|Winkel Tripel Graphics|
|Winkel Tripel superimposed over Robinson||Tissot Indicatrix||Superimposed Icosahedron|
|Lines of Equal
|Lines of Equal
"Area Scale Factors"
|Winkel's "Oikumene" (MicroCAM)||Color Shaded Relief (Geocart)||Color Relief (ETOPO5 Data)|
|B&W Outline Map (Political Boundaries) - 578K GIF (P. Voxland's World)|
In 1998 the NGS decided to change from the Robinson (bottom of page) to the Winkel Tripel projection (above) on their
World Reference Map. An internet site that discusses the change is:
The Winkel Tripel was the last of three projections developed by Oswald Winkel in 1921. John Parr Snyder refers to it as a modified Azimuthal, however, by using L. P. Lee's definitions [Lee_1944.pdf] the Tripel can also be classified as a Polyconic. It is neither conformal nor equal-area. On this projection the percentage of area distortion is less than the degrees of angular distortion. The Tripel is constructed by averaging the X then the Y outputs of the Aitoff and Equirectangular projection formulas. Winkel chose 50 degrees 28 minutes North & South as the standard parallels for the Equirectangular portion.
The formulas and paraphrased text (in Spanish) for the Winkel Tripel as presented on page 57 of "The World in Perspective" by Frank Canters and Hugo Decleir (1989) can be found at this UniversitÓria PolitŔcnica Barcelona site.
John Bartholomew [& Son, Ltd.] was the first to use the Winkel Tripel in an atlas: "The Times Atlas of the World - Mid-Century Edition" (5 volumes) 1955-60. Bartholomew still uses it for the major thematic maps and smaller inset maps in the "Times Atlas of the World - Comprehensive Edition" 1967-1997 and in various editions of the "Reader's Digest Great World Atlas" from 1961. The Bartholomew version uses 40 degrees North & South as the Equirectangular's standard parallels. The Bartholomew version superimposed over the NGS version.
The National Geographic Society has recently produced a map of Mars in the Winkel Tripel projection: http://ltpwww.gsfc.nasa.gov/tharsis/ngs.html
Dr. Fritz Kessler has written a computer program that plots the Winkel Tripel on a computer display. You can find both the program and its Visual Basic source code at his personal web site:
In 1921 Oswald Winkel wrote an article describing the Tripel and his other projections entitled Neue Gradnetzkombinationen: Petermanns Mitteilungen, v. 67, Dec., p. 248-252.
In addition to the above, Albert H. Christensen has provided scans of later articles [in German] about the Winkel Tripel. They will appear here soon.
The Microcomputer Specialty Group of the Association of American Geographers is now offering MicroCAM, polyline data from the CIA's 1995 Relational World Data Bank II, and other smaller databases/ utilities on CD for $20.00 (US). Profits from the sale of this CD will be used to support various AAG scholarships.
MicroCAM (Link at bottom of page) now has the capability of plotting the Winkel Tripel projection.
The NGS began providing FREE copies of their World Reference Map in the Winkel Tripel projection to schools around the USA [NGS Press release]. Political, satellite [NASA/JPL Press release], and physical versions, in 3 sizes, will be offered for sale by October 1998.
Bugayevskiy, L.M., and Snyder, J.P., 1995, Map projections - a reference manual:
London, Taylor & Francis, 328 p. [An extensive revision in English of Bugayevskiy and
Vakhrameyeva, 1992, Kartograficheskiye proyektsii.]
Snyder, J.P., and Voxland, P.M., 1989, An album of map projections: U.S. Geological Survey Prof. Paper 1453, 249 p. Reprinted 1994 with corrections. [Graticules for 90 projections, with brief descriptions and formulas.]
Snyder, J.P., 1993, Flattening the Earth - two thousand years of map projections: Chicago, University of Chicago Press. 365 p.
The color shaded relief map is courtesy of Daan Strebe. Mapthematics is where you can find Daan's Geocart map projection software for the Macintosh. He was also a consultant to the NGS on their change to the Winkel Tripel.
The black & white outline map with political boundaries was produced with Philip M. Voxland's "World". This DOS based program is capable of producing both raster and vector base maps in a large variety of different map projections.
The rest of the graphics were developed from software written by Paul Bryan Anderson. The small scale mapping database used, "MWDB-POLY", can be downloaded from the "MicroCAM for Windows" link at the bottom of this page.
- Revised Mar, 2001 by Paul Bryan Anderson -