Great Circle and Rhumb Line Navigation

Great Circle and Rhumb Line Tracks

• Great Circle Track: The shortest distance between two points on the Earth's surface, following a curve along the sphere's surface.
• Rhumb Line Track: A line of constant true bearing, cutting meridians at a constant angle.
• Convergency: The angular difference between meridians at a given latitude, crucial for navigation; greater using rhumb lines than great circles.
• Formula for Convergency: Convergency = dlong * cos(mean latitude), where dlong is the difference in longitude between the two meridians and mean latitude is the average of latitudes.
• Shortest Distance: A great circle track is the shortest distance between two points on the Earth's surface.
• Latitude Difference: Calculated by subtracting the smaller latitude from the larger latitude.

Convergency Calculations

• Convergency Example: At 50°N latitude, the convergency between 10°W and 14°W meridians is approximately 30.6°. This is crucial for navigation.
• Relationship between Track and Convergency: The turning rate of a great circle track from one point to another changes as a function of convergency and latitude.

Positional Considerations

• Positional Changes: The great circle track from one position to another may change more in magnitude (increase or decrease) depending on latitude. This is an important concept in navigation; for example, the great circle track at A may increase by 3 degrees compared to the one at B.
• Turning Angle: The turning angle differs between great circle and rhumb line paths.

Earth's Shape

• Earth's Shape: The Earth is an oblate spheroid, slightly flattened at the poles and bulging at the equator.
• Equatorial Diameter: The equatorial diameter is greater than the polar diameter.

Rhumb Line Track and Great Circle Track

• Conversion angle: The conversion angle accounts for the fact that true course may be different in relation to the rhumb line or great circle tracks. Note: conversion angle = 0.5 convergency.
• Maintaining Constant True Course: To maintain a constant true course, a rhumb line must be followed. A great circle track will result in varying true courses.
• Rhumb Line and Final Position: An aircraft following a series of rhumb line segments will return to its initial position; if a great circle track is followed, it will not.

Meridians

• Direction of Meridians: Meridians run north-south (true direction) on both hemispheres.
• Constant Distance Between Meridians: The distance between meridians varies with latitude—greater at the equator, smaller at the poles.

Great Circle Track Calculations

• Calculating Initial Great Circle Track: Methods for determining the initial great circle track are important for accurate navigation, such as using formulas or tools.
• Example: Initial Great Circle Track: An example illustrating determination of the initial great-circle track between specific locations at latitude and longitude, considering both the northern and southern hemispheres. This process is crucial for accurate navigation.