1. The angles of a triangle ABC are, A 69°45’47”, B 48°04’18” and C 62°09’55”. The coordinates of A
and B (m) are:
Station E (m) N (m)
A -21 226.98 -140 959.77
B -20 944.56 -141 107.20
If A, B and C are in clockwise order around the triangle, determine the coordinates of C.
2. From the same two points A and B as in question 1, the bearings to a point D are; Bearing AD 86°21’53”, bearing BD 328°46’53”. Determine the coordinates of D.
3. Describe with the aid of an example the rise and fall and height of collimation methods of booking levelling methods. What particular advantages does each method offer?
4. What simple technique can be applied to ensure that the reading taken off a levelling staff is the minimum possible reading?
5. Describe the techniques of intersection, resection, triangulation, trilateration, radiation and rectangular offsets.
6. A properly adjusted tilting level was set up at a point P and the following consecutive readings were taken on a staff positioned at points A, B and C respectively: 0.663, -0.841 and 0.939.
The level was then moved to a point Q and further readings at C and D respectively were
taken as follows: 1.198 and 1.100.
Use this example to explain what is meant by the term backsight, intersight, foresight and change
point. Book, reduce and check the levels using both of the standard methods, given that the
reduced level of point A is 94.115 m above datum. (Please note that the reading at point B was
taken on an inverted staff and as such has been recorded with a negative sign.
7. Reduce the levels outlined in the table overleaf using the collimation method, apply only the appropriate checks. Point I is a benchmark with a level of 56.174m above datum. Adjust the calculated levels so that the results at I agree with the specified level. If the distance from A to H
is 220m calculate the mean gradient between the two points. Outline the practical precautions that must be taken for accurate levelling.
BS IS FS Remarks
0.599 BM 58.031 m AOD
2.587 3.132 A
2.244 1.522 E
1.334 1.985 G
8. Levels are taken to determine the height of two pegs a and b, and to determine the soffit level of an overbridge. Using the values of levels indicated in the table below, given that the first backsight was taken from a bench mark at a church (RL = 60.270 m) and the final foresight was taken on a benchmark at a school (RL = 59.960 m), determine the closing error and the height between the underside of the bridge and the ground immediately below it. Use both the collimation and rise and fall methods to undertake the calculations and apply the usual checks.
Level (m) Remarks
1.275 Backsight to BM on church
2.812 Foresight CP1
0.655 Backsight CP 1
-3.958 Inverted staff to soffit level of bridge
1.515 Ground level beneath bridge (centre)
1.138 Foresight CP 2
2.954 Backsight CP 2
2.706 Peg a
2.172 Peg b
1.240 Foresight to BM at School
9. The rail levels of an existing railway were to be checked and raised as required. Points A, B, C, D, E, F and G were marked on the rails at regular 20m intervals and the following levels in metres were taken.
Backsight 2.80 m on BM 25.10 m
Intermediate sights on A, B and C: 0.94, 0.76 and 0.57 respectively.
Foresight and backsight on Change point D: 0.37 and 1.17 respectively.
Intermediate sights on E and F: 0.96 and 0.75 respectively.
Foresight on G of 0.54.
Book and reduce these readings using the rise and fall method and carry out appropriate
Assuming that the levels at A and G were correct, determine the amount by which the rails will
have to be lifted at the intermediate points to give a uniform gradient throughout.
10. A straight section of road XY is to be reconstructed such that it has a constant grade of 1 in 40, falling from X to Y. The level of the road at X is to remain unaltered. The levels detailed in the table below were recorded along the centre line of the existing road. i. Draw up and complete the level book for these readings applying the usual arithmetic checks. ii. Determine the height of the underside of the bridge above the centre line level when the
road has been reconstructed. iii. Calculate the depth of fill or cut at Y when the road has been reconstructed.
Backsight Intermediate sight Foresight Remarks
0.738 BM 112.309 above datum
1.094 Point X
1.713 30m from X
2.265 60m from X
0.942 2.685 CP
1.100 90m from X
1.533 120m from X
-3.133 Inverted staff on underside of bridge
126.8 m from X
0.741 1.887 CP
1.634 150m from X
2.472 Point Y 170m from X
2.265 BM 107.895 above datum
11. A survey line was measured with a tape, believed to be 20m in length, and a length of 284.62m resulted. On checking the tape was found to measure 19.95m in length. i. What was the correct length of the line? ii. If the line lay on a slope of 1 in 20 what would be the reduced horizontal length used in
plotting the survey? iii. What reading is required to produce a horizontal distance of 15.08 m between two site
pegs, one being 0.66 m above the other?
12. The information supplied in Table 1 was obtained when measuring the length of a line by tape suspended in catenary under a pull of 134 N, the mean temperature being 16°C.
Bay Length (m) Difference in level (m)
1 29.898 + 0.382
2 29.950 – 0.234
3 29.883 + 0.271
4 29.901 – 0.075
If the tape was standardised on the flat under a pull of 89 N at 20°C how long is the line?
