The document discusses tacheometry, which uses a theodolite fitted with a stadia diaphragm to measure distances. It describes the key components of tacheometry including the tacheometer, stadia rod, and stadia interval. The document explains that tacheometric distance (D) can be calculated using the formula D=Ks+C, where K is the multiplying constant, s is the stadia interval, and C is the additive constant. It also provides methods for determining the tacheometric constants K and C, including direct measurement and computation from multiple measured distances. Examples of solving tacheometry problems involving distance, elevation, and reduced level calculations are given.

1. BY ---- MOHIT DUREJA

2. BY ---- MOHIT DUREJA

3. BY ---- MOHIT DUREJA

4. INSTRUEMENT USED IN TACHEOMETRY
1) TACHEOMETER
• IT IS A TRANSIT
THEODOLITE FITTED WITH
A STADIA DIAPHRAGAM.
• THE STADIA DIAPHRAGAM
CONSIST OF ONE STADIA
ABOVE AND OTHER AN
EQUAL DISTANCE BELOW
THE HORIZONTAL CROSS
HAIR
BY ---- MOHIT DUREJA

5. DIFFERENT TYPES OF DIAPHRAGAM
CROSS HAIR DIAPHRAGAM
STADIA HAIR DIAPHRAGAM
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6. 2) STADIA ROD
• For small sights
ordinary leveling staff
is used. It has a least
count of 5mm.
• For long sight stadia
rod is used. The least
count is 5mm or 10mm
cont… INSTRUEMENT USED IN TACHEOMETRY
BY ---- MOHIT DUREJA

7. Requirement/ Characteristics of
Tacheometer
• The value of multiplying constant should be
100
• The central horizontal hair must be exactly
mid way between the other two horizontal
hair
• The value of additive constant should be zero.
• In order to have bright image the aperture of
objective should be 35 to 45 mm.
BY ---- MOHIT DUREJA

8. METHODS OF TECHEOMETRY
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9. STADIA INTERVAL
0R
STAFF INTERCEPT (S)
S=(12.38 - 11.98)
S= 0.40 M
BY ---- MOHIT DUREJA

10. BY ---- MOHIT DUREJA

11. :-The stadia method is based on the principle that
the ratio of the perpendicular to the base is
constant in similar isosceles
triangles
D
BY ---- MOHIT DUREJA

12. D= K s + C
WHERE;
K= MULTIPLYING CONSTANT
C = ADDITIVE CONSTANT TACHEOMETRIC CONSTANT
Multiplying constant is usually taken as 100
Additive constant is taken as zero(0)
There values are generally provide by manufacturers BY ---- MOHIT DUREJA

13. DETERMINATION OF STADIA CONSTANT
1) BY DIRECTLY MEASURE FROM THE INSTRUMENT
D= f s + (f+d)
i
f
BY ---- MOHIT DUREJA

14. 2) BY COMPUTATION
D1= f S1 + (f+d)
i
D2= f S2 + (f+d)
i
D3= f S3 + (f+d)
i
…………..1
…………..2
…………..3
SOLVE
EQ. 1 & 2
EQ. 2 & 3
EQ. 3 & 1
And find exact value by
their mean
f
i
(f+d) = ?
= ?K
C
BY ---- MOHIT DUREJA

15. Q .) Two distance of 90m and 250m were accurately measured out and the
intercepts on the vertical were 0.895 & 2.495m respectively. Calculate
Tacheometric constant.
BY ---- MOHIT DUREJA

16. Q. With telescope horizontal, the readings taken by upper and
lower wires were 3.840 and1.060 m. Find the horizontal distance
and elevation of staff station if the RL of instrument axis is
341.540m. The central hair reading was 2.450. (K=100, c=0.4)
BY ---- MOHIT DUREJA

17. Distance and elevation formula with inclined sight
D=K Cos α S Cos α + C Cos α
V=K Sin α S Cos α + C Sinα
D= K S + C ……from Case 1
RL of staff station (M)= RL of Inst. Axis + (V-h)
D
α =ANGLE OF ELEVATION
BY ---- MOHIT DUREJA

18. Distance and elevation formula with inclined sight
D=K Cos α S Cos α + C Cos α
V=K Sin α S Cos α + C Sinα
D= K S + C ……from Case 1
RL of staff station (M)= RL of Instrument Axis - (V+h)
α =ANGLE OF DEPRESSION
BY ---- MOHIT DUREJA

19. Q.) A tacheometer was set up at A and the readings on staff held
vertical at B were 1.215, 1.825, 2.435, the line of sight at
elevation of 6ᴼ30’. Calculate distance between them and RL of
point B if the RL of the sight is 350.700 m. ( K=100 ,C=0.35)
BY ---- MOHIT DUREJA

20. Tangential method
• Stadia hairs are not used to bisect the staff.
• Two vanes are fixed at a constant distance apart
on the staff.
• Each vane is bisected by the cross hair.
• Staff reading and vertical angle corresponding
to each vane is measured and recorded.
D
S
V

21. Case 1: When observed angles are angle of elevation

22. Case 2: When observed angles are angle of Depression

23. Case 3: When one angle is angle of Depression and other is elevation