Hölzel projection

World map in Hölzel projection

The Hölzel projection , also known as the Hölzel planisphere , is one from the Viennese publisher Ed. Hölzel developed sinusoidal pseudo-cylindrical map projection . It was first used for the Kozenn Atlas of 1951 and is still widespread in Austria today.

properties

The projection is a map network design with parallel, equally spaced degrees of latitude of unequal length , with the poles being shown in the form of a polar line . The longitudes are shown as sine curves up to a latitude of 80 ° , and further north as an ellipsoid to the pole. It is neither conformal (conformal) nor equal area , and no point of the card is free of distortion.

The projection is a variant of the Eckert V projection , with which it shares other properties.

calculation

The Eckert V projection is basically the arithmetic mean of a sinusoidal projection and a flat map . For the Hölzel projection, the dimensions are slightly changed and the poles modified, which avoids the edge at the transition to the pole line.

If the radius of a sphere (whose surface serves as a model for the earth's surface), the central meridian and a point with the polar coordinates are given, the coordinates and the image point on the map can be calculated using the following formulas: ${\displaystyle R}$ ${\displaystyle \lambda _{0}}$ ${\displaystyle (\varphi ,\lambda )}$ ${\displaystyle x}$ ${\displaystyle y}$

${\displaystyle x=R(\lambda -\lambda _{0}){\begin{cases}{0},441013\,(1+\cos {\varphi }),&{\text{wenn }}|\varphi |<{1},39634,\\{0},322673+{0},369722\,{\sqrt {1-\left({\frac {|\varphi |-{0},40928}{{1},161517}}\right)^{2}}},&{\text{andernfalls}},\end{cases}}}$

${\displaystyle y=\varphi }$.

use

Human development index (UN prosperity indicator), on a Hölzel planisphere

The Hölzel projection is only useful for a world map . It adopts the harmonious arrangement of the land masses in the Eckert projection (first published in 1909). Its smallest deviations are around the middle latitudes, so it is suitable to relate these to the total surface. The equidistant parallel latitudes are particularly suitable for zone models, for example for climatological, biological and similar thematic maps, but the well-proportioned land areas according to Eckert are also suitable for numerous other specialist topics.

The map design was first used for the Austrian Middle School Atlas (Kozenn School Atlas) , published in 1951 , and is still the standard network for world maps from Ed. Hölzel. In the classic format of the school atlas, 22.5 × 31.5 cm or currently 23.5 × 32.5 cm, the projection is full-length, with the equatorial ends slightly trimmed on both sides.

Web links

Commons : Maps with Hölzel projection  - collection of images, videos and audio files

• Hölzel projection , detailed map network, on csiss.org.

Individual evidence

1. ↑ ^{a b} 1951 | A new beginning after the Second World War ( Memento of the original from February 7, 2015 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. , hoelzel.at → Large Kozenn Atlas .  
2. ^ John P. Snyder: An Album of Map Projections . USGS Professional Paper 1453. Denver 1989, ISBN 0-226-76747-7 , pp. 46 f . ( Web link to pdf , usgs.gov [accessed February 11, 2015]).
3. ↑ Gerald I. Evenden: libproj4: A Comprehensive Library of Cartographic Projection Functions. (Preliminary Draft), March 2005, 5.2.15, p. 58 ( pdf , maptools.org, accessed February 10, 2015).
4. ↑ In 1943 Mercator had switched to Mollweide. 1943 | From Austria to Ostmark and back ( Memento of the original from February 7, 2015 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , hoelzel.at.  
5. ↑ cf. about screenshot from the Geothek-school atlas on CD in 2011 (jpg, hoelzel.at).