Cross-sectional area of tape = 3.24 mm2
Mass of Tape = 0.026 kg/m
Coefficient of linear expansion = 0.0000009 /°C
Young’s Modulus = 15.5 x 104 MN/m
Mean height of line above sea level = 53.78 m
Radius of the earth = 6367 km
13. As part of a freeway-widening contract it is proposed to increase the gradient of the sideslope of
an existing embankment to 1 vertical by 1.5 horizontal. At a critical section the difference in level
between the toe of the embankment and the road surface was found to be 14.346 m. The
length of the existing embankment slope was measured to be 29.271 using a steel tape under a
tension of 147 N at an air temperature of 25°. If the tape was standardised on the flat at 20°C
under a pull of 49 N what is the gradient of the existing sideslope and how much additional
width can be obtained with the new slope? (assume: cross-sectional area of tape = 6 mm2,
young’s modulus = 207000 MN/mm2, Coefficient of linear expansion = 0.000011/°C)
14. A Closed loop traverse has be carried out between stations P, Q, R and S. Using the following information, calculate the adjusted coordinates of Q, R and S after applying Bowditch’s rule.
Bearing of reference object from P = 273°50’00”
Coordinates of P = (400.000m E, 200.000m N)
Plan Lengths (m) Included angles
RO-P-Q = 138°15’00”
PQ = 251.23 P-Q-R = 225°36’00”
QR = 213.67 Q-R-S = 272°42’00”
RS = 273.44 R-S-P = 281°14”00”
SP = 388.00 S-P-Q = 300°24’00”
Note: RO = Reference Object
15.A closed tied traverse has been conducted between A and E via stations B, C and D. From A reference object 1 (RO1) with a bearing of 64°30’00” was sighted; from E reference object 2 (RO2) with a bearing of 118°46’00” was sighted. Using the following data, determine the adjusted coordinates of B, C and D applying Bowditch’s method.
Fixed station coordinates:
A (150.000m E, 407.000m N)
E (487.020m E, 151.470m N)
Line Length Angle Value
16. Briefly explain the following terms
• True north
• Magnetic north
• Whole circle bearings
The included angles given in the table below are recorded at stations forming a closed traverse
survey around the perimeter of a field.
Station Included angle
Determine the amount of angular error in the survey and adjust the values of the included angles.
17. A and B are points on the centre line of a level mine roadway and Cand D are points on the centre line of a lower roadway having a uniform gradient between C and D. It is proposed to connect the roadways by a drivage from point B on a bearing of 165°35’. Given the data in the table below:
Point Northing (m) Easting (m) RL (m)
A 2653 1321 462.5
B 2763 1418 462.5
C 2653 1321 418.2
D 2671 1498 441.8
i) The actual length and gradient of the drivage, and ii) The coordinates of the point at which it meets the lower roadway.
18. Measurements of the traverse ABCDE, as shown in the figure below are given in the table below.
Station Clockwise Angle Length (m)
260° 31’ 18”
123° 50’ 42”
233° 00’ 06”
158° 22’ 48”
283° 00’ 18”
The measured angles are shown as in the figure. Keeping the bearings of XA and EY and also the
coordinates of A and E fixed, obtain the adjusted coordinates for B, C and D.
19. The following survey was carried out from the bottom of a shaft at A, along an existing tunnel to the bottom of a shaft at E.
Line WCB Measured
AB 70°30’00” 150.00 Rising 1 in 10
BC 0°00’00” 200.50 Level
CD 154°12’00” 250.00 Level
DE 90°00’00” 400.56 Falling 1 in 30
If the two shafts are to be connected by a straight tunnel, calculate the bearing A to E and the
If a theodolite is to be set up at A and backsighted to B, what is the value of the clockwise angle
to be turned off, to give the line of the new tunnel?
20. An open traverse was run from A to E in order to obtain the length and bearing of the line AE which could not be measured directly, with the following results:
Line AB BC CD DE
Length (m) 1025 1087 925 1250
WCB 261°41’ 09°06’ 282°22’ 71°31’
Find by calculation the required information.
21. Describe the methods available for vertical transfer of coordinates from surface to underground.
22. The grid bearing of an underground base line, CD in the figure overleaf, is established by co- planning at the surface onto two wires, W1 and W2, hanging in a vertical shaft and then using a Weisbach triangle underground. The measured data is as follows:
Grid bearing AB 78°28’34”
Grid coordinates of A E 304 625m, N511 612m
Determine the grid bearing of line CD.
23. Describe a method that can be used to survey a no access open stope in an underground mine.
24. Briefly describe how the GPS system works. What applications of GPS can be employed in an open pit mine citing examples wherever possible?
25. Describe with the aid of diagrams methods that can be used to determine the volume and tonnage
contained in mine waste tips and ore stockpiles.
26. It is proposed to sink a vertical shaft to connect X on a roadway CD in the upper horizon with a roadway GH in the lower horizon which passes under CD. From surveys in the two horizons the following data are compiled:
Station Horizontal Angle Inclination Inclined length
A Coordinates of A
+ 1 in 200 260.412
+ 1 in 400 287.490
Station Horizontal Angle Inclination Inclined length
E Coordinates of E
+ 1 in 50 99.417
+ 1 in 20 84.936
Calculate the coordinates of X
27. Levelling carried out at an open cast coal site yielded the following results:
Grid Co-ordinates Ground Level (m)
100 100 87.6
200 100 89.0
300 100 90.0
100 200 88.4
200 200 89.7
300 200 90.8
100 300 89.3
200 300 90.6
300 300 91.9
A borehole at coordinates (200,200) has revealed that the top of the coal seam 1.68 m thick is located
8.4 m below ground level. The seam is known to dip towards the north at a gradient of 1 in 50
i. Calculate the volume of overburden contained in the gridded area ii. If the ground level rises to the north at a mean gradient of 1 in 80 from 300 mN and the
maximum ratio of overburden thickness for economic working is 15 to 1, estimate the grid northing at easting 200 m to which an east to west working face may be advanced before the site becomes uneconomic.