR Learning Objectives 1. Reconnaissance 2.
Preliminary and location surveys for engineering projects – layout – setting out works
3. CURVES : Curve ranging – Horizontal and Vertical curves – Simple curves –setting with chain and tapes, 4. Tangential angles by theodolite. 5. CONTOUR : Contouring – Methods – Characteristics and uses of contours – Plotting – Calculation of areas and volumes. .
5.1 ENGINEERING SURVEYS Engineering Surveys are a single source provider of survey services to the construction and Building industries. Operating from our base in Hong Kong we have a peak workforce of over 120 staff and have been involved in some of the largest infrastructure and building projects undertaken in the region over the last 10 years. In addition to providing site surveying staff and equipment our vision is one of converging technologies where surveyors provide an increasingly diverse range of products and deliverables driven by the huge increase in quality and quantity of spatial data being collected. From Topographic and Building Surveys to High Definition Laser Scanning and from CAD Drafting to 3D BIM Models the market for collecting and presenting spatial data has never been larger. Engineering Surveys, as a multi-disciplined, single source provider of survey services are well placed to serve this market.
5.2 Reconnaissance Reconnaissance is the military term for exploring beyond the area occupied by friendly forces to gain vital information about enemy forces or features of the environment for later analysis and/or dissemination. Often referred to as recce (British and Canadian English) or recon (American English, Australian English), the associated verb isreconnoitre in British and Canadian English or reconnoiter in American English. Examples of reconnaissance include patrolling by troops (LRRPs, Rangers, scouts, or military intelligence specialists), ships orsubmarines, manned/unmanned aircraft, satellites, or by setting up covert observation posts. Espionage normally is not reconnaissance, because reconnaissance is a military force's operating ahead of its main forces; spies are non-combatants operating behind enemy lines. History Traditionally, reconnaissance was a role that was adopted by the cavalry. Speed was key in these maneuvers, thus infantry was ill suited to the task. From horses to vehicles, for warriors throughout history, commanders procured their ability to have speed and mobility, to mount and dismount, during maneuver warfare. Military commanders favored specialized small units for speed and mobility, to gain valuable information about the terrain and enemy before sending the
main (or majority) troops into the area, screening, covering force, pursuit and exploitation roles. Skirmishing is a traditional skill of reconnaissance, as well as harassment of the enemy. Overview Reconnaissance conducted by ground forces includes special reconnaissance, amphibious reconnaissance and civil reconnaissance.
Aerial reconnaissance is reconnaissance carried out by aircraft (of all types including balloons and unmanned aircraft). The purpose is to survey weather conditions, map terrain, and may include military purposes such as observing tangible structures, particular areas, and movement of enemy forces. Naval forces use aerial and satellite reconnaissance to observe enemy forces. Navies also undertake hydrographic surveys and intelligence gathering. Reconnaissance satellites provide military commanders with photographs of enemy forces and other intelligence. Military forces also use geographical and meteorological information from Earth observation satellites. Discipline
5.2.1 Types of reconnaissance: 1. Terrain-oriented reconnaissance is a survey of the terrain (its features, weather, and other natural observations). 2. Force-oriented reconnaissance focuses on the enemy forces (number, equipment, activities, disposition etc.) and may include target acquisition. 3. Civil-oriented reconnaissance focuses on the civil dimension of the battlespace (areas, structures, capabilities, organizations, people and events or ASCOPE). The techniques and objectives are not mutually exclusive; it is up to the commander whether they are carried out separately or by the same unit. Reconnaissance-in-force Some military elements tasked with reconnaissance are armed only for self-defense, and rely on stealth to gather information. Others are well-enough armed to also deny information to the enemy by destroying their reconnaissance elements. Reconnaissance-in-force (RIF) is a type of military operation or military tactics used specifically to probe an enemy's disposition. By mounting an offensive with considerable (but not decisive) force, the commander hopes to elicit a strong reaction by the enemy that reveals its own strength, deployment, and other tactical data. The RIF commander retains the option to fall back with the data or expand the conflict into a full engagement. Other methods consist of hit-and-run tactics using rapid mobility, and in some cases lightarmored vehicles for added fire superiority, as the need arises. Reconnaissance-by-fire
Reconnaissance by fire (or speculative fire) is the act of firing at likely enemy positions, in order to cause the enemy force to reveal their location by moving or by returning fire. Reconnaissance-pull Reconnaissance-pull is a tactic that is applied at the regiment to division level and defined as locating and rapidly exploiting enemy weaknesses. It is the ability to determine enemy positions and create exploitable gaps through which friendly forces can pass while avoiding obstacles and strong points. A textbook example of reconnaissance-pull was documented during the Tinian landings during World War II, utilized by the United States Marine Corps's Amphibious Reconnaissance Battalion, from V Amphibious Corps. Aerial photography, and the confirmation by the amphibious reconnaissance platoons determined that the Japanese defenders had largely ignored the northern beaches of the island focusing most of their defensive effort on beaches in the south-west which were more favorable for an amphibious landing. American forces quickly changed their landing location to the northern beaches and planned a small and hasty "deception" operation off the southern beach, which resulted in a complete surprise for the Japanese forces. As a result, American forces were able to fight the Japanese force on land where they had the advantage leading to light losses and a relatively short battle that lasted only 9 days. Types When referring to reconnaissance, a commander's full intention is to have a vivid picture of his battlespace. The commander organizes the reconnaissance platoon based on: 1) mission, 2) enemy, 3) terrain, 4) troops and support available, (5) time available, (6) and civil considerations. This analysis determines whether the platoon uses single or multiple elements to conduct the reconnaissance, whether it pertains to area, zone, or route reconnaissance, the following techniques may be used as long as the fundamentals of reconnaissance are applied. Scouts may also have different tasks to perform for their commanders of higher echelons, for example: