Distance measurement lecture notes

1. KMJ16303
GEOMATICS ENGINEERING
MRS SITI KAMARIAH MD SA’AT
LECTURER
AGRICULTURAL ENGINEERING
FKTM, UNIMAP
Email: sitikamariah@unimap.edu.my
Phone: 019-5706232

2. DISTANCE
MEASUREMENT:
TAPING & ELECTRONIC DISTANCE MEASUREMENT (EDM)

3. INTRODUCTION
 One of the fundamentals of surveying is the need to measure
distance.
 Distances are not necessarily linear, especially if they occur on
the spherical earth.
 In this course we will deal with distances in geometric space,
which we can consider a straight line from one point or
feature to another.

4. DISTANCE MEASUREMENTS
• Distance between two points can be horizontally, slope or vertically
recorded in feet/meters.
• Horizontal and slope distance can be measured using fibreglass
tape/steel tape/using electronic distance measuring device.
• Vertical distance can be measured using a tape, as in construction
work, with a autolevel and staff. It also can be determine by
trigonometry.

5. SLOPE, VERTICAL AND HORIZONTAL DISTANCES

6. DISTANCE MEASUREMENTS
Direct
(length measurement)
eg measuring tape
Geometrical
(Optical)
Electronic
(Wave Physics)
Indirect
(distance measurement)
Distance Measurement

7. DISTANCE MEASUREMENT
EQUIPMENT

8. ELECTRONIC DISTANCE
MEASUREMENT (EDM)
 EDM is very useful in measuring distances that are
difficult to access or long distances.
 It measures the time required for a wave to sent to a
target and reflect back.
 Laser distance meter is an accurate and handy
measuring device used especially in length, area,
volume of a building.

9. TAPING
 Taping is applied to measurement with a steel tape or synthetic tape
(plastic or fiberglass).
 All standard in lengths
 100 m, 50m, 30 m, 20 m.
 It is fairly quick, easy and cheap, and hence is the most common form
of distance measurement.

10. TAPING
 Unfortunately, taping is prone to errors and mistakes.
 For high accuracy, steel tape should be used which is graduated
in mm and calibrated under standard temp (20 degree) and
tension (5kg). Be careful, easily break.
 Synthetic tape is more flexible graduated in 10mm

11. TAPING EQUIPMENT &
ACCESSORIES
a) Fiberglass Tapes
b) Nickel tape
c) Chain/Taping pin
d) Hand level
e) Ranging poles
f) Plumb bob

12. TAPING ON SMOOTH
LEVEL/SLOPING GROUND
 Tape must always be straight
 Tape must not be twisted
 Use chaining arrows for intermediate points
 Tape horizontally if possible
 Tape on the ground if possible
 Slope taping needs to be reduced
 Catenary taping requires correction
 Step taping suits some applications

13. TAPE MUST BE STRAIGHT…
obstruction
measured distance  required distance

14. FOR VERY LONG DISTANCE

15. Length AB = 4 x Full tape distance + 1 Short section
REMEMBER !
It works only on smooth ground or uniform slope surfaces
For very long distance

16. USE CHAINING PIN
measured distance  required distance

17. SLOPING GROUND
MEASUREMENT

18. SLOPE MEASUREMENT

19. SOURCES OF ERROR IN
TAPING
 Instrumental errors
 actual length can be different from nominal length because of a
defect in manufacture or repair on as a result of kinks.
 Natural errors
 the horizontal distance of a tape varies because of effects of
temperature, wind and weight of tape itself.
 Personal errors
 Tape persons may be careless in setting pins, reading tape or
manupulating equipment.

20. TAPING ERRORS
Systematic Taping
Errors
Random Taping Error
1. Slope 1. Slope
2. Standardization length 2. Temperature
3. Temperature 3. Tension and Sag
4. Tension & Sag 4. Alignment
5. Marking & Plumbing
Typical taping errors:
•Incorrect length of tape
•Temperature other than standard

21. TAPING CORRECTIONS
 For synthetic tapes, only Standardized Tape Length correction and
Slope corrections will be applied
 The best accuracy that can be achieved is the order of 1:1000
 When using steel tapes, if only Standardized Tape Length and slope
corrections are considered, the best possible accuracy that can be
obtained in the range 1:5000.
 If tension and temperature are added into consideration, accuracy
can be increased to better than 1:10000 ~ 1: 20000
 Sag only applies if tape is supported only at ends

22. STANDARD LENGTH CORRECTION
 Example: A distance of 220.450 m was measured with a steel band of nominal length
30 m. On standardization the tape was found to be 30.003 m. Calculate the correct
measured distance, assuming the error is evenly distributed throughout the tape.
 Error per 30 m, C = 3 mm
 Correction for total length =
= 220.45(0.003)/30 =0.022 m
 Correct length is 220.450 + 0.022 = 220.472 m
l
LC
Ca 
Where
Ca = correction of absolute length
C = correction to be applied to the tape= l’-l
L= measured length
l’= standardized length of field tape
l = nominal length of the tape
l
LC
Ca 

23. SLOPE CORRECTION
 Consider a 50-m tape measuring on a slope with a difference in
height of 5 m. The correction for slope is
= –25/100 = –0.250 m
L
h
Csl
2
2



L
h
Csl
2
2



OR L(1- cosθ)

24. TENSION CORRECTION
 E is modulus of elasticity of tape in N/mm2
= 2.0 x 105 N/mm2 for steel
 A is cross-sectional area of the tape in mm2
 L is measured length in m; and
 TS is the standard pull
 TF is pull applied during field measurement
 As the tape is stretched under the extra tension, the correction is positive.
If less than standard, the correction is negative.
 
