Orthodromic navigation

Orthodromic course drawn on the earth globe.

The orthodromic navigation (related to orthodromic course; from the Greek ορtóς, right angle, and δρóμος, path) is a way to navigate following an arc of great circle corresponding to the shortest distance between two points on the globe.^[1]

Since the Earth is roughly a sphere, the orthodromic distance of the is often used by mariners to find the distance between two coordinates (knowing its longitude and its latitude) on a map, and the course to be taken to go from one to the other.

Calculation

$\operatorname{gc}(\delta, \lambda, \delta', \lambda') =2R \arcsin\sqrt{\sin^2{\left(\frac{\delta' - \delta}{2}\right)} + \cos{\delta} \cdot \cos{\delta'} \cdot \sin^2{\left(\frac{\lambda' - \lambda}{2}\right)}\ }$

$R \,$ is the radius of the earth $\approx$ 6.367.000 meter).

$\delta \,$ is the latitud (in radians).

$\lambda \,$ is the longitude (in radians).

$gc \,$is the great circle arc, the shortest path between two points on the earth's globe

Comparison Chart

Comparison, of orthodromic course (white) compared with a loxodromic course (red).

See also

• Loxodromic navigation.
• Windrose network.
• Map
• Portolan map
• Marine sandglass
• Compass rose
• Isoazimuthal

References

1. Adam Weintrit; Tomasz Neumann (7 June 2011). Methods and Algorithms in Navigation: Marine Navigation and Safety of Sea Transportation. CRC Press. pp. 139–. ISBN 978-0-415-69114-7.

• http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=6233256

External links

• assistance program for orthodromic navigation