the engineer reconnaissance detachments will try to identify difficult terrain in the path of their formation, and attempt to reduce the time it takes to transit the terrain using specialist engineering equipment such as a pontoon bridge for crossing water obstacles. Sanitary epidemiological reconnaissance implies collection and transfer of all data available on sanitary and epidemiological situation of the area of possible deployment and action of armed forces, the same data for the neighboring and enemy armed forces. The aim for the reconnaissance is to clear up the reasons of the specific disease origin- sources of the infection in various extreme situations, including local wars and armed conflicts, the ways of the infection transfer and all factors promoting to the infestation. After the armed forces have become stationary during wartime and emergency of peace time the sanitary epidemiological reconnaissance turns into sanitary and epidemiological surveillance and medical control of vital and communal activity of the armed forces . Area Area reconnaissance refers to the observation, and information obtained, about a specified location and the area around it; it may be terrain-oriented and/or force-oriented. Ideally, a reconnaissance platoon, or team, would use surveillance or vantage (static) points around the
objective to observe, and the surrounding area. This methodology focuses mainly prior to moving forces into or near a specified area; the military commander may utilize his reconnaissance assets to conduct an area reconnaissance to avoid being surprised by unsuitable terrain conditions, or most importantly, unexpected enemy forces. The area could be a town, ridge-line, woods, or another feature that friendly forces intend to occupy, pass through, or avoid. Within an Area of operation (AO), area reconnaissance can focus the reconnaissance on the specific area that is critical to the commander. This technique of focusing the reconnaissance also permits the mission to be accomplished more quickly. Area reconnaissance can thus be a stand-alone mission or a task to a section or the platoon. The commander analyzes the mission to determine whether the platoon will conduct these types of reconnaissance separately or in conjunction with each other. Civil Civil Reconnaissance is the process of gathering a broad spectrum of civil information about a specific population in support of military operations. It is related to and often performed in conjunction with infrastructure reconnaissance (assessment and survey). Normally the focus of collection in the operational area for civil reconnaissance is collecting civil information relating to the daily interaction between civilians and military forces. Civil information encompasses relational, temporal, geospatial and behavioral information captured in a socio-cultural backdrop. It is information developed from data related to civil areas, structures, capabilities, organizations, people, and events, within the civil component of the commander’s operational environment that can be processed to increase situational awareness and understanding. The type of civil information that is needed in order to support military operations varies based on the environment and situation. Route Route reconnaissance is oriented on a given route: e.g. a road, a railway, a waterway; a narrow axis or a general direction of attack, to provide information on route conditions or activities along the route. A military commander relies on information about locations along his determined route: which those that would provide best cover and concealment; bridge by construction type, dimensions, and classification; or for landing zones or pickup zones, if the need arises. In many cases, the commander may act upon a force-oriented route reconnaissance by which the enemy could influence movement along that route. For the reconnaissance platoons, or squads, stealth and speed —in conjunction with detailed intelligence-reporting—are most important and crucial. The reconnaissance platoon must remain far enough ahead of the maneuver force to assist in early warning and to prevent the force from becoming surprised. Even it is paramount to obtain information about the available space in which a force can maneuver without being forced to bunch up due to obstacles.Terrain-oriented route reconnaissance allows the commander to obtain information and capabilities about the adjacent terrain for maneuvering his forces, to include, any obstacles (minefields, barriers, steep ravines, marshy areas, or chemical, biological, radiological, and nuclear contamination) that may obstruct vehicle movement—on routes to, and in, his assigned area of operations. This requirement
includes the size of trees and the density of forests due to their effects on vehicle movement. Route reconnaissance also allows the observation for fields of fire along the route and adjacent terrain. This information assists planners as a supplement to map information. Zone Zone reconnaissance focuses on obtaining detailed information before maneuvering their forces through particular, designated locations. It can be terrain-oriented, force-oriented, or both, as it acquire this information by reconnoitering within—and by maintaining surveillance over— routes, obstacles (to include nuclear-radiological, biological, and chemical contamination), and resources within an assigned location. Also, force-oriented zone reconnaissance is assigned to gain detailed information about enemy forces within the zone, or when the enemy situation is vague by which the information concerning cross-country traffic-ability is desired. The reconnaissance provides the commander with a detailed picture of how the enemy has occupied the zone, enabling him to choose the appropriate course-of-action. As the platoon conducts this type of zone reconnaissance, its emphasis is on determining the enemy's locations, strengths, and weaknesses. This is the most thorough and complete reconnaissance mission and therefore is very time-intensive The survey which is conducted for determining quantities and for collecting data for the designing of engineering works such as roads, railways, etc., is known as Engineering Survey. Engineering survey have following types: Reconnaissance* Survey The Survey which is done for the feasibility* and rough cost of the project is known as Reconnaissance Survey. Preliminary Survey The survey in which more precise information is required for the choice of best location for the project and to estimate the exact quantities and costs of project is known as Preliminary Survey. Location Survey The survey for setting out the work on the ground is known as location survey. Reconnaissance means military observation of an area to gain information. Feasibility means either the project will complete or not.
5.3 Horizontal and Vertical curves The center line of a road consists of series of straight lines interconnected by curves that are used to change the alignment, direction, or slope of the road. Those curves that change the alignment or direction are known as horizontal curves, and those that change the slope are vertical curves.
