# Transverse cylindrical equal-area

## Description

The transverse cylindrical equal-area is a transverse aspect of the cylindrical equal-area projection. This projection is appropriate for maps with a predominantly north-to-south extent along a specified meridian.

The transverse cylindrical equal-area projection was presented by Johann H. Lambert in 1772. Equations for an ellipsoid of revolution were developed by John P. Snyder in 1985. It is available in ArcGIS Pro 1.3 and later and in ArcGIS Desktop 10.4.1 and later.

## Projection properties

The subsections below describe the transverse cylindrical equal-area projection properties.

### Graticule

The transverse cylindrical equal-area projection is transverse cylindric. The central meridian and antimeridian lines are presented as one vertical line in the middle of the projection.

Northern parts of meridians 90° away from the central meridian project as a horizontal straight line through the North Pole. Similarly, southern parts of those meridians are projected as a horizontal line though the South Pole. Other meridians project as complex curves that perpendicularly intersect with the equator.

The equator is split into two parts. The first part, which contains meridians within 90° of the central meridian, projects as a horizontal straight line in the middle of the map, splitting the projected area into two (north and south) hemispheres. The second part of the equator is projected as two straight lines at the top and bottom of the map.

Other parallels are complex curves. Both poles are projected as points, each being in the center of its hemisphere. Two points on the equator, exactly 90° away from the central meridian, project as straight vertical lines, representing the left and right edge of the projection. On ellipsoids of revolution, these two lines are curved, convex toward each pole.

### Distortion

This is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are distorted. Scale is true along the projected central meridian and antimeridian. Shapes near 90° away from the central meridian are extremely distorted and stretched vertically. If the scale factor is less than 1, the line of true scale is somewhere between the central meridian and the edge of the projection and the map is less vertically elongated.

## Usage

The transverse cylindrical equal-area projection is appropriate for large-scale maps with predominant north-south extents.

## Parameters

Transverse cylindrical equal-area parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Scale Factor
• Latitude Of Center

## Sources

Snyder, J. P. (1985). "The Transverse and Oblique Cylindrical Equal-Area Projection for the Ellipsoid." Annals of the Association of American Geographers, 75 (3), p. 431-442.

Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.

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.