How to calculate RL & distance in a tacheometric surveying? (Type-1)/ Finding RL of a station by using tacheometer.

Eg:

The following observations were made in a tacheometric surveying. A tacheometer was set up at the intermediate point on line AB.

Multiplying constant (f /i) = 100,  additive constant (f +d) = 0.1

Calculate the horizontal distance AB & RL of station B. RL of station A is 465m.

Calculation:

The formula for calculating the horizontal distance 

D = (f/i ) S cos²θ + (f +d ) cosθ

Now,

D1 =  = (f/i ) S1 cos²θ1 + (f +d ) cosθ1

Here,

S1 = staff intercept at station A = 2.425

θ1 = Vertical angle = 6°30'

D1 = [(100 ✕ 2.425 ✕ cos² 6°30') + ( 0.1  ✕ cos6°30')]

      = [239.39 + 0.0993]

  D1  = 239.49 m.

Similarly,

  D2 = [(100 ✕ 1.950 ✕ cos² 9°15') + ( 0.1  ✕ cos9°15')]

        = [189.962 + 0.0987]

 D2  = 190.06 m.

    

The formula for vertical distance

 V = [(f/i ) S sin2θ /2 +  (f +d ) sinθ]

   Now,

 V1 = [(f/i ) S1 sin2θ1 /2 +  (f +d ) sinθ1]

       = [ {100 ✕ 2.425  ✕ sin(2 ✕ 6°30') /2} + (0.1 ✕ sin6°30')]

      =[ 27.275 + 0.0113]

 V1 = 27.29 m.

Similarly,

V2 = [(f/i ) S2 sin2θ2 /2 +  (f +d ) sinθ2]

       = [ {100  ✕ 1.95 ✕ sin(2 ✕ 9°15') /2} + (0.1 ✕ sin9°15')]

      =[ 30.937 + 0.0161]

 V2 = 30.95 m.

RL of a central axis of the instrument at station P

= [RL at station A + axial hair reading of staff at A - V1]

= [ 465m. + 2.150 - 27.29]

= 439.86m.

Find: 👇

1. Horizontal distance AB

            = [D1 +D2]

            = [239.49m. + 190.06m.]

            = 429.55m.

2. RL of station B

         = [RL of instrument axis at P + V2 - axial hair reading of staff at B]

         = [ 439.86m. + 30.95m. - 1.865]

          = 468.945m.

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

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