Problem Statement
The magnetic bearing of a line CD is S 30°15′ W. Find its true bearing, if the declination is 10°15′ E.
Step-by-Step Solution
Key Information & Setup
- Magnetic bearing of line CD = S 30°15′ W
- Declination = 10°15′ E
- Goal: Find the true bearing of line CD
Step 1: Convert 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 SW quadrant (S 30°15′ W):
WCB = 180° + angle from south
WCB = 180° + 30°15′
WCB = 210°15′
Step 2: Apply Declination to Find True Bearing
When declination is easterly (E), we add it to the magnetic bearing to get the true bearing:
True Bearing (WCB) = Magnetic Bearing (WCB) + Declination (east)
True Bearing (WCB) = 210°15′ + 10°15′
True Bearing (WCB) = 220°30′
Step 3: Convert True Bearing from WCB to Reduced Bearing (RB)
Now we convert the true bearing back to a reduced bearing format:
The WCB of 220°30′ lies in the SW quadrant (between 180° and 270°).
For SW quadrant: RB = S (WCB – 180°) W
RB = S (220°30′ – 180°) W
RB = S 40°30′ W
Final Result
Explanation of Magnetic vs. True Bearings
Understanding Magnetic Declination in Surveying:
- Magnetic Bearing: The angle measured from magnetic north as indicated by a compass.
- True Bearing: The angle measured from true (geographic) north.
- Magnetic Declination: The angle between magnetic north and true north at a given location.
- Easterly Declination: When magnetic north is east of true north, we add the declination to the magnetic bearing to get the true bearing.
- Westerly Declination: When magnetic north is west of true north, we subtract the declination from the magnetic bearing to get the true bearing.
General Formulas:
True Bearing = Magnetic Bearing + Easterly Declination
True Bearing = Magnetic Bearing – Westerly Declination
In surveying and navigation, understanding and accounting for magnetic declination is essential for accurate direction determination, especially in areas where the declination is significant or where precise bearings are required.