Finding RL & distance by using tacheometer. (Type-2)/Tacheometer surveying./Tacheometric surveying in construction.

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 Eg:

A tacheometer was established at station P & the readings over vertical staff at stations A & B are as follows.

Staff station	Vertical angle	Hair readings
A	- 5°15'	2.300	2.365	2.430
B	11°0'	1.675	1.765	1.855

 

The RL of station A is 345.50m. The multiplying constant = 100 & additive constant = 0.1. Find the horizontal distance AB & the RL of station B.

Calculation:

The vertical angle observed at station A is -ve & station B is +ve. It means station A is downhill & B is in an uphill position as shown below.

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

      = [upper hair reading - lower hair reading]

      = [2.430 - 2.30]

   S1  = 0.13 m.

θ1 =  5°15'

   (f/i ) = multiplying constant = 100

  (f +d ) = additive constant = 0.1

D1 = [(100 ✕ 0.13 ✕ cos² 5°15') + ( 0.1  ✕ cos5°15')]

      = [12.483 + 0.0996]

  D1  = 12.583 m.

Similarly,

D2 = (f/i ) S2 cos²θ2 + (f +d ) cosθ2

Here,

S2 = staff intercept at station B

     = [1.855 - 1.675]

 S2  = 0.18m.

θ2 = 11°

  D2 = [(100 ✕ 0.18 ✕ cos² 11°0') + ( 0.1  ✕ cos11°0')]

        = [17.345 + 0.0981]

 D2  = 17.443 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]

Here,

S1 = 0.13 m.

θ1 =  5°15'

   (f/i ) = multiplying constant = 100

  (f +d ) = additive constant = 0.1

 V1   = [{100 ✕ 0.13  ✕ sin(2 ✕ 5°15') /2} + (0.1 ✕ sin5°15')]

         =[ 1.184 + 0.0092]

  V1 = 1.194m.

Similarly,

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

Here,

S2  = 0.18m.

θ2 = 11°

     = [ {100  ✕ 0.18 ✕ sin(2 ✕ 11°0') /2} + (0.1 ✕ sin11°0')]

      =[ 3.371 + 0.0191]

 V2 = 3.391 m.

RL of the instrument axis at station P

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

    (axial hair reading means mid-hair reading )

= [ 345.5 m. + 2.365 + 1.194]

= 349.059m.

Find: 👇

1. Horizontal distance AB

            = [D1 +D2]

            = [12.583m. + 17.443m.]

            = 30.026m.

2. RL of station B

         = [RL of instrument axis at P + vertical distance V2 - axial hair reading of staff at B i.e. h2]

        = [ 349.059m. + 3.391m. - 1.765]

          = 350.685m.

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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