--- title: "Corrected and true bearings, 5°E declination" subject: "Surveying I" chapter: 4 key: "semester_3/surveying_i:local-attraction-true-bearings-5-deg" source: https://www.bctengineer.com/q/semester_3/surveying_i/local-attraction-true-bearings-5-deg site: BCT Engineering --- # Corrected and true bearings, 5°E declination Surveying I · Chapter 4: The Compass - Asked in: 2062 Poush, 10 marks - Video: [17. How to find true bearing l Magnetic declination l English l GATE 2021](https://www.youtube.com/watch?v=qTeKqJxn7p8) — The Civil Girl - Page: https://www.bctengineer.com/q/semester_3/surveying_i/local-attraction-true-bearings-5-deg - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4 ## Question The following bearings were taken while conducting a closed traverse with a compass. | Line | FB | BB | |---|---|---| | AB | 80°45′ | 260°00′ | | BC | 130°30′ | 311°35′ | | CD | 240°15′ | 60°15′ | | DA | 290°30′ | 110°10′ | At what stations do you suspect local attraction? Find the corrected bearings and also the true bearings of each line if the magnetic declination was 5°E. ## Short answer Local attraction at A and B. Corrected fore bearings: AB 81°05', BC 131°35', CD 240°15', DA 290°30'. True bearings (+5°): AB 86°05', BC 136°35', CD 245°15', DA 295°30'. ## Answer Line CD has FB − BB = 180°00′, so stations C and D are free. A and B are suspected (from DA and BC). Declination is 5° East, so **true bearing = magnetic bearing + 5°**. 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 | 80°45′ | 260°00′ | 180°45′ | Differs by +0°45′ | | BC | 130°30′ | 311°35′ | 178°55′ | Differs by −1°05′ | | CD | 240°15′ | 60°15′ | 180°00′ | Free, difference = 180° | | DA | 290°30′ | 110°10′ | 180°20′ | Differs by +0°20′ | Line CD has a difference of exactly 180°, so stations C and D are free from local attraction. The other stations are corrected one after another from these. #### Step 2: Correct the stations in turn - Line DA: FB at D = 290°30′ is correct. Correct BB should be 110°30′, observed 110°10′, so the correction at A is +0°20′. - Line AB: FB at A = 80°45′ with correction +0°20′ gives 81°05′. Correct BB should be 261°05′, observed 260°00′, so the correction at B is +1°05′. | Station | A | B | C | D | |---|---|---|---|---| | Correction | +0°20′ | +1°05′ | 0 | 0 | Stations affected by local attraction: A, B. #### Step 3: Corrected bearings | Line | Observed FB | Correction | Corrected FB | Observed BB | Corrected BB | True FB | True BB | |---|---|---|---|---|---|---|---| | AB | 80°45′ | +0°20′ | 81°05′ | 260°00′ | 261°05′ | 86°05′ | 266°05′ | | BC | 130°30′ | +1°05′ | 131°35′ | 311°35′ | 311°35′ | 136°35′ | 316°35′ | | CD | 240°15′ | 0 | 240°15′ | 60°15′ | 60°15′ | 245°15′ | 65°15′ | | DA | 290°30′ | 0 | 290°30′ | 110°10′ | 110°30′ | 295°30′ | 115°30′ | Check: corrected FB − corrected BB = 180° for every line. **Answer:** Corrected bearings (FB): AB = 81°05′, BC = 131°35′, CD = 240°15′, DA = 290°30′. True bearings (FB): AB = 86°05′, BC = 136°35′, CD = 245°15′, DA = 295°30′. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which line shows no local attraction and where do the corrections start? A. AB, starting from A B. BC, starting from B C. CD, so C and D are free and corrections start from there D. DA, starting from A Answer: C. CD has 240°15′ − 60°15′ = 180°00′, so C and D are free. (Key point: Free line) 2. Line DA: FB at D = 290°30′ is correct, observed BB = 110°10′. What is the correction at A? A. −0°20′ B. +0°20′ C. +0°45′ D. 0 Answer: B. Correct BB = 110°30′; observed 110°10′, so the correction is +0°20′. (Key point: Correction at A) 3. FB of AB is 80°45′ with +0°20′ at A, giving 81°05′. Observed BB is 260°00′. What is the correction at B? A. +1°05′ B. +0°45′ C. −1°05′ D. +0°20′ Answer: A. Correct BB = 261°05′, observed 260°00′, so correction is +1°05′. (Key point: Correction at B) 4. With declination 5°E, what is the true FB of CD (corrected 240°15′)? A. 235°15′ B. 240°15′ C. 245°15′ D. 65°15′ Answer: C. East declination is added: 240°15′ + 5° = 245°15′. (Key point: True bearing) ## Related in Surveying I - [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 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: 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, 8°40′E](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atrue-bearings-declination-8-40e) — Surveying I, chapter 4 - [Corrected bearings of closed traverse PQRST](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-traverse-pqrst-correct-bearings) — Surveying I, chapter 4 - [Corrected bearings, closed link traverse T1-T2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-t1-t2-corrected-bearings) — Surveying I, chapter 4 ## Related in other subjects - [Missing bearings of BC and DE in traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-bearings-bc-de) — Surveying II, chapter 1 - [Closed traverse missing EA bearing, BC length](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcdea-missing-ea-bc) — Surveying II, chapter 1 - [Bearings of BC and CD in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-bc-cd) — Surveying II, chapter 1, asked 2× - [Bearings of DE and EA in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-de-ea) — Surveying II, chapter 1, asked 2×