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Differential Equation of a Loxodrome on a Sphere

Published online by Cambridge University Press:  01 September 1999

Sergio Kos ,
Duško Vranić  and
Damir Zec
Sergio Kos
Affiliation:
Rijeka College of Maritime Studies, Croatia
Duško Vranić
Affiliation:
Rijeka College of Maritime Studies, Croatia
Damir Zec
Affiliation:
Rijeka College of Maritime Studies, Croatia
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Abstract

A curve that cuts all meridians of a rotating surface at the same angle is called a loxodrome. If the shape of the Earth is approximated by a sphere, then the loxodrome is a logarithmic spiral that cuts all meridians at the same angle and asymptotically approaches the Earth's poles but never meets them. Since maritime surface navigation defines the course as the angle between the current meridian and the longitudinal direction of the ship, it may be concluded that the loxodrome is the curve of the constant course, which means that whenever navigating on an unchanging course we are navigating according to a loxodrome.

Type
Forum
Information
The Journal of Navigation , Volume 52 , Issue 3 , September 1999 , pp. 418 - 420
Copyright
© 1999 The Royal Institute of Navigation

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