Linear Distance Measurement: Types, Methods, and Corrections, Lecture notes of Survey Sampling Techniques

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LINEAR DISTANCE

MEASUREMENT

Conventional

Contents

• Types of distance measurements

• Distance measurement methods/devices

• Taping/chaining

– methods/techniques

– Errors and corrections in distance measurements

– Numeric example

Linear measurements

• Distance

• Displacement between two or more points
• Used do define dimension of an object

• Distances could either be true horizontal or slope

distances.

• Horizontal distance is distance between two points in a

horizontal plane.

• It is primarily used for legal work
• Where a distance is measured along a slope, additional

data is required to project the slope distance.

• Slope, vertical angle or difference in elevation.

5

Methods of Measurement

• Direct Method

– Pacing

– Taping

– odometer

• Optical Method

– Stadia tacheometry

• Electronic Method

– Electronic Distance Measurement (EDM)

– Hand held Laser

– GPS

Indirect

1:20 to 1 : 100

1:500 to 1 : 20,

1:500 to 1 : 1,

(1mm + 1ppm)

Accuracy

1:50 to 1 : 200

Choice of device to use depends on the use of data

Taping

• Direct distance measurement

– Physically measuring distances

• Equipment for measurement of lines

Equipment Material Chain Tempered steel Steel band steel tapes Varies (synthetic material, glass fibre, coated steel

1 chain = 100 links = 20.1168m 1 chain = 150 links

Manufactured under fixed conditions of temperature and tensile force

Other equipment

• Optical square
  • Used to measure right angles
  • Either made of prism or mirror
• Ranging rods
  • Used for marking any points that needs to be seen or align
• Abney level
  • Measures ground slope
• Pegs
  • Used to mark points that need to be permanently placed on the ground
• Tension handle
  • Allows user to apply a specified tensile force
• Plumb bob
  • Locate tape precisely over specified point
• Chaining arrows
  • Mark tape length

• 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 (A source of error).

• Easier to work downhill than up hill
• Should be avoided when high accuracy is required

Sources of errors in taping

Instrumental A tape may be faulty due to a defect in its manufacturing or from kinking. For example actual length different from nominal length.

Natural The actual horizontal distance between the ends of the tape can vary due to the effects of:  temperature,  elongation due to tension, and  sagging.

Personal Errors will arise from carelessness by the survey crew:  poor alignment  tape not horizontal  improper plumbing  faulty reading of the tape

Errors and corrections

• Systematic errors

– Incorrect length of tape

– Slope

– Tension

– Temperature

– Sag

Correction

• Incorrect length of tape

– Occurs when the length of the tape is not equal to

the standard tape or distance.

• Due to wear and tear (tape tends to stretch) or
• Manufacturing errors

– The error per tape length can be measured by

checking the tape against a standard tape.

• Standard tape – kept in office and not used for any field

work.

1. The Figure shows that when the tape is too long, the distance measured appears too short, and the correction is therefore positive. The reverse is the case when the tape is too short.

2. When setting out a distance with a tape the rules in (1) are reversed.
3. It is better the correction, rather than the total corrected length. In this way fewer significant figures are required.

Source: Schofield 2007

• Slope
  • Measurement should be on the horizontal plane
  • Slope lines must be reduced to horizontal
  • Correction is always negative

a) Step taping

• No need to measure slope angle or vertical distance
• No corrections needed

∆ℎ^2

ii. Using difference in level between the two points

• If slope is gentle
•  h = height difference between the two points

Slope considered gentle if  h / L is less than 20%

Obtained from first term of binomial expansion of Pythagorean theorem

• Tension
  • Caters for elasticity of tape material
  • Occurs when the tape is pulled with a tension

greater than the standard value

P = tension applied on the tape in the field (N) Ps = tension at which the tape was standardized (N) A = cross sectional area of band (mm^2 ) E = Young’s modulus of elasticity (N mm-2) L = length measured (m)

For Steel tapes

E is 210 kN/ mm^2

The sign of correction is given by magnitude of P and Ps