CHAPTER 4 - Levelling Detail

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LEVELLING

In this chapter you will learn about: • • • • • •

The types and operation of leveling instruments, with emphasis on automatic and digital levels and staves The Observation procedure in leveling, with clear definitions of the categories of sights The methods of booking and reducing levels, with guidance on the use of the appropriate method in differing circumstances The errors which arise in leveling operations and the procedures used to minimize or eliminate them The permanent adjustment of levels with emphasis on the two-peg test and associated calculation The effect of curvature and refraction on leveling operations and the method of reciprocal leveling.

4.1

Definition

Leveling is the procedure used when one is determining differences in elevation between points that are remote from each other. An elevation is a vertical distance above or below a reference datum. In surveying, the reference datum that is universally employed is that of Mean sea level (MSL). In North America, 19 years of observations at tidal stations in 26 locations on the Atlantic, Pacific, and Gulf of Mexico shorelines were reduced and adjusted to provide the national Geodetic Gravimetric and other anomalies in the 1988 general control readjustments (North American Vertical Datum-NAVD 88). Although, strictly, the NAVD datum may not precisely agree with mean sea level at specific points on the earth’s surface, the term mean sea level (MSL) is generally used to describe the datum. MSL is assigned a vertical value (elevation) of 0.000 ft or 0.000 m. See figure 1 below:

Figure 1. Mean Sea Level A vertical line is a line from the surface of the earth to the earth’s center. It is also referred to as being plumb line or a line of gravity. A level line is a line in a level surface. A level surface is a curved surface parallel to the mean surface of the earth. A level surface is best visualized as being the surface of a large body of water at rest. A horizontal line is a straight line perpendicular to a vertical line. 1

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4.2

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Introduction

Measuring the difference in elevation between points on the earth’s surface is a fundamental of surveying. These differences in elevation can be determined by various methods of leveling. Leveling is the operation of determining the difference in elevation between points on the earth’s surface. A level reference surface, or datum, is established and an elevation assigned to it. Differences in the determined elevations are subtracted from or added to this assigned value and result in the elevations of the point. A level surface is one in which every point is perpendicular to the direction of the plumb line. It differs from a plane surface, which is flat and is perpendicular to the direction of the plumb line at only one point. A body of still water will assume a level surface. If the changes in the surface of the ocean caused by such influences as tides, currents, winds, atmospheric pressure, and the rotation of the earth could be eliminated, the resulting surface would be level. The oceans’ level surface is determined by averaging a series of tidal height observations over a Metonic cycle (Approximately 19 calendar years). This average, called mean sea level, is the most common datum for leveling and usually assigned an elevation of zero. This datum remains in effect until continuing observations show a significant difference and it becomes worthwhile to change the datum. In the United State, the mean seal level datum of 1929 is still in effect.

4.3

Types of Leveling

Leveling operations are divided into two major categories. Direct leveling is usually referred to as differential, or spirit, leveling. In this method the difference in elevation between a known elevation and the height of the instrument, and then the difference in elevation from the height of the instrument to an unknown point, are determined by measuring the vertical distance with a precise or semi precise level and leveling rods. This is only method that will yield accuracies of the third or a higher order. The second method of leveling, indirect leveling is further subdivided into two separate methods, trigonometric and barometric. The trigonometric method applies the principles of trigonometry to determine differences in elevation; a vertical angle (above or below a horizontal plan) and a horizontal distance or slope distance (measured or computed are used to compute the vertical distance between two points. This method is generally used for lower-order leveling where the terrain is prohibitive to direct leveling. Barometric leveling uses the differences in atmospheric pressure as observed with a barometer or altimeter to determine differences in elevation. This is the least used and least accurate method of determining differences in elevation. It should only be used in surveys where one of the other methods is unfeasible or would involve large amounts of time or money. Because of its limited use, barometric leveling will not be discussed further. 4.3.1 Definitions For Leveling 2

