Closed level loop tested against a tolerance and adjusted
A four-leg level loop returns to its starting benchmark 0.060 ft out. Test the misclosure against a C times root-M tolerance, then distribute it in proportion to leg length and compute adjusted elevations.
Apply· about 20 minutes by hand· 6 steps
Given
A closed level loop that starts and ends on BM-101, whose published elevation is 1,042.180 ft (US survey feet). Elevations are carried to 0.001 ft.
Leg 1, BM-101 to TP-A: observed difference +18.462 ft over 0.80 mile.
Leg 2, TP-A to BM-102: observed difference -7.235 ft over 1.20 miles.
Leg 3, BM-102 to TP-B: observed difference +11.908 ft over 1.60 miles.
Leg 4, TP-B back to BM-101: observed difference -23.075 ft over 1.40 miles.
The specification for this order of work allows a misclosure of C times the square root of the loop length in miles, with C = 0.05 ft.
Required
The loop misclosure.
The allowable misclosure, and whether the work is acceptable.
The correction to each leg and the adjusted elevations of TP-A, BM-102 and TP-B.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
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