Elementary Surveying _ Distance Measurement

Distance measurement

1. DISTANCE
MEASUREMENT
CESURV30

2. INTRODUCTION
»Distance measurementis regarded as the most
fundamental of all surveying observations.
»Distances are not necessarily linear, especially
if they occur in the spherical earth
»For relatively small distances, we can consider
straight line as one existing in the Euclidean
(geometric) space.
2023 DISTANCE MEASUREMENT 2

3. METHODS OF
MEASURING
DISTANCES
1.Pacing
2.Odometer Readings
3.Optical Rangefinders
4.Tacheometry (Stadia)
5.Subtense Bars
6.Taping
7.Electronic Distance Measurement
8.Satellite Systems
2023 DISTANCE MEASUREMENT 3

4. PACING
2023 DISTANCE MEASUREMENT 4
»Pacing is a practical measure of distance.
»Pacing consists of counting the number of steps, or paces, in a
required distance.
»No equipment is needed for pacing.
»Pacing offers relatively low accuracy.

5. PACING
Pace
»Length of a step in
walking
»May be measured from
heel to heel or toe to toe
Pace Factor
»Ratio of the measured
distance to the number of
paces made by an individual
to cover the measured
distance.
��=
�������� ��������
������ �� �����

6. ODOMETER READINGS
2023 DISTANCE MEASUREMENT 6
»Converts the number of revolution of a wheel of known circumference
to a distance

7. OPTICAL RANGEFINDERS
2023 DISTANCE MEASUREMENT 7
»Operated by looking through the lens, adjusting the focus until a
distant object viewed is focused, whereupon the distance to that
object is obtained

8. TACHEOMETRY (STADIA)
2023 DISTANCE MEASUREMENT 8
»Sometimes called Tachymetry which
means swift measurements
»This is a surveying method used to
quickly determine the horizontal
distance to, and elevation of, a point.
»Stadia observations are obtained by
sighting through a telescope with two or
more horizontal cross wires at a known
spacing.
»Stadia was introduced in 1771 by James
Watt.

9. TACHEOMETRY (STADIA)
2023 DISTANCE MEASUREMENT 9
»Its precision depends upon the
following factors:
oRefinement of the instruments
oSkill of the observer
oLength of the measurement
oEffect of refraction
»This method employs the use of
the following instruments:
oStadia rod / Leveling rod
oTelescope / Theodolite

10. TACHEOMETRY (STADIA)
2023 DISTANCE MEASUREMENT 10
»Distance formula:
�=�??????cos??????+??????
where: K = stadia interval factor
s = stadia interval
c = stadia constant
»Additional Notes:
oK = 100 if not given
oS = upper reading – lower reading
oC = 0.3 for externally focusing
instrument
oC = 0 for internally focusing
instrument
oAssume internal focusing if not given

11. TACHEOMETRY (STADIA)
2023 DISTANCE MEASUREMENT 11

12. SUBTENSE BARS
2023 DISTANCE MEASUREMENT 12
»This indirect distance measuring procedure involves using a theodolite
to read the horizontal angle subtended by two targets precisely spaces
at a fixed distance.
»The length between the two targets is commonly 2 meters.
»By using trigonometry, the following formula can be derived:
1m
1m
HD
θ/2
θ/2

13. SUBTENSE BARS
2023 DISTANCE MEASUREMENT 13
»This indirect distance measuring procedure involves using a theodolite
to read the horizontal angle subtended by two targets precisely spaces
at a fixed distance.
»The length between the two targets is commonly 2 meters.
»By using trigonometry, the following formula can be derived:
��=
1
tan
??????
2

14. TAPING (OR CHAINING)
2023 DISTANCE MEASUREMENT 14
»Taping or chaining is a method of measurement utilizing a steel tape
or synthetic tape.
»It is fairly quick, easy and cheap, and hence is the most common form
of distance measurement.
»Taping accessories:
oRange poles
oChaining pins
oPlumb bob

15. TAPING (OR CHAINING)
Level or even ground Sloping or uneven ground
2023 DISTANCE MEASUREMENT 15

16. TAPING (OR CHAINING)
2023 DISTANCE MEASUREMENT 16
»Breaking Tape
oOn steeper slopes where the length of the tape cannot be held
horizontally , shorter distances are measured and accumulated to
total of a fill tape length.

17. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 17
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
2.If the corrected length of the line is 621.6m, determine the relative precision.

18. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 18
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4

19. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 19
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4

??????
1=144 ??????????????????????????????

20. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 20
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4

??????
1=144 ??????????????????????????????
��=
100 ??????
144 �????????????????????????

21. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 21
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4

??????
1=144 ??????????????????????????????
��=
100 ??????
144 �????????????????????????

��=0.6944444 ??????/????????????????????????

22. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 22
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4
??????
2=
894.5+892+891.5+895
4
??????
1=144 ??????????????????????????????
��=
100 ??????
144 �????????????????????????

��=0.6944444 ??????/????????????????????????

23. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 23
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4
??????
2=
894.5+892+891.5+895
4
??????
1=144 ?????????????????????????????? ??????
2=893.25 ??????????????????????????????
��=
100 ??????
144 �????????????????????????

��=0.6944444 ??????/????????????????????????

24. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 24
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4
??????
2=
894.5+892+891.5+895
4
??????
1=144 ?????????????????????????????? ??????
2=893.25 ??????????????????????????????
��=
100 ??????
144 �????????????????????????
�=��??????
2
��=0.6944444 ??????/????????????????????????

25. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 25
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4
??????
2=
894.5+892+891.5+895
4
??????
1=144 ?????????????????????????????? ??????
2=893.25 ??????????????????????????????
��=
100 ??????
144 �????????????????????????
�=��??????
2
��=0.6944444 ??????/???????????????????????? �=0.6944444
??????
�??????????????????
893.25??????????????????????????????

26. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 26
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
1.Determine the length of the line.
Solution:
??????
1=
143+146.5+142.5+144
4
??????
2=
894.5+892+891.5+895
4
??????
1=144 ?????????????????????????????? ??????
2=893.25 ??????????????????????????????
��=
100 ??????
144 �????????????????????????
�=��??????
2
��=0.6944444 ??????/???????????????????????? �=0.6944444
??????
�??????????????????
893.25??????????????????????????????
�=620.3125 ??????

27. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 27
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
2.If the corrected length of the line is 621.6m, determine the relative precision.
Solution:

28. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 28
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
2.If the corrected length of the line is 621.6m, determine the relative precision.
Solution:
��=
??????�−��
??????�

29. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 29
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
2.If the corrected length of the line is 621.6m, determine the relative precision.
Solution:
��=
??????�−��
??????�
��=
621.6−620.3125
621.6

30. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 30
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
2.If the corrected length of the line is 621.6m, determine the relative precision.
Solution:
��=
??????�−��
??????�
��=
621.6−620.3125
621.6
��=
1
482.796

31. SAMPLE PROBLEM 1 (PACING)
2023 DISTANCE MEASUREMENT 31
»CE Board November 1998
»A line 100m long was paced four times by a surveying with the following data: 143, 146.5, 142.5,
and 144. Another line was paced four times by the same surveyor with the following data: 894.5,
892, 891.5, and 895.
2.If the corrected length of the line is 621.6m, determine the relative precision.
Solution:
��=
??????�−��
??????�
��=
621.6−620.3125
621.6
��=
1
482.796
��=
1
480

32. SAMPLE PROBLEM 2 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 32
»A stadia rod, held at a distance point B, is sighted by an instrument set-up at A. The upper and
lower stadia hair readings were observed as 1.506m and 0.742m, respectively. If the stadia
interval factor (K) is 100, and the instrument is external focusing, determine the length of the line
AB

33. SAMPLE PROBLEM 2 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 33
»A stadia rod, held at a distance point B, is sighted by an instrument set-up at A. The upper and
lower stadia hair readings were observed as 1.506m and 0.742m, respectively. If the stadia
interval factor (K) is 100, and the instrument is external focusing, determine the length of the line
AB
»Solution:
�=�??????cos??????+�

34. SAMPLE PROBLEM 2 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 34
»A stadia rod, held at a distance point B, is sighted by an instrument set-up at A. The upper and
lower stadia hair readings were observed as 1.506m and 0.742m, respectively. If the stadia
interval factor (K) is 100, and the instrument is external focusing, determine the length of the line
AB
»Solution:
�=�??????cos??????+�
�=1001.506−0.743cos0+0.3

35. SAMPLE PROBLEM 2 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 35
»A stadia rod, held at a distance point B, is sighted by an instrument set-up at A. The upper and
lower stadia hair readings were observed as 1.506m and 0.742m, respectively. If the stadia
interval factor (K) is 100, and the instrument is external focusing, determine the length of the line
AB
»Solution:
�=�??????cos??????+�
�=1001.506−0.743cos0+0.3
�=76.6??????