5.3.1 Horizontal Curve When a highway changes horizontal direction, making the point where it changes direction a point of intersection between two straight lines is not feasible. The change in direction would be too abrupt for the safety of modem, high-speed vehicles. It is therefore necessary to interpose a curve between the straight lines. The straight lines of a road are called tangents because the lines are tangent to the curves used to change direction. In practically all modem highways, the curves are circular curves; that is, curves that form circular arcs. The smaller the radius of a circular curve, the sharper the curve. For modern, highspeed highways, the curves must be flat, rather than sharp. That means they must be large-radius curves. In highway work, the curves needed for the location or improvement of small secondary roads may be worked out in the field. Usually, however, the horizontal curves are computed after the route has been selected, the field surveys have been done, and the survey base line and necessary topographic features have been plotted. In urban work, the curves of streets are designed as an integral part of the preliminary and final layouts, which are usually done on a topographic map. In highway work, the road itself is the end result and the purpose of the design. But in urban work, the streets and their curves are of secondary importance; the best use of the building sites is of primary importance. The principal consideration in the design of a curve is the selection of the length of the radius or the degree of curvature (explained later). This selection is based on such considerations as the design speed of the highway and the sight distance as limited by headlights or obstructions. Some typical radii you may encounter are 12,000 feet or longer on an interstate highway, 1,000 feet on a major thoroughfare in a city, 500 feet on an industrial access road, and 150 feet on a minor residential street.
.—Lines of sight
220.127.116.11 TYPES OF HORIZONTAL CURVES There are four types of horizontal curves. They are described as follows: 1. SIMPLE. The simple curve is an arc of a circle. The radius of the circle determines the sharpness or flatness of the curve. 2. COMPOUND. Frequently, the terrain will require the use of the compound curve. This curve normally consists of two simple curves joined together and curving in the same direction 3. REVERSE. A reverse curve consists of two simple curves joined together, but curving in opposite direction. For safety reasons, the use of this curve should be avoided when possible 4. SPIRAL. The spiral is a curve that has a varying radius. It is used on railroads and most modem highways. Its purpose is to provide a transition from the tangent to a simple curve or between simple curves in a compound curve. 18.104.22.168 ELEMENTS OF A HORIZONTAL CURVE The elements of a circular curve are shown in figure 11-3. Each element is designated and explained as follows: PI POINT OF INTERSECTION. The point of intersection is the point where the back and forward tangents intersect. Sometimes, the point of intersection is designated as V (vertex). I INTERSECTING ANGLE. The intersecting angle is the deflection angle at the PI. Its value is either computed from the preliminary traverse angles or measured in the field. A CENTRAL ANGLE. The central angle is the angle formed by two radii drawn from the
0 Figure.—Elements of a horizontal curve. center of the circle (O) to the PC and PT. The value of the central angle is equal to the I angle. Some authorities call both the intersecting angle and central angle either I or A. RADIUS. The radius of the circle of which the curve is an arc, or segment. The radius is always perpendicular to back and forward tangents. POINT OF CURVATURE. The point of curvature is the point on the back tangent where the circular curve begins. It is sometimes designated as BC (beginning of curve) or TC (tangent to curve). POINT OF TANGENCY, The point of tangency is the point on the forward tangent where the curve ends. It is sometimes designated as EC (end of curve) or CT (curve to tangent). POC POINT OF CURVE. The point of curve is any point along the curve. LENGTH OF CURVE. The length of curve is the distance from the PC to the PT, measured along the curve. TANGENT DISTANCE. The tangent distance is the distance along the tangents from the PI to the PC or the PT. These distances are equal on a simple curve.
LONG CHORD. The long chord is the straight-line distance from the PC to the PT. Other types of chords are designated as follows: C The full-chord distance between adjacent stations (full, half, quarter, or onetenth stations) along a curve. c] The subchord distance between the PC and the first station on the curve. c? The subchord distance between the last station on the curve and the PT. EXTERNAL DISTANCE. The external distance (also called the external secant) is the distance from the PI to the midpoint of the curve. The external distance bisects the interior angle at the PI. MIDDLE ORDINATE. The middle ordinate is the distance from the midpoint of the curve to the midpoint of the long chord. The extension of the middle ordinate bisects the central angle. DEGREE OF CURVE. The degree of curve defines the sharpness or flatness of the curve. DEGREE OF CURVATURE The last of the elements listed above (degree of curve) deserves special attention. Curvature may be expressed by simply stating the length of the radius of the curve. That was done earlier in the chapter when typical radii for various roads were cited. Stating the radius is a common practice in land surveying and in the design of urban roads. For highway and railway work, however, curvature is expressed by the degree of curve. Two definitions are used for the degree of curve. These definitions are discussed in the following sections. Degree of Curve (Arc Definition) The arc definition is most frequently used in highway design. This definition, , states that the degree of curve is the central angle formed by two radii that extend from the center of a circle to the ends of an arc measuring 100 feet long (or 100 meters long if you are using metric units). Therefore, if you take a sharp curve, mark off a portion so that the distance along the arc is exactly 100 feet, and determine that the central angle is 12°, then you have a curve for which the degree of curvature is 12°; it is referred to as a 12° curve. By studying, you can see that the ratio design speed and allowable superelevation. Then the between the degree of curvature (D) and 360° is the radius is calculated. same as the ratio between 100 feet of arc and the circumference (C) of a circle having the same radius. That may be expressed as follows:
For a 1° curve, D = 1; therefore R = 5,729.58 feet, or meters, depending upon the system of units you are using. In practice the design engineer usually selects the 5,729.65 feet, or meters, depending upon the system of degree of curvature on the basis of such factors as the design speed and allowable superelevation. Then the between the degree of curvature (D) and 360° is the radius is calculated. Degree of Curve (Chord Definition) The chord definition is used in railway practice and in some highway work. This definition states that the degree of curve is the central angle formed by two radii drawn from the center of the circle to the ends of a chord 100 feet (or 100 meters) long. If you take a flat curve, mark a 100-foot chord, and determine the central angle to be 0°30’, then you have a 30-minute curve (chord definition). From observation of figure 11-5, you can see the following trigonometric relationship:
For a 10 curve (chord definition), D = 1; therefore R = In practice the design engineer usually selects the 5,729.65 feet, or meters, depending upon the system of degree of curvature on the basis of such factors as the units you are using. Degree of curve (chord definition). 11-
.—Degree of curve (chord definition).
