- 2062 Baisakh · 10 marks
Corrected and true bearings, 8°40′E
Short answer
Corrected fore bearings: AB 66°15', BC 132°00', CD 217°30', DA 306°45'. True bearings (magnetic +8°40'): AB 74°55', BC 140°40', CD 226°10', DA 315°25'.
The following bearings were observed in running a compass traverse.
| Line | Fore bearing | Back bearing |
|---|---|---|
| AB | 66°15′ | 244°0′ |
| BC | 129°45′ | 313°0′ |
| CD | 218°30′ | 37°30′ |
| DA | 306°45′ | 126°45′ |
Find the corrected fore and back bearings, and the true bearings of the lines, given that the magnetic declination is 8°40′E.
Line DA has FB − BB = 180°00′, so stations D and A are free; B and C are suspected. Declination is 8°40′ East, so true bearing = magnetic bearing + 8°40′.
Local attraction at a station is detected by comparing the fore bearing (FB) and back bearing (BB) of each line: if there is no local attraction at either end, exactly.
Step 1: Check each line
| Line | FB | BB | FB − BB | Remark |
|---|---|---|---|---|
| AB | 66°15′ | 244°00′ | 182°15′ | Differs by +2°15′ |
| BC | 129°45′ | 313°00′ | 176°45′ | Differs by −3°15′ |
| CD | 218°30′ | 37°30′ | 181°00′ | Differs by +1°00′ |
| DA | 306°45′ | 126°45′ | 180°00′ | Free, difference = 180° |
Line DA has a difference of exactly 180°, so stations D and A are free from local attraction. The other stations are corrected one after another, starting from A.
Step 2: Correct the stations in turn
- Line AB: FB at A = 66°15′ is correct. The correct BB is 246°15′, observed 244°00′, so the correction at B is +2°15′.
- Line BC: FB at B = 129°45′ with correction +2°15′ gives 132°00′. The correct BB is 312°00′, observed 313°00′, so the correction at C is −1°00′.
- Line CD (check): FB at C = 218°30′ with correction −1°00′ gives 217°30′. The correct BB is 37°30′, which equals the observed value, so D needs no correction, as expected.
| Station | A | B | C | D |
|---|---|---|---|---|
| Correction | 0 | +2°15′ | −1°00′ | 0 |
Stations affected by local attraction: B, C.
Step 3: Corrected bearings
| Line | Observed FB | Correction | Corrected FB | Observed BB | Corrected BB | True FB | True BB |
|---|---|---|---|---|---|---|---|
| AB | 66°15′ | 0 | 66°15′ | 244°00′ | 246°15′ | 74°55′ | 254°55′ |
| BC | 129°45′ | +2°15′ | 132°00′ | 313°00′ | 312°00′ | 140°40′ | 320°40′ |
| CD | 218°30′ | −1°00′ | 217°30′ | 37°30′ | 37°30′ | 226°10′ | 46°10′ |
| DA | 306°45′ | 0 | 306°45′ | 126°45′ | 126°45′ | 315°25′ | 135°25′ |
Check: corrected FB − corrected BB = 180° for every line.
Answer: Corrected bearings: AB = 66°15′ / 246°15′, BC = 132°00′ / 312°00′, CD = 217°30′ / 37°30′, DA = 306°45′ / 126°45′ (FB / BB). True bearings (FB): AB = 74°55′, BC = 140°40′, CD = 226°10′, DA = 315°25′.
✓ Answer checked by Claude Opus 5.5 (high effort)
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