BASIC DISTANCE MEASUREMENT

contents Types of distance measurements Measurement methods Taping methods Errors and corrections in distance measurements

Linear measurements Linear distance measurements in plane surveying are made in such a way that they are horizontal. Where a distance is measured along a slope it will have to be projected.

Types of Distance Measurement

Types of Distance Measurement

Types of Distance Measurement

Methods of Measurement Pacing Accuracy 1 : 100 Taping Accuracy 1 : 10,000 Electronic Distance Measurement (EDM) Accuracy 1 : 10,000 to 1:100,000

Taping Direct distance measurement Equipment for measurement of lines Material Chain Tempered steel Steel band steel tapes Varies (synthetic material, glass fibre, coated steel

Other equipment Optical square Ranging rods Abney level Pegs Used to measure right angles Either made of prism or mirror Ranging rods Used for marking any points that needs to be seen Abney level Measures ground slope Pegs Used to mark points that need to be permanently placed on the ground

Tape measurements techniques Surface taping Tape is laid on the ground and fully supported on the ground. Usually done where the ground is even. Catenary taping Tape is suspended clear of the ground. This eliminates the effects of surface irregularities. Reduces uncertainty in the determination of tape temperature

Step taping Used in ground with variable slope. The distance is measured in steps with the tape held horizontally. Measurements are done in steps of 5 – 10 m A plumb bob is used to transfer the distance to the ground. Easier to work downhill than up hill

Errors and corrections Systematic errors Standardisation Slope Tension Temperature Sag alignment

Correction Standardisation Occurs when the length of the tape is not equal to the standard one Due to wear and tear, tape tends to stretch The error per tape length can be measured by checking the tape against a standard.

ls = standard length of tape (m) l = nominal length of tape (m) L = measured length (m) ls = standard length of tape (m) l = nominal length of tape (m) The sign of correction is given by magnitude of l and ls

Slope Measurement should be on the horizontal plane Slope lines must be reduced to horizontal Correction is always negative Step taping No need to measure slope angle or vertical distance No corrections needed Correction always -ve

Projecting slope distance to horizontal plane Applicable where the ground runs in long regular slopes Slope measured by Leveling Abney level or Procedure which gives surface heights at points along slope Using slope angle Slope angle Measured length

Using difference in level between the two points h = height difference between the two points Acceptable if h/L is less than 1 in 25

Tension Caters for elasticity of tape material Occurs when the tape is tensioned to a value at which it was not standardized at For Steel tapes E is 200,000 N/ mm2 P, Ps = field and standard tension respectively (N) A = cross sectional area of band (mm2) E = Young’s modulus of elasticity (N mm-2) L = length measured (m) The sign of correction is given by magnitude of P and Ps

Temperature Due to thermal characteristics Required if the temperature is not the same as when the tape was standardized For Steel tapes  is 0.0000112 per °C coefficient of linear expansion temperature Standard temperature Measured length The sign of correction is given by magnitude of t and ts

Sag If a tape was standardized on flat level, using catenary will introduce a sag error due to its weight. w = weight per unit length (N/m) W = total weight of tape (N) l = measured length of span (m) = angle of slope between supports P = tension applied Correction always -ve

Alignment Applied when there is an obstruction that causes the tape to be misaligned Correction is usually small e = amount of deviation from tape L = measured length

Combined Formula Steel Taping: Examples Actual length is: For vertical length is:

A steel tape of nominal length 30 m was used to measure a line AB by suspending it between supports. The following measurements were recorded Line Length Measured Slope Angle Mean Temp. Tension AB 29.872 m 3o 40’ 5oC 120 N The standardisation length of the tape against a reference tape was known to be 30.014 m at 20oC and 50 N. If the tape weighs 0.17 N/m and has a cross sectional area of 2 mm2, calculate the horizontal length of AB.

Mistakes/ Gross errors Inexperience or carelessness of surveyor Mis – reading Erroneous booking Omitting entire band/tape length Displacement of station errors Mis alignment of tape