Predicted traverse closure error against the observed misclosure
What misclosure should a five-course traverse produce, given the instrument that ran it? Propagate the per-course errors, predict the closure, and compare it with what the field actually returned.
Analyze· about 30 minutes by hand· 5 steps
Given
A five-course closed boundary traverse, observed with a total station:
A-B azimuth 26°59′20″, 423.12 ft
B-C azimuth 124°10′45″, 519.74 ft
C-D azimuth 199°03′50″, 431.68 ft
D-E azimuth 248°22′05″, 379.80 ft
E-A azimuth 344°32′50″, 480.37 ft
Each distance carries a standard error of σ_D = ±0.020 ft, and each course azimuth a standard error of σ_α = ±10″, treated as independent between courses.
The traverse as observed returned ΣLat = +0.0488 ft and ΣDep = −0.0467 ft.
Distances in US survey feet, perimeter 2234.71 ft.
Required
The predicted standard error of the latitude and departure of each course.
The predicted linear misclosure of the traverse and the precision it implies.
A judgement on whether the observed misclosure is consistent with that prediction, or points to a blunder.
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.
Premium
The worked solution is part of Premium
This problem is 5 steps of computation, with the arithmetic shown at every stage and an independent check at the end. Several problems from every category are free to read in full so you can judge the format first.
Every calculator, the whole reference library and all the guides are free to use forever - the practice bank, the full problem library and the printable job paperwork are the paid upgrade.