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Bench Mark (BM) is a permanent point of known elevation. Bench marks are established by using precise leveling techniques and instrumentation. Bench marks are bronze disks of plugs set into vertical (usually) wall faces. It is important that the bench mark be placed in a structure that has substantial footings (at least below minimum frost depth penetration). Bench mark elevations and locations are published be federal, state or provincial, and municipal agencies and are available to surveyors for a nominal fee. Temporary bench mark (TBM) is a semipermenant point of known elevation. TBMs can be flange bolts on fire hydrants, nails in the roots of trees, top corners of concrete culvert headwalls, and the field notes of various surveying agencies. Turning point (TP) is a point temporarily used to transfer an elevation. Backsight (BS) is a rod (staff) reading taken on a point of known elevation in order to establish the elevation of the instrument line of sight. Height of instrument (HI) is the elevation of the line of sight through the level. (i.e. Elevation of BM + BS = HI) Foresight (FS) is a rod reading taken on a turning point, bench mark or temporary bench mark in order to determine its elevation (i.e. Hi – FS = elevation of TP (BM or TBM). Intermediate foresight (IS) is a rod (staff) reading taken at any other point where the elevation is required. HI – IS elevation. Most engineering leveling projects are initiated so as to determine the elevations of intermediate points (as profiles, cross sections etc.) The addition of backsights to elevations to obtain heights of instrument and the subtraction of foresights from heights of instrument to obtain new elevations are known as note reductions. The arithmetic can be verified by performing the arithmetic check (page check). Since all BS are added, and all FS are subtracted, when the sum of BS is added to the original elevation, and then the sum of FS is subtracted from that total, the remainder should be the same as the final elevation calculated. Original elevation + ∑ BS - ∑ FS = New Elevation

4.4

Leveling Equipment 4.4.1 Levels 3

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The engineer’s level can be compared to a carpenter’s level. The difference is that the engineer’s level is used by mounting it on a tripod (to hold its steady) and sighting through a telescope in order to transfer the level line to another point. While the carpenter’s level can be used to determine if two points a few inches apart are on a level surface, the engineer’s level can tell if two points a few hundred feet apart are on a level line. Just as there are many different types of carpenter’s levels – for example, water levels and line levels - so too there are many different types of engineer’s levels. Although some of these levels have certain features that others do not have, they all share certain basic parts.

Figure 2 identifies the important parts of an engineer’s level. 1. Eyepiece. The adjustable lens through which the observer looks. The eyepiece is rotated to bring the cross hairs into focus. 2. Telescope. The tube which holds all the lenses and focusing gears in their proper positions. 3. Sunshade. A metal or plastic extension which can be placed over the objective lens to protect the lens form damage and to reduce glare when the level is in use. 4. Focusing Knob. An adjustment knob which internally focuses the level on the desired target. 5. Horizontal circle. 6. Leveling screws. Adjustment screws used to level the instrument. 1 7. Base. A 3 in 8 in (89 by 203mm) threaded base which secures the instrument to the tripod. 2 8. Plumb bob, hook, and chain. A hook and chain, centered under the level, to which the plumb bob is attached if angles will be turned. These items are not illustrated. 9. Shifting center. A design feature which permits exact placement over a given point. 10. Name and serial number plate. 4

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11. Horizontal tangent screw. An adjustment screw which allows exact alignment of the cross hairs and the target within the horizontal plane. 12. Horizontal clamp screw. An adjustment screw which allows approximate alignment of the cross hairs and the target within the horizontal plane. 13. Level vial. A graduated, liquid-filled glass vial which is parallel to the line of sight of the telescope.

4.4.2 Categories of Levelling Instrument Levels are categorized loosely into two groups; (1) Automatic levels which, as the name suggests, set out a horizontal plane automatically compensator. (2) Digital levels, also automatic, which establish and store the elevation of a point by using a bar-coded staff and indicate it digitally on an LCD screen. 1. Automatic Levels All leveling instruments create a horizontal plane through the telescope. This horizontal plane is called the plane of collimation. Traditionally, this plane was established by using a spirit level attached to the telescope or body of the instrument. The plane was horizontal when the properly adjusted spirit level was centralized. In automatic levels, the line of collimation is established automatically by means of an optical compensator inserted into the path of the rays through the telescope. In order to allow the compensator to function correctly, the instrument is firstly leveled by means of a small circular spirit 1 level (pond bubble) which sets the instrument to within degree of the 4 vertical axis position. Figure 3 shows the sokkia C310 automatic level, which is a typical example of this kind of level manufactured for use by engineers and builders. It is compact, lightweight and sturdy and is an ideal basic level for use on construction sites. The compensator is a prism which acts as a pendulum to direct the incoming ray from the staff through the centre of the reticule. It is situated in front of the eyepiece and since it is light in weight, is stabilized against oscillation and vibration by four suspension wires and some from of magnetic damping action. Figure 4.4 shows exactly how this is achieved by Sokkia.

