Problem Statement
The magnetic bearing of a line in MNNIT Allahabad was found to be N60°30′W in 1992, when the declination was 5°10′E. Find its present magnetic bearing, if declination is 3°W.
Step-by-Step Solution
Key Information & Setup
- Original magnetic bearing (1992) = N60°30′W
- Original declination (1992) = 5°10′E
- Current declination = 3°W
- Goal: Find the current magnetic bearing of the line
Step 1: Convert Original Magnetic Bearing to Whole Circle Bearing (WCB)
First, we need to convert the Reduced Bearing (RB) to Whole Circle Bearing (WCB):
For a bearing in the NW quadrant (N60°30′W):
WCB = 360° – angle from north
WCB = 360° – 60°30′
WCB = 299°30′
Step 2: Calculate Original True Bearing
When declination is easterly (E), we add it to the magnetic bearing to get the true bearing:
True Bearing = Magnetic Bearing + Declination (east)
True Bearing = 299°30′ + 5°10′
True Bearing = 304°40′
Step 3: Apply Principle of Constant True Bearing
The true bearing of a fixed line on Earth’s surface remains constant over time, even as magnetic declination changes.
Current True Bearing = Original True Bearing
Current True Bearing = 304°40′
Step 4: Calculate Current Magnetic Bearing from True Bearing
When declination is westerly (W), we add it to the true bearing to get the magnetic bearing:
Current Magnetic Bearing = True Bearing + Declination (west)
Current Magnetic Bearing = 304°40′ + 3°0′
Current Magnetic Bearing = 307°40′
Step 5: Convert Current Magnetic Bearing to Reduced Bearing Format
Now we convert the current magnetic bearing back to a reduced bearing format:
The WCB of 307°40′ lies in the NW quadrant (between 270° and 360°).
For NW quadrant: RB = N (360° – WCB) W
RB = N (360° – 307°40′) W
RB = N 52°20′ W
Final Result
Explanation of Declination Reversal
Understanding Declination Direction Reversal:
- Direction Change: In this problem, the declination has not only changed in magnitude but also in direction (from East to West).
- Impact on Calculations: When declination changes direction, we must be particularly careful with the formulas used. For easterly declination, we add to magnetic bearing to get true bearing; for westerly declination, we subtract.
- Total Declination Shift: The total change in declination in this problem is significant: from 5°10′E to 3°W, which is a total shift of 8°10′.
- Bearing Format Conversion: This problem demonstrates the importance of working with whole circle bearings for calculations and then converting back to the desired format for the final answer.
Summary of the Process:
1. Convert original magnetic bearing to WCB
2. Calculate original true bearing using easterly declination
3. Apply principle that true bearing remains constant
4. Calculate current magnetic bearing using westerly declination
5. Convert final WCB to reduced bearing format
This methodology can be applied to any problem involving changes in magnetic declination over time, regardless of whether the declination changes in magnitude, direction, or both.
