--- title: "Local attraction and true bearings, 7°W" subject: "Surveying I" chapter: 4 key: "semester_3/surveying_i:local-attraction-true-bearings-7w" source: https://www.bctengineer.com/q/semester_3/surveying_i/local-attraction-true-bearings-7w site: BCT Engineering --- # Local attraction and true bearings, 7°W Surveying I · Chapter 4: The Compass - Asked in: 2066 Jestha, 8 marks - Video: [4.6 Compass Surveying: Local Attraction Correction by Bearings (Complete Numerical)](https://www.youtube.com/watch?v=JvOphyhwV44) — Civil Modules - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/local-attraction-true-bearings-7w - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4 ## Question The following bearings were observed with a compass for traversing. Find the amount of local attraction and correct the bearings as well as the true bearings if the magnetic declination is 7°W. | Line | FB | BB | |---|---|---| | AB | 59°00′ | 239°00′ | | BC | 139°30′ | 317°00′ | | CD | 215°15′ | 36°30′ | | DE | 208°00′ | 29°00′ | | EA | 318°30′ | 138°45′ | ## Short answer Local attraction at C, D, E: corrections to observed bearings are +2°30′, +1°15′, +0°15′. Corrected magnetic FB: AB 59°00′, BC 139°30′, CD 217°45′, DE 209°15′, EA 318°45′. True FB (declination 7°W): AB 52°00′, BC 132°30′, CD 210°45′, DE 202°15′, EA 311°45′. ## Answer Line AB has FB − BB = 180°, so A and B are free. Stations C, D and E are suspected. Declination is 7° West, so **true bearing = magnetic bearing − 7°**. 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, $\text{FB} - \text{BB} = 180^\circ$ exactly. #### Step 1: Check each line | Line | FB | BB | FB − BB | Remark | |---|---|---|---|---| | AB | 59°00′ | 239°00′ | 180°00′ | Free, difference = 180° | | BC | 139°30′ | 317°00′ | 182°30′ | Differs by +2°30′ | | CD | 215°15′ | 36°30′ | 178°45′ | Differs by −1°15′ | | DE | 208°00′ | 29°00′ | 179°00′ | Differs by −1°00′ | | EA | 318°30′ | 138°45′ | 179°45′ | Differs by −0°15′ | Line AB has a difference of exactly 180°, so stations A and B are free from local attraction. The other stations are corrected one after another, starting from B. #### Step 2: Correct the stations in turn - Line BC: FB at B = 139°30′ is correct. The correct BB is 319°30′, observed 317°00′, so the correction at C is +2°30′. - Line CD: FB at C = 215°15′ with correction +2°30′ gives 217°45′. The correct BB is 37°45′, observed 36°30′, so the correction at D is +1°15′. - Line DE: FB at D = 208°00′ with correction +1°15′ gives 209°15′. The correct BB is 29°15′, observed 29°00′, so the correction at E is +0°15′. - Line EA (check): FB at E = 318°30′ with correction +0°15′ gives 318°45′. The correct BB is 138°45′, which equals the observed value, so A needs no correction, as expected. | Station | A | B | C | D | E | |---|---|---|---|---|---| | Correction | 0 | 0 | +2°30′ | +1°15′ | +0°15′ | Stations affected by local attraction: C, D and E. The amount of local attraction at each is equal and opposite to the correction: C −2°30′, D −1°15′, E −0°15′ (the observed bearings there are too small). #### Step 3: Corrected bearings | Line | Observed FB | Correction | Corrected FB | Observed BB | Corrected BB | True FB | True BB | |---|---|---|---|---|---|---|---| | AB | 59°00′ | 0 | 59°00′ | 239°00′ | 239°00′ | 52°00′ | 232°00′ | | BC | 139°30′ | 0 | 139°30′ | 317°00′ | 319°30′ | 132°30′ | 312°30′ | | CD | 215°15′ | +2°30′ | 217°45′ | 36°30′ | 37°45′ | 210°45′ | 30°45′ | | DE | 208°00′ | +1°15′ | 209°15′ | 29°00′ | 29°15′ | 202°15′ | 22°15′ | | EA | 318°30′ | +0°15′ | 318°45′ | 138°45′ | 138°45′ | 311°45′ | 131°45′ | Check: corrected FB − corrected BB = 180° for every line. **Answer:** Corrected bearings (FB): AB = 59°00′, BC = 139°30′, CD = 217°45′, DE = 209°15′, EA = 318°45′. True bearings (FB): AB = 52°00′, BC = 132°30′, CD = 210°45′, DE = 202°15′, EA = 311°45′. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the presence of local attraction at the ends of a line detected? A. Compare FB and BB: if FB − BB is not exactly 180°, attraction is present at one or both ends B. Check whether the sum of FB and BB equals 360° C. Compare the observed bearing with the true meridian D. Check whether the FB is greater than the BB Answer: A. Without local attraction at either end, FB − BB = 180° exactly. A line with exactly 180° has both stations free. (Key point: Detecting free stations) 2. For line BC, FB at B = 139°30′ is correct and the observed BB is 317°00′. What is the correction at C? A. −2°30′ B. +2°30′ C. +1°15′ D. 0 Answer: B. The correct BB is 139°30′ + 180° = 319°30′. Observed is 317°00′, so the correction is +2°30′. (Key point: Correction at C) 3. For line CD, what correction is applied to the FB at C before finding the correction at D? A. None, since C is free B. +1°15′ C. +2°30′ (the correction already found at C) D. −2°30′ Answer: C. Station C has +2°30′, so the FB of CD becomes 217°45′. The correct BB is then 37°45′ against 36°30′ observed, giving +1°15′ at D. (Key point: Chain of corrections) 4. With a declination of 7° West, how is the true bearing obtained from the corrected magnetic bearing? A. True = magnetic + 7° B. True = magnetic − 7° C. True = magnetic + 7° only for back bearings D. True = magnetic, since declination only affects BB Answer: B. West declination means the needle points west of true north, so true = magnetic − 7°. True FB of AB = 59°00′ − 7° = 52°00′. (Key point: Magnetic declination west) ## Related in Surveying I - [Local attraction and true bearings, 1°30′E](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Acompass-closed-traverse-declination-1-30-east) — Surveying I, chapter 4 - [Local attraction, bearings AB 305°00′ (EA 45°)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-305-00) — Surveying I, chapter 4, asked 2× - [Local attraction, bearings AB 305°30′](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-bb-44-00) — Surveying I, chapter 4, asked 2× - [Local attraction: AB 69°30′ compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-69-30-reordered) — Surveying I, chapter 4 - [Corrected and true bearings, 5°E declination](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-true-bearings-5-deg) — Surveying I, chapter 4 - [Local attraction, BC 79°30′ and DE 82°15′](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-191-30-bc-79-30) — Surveying I, chapter 4