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Difficulty: Very hardElementary Surveying Instruments and Fieldwork

A surveyor conducting a prismatic compass traverse along stations PP, QQ, RR, and SS records the following observed bearings:

- Line P−QP-Q: Forward Bearing =142∘00′= 142^\circ 00', Back Bearing =322∘00′= 322^\circ 00'
- Line Q−RQ-R: Forward Bearing =075∘30′= 075^\circ 30', Back Bearing =258∘00′= 258^\circ 00'
- Line R−SR-S: Forward Bearing =190∘00′= 190^\circ 00'

If the local magnetic declination in the survey area is 5∘30′ W5^\circ 30'\text{ W}, what is the true geographic forward bearing of line R−SR-S?

  1. 182∘00′182^\circ 00'Answer
  2. B
    184∘30′184^\circ 30'
  3. C
    187∘00′187^\circ 00'
  4. D
    193∘00′193^\circ 00'

Answer

The true geographic forward bearing of line R-S is 182∘00′182^\circ 00'.
The correct answer is 182∘00′182^\circ 00'. Evaluating line P-Q shows a difference of exactly 180∘00′180^\circ 00' between its forward bearing (142∘00′142^\circ 00') and back bearing (322∘00′322^\circ 00'), confirming that stations P and Q are free from local attraction. Consequently, the forward bearing of line Q-R (075∘30′075^\circ 30') measured at station Q is accurate, making its theoretical back bearing at station R equal to 075∘30′+180∘00′=255∘30′075^\circ 30' + 180^\circ 00' = 255^\circ 30'. Comparing this with the observed back bearing at station R (258∘00′258^\circ 00') identifies a local attraction error of +2∘30′+2^\circ 30' at station R. Applying this correction to the observed forward bearing of line R-S (190∘00′190^\circ 00') gives a corrected magnetic bearing of 187∘30′187^\circ 30'. Finally, subtracting the 5∘30′ W5^\circ 30'\text{ W} magnetic declination (True Bearing=Magnetic Bearing−West Declination\text{True Bearing} = \text{Magnetic Bearing} - \text{West Declination}) yields 182∘00′182^\circ 00'.

Step-by-Step Solution

1
Identify stations free from local attraction
Difference for line P-Q =322∘00′−142∘00′=180∘00′= 322^\circ 00' - 142^\circ 00' = 180^\circ 00'. Both station P and station Q are free from local attraction.
When the difference between the forward bearing and back bearing of a line is exactly 180∘180^\circ, neither instrument station suffers from local attraction.
2
Determine local attraction at station R
Since station Q is correct, the true magnetic forward bearing of Q-R is 075∘30′075^\circ 30'. The correct back bearing at station R should be 075∘30′+180∘00′=255∘30′075^\circ 30' + 180^\circ 00' = 255^\circ 30'. The observed back bearing at station R is 258∘00′258^\circ 00'. Local attraction at station R =258∘00′−255∘30′=+2∘30′= 258^\circ 00' - 255^\circ 30' = +2^\circ 30'.
Any bearing taken FROM station R reads 2∘30′2^\circ 30' too high due to local magnetic interference.
3
Calculate corrected magnetic forward bearing of line R-S
Corrected Magnetic FB =190∘00′−2∘30′=187∘30′= 190^\circ 00' - 2^\circ 30' = 187^\circ 30'.
Subtracting the positive local attraction error adjusts the reading to the correct magnetic orientation.
4
Convert magnetic bearing to true geographic bearing
True Geographic Bearing =Magnetic Bearing−West Declination=187∘30′−5∘30′=182∘00′= \text{Magnetic Bearing} - \text{West Declination} = 187^\circ 30' - 5^\circ 30' = 182^\circ 00'.
When magnetic declination is West, True Bearing equals Magnetic Bearing minus Declination (TB=MB−W\text{TB} = \text{MB} - \text{W}).

Key Concept

Correction of Prismatic Compass Bearings for Local Attraction and Magnetic Declination
Estimated Time:2m 0s
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Topics

Elementary Surveying Instruments and Fieldwork

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