- 2078 Kartik · 6+2 marks
Reiteration method with VCR, least count 1′
Short answer
Adjusted horizontal angles: AOB=100°40′00″, BOC=60°40′00″, COA=198°40′00″. Missing VCR: A face right=294°15′00″, B face left=91°05′00″, C face left=59°20′00″.
The following angular observations were made during reiteration method of measurement by a theodolite. Compute the horizontal angles included between survey lines OA, OB and OC by mean direction method. Apply necessary check and corrections if the least count of the instrument is 1 minute. Also find the missing data in VCR.
| Inst stn | Sighted to | Face | HCR (D M S) | VCR (D M S) |
|---|---|---|---|---|
| O | A | L | 00 00 00 | 65 45 00 |
| R | 180 00 00 | ? ? ? | ||
| B | L | 100 40 40 | ? ? ? | |
| R | 280 39 50 | 268 55 00 | ||
| C | L | 161 20 40 | ? ? ? | |
| R | 341 20 20 | 300 40 00 | ||
| A | L | 00 00 20 | ||
| R | 180 00 00 |
Method. The reiteration (direction) method: all directions are observed from the reference object A, and the horizon is closed on A again. Mean direction = [Face L + (Face R ∓ 180°)]/2. The angles are differences of the mean directions.
Check on the observations
For each target the difference between Face L and (Face R - 180°) should not exceed the least count (1′ = 60″). All differences are below 60″, so the observations are accepted. The closing reading on A must agree with the first reading within the least count.
| Stn | Face L | Face R | R - 180° | Difference (L vs R-180°) | Mean direction | Direction from A |
|---|---|---|---|---|---|---|
| A | 0°00′00″ | 180°00′00″ | 0°00′00″ | 0°00′00″ | 0°00′00″ | 0°00′00″ |
| B | 100°40′40″ | 280°39′50″ | 100°39′50″ | 0°00′50″ | 100°40′15″ | 100°40′15″ |
| C | 161°20′40″ | 341°20′20″ | 161°20′20″ | 0°00′20″ | 161°20′30″ | 161°20′30″ |
| A (closing) | 0°00′20″ | 180°00′00″ | 0°00′00″ | 0°00′20″ | 0°00′10″ | 0°00′10″ |
Closing error on A = 0°00′10″, which is less than 1′, so the round is accepted.
Mean angles and adjustment
Sum of the three angles AOB + BOC + COA should be 360°. Distributing the closing error 0°00′10″ equally (correction -0°00′03.33″ per angle):
| Angle | Observed | Correction | Adjusted angle | Rounded to least count (1′) |
|---|---|---|---|---|
| AOB | 100°40′15″ | -0°00′03.33″ | 100°40′11.67″ | 100°40′00″ |
| BOC | 60°40′15″ | -0°00′03.33″ | 60°40′11.67″ | 60°40′00″ |
| COA | 198°39′40″ | -0°00′03.33″ | 198°39′36.67″ | 198°40′00″ |
| Sum | 360°00′10″ | -0°00′10″ | 360°00′00″ | 360°00′00″ |
Missing VCR
FL + FR = 360° for each target.
| Observation | VCR Face left | VCR Face right | Vertical angle (90° - Z) |
|---|---|---|---|
| A (R) | 65°45′00″ | 294°15′00″ | +24°15′00″ |
| B (L) | 91°05′00″ | 268°55′00″ | -1°05′00″ |
| C (L) | 59°20′00″ | 300°40′00″ | +30°40′00″ |
Answer: AOB = 100°40′00″, BOC = 60°40′00″, COA = 198°40′00″ (to the least count of 1′); missing VCR: A (face R) = 294°15′00″, B (face L) = 91°05′00″, C (face L) = 59°20′00″.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Direction theodolite, least count 6″, station D · Surveying I, chapter 7
- Mean direction angles with VCR (125°25′20″) · Surveying I, chapter 7
- Theodolite traverse ABCDA with missing VCR (68°30′10″) · Surveying I, chapter 7
- Theodolite traverse ABCDA, booking format with VCR · Surveying I, chapter 7
- Mean angles; VCR and VA from A · Surveying I, chapter 7
- Horizontal angles from field notes, triangle ABC · Surveying I, chapter 7
- Distances OA and OC by resection on A, B, C · Surveying II, chapter 5
- 8086 ALP: words on lines and word count · Microprocessor, chapter 3