Magnetic bearing of a line is 10° 30' and the magnetic declination is 2° East. If, due to seasonal variations, the magnetic declination changes to 2° West, find the magnetic bearing of the line in quadrantal bearing system.
🧭 Understanding Bearings and Declination
This problem involves converting between magnetic and true bearings. The key is to remember that the True Bearing of a fixed survey line is constant, while the Magnetic Bearing changes as the magnetic declination changes.
- True Bearing (TB): The angle of a line measured with respect to the True North (Geographic North Pole). This value does not change.
- Magnetic Bearing (MB): The angle of a line measured with respect to the Magnetic North. This value changes as the Earth's magnetic field fluctuates.
- Magnetic Declination: The horizontal angle between True North and Magnetic North at a specific location.
The fundamental relationship is: True Bearing = Magnetic Bearing ± Declination
🔬 Step-by-Step Calculation
The problem can be solved in two main steps:
Step 1: Find the True Bearing of the Line
First, we use the initial measurements to calculate the constant True Bearing.
- Initial Magnetic Bearing (MB) = 10° 30'
- Initial Declination = 2° East
For an East declination, Magnetic North is to the east of True North, so we add the declination to the Magnetic Bearing:
True Bearing = 10° 30' + 2° = 12° 30'
Step 2: Calculate the New Magnetic Bearing
Next, we use the constant True Bearing and the new declination to find the new Magnetic Bearing.
- True Bearing (TB) = 12° 30'
- New Declination = 2° West
For a West declination, Magnetic North is to the west of True North, so we subtract the declination from the True Bearing:
True Bearing = New Magnetic Bearing - Declination (West)
12° 30' = New MB - 2°
New Magnetic Bearing = 12° 30' + 2° = 14° 30'
🔄 Convert to Quadrantal Bearing (QB)
The final step is to convert the new magnetic bearing from a Whole Circle Bearing (WCB) to the Quadrantal Bearing (QB) system.
- New Magnetic Bearing (WCB) = 14° 30'
Since this angle is between 0° and 90°, it lies in the first quadrant (North-East). In the QB system, this is expressed as:
N 14° 30' E
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