Lec2_Elementary and Higher Surveying_2013-2014

III. MEASUREMENT OF HORIZONTAL DISTANCES Choice of determining distances depends in  Purpose for which the measurement is intended  Accuracy Required  Cost and other conditions

A. METHODS 1. 2. 3. 4. 5. 6. 7. 8.

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Estimation Scaling from a Map Pacing Odometer Tacheometry (Tachometric Surveys) Taping Photogrammetry Inertial Systems Electronic Distance Measurement

B. PACING Pacing – counting of steps or paces by walking naturally along the line to be measured. RP: ranges from1/50 to 1/200 Distance = (pace factor) x (Number of Paces) Pace factor or unit pace is expressed in m/pace or ft/pace. It can be determined by taking the ratio of the known distance and average number of paces.

Two Methods To Calibrate One’s Pace 1. Determine the average length of an individual’s normal step 2. Adjust one’s pace to some predetermined length such as 1 meter Problem 1 A surveying student walks along a given line that was known to be 50.00 m long, in order to determine his average unit pace. He paced the line 5 times 69, 70.50, 68.75, 86 and 70 paces respectively in her field notebook. Determine the following: a. Pace factor in m/pace, ft/pace b. If the surveyor then counted three times 250.25, 254, 255.50 paces while pacing of unknown distance, what is the distance? c. Relative Precision of the paces Problem 2 A surveyor has a unit pace of 0.68 m/pace a. He counts 48 paces while walking from X to Y. What is the distance between X to Y? b. How many paces should the same surveyor count in order to layout a line roughly 357 m long?

C. MILEAGE RECORDER It is attached to an ordinary automobile speedometer and registers the distance to 0.10 mi and may be read by estimate to 0.01 mi.

general, boundary, control and construction surveys involving long lines and large areas can be performed most accurately and economically using modern EDM equipment.

I. TAPING It is direct measurement of distances using tape varying in length from 1 m to 100 m. Relatively short distances or specific construction layout requirements are present, taping the distances can be more practical.

J. ERRORS IN MEASUREMENT OF DISTANCES 1. Tape Not Standard Length

Where: c = correction per tape length Nominal Length – length stated by manufacturer True Length – length derived by comparison of temperature, tension, support. In measuring distances:  Positive correction is applied for tape too long  Negative correction is applied for tape too short In laying distances:  Negative correction is applied for tape too long  Positive correction is applied for tape too short Problem 3 A 50-m tape which is 0.035 m too long is used to measure distance AB. The recorded length was 624.76 m. find the corrected horizontal distance of line AB. Problem 4 A rectangular lot 250 m x 420 m is to be laid out using a 30-m tape. It was found out that the actual length of the tape was 29.98 m. What dimension should be laid out in order to have the desired area of the lot? Problem 5 The sides of a square lot having an area of 22500 sq.m. was measured by a 100-m tape that is 0.025 m too short. Calculate the error in the area.

2. Imperfect Alignment of Tape Problem 6 The distance measured over smooth level ground between two monuments was recorded as 108.00 m. Measurements consisted of three full tape lengths and one partial tape length. If the first taping point was misaligned 0.30 dm left, the second 7.2 dm right, and the third 4.1 dm left, compute the correct distance between the points.

3. Variation in Temperature (Correction due to Temperature) Tape expands s temperature rises and contracts as the temperature falls. If the tape is standardized at a given temperature and measurements are taken at a higher temperature the tape will be too long. Errors are reduced by attaching one or more tape thermometers to it and observing temperatures for each tape length.

D. ODOMETER It is a simple device that can be attached to any vehicle and register the number of revolutions of a wheel. With the circumference of the wheel known, the relation between revolutions and distance is fixed.

E. TIME INTERVAL OF TRAVEL F. MATHEMATICS AS EXPONENTIAL METHODS Unknown distances may be determined through their relation to one or more distances. It is used in triangulation (Topographic and Control Surveys) and plane table work.

G. TACHEOMETRY 1. 2.

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Stadia Method Distance Wedge Using a subtense bar and a transit/theodolite

H. ELECTRONIC DISTANCE MEASUREMENT Measurement of distance measuring equipment is based on the invariant speed of light or electromagnetic waves in vacuum. In

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Where: cT = correction per tape length, m or ft = coefficient of linear expansion, /C° or /F° For steel tape: = 0.0000116/C° = 0.00000645/F° T = observed temperature, °C or °F To = standard temperature, °C or °F To : If not given, use 20°C or 68°F L = nominal/standard length of the tape, m or ft Total Correction to be applied in measured length: (

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Problem 7 A distance was measured with a 30-m steel tape and recorded as 130.45 m when the average tape temperature was 8°C. What is the adjusted distance?