- 2078 Kartik · 6 marks
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.
| Station | Deflection angle (degrees) | Leg | Bearing (degrees) |
|---|---|---|---|
| M2 | -70 | M1-M2 | 105 |
| A | +20 | M2-A | |
| B | -90 | A-B | |
| M8 | +70 | B-M8 | |
| M8-M9 | 36 |
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
| Leg | Working | Computed bearing |
|---|---|---|
| M1-M2 | given | 105° |
| M2-A | 105° − 70° | 35° |
| A-B | 35° + 20° | 55° |
| B-M8 | 55° − 90° = −35° | 325° |
| M8-M9 | 325° + 70° = 395° | 35° |
Computed bearing of M8-M9 = 35°, observed = 36°.
Step 2: Check of accuracy
Permissible misclosure (n = 4 deflection angles). Since , the work is acceptable, but the bearings of the link legs are adjusted.
Step 3: Correction
Correction per angle . The correction to a leg increases by 15′ at each station.
| Leg | Computed | Correction | Corrected bearing |
|---|---|---|---|
| M2-A | 35°00′ | +0°15′ | 35°15′ |
| A-B | 55°00′ | +0°30′ | 55°30′ |
| B-M8 | 325°00′ | +0°45′ | 325°45′ |
| M8-M9 | 35°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)
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