Tutorial Geomatics
Distance Measurement
1. A tape of 30 m length suspended in catenary measured the length of a base line. After applying all
corrections the deduced length of the base line was 1462.36 m. Later on it was found that the actual pull
applied was 155 N and not the 165 N as recorded in the field book. Correct the deduced length for the
incorrect pull.
The tape was standardized on the flat under a pull of 85 N having a mass of 0.024 kg/m and crosssectional area of 4.12 mm2. The Young’s modulus of the tape material is 152000 MN/m2 and the
acceleration due to gravity is 9.806 m/s2.
*Final Exam 2011/2012
2. The depth of a mine shaft was measured as 834.66 m using a 1000 m steel tape having a cross-section
of 10 mm2 and a mass of 0.08 kg/m. Calculate the correct depth of the mine shaft if the tape was
standardized at a tension of 182 N. The Young’s modulus of elasticity of the tape material is 21 × 10 4
N/mm2 and g = 9.806 m/s2.
3. A steel tape of nominal length 30 m was used to check the distance between two offset pegs A1 and A2.
The following results were obtained.
Length recorded on
Height
Temperature
Tension applied
tape
A1
A2
23.512 m
21.50 m
23.50 m
28oC
100 N
Compared to 25.000 m baseline, the tape read 24.994 m with 50 N tensions applied to at 15oC. The
cross sectional area of the tape is 2.0 mm2 and it wigh 4.5 N.
Calculate the horizontal length A1 to A2.
Tacheometry
1. To determine the distance between two points A and B, a tacheometer was set up at P and the following
observations were recorded.
(a) Staff at A
Staff readings = 2.225, 2.605, 2.985
Vertical angle = + 7°54′
(b) Staff at B
Staff readings = 1.640, 1.920, 2.200
Vertical angle = – 1°46′
(c) Horizontal angle APB = + 68°32′30″
Elevation of A = 315.600 m
k = 100 m
c = 0.00 m
Determine the distance AB and the elevation of B.
2. The following tacheometric observations were made on two points P and Q from station A.
The height of the tacheometer at A above the ground was 1.55 m. Determine the elevations of P and Q if the
elevation of A is 75.500 m. The stadia constant k and c are respectively 100 and 0.00 m.
3. The following tacheometric observations were made from station A to stations 1 and 2.
Calculate the errors in horizontal and vertical distances if the staff was inclined by 1° to the vertical in the
following cases:
(a) Staff inclined towards the instrument for the line A–1.
(b) Staff inclined away from the instrument for the line A–2.
(c) If the elevation of the point 1 is 115.673 m, determine the correct elevation of the point 2. The height of the
instrument above ground is 1.52 m.
The height of the instrument above ground was 1.52 m. Take stadia constants as 100 and 0.0 m.
4. A theodolite has a multiplying constant of 100 and an additive constant of zero. When set 1.35 m above
station B, the following readings were obtained.
The coordinates of A are E 163.86, N 0.0, and those of B, E 163.86, N 118.41. Find the coordinates of C and its
height above datum if the level of B is 27.3 m AOD.
5. A tacheometric observation was carried out at an intermediate station C of the line AB and the following
readings were obtained:
Staff Station
[Stesen Staf]
A
B
Vertical Angle
[Sudut Pugak]
θ
- 06o25’40”
+ 04o 36’ 10”
Staff Reading
[Bacaan Staf]
Lower
[Bawah]
0.445
0.950
Middle
[Tengah]
1.675
1.880
Upper
[Atas]
2.905
2.810
The instrument was fitted with an anallactic lens and the constant was 100. Find the gradient of the line joining
stations A and B.
*Final Exam 2010/2011
6. A line XY is measured at both ends as follows:
Instrument at X, slope distance = 879.209 m; vertical angle = +1o26’50”
Instrument at Y, slope distance = 879.230 m; vertical angle = -1o26’38”
The height of instrument, reflector and target are equal for each observation.
i) Compute the horizontal distance XY
ii) If the elevation at X is 163.772m, calculate the elevation at position Y.
*Final Exam 2009/2010
Traverse
1. The following data were collected while running a closed traverse ABCDA. Calculate the missing data.
2. P, Q, R, and S are four stations whose coordinates are as below:
Another station X is to be fixed at the intersection of the lines PR and QS. What are the coordinates of X ?
3. In a traverse ABCDEFG, the line BA is taken as the reference meridian. The coordinates of the sides AB, BC,
CD, DE and EF are:
If the bearing of FG is 284°13_ and its length is 896.0 m, find the length and bearing of GA
4. A four-sided traverse work is run at Agrotechnology Unit, Sg.Chuchuh. The coordinates of four-sided
polygon traverse RSTU are shown in Table Q2
Table Q2/[Jadual Q2]
Point
mE
mN
(i)
(ii)
R
1761.32
1111.17
S
1959.77
1435.43
T
2168.32
1276.18
U
1994.81
972.36
Calculate the plan area contained within the traverse in hectares.
Calculate bearing and distance of each side.
*Final Exam 2011/2012
5. Closed traverse ABCD has the following bearings: AB = N60o50’E, BC = S42o48’E, CD = S7o33’W,
and DA = N66o03’W.
(i)
Compute the interior angles and provide a geometry check for your works.
(ii)
If the bearing of AB is reduced to N45o55’E, proposed bearing of remaining sides in the
clockwise direction.
*Final Exam 2011/2012
6. A six-sided traverse has the following coordinates: A (559.319 N, 207.453 E), B (738.562 N, 666.737
E), C (541.742 N, 688.350 E), D (379.861 N, 839.008 E), E (296.099 N, 604.048 E), F (218.330 N,
323.936 E).
i)
Determine the distance and bearing of each side.
ii)
Calculate the area (in hectares) enclosed by the traverse.
*Final Exam 2010/2011
7. Question (c) and (d) refering to Table Q2.
Table Q2/Jadual Q2
Line
[Garis]
AB
BC
CD
DE
EA
Length (m)
[Panjang]
110.20
145.31
98.75
163.20
52.34
Bearing
[Sudut]
156o40’00”
75o18’00”
351o08’00”
276o29’00”
187o27’00”
a) Calculate the closing error and accuracy of the traverse survey
b) Distribute the closing error by Bowditch’s rule and calculate the corrected latitude and departure.
*Final Exam 2009/2010
8. Compute the interior angles for the trapezoidal layout
1. 9. Given the following information;
Course
Bearing
Azimuth
Distance
A..B
N60o00’W
300o00’
371.006
B..C
N40 38’W
o
220 38’
110.222
C..D
S10o28’W
190o28’
139.872
D..E
o
S83 33’E
o
96 27’
103.119
E..A
N81 30’E
81 30’
319.860
o
o
o
a) Compute the linear error of closure
b) Compute the precision ratio
c) Compute the adjusted latitude and departure (compass rules)
Areas and Volume
1. The coordinates of traverse stations of a closed traverse ABCDE are given
Calculate the area enclosed by the traverse.
2. A road is to run on an embankment between chainages 230m and 307m. The cross-sectional area every
10m of chainage is shown in Table Q1 below. Determine the volume of fill required, by both the
trapezoidal and prismoidal method.
Table Q1/Jadual Q1
Chainage (m)
[Rantaian]
Area
(m2)
[Luas]
230
240
250
260
270
280
290
300
307
0.0
20.5
45.7
96.6
127.3
125.9
88.9
45.2
0.0
*Final Exam 2009/2010