--- title: "Corrected bearings, closed link traverse T1-T2" subject: "Surveying I" chapter: 4 key: "semester_3/surveying_i:closed-link-traverse-t1-t2-corrected-bearings" source: https://www.bctengineer.com/q/semester_3/surveying_i/closed-link-traverse-t1-t2-corrected-bearings site: BCT Engineering --- # Corrected bearings, closed link traverse T1-T2 Surveying I · Chapter 4: The Compass - Asked in: 2057 Chaitra, 10 marks - Video: [Azimuths and Bearings Traverse Surveying: A Complete Solved Land Problem in Civil & Construction](https://www.youtube.com/watch?v=mXMEPFJLpKo) — Kelvin Academy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/closed-link-traverse-t1-t2-corrected-bearings - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4 ## Question The following data apply to a closed "link" traverse. Compute the corrected bearings and the angular misclosure. | Station | Measured angle (angle to the right) | |---|---| | T1 | | | A | 272°40′00″ | | B | 267°27′28″ | | C | 87°02′31″ | | D | 109°35′39″ | | E | 270°29′59″ | | T2 | | Corrected bearing of the starting line (T1 to A) = 310°17′20″; corrected bearing of the closing line (E to T2) = 57°32′52″. ## Short answer Angular misclosure = -5″ (computed bearing 5″ too large, known minus computed). Corrected bearings: T1-A 310°17′20″, A-B 42°57′19″, B-C 130°24′46″, C-D 37°27′16″, D-E 327°02′54″, E-T2 57°32′52″. ## Answer The bearings of the first line (T1A) and the last line (ET2) are known (corrected). The bearing of ET2 is computed through the five angles to the right at A, B, C, D and E, and compared with its known value. **Rule (angles to the right):** $\text{FB of next line} = \text{FB of previous line} + 180^\circ + \text{angle to the right}$ (add or subtract $360^\circ$ to bring the result between $0^\circ$ and $360^\circ$). #### Step 1: Bearings computed from the observed angles | Line | Working | Computed FB | |---|---|---| | T1-A | given | 310°17′20″ | | A-B | 310°17′20″ + 180° + 272°40′00″ − 720° | 42°57′20″ | | B-C | 42°57′20″ + 180° + 267°27′28″ − 360° | 130°24′48″ | | C-D | 130°24′48″ + 180° + 87°02′31″ − 360° | 37°27′19″ | | D-E | 37°27′19″ + 180° + 109°35′39″ | 327°02′58″ | | E-T2 | 327°02′58″ + 180° + 270°29′59″ − 720° | 57°32′57″ | Computed FB of E-T2 = 57°32′57″; given (known) FB of E-T2 = 57°32′52″. #### Step 2: Angular misclosure $$ \text{Misclosure} = \text{given} - \text{computed} = -0^\circ 00'05'' $$ The computed bearing is 5″ too large. The misclosure is small (a few seconds), so it is distributed equally among the five angles. #### Step 3: Adjustment Total correction = −0°00′05″ (added to the computed bearing of the last line). It is distributed equally over the 5 observed angles: −0°00′05″ / 5 = −0°00′01″ per angle. The correction to a line is −0°00′01″ multiplied by the number of angles used to reach it. | Line | Computed FB | Correction | Corrected FB | Corrected BB | |---|---|---|---|---| | T1-A | 310°17′20″ | 0 | 310°17′20″ | 130°17′20″ | | A-B | 42°57′20″ | −0°00′01″ | 42°57′19″ | 222°57′19″ | | B-C | 130°24′48″ | −0°00′02″ | 130°24′46″ | 310°24′46″ | | C-D | 37°27′19″ | −0°00′03″ | 37°27′16″ | 217°27′16″ | | D-E | 327°02′58″ | −0°00′04″ | 327°02′54″ | 147°02′54″ | | E-T2 | 57°32′57″ | −0°00′05″ | 57°32′52″ | 237°32′52″ | Check: the corrected FB of the last line equals the given value 57°32′52″. **Answer:** angular misclosure = −5″ (known − computed; the computed bearing is 5″ too large). Corrected bearings: T1A 310°17′20″, AB 42°57′19″, BC 130°24′46″, CD 37°27′16″, DE 327°02′54″, ET2 57°32′52″. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the bearing of ET2 computed in a link traverse? A. By averaging the known bearings of T1A and ET2 B. By carrying the known T1A bearing through the five angles using FB = previous FB + 180° + angle C. By adding all angles and subtracting 360° D. By measuring it directly with a compass Answer: B. The starting bearing is carried forward through each angle to the last line and then compared with the known bearing. (Key point: Method of computing) 2. Computed ET2 = 57°32′57″ and known ET2 = 57°32′52″. What is the misclosure (known − computed)? A. +5″ B. −5″ C. −57″ D. 0″ Answer: B. 57°32′52″ − 57°32′57″ = −5″. (Key point: Misclosure sign) 3. How is the correction applied along the lines? A. −5″ to every line B. −1″ per angle, so line k gets −1″ × k C. Only the last line is corrected D. −5″ at the first line and nothing after Answer: B. −5″/5 angles = −1″ per angle, and each line's correction is multiplied by the number of angles used to reach it (−1″ at AB up to −5″ at ET2). (Key point: Equal distribution) 4. What shows the adjustment is correct? A. Corrected FB of ET2 equals the known value 57°32′52″ B. Corrected FB of ET2 equals 310°17′20″ C. All corrected bearings are below 180° D. The sum of corrections is zero Answer: A. After adjustment the last bearing must agree with the known bearing of ET2. (Key point: Closing check) ## Related in Surveying I - [Angle misclosure, closed link traverse AT1-ET2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-at1-et2) — Surveying I, chapter 4 - [Angular misclosure, link traverse ABCDEFG](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-initial-154-50-last-335-30) — 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 - [Link traverse XP to TY, angles to right](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-xp-ty-angles-to-right) — Surveying I, chapter 4 - [Link traverse PABCQ: permissible misclosure](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-pabcq-permissible-misclosure) — Surveying I, chapter 4 - [Link traverse M2 to M8 bearings](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-m2-to-m8) — Surveying I, chapter 4 ## Related in other subjects - [Closed loop/link traverse, misclosure terms](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-misclosure) — Surveying II, chapter 1 - [Closed loop/link traverse, misclosure balancing](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-angular-misclosure) — Surveying II, chapter 1 - [Adjust traverse A-X to E-Y bearings](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-adjust-latitude-departure-ax-ey) — Surveying II, chapter 1 - [Closed traverse ABCDA missing data, C(1200, 2000)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcda-c-1200-2000) — Surveying II, chapter 1