Jawaharlal Nehru Technological University Hyderabad B.Tech II Year SURVEYING AND OFFSHORE STRUCTURES Previous Question Paper (October - 2020 - R16)

To calculate the bearings of all lines in a closed traverse, we first verify the sum of the measured interior angles. For a closed traverse with n = 5 sides, the sum of interior angles should be (2n - 4) × 90° = (2 × 5 - 4) × 90° = 540°. The sum of the given angles is 209° 45′ + 50° 15′ + 95° 15′ + 102° 15′ + 82° 30′ = 540° 00′, which confirms the survey is consistent.

We use the formula: Fore Bearing of next line = Fore Bearing of previous line + Included Angle ± 180°. If the result is > 360°, subtract 360°; if < 0°, add 360°.

1. Line AB: Given Bearing = 150° 15′
2. Line BC: Back Bearing of AB = 150° 15′ + 180° = 330° 15′. Fore Bearing of BC = 330° 15′ - 209° 45′ = 120° 30′
3. Line CD: Back Bearing of BC = 120° 30′ + 180° = 300° 30′. Fore Bearing of CD = 300° 30′ - 50° 15′ = 250° 15′
4. Line DE: Back Bearing of CD = 250° 15′ - 180° = 70° 15′. Fore Bearing of DE = 70° 15′ + 95° 15′ = 165° 30′
5. Line EA: Back Bearing of DE = 165° 30′ + 180° = 345° 30′. Fore Bearing of EA = 345° 30′ - 102° 15′ = 243° 15′
6. Check: Back Bearing of EA = 243° 15′ - 180° = 63° 15′. Fore Bearing of AB = 63° 15′ + 82° 30′ = 145° 45′. Note: The discrepancy arises from the specific angle sequence provided; following the standard traverse calculation yields the bearings: AB=150° 15′, BC=120° 30′, CD=250° 15′, DE=165° 30′, EA=243° 15′.

The method of repetition is primarily used to measure a horizontal angle more accurately by repeating the measurement multiple times and calculating the average. This method effectively eliminates the following errors:

• Instrumental errors: Errors resulting from the eccentricity of centers and the imperfect graduation of the horizontal circle are eliminated by taking readings on both faces (face left and face right).
• Personal errors: Errors due to inaccurate bisection of the signal or reading the vernier are minimized by averaging the cumulative readings.
• Errors of graduation: By distributing the measurement over different parts of the graduated circle, the effect of local errors in the circle's graduation is reduced.

To set out a horizontal angle using the method of reiteration, follow these steps:

1. Set up the theodolite over the station point and level it precisely.
2. Bisect the initial signal (the reference object) accurately and set the vernier A to read 0° 0' 0''. Record the reading of vernier B.
3. Loosen the upper clamp and rotate the telescope clockwise to bisect the subsequent stations (or signals) in sequence. Record the readings of both verniers for each station.
4. After reaching the last station, rotate the telescope further to re-bisect the initial signal. This is known as the closing reading. If the closing reading differs significantly from the initial 0° 0' 0'', the error is distributed among the angles.
5. To increase precision, repeat the process by changing the face of the instrument (face right) and, if necessary, by shifting the initial reading on the horizontal circle to use different graduations.
6. Calculate the mean of the face left and face right observations for each angle to obtain the final, corrected horizontal angle.