Notice that in both the arc definition and the chord definition, the radius of curvature is inversely proportional to the degree of curvature. In other words, the larger the degree of curve, the shorter the radius; for example, using the arc definition, the radius of a 1° curve is 5,729.58 units, and the radius of a 5° curve is 1,145.92 units. Under the chord definition, the radius of a 1° curve is 5,729.65 units, and the radius of a 5° curve is 1,146.28 units.
5.4 CURVE FORMULAS The relationship between the elements of a curve is expressed in a variety of formulas. The formulas for radius (R) and degree of curve (D), as they apply to both the arc and chord definitions, were given in the preceding discussion of the degree of curvature. Additional formulas you will use in the computations for a curve are discussed in the following sections. Tangent Distance Length of Curve By studying, you can see that the solution for the tangent distance (T) is a simple right-triangle solution. In the figure, both T and R are sides of a right triangle, with T being opposite to angle N2. Therefore, from your knowledge of trigonometric functions you know that
and solving for T,
Chord Distance By observing figure 11-7, you can see that the solution for the length of a chord, either a full chord (C) or the long chord (LC), is also a simple right-triangle solution. As shown in the figure, C/2 is one side of a right triangle and is opposite angle N2. The radius (R) is the hypotenuse of the same triangle. Therefore,
and solving for C:
Length of Curve In the arc definition of the degree of curvature, length is measured along the arc, In this figure the relationship between D, & L, and a 100-foot arc length may be expressed as follows:
Then, solving for L,
This expression is also applicable to the chord definition. However, L., in this case, is not the true arc length, because under the chord definition, the length of curve is the sum of the chord lengths (each of which is usually 100 feet or 100 meters), As an example, if, as shown in view B, , the central angle (A) is equal to three times the degree of curve (D), then there are three 100-foot chords; and the length of “curve” is 300 feet. Middle Ordinate and External Distance Two commonly used formulas for the middle ordinate (M) and the external distance (E) are as follows
DEFLECTION ANGLES AND CHORDS From the preceding discussions, one may think that laying out a curve is simply a matter of locating the center of a circle, where two known or computed radii intersect, and then swinging the arc of the circular curve with a tape. For some applications, that can be done; for example, when you are laying out the intersection and curbs of a private road or driveway with a residential street. In this case, the length of the radii you are working with is short. However, what if you are laying out a road with a 1,000- or 12,000- or even a 40,000-foot radius? Obviously, it would be impracticable to swing such radii with a tape. In usual practice, the stakeout of a long-radius curve involves a combination of turning deflection angles and measuring the length of chords (C, Cl, or CZ as appropriate). A transit is set up at the PC, a sight is taken along the tangent, and each point is located by turning deflection angles and measuring the chord distance between stations. This procedure In below figure, you see a portion of a curve that starts at the PC and runs through points (stations) A, B, and C. To establish the location of point A on this curve, you should set up your instrument at the PC, turn the required deflection angle (all/2), and then measure the required chord distance from PC to point A. Then, to establish point B, you turn deflection angle D/2 and measure the required chord distance from A to B. Point C is located similarly. As you are aware, the actual distance along an arc is greater than the length of a corresponding chord; therefore, when using the arc definition, either a correction is applied for the difference between arc
.-Deflection angles and chords.
length and chord length, or shorter chords are used to make the error resulting from the difference negligible. In the latter case, the following chord lengths are commonly used for the degrees of curve shown: 100 feet—0 to 3 degrees of curve 50 feet—3 to 8 degrees of curve 25 feet—8 to 16 degrees of curve 10 feet-over 16 degrees of curve The above chord lengths are the maximum distances in which the discrepancy between the arc length and chord length will fall within the allowable error for taping. The allowable error is 0.02 foot per 100 feet on most construction surveys; however, based on terrain conditions or other factors, the design or project engineer may determine that chord lengths other than those recommended above should be used for curve stakeout. The following formulas relate to deflection angles: (To simplify the formulas and further discussions of deflection angles, the deflection angle is designated simply as d rather than d/2.)