36. SAMPLE PROBLEM 3 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 36
»CE Board November 1998
»A stadia intercept of 3.60m was measured on a stadia rod by a transit with stadia constant and
stadia interval factor of 0.3m and 100, respectively. If the line of sight was inclined at an angle of
3
�
30′ with the horizontal, determine the horizontal distance from the transit to the rod.

37. SAMPLE PROBLEM 3 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 37
»CE Board November 1998
»A stadia intercept of 3.60m was measured on a stadia rod by a transit with stadia constant and
stadia interval factor of 0.3m and 100, respectively. If the line of sight was inclined at an angle of
3
�
30′ with the horizontal, determine the horizontal distance from the transit to the rod.
»Solution:
�=�??????cos??????+�

38. SAMPLE PROBLEM 3 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 38
»CE Board November 1998
»A stadia intercept of 3.60m was measured on a stadia rod by a transit with stadia constant and
stadia interval factor of 0.3m and 100, respectively. If the line of sight was inclined at an angle of
3
�
30′ with the horizontal, determine the horizontal distance from the transit to the rod.
»Solution:
�=�??????cos??????+�
�=1003.6cos3
�
30′+0.3

39. SAMPLE PROBLEM 3 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 39
»CE Board November 1998
»A stadia intercept of 3.60m was measured on a stadia rod by a transit with stadia constant and
stadia interval factor of 0.3m and 100, respectively. If the line of sight was inclined at an angle of
3
�
30′ with the horizontal, determine the horizontal distance from the transit to the rod.
»Solution:
�=�??????cos??????+�
�=1003.6cos3
�
30′+0.3
�=359.6285 ??????

40. SAMPLE PROBLEM 3 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 40
»CE Board November 1998
»A stadia intercept of 3.60m was measured on a stadia rod by a transit with stadia constant and
stadia interval factor of 0.3m and 100, respectively. If the line of sight was inclined at an angle of
3
�
30′ with the horizontal, determine the horizontal distance from the transit to the rod.
»Solution:
�=�??????cos??????+�
�=1003.6cos3
�
30′+0.3
�=359.6285 ??????
��=�cos??????

41. SAMPLE PROBLEM 3 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 41
»CE Board November 1998
»A stadia intercept of 3.60m was measured on a stadia rod by a transit with stadia constant and
stadia interval factor of 0.3m and 100, respectively. If the line of sight was inclined at an angle of
3
�
30′ with the horizontal, determine the horizontal distance from the transit to the rod.
»Solution:
�=�??????cos??????+�
�=1003.6cos3
�
30′+0.3
�=359.6285 ??????
��=�cos??????
��=359.6285cos3
�
30
′

42. SAMPLE PROBLEM 3 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 42
»CE Board November 1998
»A stadia intercept of 3.60m was measured on a stadia rod by a transit with stadia constant and
stadia interval factor of 0.3m and 100, respectively. If the line of sight was inclined at an angle of
3
�
30′ with the horizontal, determine the horizontal distance from the transit to the rod.
»Solution:
�=�??????cos??????+�
�=1003.6cos3
�
30′+0.3
�=359.6285 ??????
��=�cos??????
��=359.6285cos3
�
30
′
��=358.9577 ??????

43. SAMPLE PROBLEM 3 (TACHEOMETRY)
2023 DISTANCE MEASUREMENT 43
»CE Board November 1998
»A stadia intercept of 3.60m was measured on a stadia rod by a transit with stadia constant and
stadia interval factor of 0.3m and 100, respectively. If the line of sight was inclined at an angle of
3
�
30′ with the horizontal, determine the horizontal distance from the transit to the rod.
»Solution:
�=�??????cos??????+�
�=1003.6cos3
�
30′+0.3
�=359.6285 ??????
��=�cos??????
��=359.6285cos3
�
30
′
��=358.9577 ??????

