Skip to main content

Link traverse M2 to M8 bearings

Short answer

Bearings of link legs: M2-A 35°, A-B 55°, B-M8 325°. Misclosure +1° is within permissible 2°, so work acceptable. Corrected bearings: M2-A 35°15′, A-B 55°30′, B-M8 325°45′.

During compass survey in a link traverse from station M2 to M8, the following observations were recorded.

StationDeflection angle (degrees)LegBearing (degrees)
M2-70M1-M2105
A+20M2-A
B-90A-B
M8+70B-M8
M8-M936

Compute the bearings of the link legs. Check the accuracy of work if the least count of the compass used is 1 degree. Correct the affected bearings if necessary.

Deflection angles: ++ = right, −- = left. A leg's bearing is the previous leg's bearing plus the deflection angle at the station between them.

Step 1: Bearings from the observed deflection angles

LegWorkingComputed bearing
M1-M2given105°
M2-A105° − 70°35°
A-B35° + 20°55°
B-M855° − 90° = −35°325°
M8-M9325° + 70° = 395°35°

Computed bearing of M8-M9 = 35°, observed = 36°.

Step 2: Check of accuracy

Misclosure=36∘−35∘=+1∘\text{Misclosure} = 36^\circ - 35^\circ = +1^\circ

Permissible misclosure =L.C.×n=1∘×4=2∘= L.C. \times \sqrt{n} = 1^\circ \times \sqrt{4} = 2^\circ (n = 4 deflection angles). Since 1∘<2∘1^\circ < 2^\circ, the work is acceptable, but the bearings of the link legs are adjusted.

Step 3: Correction

Correction per angle =+1∘/4=+0.25∘=+0°15′= +1^\circ/4 = +0.25^\circ = +0°15′. The correction to a leg increases by 15′ at each station.

LegComputedCorrectionCorrected bearing
M2-A35°00′+0°15′35°15′
A-B55°00′+0°30′55°30′
B-M8325°00′+0°45′325°45′
M8-M935°00′+1°00′36°00′ (agrees with observed)

Corrected deflection angles: M2: −69°45′ (left), A: +20°15′ (right), B: −89°45′ (left), M8: +70°15′ (right).

Answer: bearings of the link legs M2-A = 35°, A-B = 55°, B-M8 = 325°; misclosure = +1° (within permissible 2°); corrected bearings M2-A = 35°15′, A-B = 55°30′, B-M8 = 325°45′.

✓ Answer checked by Claude Opus 5.5 (high effort)

All Surveying I chapter 4 questions →