(Case : 1 When the line of sight is horizontal and staff is held Vertical) Example 3

Example 3

A staff held vertically at a distance of 50 m and 100m from the centre of the theodolite with a stadia hair, the staff intercept with the telescope is 0.500 and 1.000 respectively. The instrument was then setup over a station P of RL 1850.95 m and the total height of the instrument was 1.475m. The hair reading on a staff held vertically at station Q were 1.050, 1.900 and 2.750 with the line of sight horizontal. Calculate the horizontal distance of PQ and RL of Q point.

Ans.=>

            D = KS + C 

D= (f/i) S + (f + d) ........... (1)

D₁= 50M S₁= 0.500M  

D₂= 100M S₂= 1.000M

Calculate the

1) horizontal distance of PQ = D=? 

(Haire reading Bottom = 1.050m, Middle =1.900M,Top = 2.750M )

2) RL of Q point.=? ( RL .of P =1850.950M) (Height of instrument = 1.475M)

D = KS + C 

50 = K(0.005) + C ................(1) 

100 = K(1.000) + C ...............(2) 

C = 50 – 0.005 K ..................(3) 

Put the value of C in Eq 2

100 = K(1.000) + C ...............(2) 

100 = 1.000 K + 50 – 0.005 K 

K = 100 (Now put the value of K in eq 3 )

C = 50 – 0.005 K ..................(3) 

C = 50 – 0.005 (100) C = 0 

Note: if K = 100 and C = 0 means your instrument is perfect

Calculation horizontal distance between  PQ

 D = KS + C ...........................(1)

  Now S = 2.750 – 1.050 = 1.700m

 K = 100 & C = 0 

Put all the value in equation no 1 

D = 100 (1.700) + 0  

D= 170m

Calculation of RL of Q point 

• RL of Q = 1850.95 + 1.475 – 1.900 

RL of Q = 1850.525m