Winkel Tripel projection

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A Winkel Tripel projection of the Earth
A Winkel Tripel projection of the Earth

The Winkel tripel projection is a modified azimuthal map projection, one of three projections proposed by Oswald Winkel in 1921. The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection[1]:

(\lambda, \phi) \mapsto \left(\frac{\lambda \cos \phi_1 + 2 B \cos \phi \sin {\frac{\lambda}{2}}}{2} , \frac{\phi + B \sin \phi}{2}\right)

where \lambda\, is the longitude from the central meridian of the projection, \phi\, is the latitude, and \phi_1\, is the standard parallel for the equi-rectangular projection, and

B = \frac{\alpha}{\sin \alpha}\,

where

\alpha = \arccos (\cos \phi \cos {\frac{\lambda}{2}})\,

noting that when \alpha = 0\, then B is explicitly defined to be 1. In his proposal, Winkel set :

\phi_1 = \arccos {\frac{2}{\pi}}\,.

In 1998, the Winkel Tripel projection replaced the Robinson projection as the standard projection for world maps made by the National Geographic Society.

  1. ^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp.231-232, ISBN 0-226-76747-7.

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