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Figure 3. Sokkia C310 Automatic Level Currently there are over fifty different automatic levels produced by the many instrument manufacturers who may use different techniques to achieve a stable horizontal line of sight in their products. These need not concern the surveyor unduly. It is sufficient to know that when the instrument is set up as in the following section a reliable horizontal line of site is established through the telescope of the instrument. Other features of various manufacturers’ automatic levels include magnification from x20 to x32: a horizontal circle which can read angles to one degree and an ability to measure distance with accuracies varying from 1 cm to 10 cm. 1a. Setting up the Automatic Level a. The instrument is set up with the leveling head approximately level and the instrument securely attached using the fastening screw. b. On all automatic levels there is a small circular spirit level which is centered in exactly the same manner as a titling level via a three-screw arrangement, a ball and socket joint or a jointed head system. c. When the spirit level has been centered the vertical axis. The compensator automatically levels the line of sight for every subsequent pointing of the instrument. d. Parallax is eliminated as before, the staff is sighted and brought into focus and the staff reading noted. 2. Digital Level With the ever-increasing rate of technological advance, it is impossible for any textbook o keep abreast with the range of models available at any given time. The following description is therefore, intentionally, an overview of the main features, capability and application of digital levels.

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Figure 4 (a) shows the Topcon DL 102C engineer’s electronic digital level. 7

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Other manufacturers produce similar models, notably the Sokkia SDL30 figure 4.b and Leica DNA figure 4. c.

Figure 5. Barcode Staff These instruments are used in conjunction with a unique patterned staff, similar to a barcode (figure 5). They are fully automatic and when properly set up, the line of sight through the telescope is horizontal, as with an automatic level. The main advantage of a digital level is that the surveyor does not need to read the staff, note the reading or calculate the results. Hence, these potential sources of error are eliminated. The instruments are robustly constructed and are protected against water penetration. The Topcon DL 102C is powered by Nickel Cadmium 7.2 V rechargeable battery. The Sokkia SDL30 is powered by a new Lithium-Ion battery 7.2V battery.

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4.4.3 Tripods The tripod supports the level base and keeps it stable during the observation. In other word, tripod is the base or foundation which supports the survey instrument and keeps is stably attached to the ground during observations. It consists of a tripod head to which the instrument is attached, there wooden or metal legs which are hinged at the head and metal tripod pointed shoes on each leg to press or anchor into the ground to achieve a firm setup. 4.4.4 Levelling Staff The leveling staff should conform to the British Standard specification. A portion of such a staff is shown in figure below.

Figure 6: Leveling Staff The length of the instrument is 3, 4 or 5 meter, while the width of the reading face must not be less than 38mm. Different colours must be used to show the graduation marks in alternate meters, the most common colours being black and red on a white ground. Major graduations occur at 100 mm intervals, the figures denoting meters and decimal parts. Minor graduations are 10mm interval, the lower three graduation marks of each 100 mm division being connected by a vertical band to form a letter E. Thus the “ E “ band covers 50mm and its distinctive shape is a valuable bid in reading the staff. Minor graduations of 1 mm may be estimated. In figure 6 above, various staff readings are shown to illustrate the method of reading.

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4.4.5 Tapes Tapes figure 3 are used in surveying to measure horizontal, vertical and slope distance. The common survey tapes are made of a ribbon or band of steel. Steel tapes are the most accurate of all survey tapes and are used to measure distances up to and including second-order accuracy.

Figure 7. Tapes

4.4.6 Orders of Accuracy When writing the specifications for a survey, it is very impractical to specify the exact degree of accuracy that is to be attained in each of the measurements. For this reason, specifications are based on the minimum degree of accuracy allowed for the particular survey. The range between the allowed degrees of accuracy is known as order of accuracy. The orders of accuracy for surveys are called first order, second order, third order, and lower order. The measurements for first order surveys are the most accurate, and the measurements for the other orders are progressively less accurate. Orders of accuracy are specified for triangulation, traverse, and leveling. For the measurements made in mapping, orders of accuracy are also specified for the astronomic observations made to establish position and azimuth. As an example of the range between orders of accuracy, let us consider the allowed traverse position closure. The first specifies 1: 25000 or better; second order, 1: 10000; third order, 1: 5000. the surveys normally considered in this book require third and lowerorder accuracy.

4.4.7 Level Bench Marks A bench mark is a relatively permanent object, natural or artificial, bearing a marked point whose elevation is known. A bench mark may be further qualified as permanent, temporary or supplementary. The purpose of a survey normally governs whether its stations will be permanently or temporarily marked. When it is known that the station may be reused over a period of several years, the station 10

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marker should be of a permanent type. A permanent bench mark is normally abbreviated BM, and a temporary or supplemental bench mark is abbreviated TBM. 4.5

Procedure with Automatic Levels Figure 8 illustrates a typical leveling situation, where the reduced levels of several points B, C. D, E, F and G are to be determined relative to a point A which is the bench mark. The leveling is to be closed on a second bench mark H.

