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The following readings were obtained during differential levelling. Reduced Level (RL) of point A is 240,000 m. The fore sight and back sight between points A and TPI is 1.420 m and 2.024 m, respectively. Fore sight and back sight between points TPI and TP2 is 2.100 m and 1.986 m, respectively. The back sight from B is 1.722 m. These are marked on the given figure. What is the RL at turning point - 2 (TP2)? All values are in metres.

The following readings were obtained during differential levelling. Reduced Level (RL) of point A is 240,000 m. The fore sight and back sight between points A and TPI is 1.420 m and 2.024 m, respectively. Fore sight and back sight between points TPI and TP2 is 2.100 m and 1.986 m, respectively. The back sight from B is 1.722 m. These are marked on the given figure. What is the RL at turning point - 2 (TP2)? All values are in metres. Correct Answer 240.490 m

Concepts:

When staff is held vertically downward, then Height of instrument is

HI = Reduce Level (RL) + Staff Reading (SR)

Also, Reduce level of any other point on ground is calculated as:

RL = HI – BS/FS                          {BS is Back Sight and FS is Fore Sight}

Calculations:

RL of Point A = 240 m

HI at A = RL at A + BS at A

(HI)A = 240 + 2.024 = 242.024 m

(RL)TP1 = (HI)A  - FS at A = 242.024 – 1.42  = 240.604 m

HI when instrument is between TP1 and TP2,(HI)1-2 =  RL at TP1 + BS between TP1 and TP2

(HI)1-2 = 240.604 + 1.986 = 242.59 m

(RL)TP2 = (HI)1-2  - FS between TP1 and TP2 = 242.59 – 2.1 = 240.49 m

∴ The reduced level of TP2 is 240.49 m.

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