44. SAMPLE PROBLEM 4 (SUBTENSE BARS)
2023 DISTANCE MEASUREMENT 44
»The following subtended angles were read on a 2m long subtense bar using a theodolite:
0
�
24
′
17“ 0
�
53
′
26“ 0
�
18
′
25“ 0
�
10;49“
Compute the horizontal distance from the theodolite to each position of the bar

45. SAMPLE PROBLEM 4 (SUBTENSE BARS)
2023 DISTANCE MEASUREMENT 45
»The following subtended angles were read on a 2m long subtense bar using a theodolite:
0
�
24
′
17“ 0
�
53
′
26“ 0
�
18
′
25“ 0
�
10;49“
Compute the horizontal distance from the theodolite to each position of the bar
Solution:
��=
1
tan
??????
2

46. SAMPLE PROBLEM 4 (SUBTENSE BARS)
2023 DISTANCE MEASUREMENT 46
»The following subtended angles were read on a 2m long subtense bar using a theodolite:
0
�
24
′
17“ 0
�
53
′
26“ 0
�
18
′
25“ 0
�
10;49“
Compute the horizontal distance from the theodolite to each position of the bar
Solution:
��=
1
tan
??????
2
��
1=
1
tan
??????
2
=
1
tan
0
??????
24
′
17“
2

47. SAMPLE PROBLEM 4 (SUBTENSE BARS)
2023 DISTANCE MEASUREMENT 47
»The following subtended angles were read on a 2m long subtense bar using a theodolite:
0
�
24
′
17“ 0
�
53
′
26“ 0
�
18
′
25“ 0
�
10;49“
Compute the horizontal distance from the theodolite to each position of the bar
Solution:
��=
1
tan
??????
2
��
1=
1
tan
??????
2
=
1
tan
0
??????
24
′
17“
2
=283.1351 ??????

48. SAMPLE PROBLEM 4 (SUBTENSE BARS)
2023 DISTANCE MEASUREMENT 48
»The following subtended angles were read on a 2m long subtense bar using a theodolite:
0
�
24
′
17“ 0
�
53
′
26“ 0
�
18
′
25“ 0
�
10;49“
Compute the horizontal distance from the theodolite to each position of the bar
Solution:
��=
1
tan
??????
2
��
1=
1
tan
??????
2
=
1
tan
0
??????
24
′
17“
2
=283.1351 ??????
��
2=
1
tan
??????
2
=
1
tan
0
??????
53
′
26“
2
=128.6716 ??????

49. SAMPLE PROBLEM 4 (SUBTENSE BARS)
2023 DISTANCE MEASUREMENT 49
»The following subtended angles were read on a 2m long subtense bar using a theodolite:
0
�
24
′
17“ 0
�
53
′
26“ 0
�
18
′
25“ 0
�
10;49“
Compute the horizontal distance from the theodolite to each position of the bar
Solution:
��=
1
tan
??????
2
��
1=
1
tan
??????
2
=
1
tan
0
??????
24
′
17“
2
=283.1351 ??????
��
2=
1
tan
??????
2
=
1
tan
0
??????
53
′
26“
2
=128.6716 ??????
��
3=
1
tan
??????
2
=
1
tan
0
??????
18
′
25“
2
=373.3291 ??????

50. SAMPLE PROBLEM 4 (SUBTENSE BARS)
2023 DISTANCE MEASUREMENT 50
»The following subtended angles were read on a 2m long subtense bar using a theodolite:
0
�
24
′
17“ 0
�
53
′
26“ 0
�
18
′
25“ 0
�
10;49“
Compute the horizontal distance from the theodolite to each position of the bar
Solution:
��=
1
tan
??????
2
��
1=
1
tan
??????
2
=
1
tan
0
??????
24
′
17“
2
=283.1351 ??????
��
2=
1
tan
??????
2
=
1
tan
0
??????
53
′
26“
2
=128.6716 ??????
��
3=
1
tan
??????
2
=
1
tan
0
??????
18
′
25“
2
=373.3291 ??????
��
4=
1
tan
??????
2
=
1
tan
0
??????
18
′
25“
2
=635.6383 ??????