Figure 8. Levelling Observation Procedure The instrument has to be set up twice in this particular case, although in a practical leveling exercise there could be many more set up points. Every time the instrument is set up, the FIRST sight taken from that position is called a BACK sight (BS). Likewise the last sight taken, prior to moving the instrument, it called a FORE sight (FS). Thus, in set up number 1, point A is a backsight, while point E is a foresight. Any other sight observed between backsight and foresight is an INTERMIDIATE sight (IS). Point B, C and D are therefore intermediate sights. A set up number 2, the sight taken to point E is a BS; point F is an IS; point G is an IS; and finally point H is a FS. It should be noted that the sight G is taken to the underside of a beam, which is higher than the instrument. In such a case, the staff is held upside down against the point while the reading is taken. 11

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Such a sight is called an inverted staff reading. Point E, where a foresight followed by a backsight is taken, is called a change point. Both readings are entered on the same line of the field book. Each point is given a separate line in the field book and its reading is entered on that line in its respective column, either BS, IS or FS. At each point of the survey, the staffholder holds the staff on the mark and ensures that it is held vertically, facing toward the instrument. The observer directs the telescope towards the staff and using the focusing screw, bring the staff clearly into focus. Parallax should already have been eliminated insetting up the instrument in which case there should be no apparent movement of the cross-hair when the head is moved up and down. The observer then reads the figure on the staff and enters the reading on the appropriate line and column in the field book. The reading is taken once more and checked against the field book entry. 4.6. Errors in Levelling As in all surveying arising operation, the sources and effects of errors must be recognized and steps taken to eliminate or minimize them. Errors in leveling can be classified under several headings. (b) Gross Errors This are mistake arising in the mind of the observer. They are usually due to carelessness, inexperience or fatigue. 1. Wrong staff readings. This is probably the most common error of all in leveling. Examples of wrong staff readings are: misplacing the decimal point, reading the wrong meter value and reading the staff wrong way up, with inverted staff readings. 2. Using the wrong cross-hair. Instead of reading the staff against the axial line, the observer reads against on of the stadia lines. This error is common in poor visibility. 3. Wrong booking. The reading is noted with the figures interchanged e.g. 3.020 instead 3.002. 4. Omission or wrong entry. A staff reading can easily be written in the wrong column or even omitted entirely. 5. Spirit level not centered. When using automatic levels, the small circular spirit level (pond bubble) must be accurately centered. If not, the compensator may become jammed, since it has only a limited amount of movement. 12

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All of these can be small or very large and every effort must be made to eliminate them. The only way to eliminate gross errors is to make a double leveling, i.e. to level from A to ZB then back from B to A. Theoretically the leveling should close without any error but this will very seldom happen. However, the error should lie within the limits. (c) Constant Errors These errors are due to instrumental defects and will always be of the same sign. 1. Non-verticality of the staff. This is a serious source of error. Instead of being held vertically the staff may be learning forward or backward. In figure 9, the staff is 3o out of vertical. If a reading of 4 meter is observed, it will be in error by 5 mm. The correct reading is: 4 x cos 3o = 3.995 meters.

Figure 9. The error can be eliminated by fitting the staff a circular spirit level. The staff holder must ensure that the bubble is centered when the staff is being read. A second method of eliminating the error is for the staff-holder to swing the staff slowly backwards and forwards across the vertical position during the observation. The observer then reads the lowest reading. 2. Collimation error in the instrument. In a properly adjusted level, the line of sight must be perfectly horizontal, when the instrument has been set up, ready for use. If not, there will be an error in the staff reading. In figure 10, the line of sight is inclined and the resultant error is  , increasing with length of sight. The error can be entirely eliminated by making backsights and foresights equal in length. The error  will be the same for each sight and true difference in level will be the difference in the readings.

Figure 10. 13

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3. Staff graduation errors. With the improvement of quality in the manufactures of leveling staves, particularly in the printing process, staff graduation errors are very uncommon. However, care should be taken when using a telescope staff, to ensure that the staff is fully extended.

