# Hammer

## Description

The Hammer projection is a modification of the Lambert azimuthal equal-area projection. It is an equal-area projection and its graticule takes a form of an ellipse. The projection is also known as the Hammer-Aitoff projection. The Hammer projection is appropriate for small-scale mapping.

The Hammer projection was developed by Ernst von Hammer in 1892 after being inspired by the Russian cartographer, David A. Aitoff. Equations for an ellipsoid were developed at Esri. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.1.1 and later.

## Projection properties

The subsections below describe the Hammer projection properties.

### Graticule

Hammer is a modified azimuthal projection. The central meridian is a straight line, half the length of the projected equator. The other meridians are complex curves, concave toward the central meridian and unequally spaced along the equator. The equator is a straight line. All other parallels are complex curves, concave toward the nearest pole and unequally spaced along the central meridian. The projection outline forms a shape of an ellipse. Poles are presented as points and they are co-vertices of the ellipse (on the minor axis). The graticule is symmetric across the equator and the central meridian.

### Distortion

Hammer is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are generally distorted. Land features near the projection's outline are skewed. Scale decreases along the equator and central meridian as distance from the origin increases. Areas near the poles are less sheared than on some pseudocylindrical projections. Distortion values are symmetric across the equator and the central meridian.

## Usage

The Hammer projection is appropriate for small-scale mapping, especially for thematic world maps illustrating area characteristics and analysis requiring accurate areas. The Hammer ellipsoidal variant is recommended for world maps centered on other latitudes besides the equator. An example of such an oblique aspect is the Briesemeister projection.

## Variants

There are two variants of the Hammer projection available in ArcGIS:

• Hammer-Aitoff is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.1.1 and later.
• Hammer ellipsoidal is available in ArcGIS Pro 1.2 and later and in ArcGIS Desktop 10.4 and later.

The Hammer ellipsoidal version supports projection for ellipsoids, while Hammer-Aitoff uses the semimajor axis for the radius and equations for a sphere. Both implementations support sphere-based Earth models.

## Limitations

Only the Hammer ellipsoidal version correctly projects an ellipsoid of revolution. The Hammer-Aitoff version does not maintain areas when using ellipsoids.

## Parameters

Hammer-Aitoff parameters are as follows:

• False Easting
• False Northing
• Central Meridian

Hammer ellipsoidal parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Latitude Of Origin

## Sources

Bugayevskiy, L. M. and Snyder, J. P. (1995). Map Projections: A Reference Manual. London: Taylor & Francis.

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.

Yang, Q., Snyder, J. P. and Tobler, W. R. (2000). Map Projection Transformation: Principles and Applications. London: Taylor & Francis Group.