What is a loxodromic measure used for?

A loxodromic measure, also known as a rhumb line, is specifically used for navigating by maintaining a constant angle with the meridians of the Earth. This means that if you were to plot a course on a globe or a map representing the Earth's surface, a loxodromic path would allow a navigator to travel in a straight line while adhering to a set bearing. This concept is crucial in maritime and aerial navigation, where it's often necessary to follow a fixed compass direction over long distances.

In contrast, calculating distances on a flat map involves different geometric principles, typically relying on Euclidean distance rather than accounting for the curvature of the Earth that loxodromic measures consider. For measuring the shortest distance between two points, the geodesic approach is more appropriate, which is based on the arc of a great circle, offering the shortest path over the Earth's surface. Finally, defining the shape of the Earth relates to geodesic studies and models like the ellipsoid, rather than navigation along lines of constant bearing.

Understanding the application of a loxodromic measure is vital for anyone involved in navigation and route planning, emphasizing its importance in maritime and aviation contexts.