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Chapter 2: Numerical on Tacheometry

1. The stadia reading with horizontal sight at a vertical staff held 50 m away from the
tacheometer were 1.385 and 2.380. the focal length of the object glass was 25cm. The
length of the object glass was 25cm. The distance between the object glass and trunion axis
of a tacheometer was 15 cm. Calculate the stadia interval (i).

2. A staff held vertically at a distance of 50 m and 100m from the centre of the theodolite with
a stadia hair, the staff intercept with the telescope is 0.500 and 1.000 respectively. The
instrument was then setup over a station P of RL 1850.95 and the total height of instrument
was 1.475m. The hair reading on a staff held vertically at station Q were 1.050, 1.900 and
2.750 with the line of sight horizontal. Calculate the horizontal distance of PQ and RL of
Q point.

3. The Following Reading were taken with a tacheometer on to a vertical staff, Calculate
tacheometric constant

4. A tachometer was setup at a station A and the following readings were obtain on a staff
held vertically, calculate the horizontal distance AB and RL of B, when the constant of
instrument is 100 and 0.15

5. To determine the gradient between two-point P and Q a tacheometer was set up at a R

station and the following observation where taken keeping the staff held vertical, if the
horizontal angle PRQ is 36020’ determine the avg. Gradient between P and Q Point take K
= 100 and C = 0 and RL of HI = 100m
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Chapter 2: Numerical on Tacheometry

6. Find out the distance between P and Q by using the bellow data given in table, the staff
held normal to the line of sight in both the cases value of the tacheometer constant is 100
and 0.3

7. A leveling staff is held vertical at distane of 100 m and 300 m from the axis of a tacheometer
and the staff intercepts for horizontal sights are 0.90 m and 3.00 m respectively. Find the
constant of the instrument.
The instrument is set up at as station A and the staff is held vertical at a point B. with the
telescope inclined at an angle of depression of 100 to the horizontal, the reading on the
staff is 2.670, 1.835, 1.000m. Calculate the RL of B and the horizontal distance from A.
The HI is 1.42 m and RL of station A is 450.5 m

8. Determine the gradient from P to Q from the following observation made with a tachometer
fitted with an anallactic lens. The constant of the instrument was 100 and 0 and the staff
was held vertical
Instrument Staff station Bearing Vertical angle Staff reading (m)
station
R P 1300 + 100 32’ 1.255,1.810,2.365
Q 220 0
+ 50 06’ 1.300,2.120,2.940

9. To determine the elevation of station P in a tacheometric survey, the following observation

were made with the staff held vertical. The instrument was fitted with an anallactic lens.
Instrument HI (m) Staff station Vertical Staff reading (m)
station angle
O 1.45 BM -60 00’ 1.335, 1.895,
2.460
O 1.45 CP +80 30’ 0.780, 1.265,
1.745
P 1.40 CP - 60 30’ 1.155, 1.615,
2.075

10. The ruins of an old fort exist on a hill. It was required to determine the distance of the fort
from the road and the height of the roof above the plinth with tacheometer. Observation
were made on a 4 m staff held vertical on the entrance gate of the fort and on the roof from
the road. Constant of the instrument were 100 and 0
Instrument station HI (m) Staff station Vertical angle Staff reading (m)
Road 1.45 Plinth level +100 30’ 2.150, 2.720, 3.290
Roof +160 24’ 1.850, 2.400, 3.040

11. A tacheometer was set up at a station A and the reading on a vertically held staff at B were
2.255, 2.605 and 2.955 the line of sight being at an inclination of +80 24’. Another
observation on the vertically held staff at BM gave the reading 1.640, 1.920 and 2.200, the
inclination of the line of sight being + 10 6’, calculate the horizontal distance between A
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Chapter 2: Numerical on Tacheometry

and B, and the elevation of B if the RL of BM is 418.685 m. The constant of the instrument
was 100 and 0.3

12. The elevation of a point P is to be detrmined by observation from two adjacent stations of
a tacheometric survey. The staff was held vertically upon the point and the instrument is
fitted within an anallactic les, the constant of the instrument being 100. Calculate the
elevation of the point P from the following data taking both observations as equal
trustworthy.
Inst. Station HI (m) Staff Vertical angle Staff reading Elevation of
point station
A 1.42 P + 2 24’
0
1.230, 2.055, 85
2.880
B 1.40 P - 30 36’ 0.785, 1.800, 97
2.815

13. The vertical angles to vanes fixed at 1 m and 3 m above the foot of the staff held vertically
at a station A were +20 30’ and + 50 48’respectively. Find the horizontal distance and the
reduced level of A if the height of the instrument determined from the observation on to a
bench mark is 438.556 m above datum.

14. A surveyor wishes to obtain the height of this instrument by observing a staff held upon a
Bench Mark which is at a lower level than the instrument. He takes two observations on
the staff, the readings being 3.260 and 1.090 and the corresponding angles of depression
being 9° 36′ and 10° 48′. Calculate the elevation of the instrument if that of the bench mark
is 85.658.

15. Two observations are taken upon a vertical staff by means of a theodolite, the reduced level
of the trunnion axis of which is 155 m. In the case of the first observation the line of sight
is directed to give staff reading of 1.0 m and the angle of elevation as 4° 58′. In the second
observation the staff reading is 3.5 m, and the angle of elevation is 5° 44′. Compute the
reduced level of the staff station and its horizontal distance from the instrument.

16. To determine the distance between two points C and D and their elevations the following
observations were taken upon a vertically held staff from two traverse stations A and B.
the tacheometer was fitted with an analatic lens.

Traverse Ht of Co-ordinates Staff Bearing Vertical Staff

station inst. St Station Angle Reading
A 1.58 N 218.3 E 164.7 C 3300 20’ +120 12’ 1.860
B 1.50 N 518.3 E 207.6 D 200 36’ +100 36’ 1.885
Calculate
a) The distance CD
b) The RL of C and D if those of A and B were 432.550 and 436.865 m
c) The gradient from C to D
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