Rhumb Line Distance

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:

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

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.

The Math / Science

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.

Key Characteristics of a Rhumb Line:

1. Constant Bearing: A rhumb line crosses each meridian at the same angle, making it a line of constant compass direction.
2. 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.
3. 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.
4. 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.

The formula for Rhumb Line Distance used in this calculator is:

`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).

Sailing and Navigation Calculators:

• Bruce Number: Computes the ratio of the square root of sail area to the cube root of displacement of a sail boat
• Sail Area / Displacement Ratio: Compute SA/D ratio for sail boats.
• Displacement-Length Ratio: Computes a metric to describe how heavy a boat is in relation to its waterline.
• Capsize Screening Formula: Computes a metric to describe a boat's stability in rough seas.
• Vessel Displacement Volume: Computes the cubic feet displacement associated with the weight displacement.
• Weight of Seawater: Computes the weight and mass of a volume of seawater.
• Time to Sink: Compute the time it takes for a breach (water in) to surpass the displacement of the boat.
• Haversine Distance (decimal degrees): Compute the Distance Between two Points on the Earth (Great Circle Arc)
• Haversine Distance (Degrees, Minutes and Seconds): Compute the Distance Between two Points on a Sphere (Great Circle Arc) using degrees, minutes and seconds verses decimal degrees.
• Rhumb Line Azimuth: Computes the azimuth heading one can navigate for a path that crosses all meridians of longitude at a constant angle.
• Rhumb Line Distance: Computes the distance traveled between two points on the globe if traveled via a rhumb line.
• Correction Angle: navigation equation that compensates for air or water currents.
• Decimal Degrees: Compute decimal degree angles from degrees, minutes and seconds,[CLICK HERE].
• Nautical Travel Cost: Computes the total cost to travel a distance based on the cost rate and distance traveled.
• Travel Time between Coordinates: Compute the time to travel between two location (latitudes and longitudes) based on a average speed
• Distance to Sea Level Horizon: Computes the distance to the horizon from a specified height using a spherical model the mean spherical radius of the Earth

Navigation Calculators:

• Haversine Distance (decimal degrees): Compute the Distance Between two Points on the Earth (Great Circle Arc)
• Haversine Distance (Degrees, Minutes and Seconds): Compute the Distance Between two Points on a Sphere (Great Circle Arc) using degrees, minutes and seconds verses decimal degrees.
• Rhumb Line Azimuth: Computes the azimuth heading one can navigate for a path that crosses all meridians of longitude at a constant angle.
• Rhumb Line Distance: Computes the distance traveled between two points on the globe if traveled via a rhumb line.
• Travel Time between Coordinates: Compute the time to travel between two location (latitudes and longitudes) based on a average speed.
• Navigation Speed: Computes the required average speed needed to go between coordinates on a great circle arc within a given amount of time.
• Distance to Sea Level Horizon: Computes the distance to the sea horizon at an altitude
• Correction Angle: navigation equation that compensates for air or water currents.
• Distance to Sea Level Horizon: Compute the distance to the horizon based on a height above the orb using a spherical Earth model.
• Decimal Degrees: Compute decimal degree angles from degrees, minutes and seconds,[CLICK HERE].