Great Circle Navigation Calculator

Bearing Formula:

\[ \text{Bearing} = \arctan2(\sin \Delta\lambda \cdot \cos \varphi_2, \cos \varphi_1 \cdot \sin \varphi_2 - \sin \varphi_1 \cdot \cos \varphi_2 \cdot \cos \Delta\lambda) \]

Latitude of Point 1 (φ₁):

degrees

Longitude of Point 1 (λ₁):

degrees

Latitude of Point 2 (φ₂):

degrees

Longitude of Point 2 (λ₂):

degrees

Initial Bearing:

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1. What is Great Circle Navigation?

Great circle navigation is the shortest path between two points on the surface of a sphere. The initial bearing is the angle measured clockwise from true north to the great circle route at the starting point.

2. How Does the Bearing Calculation Work?

The calculator uses the bearing formula:

\[ \text{Bearing} = \arctan2(\sin \Delta\lambda \cdot \cos \varphi_2, \cos \varphi_1 \cdot \sin \varphi_2 - \sin \varphi_1 \cdot \cos \varphi_2 \cdot \cos \Delta\lambda) \]

Where:

\( \varphi_1, \lambda_1 \) — Latitude and longitude of point 1 (radians)
\( \varphi_2, \lambda_2 \) — Latitude and longitude of point 2 (radians)
\( \Delta\lambda \) — Difference in longitude between the two points
\( \arctan2 \) — Two-argument arctangent function

Explanation: The formula calculates the initial bearing (forward azimuth) from point 1 to point 2 along the great circle path.

3. Importance of Bearing Calculation

Details: Great circle bearings are essential for navigation, aviation, and maritime applications where the shortest path between two points is crucial for efficiency and fuel savings.

4. Using the Calculator

Tips: Enter coordinates in decimal degrees (positive for N/E, negative for S/W). Valid ranges: latitude -90 to 90, longitude -180 to 180.

5. Frequently Asked Questions (FAQ)

Q1: Why doesn't the bearing remain constant along the route?
A: On a great circle route (except due north/south or along the equator), the bearing changes continuously as you move along the path.

Q2: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect sphere. Earth's ellipsoidal shape introduces small errors (typically < 0.5°).

Q3: What's the difference between initial and final bearing?
A: Initial bearing is the direction at the start point. Final bearing (arrival bearing) is the direction when approaching the destination.

Q4: Can I use this for rhumb line navigation?
A: No, this calculates great circle bearings. Rhumb lines maintain constant bearing but are longer paths.

Q5: How does this relate to compass navigation?
A: The result is true bearing. For magnetic compass use, you must account for magnetic declination at your location.