Where: d = Deflection angle (expressed in degrees) C = Chord length D = Degree of curve d = 0.3 CD Where: d = Deflection angle (expressed in minutes) C = Chord length D = Degree of curve
5.5 SOLVING AND LAYING OUT A SIMPLE CURVE Now let’s solve and lay out a simple curve using the arc definition, which is the definition you will more often use as an EA. let’s assume that the directions of the back and forward tangents and the location of the PI have previously been staked, but the tangent distances have not been measured. Let’s also assume that stations have been set as far as Station 18 + 00. The specified degree of curve (D) is 15°, arc definition. Our job is to stake half-stations on the curve. Solving a Simple Curve We will begin by first determining the distance from Station 18 + 00 to the location of the PI. Since these points have been staked, we can determine the distance by field measurement. Let’s assume we have measured this distance and found it to be 300.89 feet. Next, we set up a transit at the PI and determine that deflection angle I is 75°. Since I always equals A, then A is also 75°, Now we can compute the radius of the curve, the tangent distance, and the length of curve as follows:
5.6 VERTICAL CURVES In addition to horizontal curves that go to the right or left, roads also have vertical curves that go up or down. Vertical curves at a crest or the top of a hill are called summit curves, or oververticals. Vertical curves at the bottom of a hill or dip are called sag curves, or underverticals.
5.6.1 COMPUTING VERTICAL CURVES As you have learned earlier, the horizontal curves used in highway work are generally the arcs of circles. But vertical curves are usually parabolic. The parabola is used primarily because its shape provides a transition and, also, lends itself to the computational methods described in the next section of this chapter. Designing a vertical curve consists principally of deciding on the proper length of the curve. the length of a vertical curve is the horizontal distance from the beginning to the end of the curve; the length of the curve is NOT the distance along the parabola itself. The longer a curve is, the more gradual the transition will be from one grade to the next; the shorter the curve, the more abrupt the change. The change must be gradual enough to provide the required sight distance. The sight distance requirement will depend on the speed for which the road is designed; whether passing or nonpassing distance is required; and other assumptions, such as one’s reaction time, braking time, stopping distance, height of one’s eyes, and height of objects. A typical eye level used for designs is 4.5 feet or, more recently, 3.75 feet; typical object heights are 4 inches to 1.5 feet. For a sag curve, the sight distance will usually not be significant during daylight; but the nighttime sight distance must be considered when the reach of headlights may be limited by the abruptness of the curve.
5.6.2 ELEMENTS OF VERTICAL CURVES the elements of a vertical curve. The meaning of the symbols and the units of measurement usually assigned to them follow: PVC Point of vertical curvature; the place where the curve begins. PVI
Point of vertical intersection; where the grade tangents intersect
PVT Point of vertical tangency; where the curve ends. POVC Point on vertical curve; applies to any point on the parabola POVT Point on vertical tangent; applies to any point on either tangent gI
Grade of the tangent on which the PVC is located; measured in percent of slope
Grade of the tangent on which the PVT is located; measured in percent of slope.
The algebraic difference of the grades: G = g2 -g,, wherein plus values are assigned to uphill grades and minus values to downhill grades; examples of various algebraic differences are shown later in this section. Length of the curve; the horizontal length measured in 100-foot stations from the PVC to the PVT. This length may be computed using the formula L = G/r, where r is the rate of change (usually given in the design criteria). When the rate of change is not given, L (in stations) can be computed as follows: for a summit curve, L = 125 x G/4; for a sag curve, L = 100 x G/4. If L does not come out to a whole number of stations using these formulas, then it is usually extended to the nearest whole number. You should note that these formulas for length are for road design only, NOT railway. L1 Horizontal length of the portion of the PVC to the PVI; measured in feet. L2 Horizontal length of the portion of the curve form the PVI to the PVT; measured in feet. e Vertical (external) distance from the PVI to the curve, measured in feet. This distance is computed using the formula e = LG/8, where L is the total length in stations and G is the algebraic difference of the grades in percent.
5.7 Contour CONTOUR • Defined as the line of intersection of a level surface with the surface of ground. • Lines drawn on the map to join points of the same height on the earth surface. • The best method of representation of features such as hills etc. CONTOUR INTERVAL 1. The constant height difference between two contour lines. 2. Depends upon the following factors: • The nature of the ground • The purpose and Extent of the survey • The scale of the map • Time and Expense of Field and Office work. EXAMPLE OF CONTOUR INTERVAL 1. For large scale maps of flat country, for building sites for detailed design work • 0.2m to 0.5m 2. For reservoirs and town planning scheme. • 0.5m to 2m 3. For location surveys • 2m to 3m 4. For small scale maps of broken country and General Topographical work • 3m, 5m, 10m or 25m. CHARACTERISTICS OF CONTOUR LINES 1. CONSAVE 2. CONVEX 3. VERTICAL SLOPE 4. CLIFF 5. VALLEY 6. HILL SPUR USE OF CONTOUR MAP AND CONTOUR PLAN 1. Study original shape of the earth surface 2. Identify most suitable site and saving cost for engineer works 3. Identify water catchments area 4. Calculate capacity or volume of a pond 5. Identify volume of cut and fill 6. Identify intervisibility between two points 7. Identify the slope of road 8. Draw longitudinal section and cross section to view the shape of earth surface.
9. Calculate horizontal distance between contour lines. METHOD OF CONTOURING 1. DIRECT METHOD • The contours to be located are directly traced out in the field by locating and making a number of points on each contour 2. INDIRECT METHOD • The points located and surveyed are not necessarily on the contour lines but the spot levels. • GRID LEVEL METHOD • CROSS SECTIONING METHOD • SPOT HEIGHT METHOD GRID LEVEL METHOD • This method is most systematic and favoured by many because the contouring process is easy to understand. • Suitable for flat and open survey area.
