Calculation

Calculating distances between two points on the surface of a sphere

Airline distance calculation

Vincenty's formulae, the Haversine formula, and the Great-circle distance method are three different approaches to calculating distances between two points on the surface of a sphere, commonly used for measuring distances on the Earth.

Vincenty's Formulae

• Accuracy: Vincenty's formulae are known for their higher accuracy compared to the Haversine formula, especially for long distances and over ellipsoidal surfaces.

• Applicability: Vincenty's formulae are suitable for calculating distances on an ellipsoidal Earth model, making them more precise for geodetic calculations.

• Complexity: These formulae are more complex mathematically than the Haversine formula.

Haversine Formula

• Simplicity: The Haversine formula is simpler and computationally less intensive than Vincenty's formulae, making it easier to implement.

• Accuracy: While accurate for short distances, the Haversine formula may exhibit limitations for long distances, as it assumes a spherical Earth model and does not account for the Earth's ellipsoidal shape.

• Popular Use: The Haversine formula is commonly used in applications where simplicity and speed are prioritized over extreme precision, such as in web and mobile applications.

Great-circle Distance Method

• Concept: The Great-circle distance method calculates the shortest distance between two points on the surface of a sphere, traveling along the surface of the sphere.

• Accuracy: It provides good accuracy for most practical purposes, especially for shorter distances.

• Applicability: The Great-circle distance method assumes a spherical Earth model, which simplifies calculations. It is suitable for applications where a balance between accuracy and computational efficiency is required.

In summary, the choice between Vincenty's formulae, the Haversine formula, and the Great-circle distance method depends on the specific requirements of the application. Vincenty's formulae are preferred for high-precision geodetic calculations, the Haversine formula is suitable for simpler applications with moderate accuracy needs, and the Great-circle distance method strikes a balance between accuracy and computational efficiency.