Determine the true length:

A sloping ground with a gradient of 1 in 10 was surveyed with a 30 m chain. The chain was checked at commencement of work, at mid station C of survey line AB and at the end of survey and was found to be 2 cm, 6 cm and 10 cm too long respectively. If the measured length of survey line AB = 6000 m, find the true length of AB.

Solution

Actual length of 30 m chain at A = 30.02 m

Actual length of 30 m chain at C = 30.06 m

Average length of chain in during measurement from A to C

= 30.02 + 30.06/2 = 30.04 m

Actual length of AC measured along with slope

= 30.04/30.0 × 3000 = 3004 m

Actual chain length at C = 30.06 m

Actual chain length at B = 30.10 m

Average length of chain during measurement from C to B

= 30.06 + 30.10/2 = 30.08 m

Actual length of CB measured along slope

= 30.08/30.0 × 3000 = 3008 m

Actual length of line AB along slope = 3004 + 3008 = 6012 m

A slope of ground is 1 in 10, that is 1 m vertical in 10 m horizontal, e.g. EF = 1 m and DE = 10 m.         

Then DF along slope =

= 10.0499

 ≈ 10.05          

Thus, when sloping length is 10.05 m, horizontal length is 10.00 m. Therefore, true horizontal distance among AB would be

= 10.00 /10.05× 6012 m = 5985.07 m.