Contour maps are very useful since they provide valuable information about the terrain. Some of the uses are as follows: i) The nature of the ground and its slope can be estimated ii) Earth work can be estimated for civil engineering projects like road works, railway, canals, dams etc. iii) It is possible to identify suitable site for any project from the contour map of the region. iv) Inter-visibility of points can be ascertained using contour maps. This is most useful for locating communication towers. v) Military uses contour maps for strategic planning. the contour map, a common type of drawing in civil engineering. It is an ideal means of representing a threedimensional surface using a single two-dimensional view. Contour maps not only convey a qualitative impression of the features of the surface but also enable, using a single view, complete quantitative information to be extracted from the drawing. Although they are often used for topographic maps, contour maps have other applications that will be briefly mentioned in the article.
1. what it is We will define what a contour map actually is by considering a simple example of representing a three-dimensional landform using only two dimensions.A three-dimensional surface is given. For example, we can consider a the landform shown in the figure to the right. The perspective view shown is obviously a two-dimensional representation of a threedimensional object. This conveys a reasonable qualitative impression of the overall characteristics of the landform, but it does have the following shortcomings: 1. Depending on the point from which the view is taken, we may miss valuable information. For example, when the landform is viewed to obtain the upper of the two views shown to the right, we have no information on what lies beyond the red line. We need to rotate to a different viewpoint to obtain this information. 2. There is no reliable way of extracting quantitative information from this drawing. For example, we may wish to know the elevation of a specific point on this landform or the difference in elevation between two given points. Not only is it difficult to locate a given point exactly in a horizontal plane, it is likewise difficult to gain more than a general impression of its elevation. It is thus not possible to use this drawing to answer questions such as “What is the elevation of a point 400 m to the north and 300 m to the east of Point A”.We can solve the first problem to some extent by using multiple views of the same landform. This is shown in the figure to the right, where we have rotated the original viewpoint by approximately 90 degrees to obtain a second view. With the help of the second view, we can see what lies beyond the ridge. By selecting a sufficient number of views, we can generally provide a correct qualitative impression of the entire landform. The problem with this approach is that it is not compact, in the sense that one view is generally not enough. Furthermore, to be of value as a basis for extracting quantitative information, this approach also requires a means of relating one view to another. This is not a straightforward task We can solve the second problem to some extent by identifying specific points and writing in the elevation of these points on the drawing. This has been done for two points in the drawing to the right. Elevations are given in metres above sea level. This increases the quantitative content of the drawing. If a sufficiently large number of such elevations were given, it would be possible to estimate, at least approximately, elevations of other points by interpolation. There is still no reliable quantitative basis, however, for locating points in the horizontal plane. It is practically impossible, for example, to know the distance and bearing of the point with elevation 1019 relative to the point with elevation 1178. Reliable answers to questions relating to the elevation of a point of known coordinates relative to a given point thus remain difficult to obtain. Neither providing multiple perspective views nor providing elevation values for given points thus allows us to represent the three dimensional surface using a single two-dimensional drawing that enables quantitative information to be extracted (i.e., the z coordinate of a point given its x and y coordinates). To accomplish this objective, we need a more suitable two dimensional representation of the three dimensional surface. To develop this representation, we return to the previous perspective views. We first imagine that the landform has been sliced by a horizontal plane of constant elevation. In this case, say its elevation is 1000 m. Where this plane cuts the landform defines
one or more curves in a horizontal plane. We can erase the plane itself but leave the line created by the intersection of the plane and the landform. This curve joints points of equal elevation. We define any curve joining points of equal elevation a contour line, or simply a contour We can repeat this construction for planes at other elevations. For example, we can do so for planes with elevation 1100 m and 900 m. We can provide greater detail by showing more contour lines. In the lower view to the right, we have shown contours at increments of 20 m. We say that the contour interval in this drawing is 20 m. This contour interval appears to cover the landform reasonably well and capture the changes in topography. Although this drawing conveyssignificantly more information than the original perspective view given on the first page of this article, it is in itself is not particularly useful, since it has most of the shortcomings of the drawings developed initially. But it can be transformed into a powerful drawing by representingthis information on a horizontal plane We do this by viewing the landform, with the contour lines, looking directly down from a point above it. By choosing this viewpoint, we gain a dimensionally true representation of the horizontal plane, which permits us to use true x-y coordinates to locate points. The vertical dimension disappears visually but is now represented in a more abstract way through the contour lines, which now appear to be drawn on a horizontal plane.A given point can now be located and measured in x-y coordinates from any other point on the map. Its elevation can be read directly from the contour that intersects the point or, for points located in between contours, by interpolation. For example, a point 500 m to the east and 500 m to the north of the origin in the lower left portion of the drawing (shown with the red dot) is found to have an elevation of approximately 1008 m It is important that contour maps always incorporate a constant contour interval. By doing this, we can get a visual sense of the threedimensional properties of the surface, even when the shading of the original landform has been removed, by considering the patterns formed by the contours.The closest path from one contour line to an adjacent contour gives the steepest path. This follows directly from the definition of slope, which is equal to rise over run. For a constant rise (fixed contour interval), the greatest slope corresponds to the smallest value of run(closest distance between contours). It therefore follows that closely spaced contours denote regions that are steep and widely spaced contours are regions that are relatively flat.Closed curves denote either “hills” or “depressions”. We distinguish between the two by considering whether the contours are increasing or decreasing. In the case of the map shown to the right, the change of the contours indicates that the triangular figure enclosed by the green rectangle would be the top of a hill.