F S
T
L T T
C
AE



25. TENSION CORRECTION
 Consider a 50-m tape with a cross-sectional area of 4 mm2, a standard
tension of 50 N and a value for the modulus of elasticity of E = 200
kN/mm2. Under a pull of 90 N the tape would stretch by
3
50000(90 50)
2.5 mm
4(200x10 )

 
 
F S
T
L T T
C
AE



26. TEMPERATURE CORRECTION
 Where Tf = mean field temperature during measurement
 Ts = temperature of standardization
 Coefficient of expansion of steel α = 0.0000112 per °C for steel
 If L = 50 m and the different of temperature and standard temperature (20oC) in
temperature is 2°C then
Ct = 0.0000112 x50 (± 2-20) = -0.0010 m
 
t f s
C L T T

 

27. SAG CORRECTION

28. SUMMARY
For converting slope distances L to horizontal distances D:
D = L – slope± standardization ± tension ± temperature – sag
Eq. (4.8)
For vertical measurements V:
V = VM ± standardization ± tension ± temperature
Eq. (4.9)
where
VM = measured vertical distance

29. EXAMPLE 1:
Question: The downhill end of 30 m
tape is held 90 cm too low. What is the
horizontal distance measured?
Answer:
Correction for slope = h2/2L
= (0.9)2/(2x30) = 0.0135 m
Hence, the horizontal distance
= 30 – 0.0135 = 29.987 m

30. EXAMPLE 2:
 Question: A 100 m tape is suspended between
the end under a pull of 200 N. The weight of the
tape is 30 N. Find the correct distance between
the tape end.
 Answer:
 Correction for sag = W2L/24P2
= 302 x 100 / 24x2002 = 0.0938 m
 Hence, the horizontal distance
= 100 – 0.0938 = 99.906 m

31. EXAMPLE 3:
 Question: A line was measured with a steel tape which exactly 30 m at
a temperature of 20 degrees and a pull of 10 kg. The measured
length was 1650 m. The temperature during measurement was 30
degrees and a pull apply was 15 kg. Find the true length of the line if
the cross sectional area of the tape was 0.025 cm2. The coefficient of
expansion of the material of the tape per degrees is 3.5 x 10-6 and
modulus of elasticity of the materials of tape is 2.1 x 106 kg/cm2.
• Answer: Correction for temperature and correction for tension
1) Correction for temperature:
= 3.5 x 10-6 x 1650 x (30-20) = 0.0578 m (+ve)
2) Correction for tension:
= 1650 (15-10)/(0.025 x 2.1 x 106 )
= 0.157 (+ve)
The true length of the line = 1650 + 0.0578+ 0.157 = 1650.215 m
 
t f s
C L T T

 
 
F S
T
L T T
C
AE



32. EXAMPLE 4: MEASURING A HORIZONTAL
DISTANCE WITH A STEEL TAPE
 Question: A steel tape of nominal length 30 m was used to measure the distance
between two points A and B on a structure. The following measurements were
recorded with the tape suspended between A and B:
Line Length measured Slope angle Mean temperature Tension apply
AB 29.872 m 3°40’ 5 °C 120 N
 The standardized length of the tape against a reference tape is 30.014 m at 20 °C
and 50 N tension. The tape weighs 0.17 N m–1 and has a cross-sectional area of 2
mm2.
 Calculate the horizontal length of AB.

33. ANSWER
 From equation (4.1):
slope correction = L (1-cosθ) = –29.872 (1 – cos 3°40') = –0.0611 m
 From equation (4.3):
standardization correction , =29.872 (30.014-30)/30 = +0.0139 m
 From equation (4.5):
tension correction, = 29.872 (120-50)/(2mm2x200000N/mm2) = +0.0052m
 From equation (4.6):
température correction = 0.0000112 x 29.872 (5-20) = –0.0050 m
 From equation (4.7):
sag correction =
= –0.0022 m
 Horizontal length AB = 29.872 -0.0611 +0.0139+0.0052-0.0050-0.0022
= 29.823 m (to the nearest mm)
l
LC
Ca 
 
t f s
C L T T

 
 
F S
T
L T T
C
AE



34. EXERCISE:
 Try Exercise 4.6 & 4.7 in textbook

35. ATTENDANCE W2

36. THANK YOU