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Calculate the value of R.L for staff being vertical and possessing staff readings as follows 3m, 2m,1m, It being an analectic lens possesses an instrumental height of 1.5m with R.L 100 m. Line of sight placed at an angle of + 5°.
120.864 m
113.864 m
116.864 m
118.864 m
116.864 m
Given: Instrument R.L = 100 m, Height of instrument (h) = 1.5 m, Angle of elevation (θ) = +5°, Staff readings = 3 m (top), 2 m (middle), 1 m (bottom), Analectic lens constant k = 100, c = 0.
Instrument R.L = 100 m, Height of instrument (h) = 1.5 m, Angle of elevation (θ) = +5°, Staff readings = 3 m (top), 2 m (middle), 1 m (bottom), Analectic lens constant k = 100, c = 0.
R.L of staff station=R.L of BM+h+V−r
Calculate Staff Intercept (s) and Central Reading (r)
The staff intercept s is the difference between the top and bottom staff readings. The central staff reading r is the middle reading.
s=3−1=2 m,r=2 m
Calculate Vertical Distance (V)
For an inclined sight with a vertical staff using an analectic lens (k=100,c=0), the formula for vertical component V is V=2k⋅ssin(2θ).
V=2100×2sin(2×5°)=100sin(10°)≈17.364 m
Calculate R.L of the Staff Station
Applying the tacheometric leveling formula for an angle of elevation: R.L of Station=R.L of BM+h+V−r.
R.L=100+1.5+17.364−2=116.864 m
C is correct because the calculated Reduced Level (R.L) of the staff station is equal to 116.864 m.
For an analectic lens, the additive constant c=0 and multiplying constant k=100, simplifying vertical distance to V=k⋅s⋅2sin(2θ).