How to calculate the RL & distance of a building using trigonometric surveying? (Type -3 )/ Finding distance of an inaccessible object in trigonometric leveling.

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Eg:

Calculate the horizontal distance of the building from station A & RL of the top of the building from the following data.

Instrument station	Staff reading on BM	Angle of elevation of top of building
A	1.750	22°15'
B	2.550	17°30'

 

BM of staff station P = 470m. The distance between the instrument station A & B is 40m. The building & the instruments at stations A & B are in the same vertical plane.

Calculation:

Before making a drawing over the above-given data, let us interpret the question.

1. Staff reading from stations A & B are different. It means the RL of the instrument axis is different for both stations.

2. Angle observed from station A is larger than station B. It means station A is nearer to the building.

3.  We have to calculate the horizontal distance of the building from station A. It means the building base is inaccessible.

1. Horizontal distance between station A & building

D =[ {d + (h cot𝝰1)} × tan𝝰1  ÷ (tan𝝰2 - tan𝝰1)]

Here,

h = difference between BS from station A & B.

    = [2.55m. - 1.75m.]

    = 0.8m.

cot𝝰1 = (1  ÷tan𝝰1)

 D =[{40m. + (0.8m. × cot17°30')} × tan17°30'  ÷ (tan22°15' - tan17°30')]

     = [{40m. + (0.8m. × 3.171)} × 0.315  ÷ (0.409 - 0.315)]

     = [13.40  ÷  0.094]

    D = 142.553m.

As you can observe in the above drawing,

2. RL on top of the building

= [BM at station P + height of instrument axis of station A + height of the top of the tower from instrument axis of station A]

= [ BM + HI2 + H2]

First, let us calculate the value of HI2 & H2.

HI2 = BS from station A over staff held at station P = 1.75m.

     

By trigonometric formula,

tan𝝰2 = [opposite side/adjascent side]

          = [H2 ÷ D]

Therefore,

 H2 = [ tan𝝰2 × D ]

     = [ tan22°15' × 142.553m. ]

     = [0.409 × 142.553m. ]

     = 58.304m.

Note:

If the value of D is unknown, then you should use the following formula to calculate H2

 H2 = [{d + (h cot𝝰1)} × (tan𝝰1× tan𝝰2)  ÷ (tan𝝰2 - tan𝝰1)]

       = [{40m. + (0.8m. × cot17°30')} × (tan17°30' × tan22°15')  ÷ (tan22°15' - tan17°30')]

       = [{40m. + (0.8m. × 3.171)} × ( 0.315 × 0.409) ÷ (0.409 - 0.315)]

     = [5.4806  ÷  0.094]

   H2 = 58.304m. ✔

 

RL on top of the building

=  [ BM + HI2 + H2]

= [ 470m. + 1.75m. +58.304m.]

= 530.054m.

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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