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` = "Rhumb Line Distance"`

Enter a value for all fields

The **Rhumb Line Distance **calculator computes the distance traveled between two points using azimuth angle (rhumb line) to travel between to latitude / longitude coordinates.

**INSTRUCTIONS**: Choose units and enter the following:

**(**Latitude One**LT1**)**(**Longitude One**LN1**)**(**Latitude Two**LT2**)**(**Longitude Two**LN2**)

**Rhumb Line Distance (d): **The distance is returned in nautical miles (nmi). However, this can be automatically converted to compatible units via the pull-down menu.

A rhumb line, also known as a loxodrome, is a path on the surface of a sphere (such as the Earth) that crosses all meridians of longitude at a constant angle. Unlike a great circle route, which is the shortest path between two points on the globe, a rhumb line maintains a constant bearing (direction) and is easier to navigate using a compass.

- Constant Bearing: A rhumb line crosses each meridian at the same angle, making it a line of constant compass direction.
- Ease of Navigation: Because the bearing remains constant, it's easier to follow using traditional navigation techniques, such as a compass, without continuously adjusting the course.
- Non-Shortest Path: On a spherical surface, a rhumb line is not the shortest distance between two points. The shortest path is a segment of a great circle.
- Spiraling towards the Poles: On a Mercator projection map, which is commonly used for navigation, rhumb lines appear as straight lines. However, on a spherical surface, rhumb lines spiral towards the poles.

Practical Usage:

- Marine and Air Navigation: Rhumb lines are particularly useful in marine and air navigation for courses that need to be followed over long distances without changing direction.
- Mercator Projection: On a Mercator projection map, rhumb lines are represented as straight lines, which simplifies the navigation process.

Example:

If a ship were to sail from London to New York City along a rhumb line, it would maintain a constant compass direction throughout the journey, even though this path is longer than the great circle route.

`d = R * sqrt(Deltaphi^2 + (cos(phi_m)*Deltalambda)^2)`

where:

- d = rhumb line distance.
- R = Earth's Mean Radius
- Δϕ = Difference in latitude between the two points (in radians).
- Δλ = Difference in longitude between the two points (in radians).
- ϕm = Mean latitude between the two points (in radians).

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