(d) Random errors These are due to physical and climatic conditions. The resulting errors are small and are likely to be compensatory. 1. Effect of wind and temperature. The stability of the instrument may be affected, causing the height of collimation to change slightly. 2. Soft and hard ground. When the instrument is set on soft ground it is likely to sink slightly as the observer moves around it. When set in frosty earth, the instrument tends to rise out of the ground. Again the height of collimation changes slightly. 3. Change points. At any change point the staff must be held on exactly the same spot for both foresight and backsight. A firm spot must be chosen and marked by chalk. If the ground is soft a change plate figure 11 must be used.

Figure 11. The plate is simply a triangular piece of metal bent at the apices to form spikes. A dome of metal is welded to the plate and the staff is held on the dome at each sighting. 4. Human deficiencies. Errors arise in estimating the millimeter readings, particularly when visibility is bad or sights are long. All of the errors in this class tend to be small and compensating and are of minor importance only, in building surveying.

4.7

Permanent Adjustment In the proceeding errors section, it was pointed out that the line of collimation might not be horizontal. The leveling will still be correct provided the sights are of equal length. This is not always possible, however, particularly when many intermediate sights are to be taken. The only way in which these errors can be eliminated is to ensure that the instrument is in good adjustment. 14

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(a) Automatic and Digital Levels 1. The vertical axis of both types of level must be within ¼ degree of the thru plumb line. This verticality is indicated by the small circular spirit level (figure 4.3) or pond level as it is frequently called. When set up, the level should remain central when the instrument is turned to any position. If this does not happen, adjustments can be made to the level vial by means of two small screws, using the tools supplied by the manufacturer. 2. The line of sight must be perfectly horizontal, when the bubble of the pond level is central. This will only happen when the compensator and reticule are set correctly, otherwise a collimation error is present. In order to detect a collimation error, a so-called “Two-Peg Test” must be carried out. (b) Two-Peg Test Test (figure (4.25).

Figure 12. 1. Hammer two pegs A and B firmly into the ground, 60 meters apart. 2. Set up a level exactly midway between the pegs at a point C and read a staff held on each peg in turn. Reading on peg A = 1.310 m Reading on peg B = 0.460 m True difference in level A and B = 0.850m This is the true difference in level between the pegs irrespective of whether the line of collimation in inclined or not. If there were a collimation error it would be equal in both directions CA and CB since the distances are equal. 3. Remove the level to a point D some distance beyond peg B. The best distance is 1/10th of distance AB, which is 6 meters. Take a second set of reading on pegs A and B Reading on peg A Reading on peg B Apparent difference in level A to B 15

= 2.090 m = 1.180 m = 0.910 m

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4. Since the true difference in level does not equal the apparent different, there is a collimation error in the line of sight of the instrument. Because the apparent difference is greater than the true difference, the line of collimation error points upwards in the case. 5. The correct staff reading required to adjust the level are now required. They are calculated by one of the following methods.

Calculation of Adjustment (i)

Let x be the collimation error at B. Therefore the true staff reading at B = (1.180 – x) By proportion, the collimation error at A is Error ( A) 66 = x 6 Therefore error A So the true staff reading at A True difference in level Also, true difference in level Therefore 0.850 10x x True reading B

= 11x = (2.090 – 11x) = 0.850 m = (2.090 – 11x)- (1.180 – x) = 2.090 – 1.180 – 10x = 0.910 – 10 x = 0.910 – 10x = 0.060 = 0.006m = 1.180 – x = 1.180 – 0.006 = 1.174 m = 2.090 – 10x = 2.090 – 0.066 = 2.090 – 0.066 = 2.024 m

Check Different in level A 2.024 – 1.174 = 0.085 m (ii) True difference in level AB 1.310 – 0.460 = +0.850 m Apparent difference in level AB = 2.090 – 1.180 = +0.910 m The line of collimation is elevated by ( 0.910- 0.850 = 0.060) m over 60 m i.e. + 0.060 m in 60 m = 0.1 % Therefore true reading at B = 1.180 – 0.1 % of 6 m = (1.10 – 0.006) = 1.174 m And true reading at A = 2.090 – 0.1% of 66 m = (2.090 – 0.066) 16

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Engineering Surveying 1 Note = 2.024 m Check: Difference in Level AB = (2.024 – 1.174) = 0.850 m. Adjustment. The line of sight through the instrument is adjusted by means of the reticule (eyepiece). On most instruments there is one screw which is moved slowly up or down using a special tool supplied by the manufacturer, until the correct reading on the staff held on point A is obtained. A check is then made to peg B. The instrument manual will give all the information on a particular instrument. It may show that the adjustment method requires and adjustment to be made to the compensator. This is definitely not a job for the amateur and the instrument should be returned to the manufacturer where it will be adjusted under laboratory conditions.

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