Surveying 1

November 2022 Review

SURVEYING 1
INSTRUCTION: Select the correct answer for each of the following 15. Assume that any distance of 100 ft can be taped with an error
questions. Mark only one answer for each item by shading the box of ±0.02 ft if certain techniques are employed. Determine the
corresponding to the letter of your choice on the answer sheet error in taping 5000 ft using this skills.
provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 2 only.
16. In trigonometric leveling, the slope distance is S = 50 ± 0.05 m
THEORY OF ERRORS and β=30⁰00’ ± 00⁰30’. Compute the probable error in the
vertical distance of the slope.
Situation 1:
Given the following data measuring a distance of a certain line 17. The area of a rectangular parcel of land is required together
with its probable error. The length is a=100±0.10 m and the
Distance No. of Measurement width is b = 40±0.08m. Determine the probable error in the
47.23 3 area.
47.21 2
47.19 4 Measurement of Horizontal Distances
47.27 2
a. Determine the most probable value of the measurements. DISTANCE BY PACING
b. Calculate the standard deviation of any single observation
Situation 6: Line AB 50 m long was paced by a surveyor four
c. Calculate the standard error of the mean
times with the following data: 72, 73, 71 and 75.
d. Calculate the probable error of any single observation Another line CB was paced for 193, 192, 195 and
e. Calculate the probable error of the mean 194.
f. Determine the relative precision 18. Determine the pace factor of the surveyor.

Situation 2: The observed angles of a triangle lot are as follows: 19. Determine the actual length of CB.
A = 34°20’36” C = 49°16’34”
B = 96°22’41” 20. A line 100 m long was paced 4 times by a surveyor with the
1. Compute the most probable value of Angle A. following data: 143, 146.50, 142.50, and 144. Another line
was paced 4 times by the same surveyor with the following
2. Compute the most probable value of Angle B. data: 894.50, 892, 891.50, and 895. Determine the length of
the line.
3. Compute the most probable value of Angle C.
DISTANCE BY TAPING
Situation 3: From the measured values of distance AB, the
following trials were recorded. 21. If the line AB was at elevation 400 m above sea level,
determine the reduced sea level distance.

22. Compute the grid distance if the grid factor is 0.9999.

23. A line was measured to have 5 tallies, 6 marking pins and 63.5
4. Compute the average mean value.
links. How long is the line in feet?
5. Compute the probable error.
24. A line was measured with a 50-m tape. There were 2 tallies, 8
pins, and the distance from the last pin to end of the line was
6. Compute the standard deviation.
2.3 m. Find the length of the line in meters.
7. Compute the standard error.
25. The distance was measured and was recorded to have a value
of 8 perch, 7 rods and 40 vara. Compute the total distance in
8. Compute the precision.
meters.
Situation 4: The distance of line AB was measured four times
CORRECTIONS
and recorded as follows: 100.02, 100.05, 100.03
Situation 7: A rectangular lot having a dimension of 218.5 m by
and 100.04.
147.2 m was measured by a 30 m tape which is 0.02
9. Determine the probable value.
m too long.
26. Compute the correct length of the lot.
10. Determine the probable error.
27. Find the error in the area.
11. Determine the precision.
28. If the same tape was used to set a baseline with length of 500
WEIGHTED MEASUREMENTS
m,
Situation 5: Given are the data below:
CORRECTION DUE TO TAPE

Situation 8: Using a 50-m tape, the measured distance between

points A and B is 170.42 m.

29. What is the correct distance if the tape used is 0.02 m too
12. What is the correct value of the angle at station A?
long?
13. What is the correct value of the angle at station C?
30. What is the correct distance if the tape used is 0.02 m too
short?
PROPAGATION OF RANDOM ERRORS
31. The correct distance between points X and Y is 213.50 m. If a
14. Three adjacent distances along the samel line were measured
100-m tape that is 0.025 m too long is used to measure, what
independently with the following result:
will be the measured distance?
X1= 51.00 m with PE1= ±0.05 m
X2= 36.50 m with PE2= ±0.04 m
X3= 26.75 m with PE3= ±0.03 m.
Compute the total distance and its probable error

Engr. Jude L. Rosales, CE, SO

 Surveying 1
November 2022 Review

CORRECTION DUE TO TEMPERATURE

44. Compute the stadia interval factor of the instrument.
32. A 30-m tape which is of standard length at a temperature of
20° is used to measure a line with a measured distance of 412 45. If it was also used to determine the difference in elevation
m. During measurement, the temperature was 52°C. If the between B and D having a stadia intercept reading of 2.42 m
coefficient of thermal expansion of the tape is 0.000016/°C, at D at a vertical angle of +6°30’, determine the difference in
determine the correct length of the line. elevation.

CORRECTION DUE TO TENSION 46. Compute the horizontal distance between B and D.

33. A steel tape is 100 m long at a standard pull of 65 N. Compute Situation 12: A transit with stadia interval factor of 100.8 was set
the pull correction if during measurement the applied pull is at C on the line between points A and B, and the
40 N. The tape has a cross-sectional area of 3.18 mm2. following stadia readings were observed.

CORRECTION DUE TO SLOPE

34. A distance of 15.94 m is measured with a tape. During

measurement, the other end was discovered to be 0.78 m If the stadia constant is 0.381 m,
lower. Find the correct distance.
47. What is the length of line AB?
CORRECTION DUE TO REDUCTION OF SEA LEVEL
48. What is the difference in elevation between points A and B?
35. At an elevation 860 m, a line was measured to be 30 km. Find
the sea level distance if the average radius of curvature is 49. What is the horizontal distance from the transit to the rod
6400 km. held at B?

COMBINED CORRECTION DISTANCE BY SUBTENSE BAR

Situation 9: A line was determined to be 2,395.25 m when 50. A subtense bar was first set up at A and subsequently at B,
measured with a 30-m steel tape supported and the subtended angles to the bar, as read from a
throughout its length under a pull of 4 kg at a mean theodolite positioned somewhere along the middle of line AB,
temperature of 35°C. tape used is of standard were recorded as 50’15” and 35’30”, respectively. Determine
length at 20°C under a pull of 5 kg. Cross-sectional the length AB.
area of the tape is 0.03 cm2. Coefficient of thermal
expansion is 0.0000116/°C. Modulus of elasticity of
tape is 2 x 109 kg/cm2
36. Determine the error of the tape due to change in
temperature.

37. Determine the error of the tape due to tension.

38. Determine the corrected length of the line

CORRECTION DUE TO SAG

Situation 10: A 50 m tape was used to measure a distance. The

measured length is 762.46 m. During measuring,
the pull at ends of the tape is recorded to be 20 kg.

39. Find the error in measurement if the tape is used with its
ends supported.

40. Find the corrected length if the tape is used with its ends
supported.

41. Find the corrected length if the tape is supported at every 25

m.

DISTANCE BY TACHYMETRY (Stadia Method)

42. A transit is set up at a distance of 194.20 m from the stadia

rod. With a horizontal line of sight, the stadia intercept was
recorded to be 1.94. if the stadia constant is 0.30, fin the
stadia interval factor.

43. A stadia intercept factor of 3.6 m was measured on a stadia

rod by a transit with stadia constant and stadia interval factor
of 0.30 m 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.

Situation 11: A transit with stadia constant equal to 0.3 is used to

determine the horizontal distance between points B
and C, with a stadia intercept reading of 1.85 m, the
distance BC is equal to 182.87 m

Engr. Jude L. Rosales, CE, SO