Landform with contours viewed from above. Contour interval is 20 m. A series of adjacent contours that all “point” in the same direction often indicates the path of a river, since this corresponds to the landform created by the flow of water through the earth. The blue line drawn onto the map to the right indicates one possible river.We can summarize the essence of contour maps as follows. Contour maps allow us to represent three-dimensional surfaces using a single two-dimensional drawing. They maintain the ability to locate points accurately in two horizontal dimensions. Everything in these two dimensions is drawn to scale. We lose a direct means of visualizing the third dimension, but are able to represent it accurately through lines joining points of equal elevation, called contour lines. These are equivalent to the curve formed by intersecting the surface of the given landform with planes of constant elevation. By working with a constant contour interval, we gain the ability to visualize the three dimensional characteristics of the surface. The data used to generate the landform considered in this example originate from the National Map of Switzerland. The corresponding section of this map is shown in the figure to the right. The contour interval in this case is 10 m 2. suitable applications Contour drawings are not the best way to represent all threedimensional objects. They are best suited to representing objects that have a single surface, a significant and well defined reference plane, and a significant third coordinate perpendicular to the reference plane.It follows from these conditions that contour drawings are well suited to the representation of landforms with a
single two-dimensional drawing. They have a single surface (the surface of ground), a well defined reference plane (the horizontal plane) and a significant third coordinate perpendicular to the reference plane (the z coordinate represents elevation, which is of primary significance).Contour drawings are not suitable for representing other types of three dimensional objects when at least one of these conditions is not satisfied. The bridge pictured in the figure to the right, for example, does not have a single surface, but rather several including a near vertical surface, a far vertical surface, and an upper surface. A single contour diagram cannot adequately represent all of these surfaces. This type of object is best represented in other ways, such as with multiple views based on standard viewing planes. In these drawings only two dimensions are depicted in each view. No quantitative (and often no qualitative) information regarding the third coordinate can be extracted from a given view. For this reason, more than one view is required to describe the object completely.
3. how to do it There are several ways to produce contour drawings from a set of x, y, and z coordinates describing a given three-dimensional surface. This section describes one way that is relatively straightforward. Given:
1. A regular square grid of points, with x, y, and z coordinates of the surface defined for each point of the grid. This grid is shown in the image to the right. It has nine points. The scale in the horizontal plane is given graphically. Elevations in metres are given for each grid point. Required: Produce a contour drawing representing the surface defined by the given x, y, and z coordinates. How to proceed: 1. Set the contour interval. To do this, it is necessary first to scan the z coordinates to extract the minimum and maximum values. Within this range, define an interval that is regular and that captures the relevant features of the surface with good fidelity. In this case, regular means taken from the series 1 m, 2 m, 5 m, 10 m, 20 m, 50 m, 100 m, etc. When working with a set of several diagrams, it is usually preferable to use a constant contour interval over the entire set of diagrams to enable comparisons across the set of drawings. In such cases, the choice of interval should be made in consideration of the properties of the entire set of data.
For this example, the minimum and maximum elevations are 12 and 45 m respectively. For simplicity, we will use a contour interval of 10 m for this example. So relevant contours will be at the 20, 30, and 40 m elevations. 2. Draw the grid to a suitable scale. As always, use regular scales (i.e., from the series 1:1, 1:2, 1:5, 1:10, 1:20, 1:50, 1:100, etc...). In this case, this has already been done for us. 3. For easy reference, write in the z values next to the corresponding points of the grid. This has already been provided. 4. For each segment joining adjacent points of the grid, identify points of intersection of contour lines with the segment, based on the assumption that the change in z within a given segment of the grid is linear. Proceed according to the following example: (a) Given: The top left horizontal segment AB of the grid has the following z values: z(A)=19.0 m, z(B)=22.0 m. (b) So one contour will intersect this segment. It is the 20 m contour, since 19 < 20 < 22.
(c) Locate the point of intersection of the contour within this segment by linear interpolation. One straightforward way to accomplish this is to use a scale in a way similar to the method used to subdivide a line into several equal segments:
(i) On the vertical gridline passing through the left end point, align the scale to a value corresponding to the elevation at that location. In this case, the scale is set to 90. (ii) On the vertical gridline passing through the right end point, align the scale to a value corresponding to the elevation at that location. In this case, the scale is set to 120. The scale remains at 90 along the left gridline. The series 90, 100, 110, 120 defined by the scale is similar to the series 19, 20, 21, 22 defined by the given elevations. So the intersection of the 20 m contour with the given line segment will correspond to 100 on the scale. (iii)Draw a line perpendicular to the given segment corresponding to the point of intersection identified with the scale. This locates the intersection of the contour with the given segment. (iv)Write the value of the contour next to the intersection point. (v) Note: the accuracy of this procedure increases as the angle between the scale and Segment AB gets smaller. So it is usually helpful to try fitting several scales to the given segment to minimize this angle. (vi)The outcome of this phase of the process is shown in the figure to the right.
(d) When all of the points of intersection of contours and segments have been thus identified, draw the contour lines. Proceed on a square by square basis. For a given square bounded by four adjacent grid points, the following two cases must be considered: (i) A given contour intersects exactly two bounding segments of the square. This is the case, for example, for the 20 m contour in the upper left-hand square. In this case, simply draw a line joining the points of intersection. This line is the path of the contour within the square. The image to the right shows the 20 m and the 30 m contours drawn for the upper left hand square in the grid.
(ii) A given contour intersects all four bounding segments of the square. In this case, it is not clear how to draw the contours. The figure to the right shows that a single arrangement of intersecting points can correspond to several arrangements of contours. In this case, only one arrangement (the middle one) corresponds to the given three-dimensional figure shown. (e) The completed contours are shown in the figure to the right. (f) Once the complete contour diagram has been drawn, trace the contours onto a new sheet of paper. This leaves only the contours and does not show the working grid and other marks that were made to produce them. It is generally necessary to label specific contours and spot elevations. As with all plan views (i.e. top views), a north arrow is required.
