# Winkel I

## Description

The Winkel I is a compromise pseudocylindrical map projection for world maps. It is an arithmetic mean of projected coordinates of sinusoidal and equidistant cylindrical projections and a general case of the Eckert V projection. The meridians are sinusoidal curves, producing undesirable bulging along the equator on the west and east edges of the map.

The projection was introduced by Oswald Winkel in 1914. In his original design, Winkel used a standard parallel at 50°28ʹ. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.

## Projection properties

The subsections below describe the Winkel I projection properties.

### Graticule

Winkel I is a pseudocylindric projection. The equator and the central meridian are projected as straight lines. The other meridians are sinusoidal curves, bulging away the central meridian and equally spaced. The parallels are equally distributed straight lines perpendicular to the central meridian. The poles project as straight lines. The lengths of the central meridian and both pole lines depend on the value of the standard parallel. The graticule is always symmetric across the equator and the central meridian.

### Distortion

The Winkel I projection is neither conformal nor equal-area. It generally distorts shapes, areas, distances, directions, and angles. The scale is constant along any given parallel and it is true along the standard parallel. The high latitude areas are exaggerated. Bulging meridians produce considerable distortion toward the edges of the projection. The distortion values are symmetric across the equator and the central meridian.

## Usage

Winkel I projection is appropriate for general world maps although its use is not advisable.

## Limitations

Winkel I is supported on spheres only. For an ellipsoid, the semimajor axis is used for the radius.

## Parameters

Winkel I parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Standard Parallel 1

### Particular parameter cases

When the standard parallel is set at the equator, the result is the Eckert V map projection.

## Sources

Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.