Tacheometric formula for horizontal distances using horizontal sights ...
Horizontal distance is given by:
D = ks + c
Where,
k = Multiplying constant
c = Additive constant
For inclined sights:
D = ks cos2θ + c cos θ
By comparing the above two equations it is clear that tacheometric formula for horizontal distances using horizontal sights can also suitably employed for inclined sights through θ by multiplying the multiplying constant by cos2 θ and additive constant by cos θ.
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Tacheometric formula for horizontal distances using horizontal sights ...
The use of correction factors. The formula is:
d = (st / 100) * (100 + h * k)
Where:
d = Horizontal distance
st = Stadia reading
h = Instrument height
k = Multiplying constant
For horizontal sights, the instrument height (h) and multiplying constant (k) are both zero, so the formula simplifies to:
d = (st / 100) * 100
For inclined sights, the instrument height and multiplying constant need to be taken into account. The instrument height (h) is the vertical distance between the center of the instrument and the ground, and the multiplying constant (k) depends on the angle of inclination.
To apply the formula for inclined sights, the stadia reading (st) needs to be corrected by multiplying it by a factor (c) to account for the angle of inclination. The corrected stadia reading (st') is given by:
st' = st * c
The correction factor (c) can be calculated using the formula:
c = 1 + (h / 100) * k
Once the stadia reading is corrected, the horizontal distance (d) can be calculated using the formula:
d = (st' / 100) * (100 + h * k)
By taking into account the instrument height and multiplying constant, the tacheometric formula for horizontal distances can be suitably employed for inclined sights.