In some cases, it is preferable to draw smooth curves for the contours. This will often provide a more realistic rendition of the features of a given landscape. All of the contour maps we will draw in this course will be done by straight line segments linking points of equal elevation along gridlines, as described in the previous section.It is common to create contour maps from survey data obtained in the field. In such cases, it is sometimes difficult to get elevation values for a square grid of points in the plane. It is also possible to create a contour map following the principles outlined in the previous section for an irregular collection of points. In such a case, it is necessary to establish a triangular network of lines joining the available points in the plane. This is shown in the leftmost diagram. Along these lines, contour values are interpolated, as shown in the middle diagram. Finally, for a given triangle, straight line segments are drawn linking points on the boundary of identical contour value. This is shown in the rightmost diagram, where contour lines have been highlighted in green.
5. examples from practice This section describes several types of contour drawing in common use in engineering. 5.1. Standard Topographic Maps Topographic maps describe, with a high level of detail and accuracy, the topography (i.e., the shape) of a given geographical area. The standard way of representing the three dimensional features of landforms is contour lines. The first example is from Canada’s National Topographic System of maps. The most detailed scale available is 1:50 000. The second example is from the National Map of Switzerland. This map is drawn to a scale of 1:50 000. The third example is also from the National Map of Switzerland, this time from their 1:25 000 series. The Swiss maps are produced with much greater detail and with additional visual cues to help the user gain a qualitative impression of the three-dimensional landforms from the contours.
This is accomplished by: (1) a relatively small contour interval (in this case 10 metres), (2) subtle shading that corresponds to the shadows that would be cast on the landforms when the sun shines from the northwest quadrant of the map, and (3) pictorial symbols such as the cliff symbol, which is used when the slope of the land is so steep as to cause excessive bunching of the contour lines 5.2. Project-specific topographic plans and diagrams When the level of detail given on standard topographic maps is insufficient, it is possible to produce topographic plans for a given site based on specific survey data. These plans are used, for example, for the layout of bridges. Inthis diagram, for example, the contour interval is 5 m, which is considerably less than the contour interval used on standard topographic maps. This type of map will generally be prepared by a specialist land survey firm.Although contour diagrams are most often used to represent natural features such as topography, they are sometimes used to represent features of the facility to be built. Contour maps are sometimes made, for example, of bridge decks to validate that drainage will work properly. 5.3. Contour graphs It is also common to use contours to represent abstract surfaces, i.e., mathematical functions of two variables z=f(x,y). In such cases, x and y need to be spatial coordinates in a well defined and meaningful plane. Function z then defines a three-dimensional surface, similar to a landform.The same principles used to draw contour maps of physical landforms can be used to draw contour graphs of such functions. The figure to the right shows one such application. This diagram is called an influence surface for a slab free along the bottom, fixed in shear and bending along the top, and extending to infinity in the other two directions. It is based on the function z = Ma(x,y), where A is a given fixed point and Ma is the bending moment at Point A due to a unit load applied at Point (x,y). It is the two-dimensional analog of the one-dimensional influence line. This type of diagram can be used to calculate bending moments in bridge deck slabs due to loads applied by the wheels of a heavy truck. Its use is illustrated in the figure to the right.
6. applications: cutting sections from contour maps Contour maps are useful in and of themselves, but they are also used as a basis for producing relevant two-dimensional drawings. These can be visualized as the curve formed by the intersection of the given three dimensional surface and a vertical plane. The curve thus formed is often referred to as a section. The process of drawing this curve from a given contour map is referred to as cutting a section.
A common application of sections cut from contour maps is the production of the elevation of a valley to be crossed by a bridge. The procedure for cutting such a section is relatively straightforward. Given: 1. Contour map of the area under consideration 2. A straight line drawn on the contour map locating the vertical plane that defines the section (Line A-A).Required:
A two-dimensional drawing (x-z view) showing the shape of the landform along the given line. How to proceed:
1. Draw a line parallel to Line A-A on a blank portion of the page. This will be the horizontal datum of the section to be cut. 2. Based on these maximum and minimum elevations intersected by Line A-A, draw a vertical scale of elevations to the left of, and perpendicular to, the horizontal datum. Provide suitable labels to this axis. Draw horizontal gridlines based on the labels given on the axis. The drawing to the right represents the progress thus far. The area just created is called the section diagram. 3. For each contour that intersects Line A-A, do the following: (a) Identify the points of intersection of the contour and Line A-A. We will call one such point Point P1. (b) Draw lines perpendicular to Line A-A from Points Pi to the section diagram. The outcome of this step is shown in the diagram to the right. (c) Draw horizontal lines in the section diagram corresponding to the contour elevations. (d) Identify the points of intersection Q1 for specific perpendiculars originating from the contours and the corresponding elevation in the section diagram. 4. Join the points Qi to form a continuous curve. The resulting curve is the section cut along Line A-A. The figure to the right shows the finished section cut along Line A-A. The location of one point of the profile is highlighted. It corresponds to the 1000 level contour.
Review Questions 1. Explain engineering surveyes? 2. What is Reconnaissance in detail? 3. What is Preliminary and location surveys for engineering projects explain? 4. What is curves? 5. Explain the all types of curves? 6. What is horizontal and vertical curves? 7. What is CONTOUR? 8. Describe the Contouring – Methods with detail? 9. What are the characteristics of contour method? 10. What are the uses of contour method?
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