Mercator

Description

Originally created to display accurate compass bearings for sea travel, an additional feature of this projection is that all local shapes are accurate and clearly defined. A sphere-based version of Mercator is used by several web mapping sites. The sphere's radius is equal to the WGS 1984 semimajor axis, 6378137.0 meters. Two methods exist for emulating the Mercator projection used by the web services. If the Mercator implementation supports spheroids (ellipsoids), the projected coordinate system must be based on a sphere-based geographic coordinate system. This will force the use of sphere equations. The implementation of Mercator auxiliary sphere has sphere equations only. In addition, it has a projection parameter that identifies what to use for the sphere radius if the geographic coordinate system is ellipsoidal based. The default value of zero (0) uses the semimajor axis.

Projection method

This is a cylindrical projection. Meridians are parallel to each other and equally spaced. The lines of latitude are also parallel but become farther apart toward the poles. The poles cannot be shown.

Lines of contact

The equator or two latitudes symmetrical around the equator

Linear graticules

All meridians and all parallels

Properties

Shape

This projection's shape is conformal. Small shapes are well represented because this projection maintains the local angular relationships.

Area

Area is increasingly distorted toward the polar regions. For example, although Greenland is only one-eighth the size of South America, Greenland appears to be larger in the Mercator projection.

Direction

Any straight line drawn on this projection represents an actual compass bearing. These true direction lines are rhumb lines and generally do not describe the shortest distance between points.

Distance

Scale is true along the equator or along the secant latitudes.

Limitations

The poles cannot be represented on the Mercator projection. All meridians can be projected, but the upper and lower limits of latitude are approximately 80° N and S. Large area distortion makes the Mercator projection unsuitable for general geographic world maps.

Uses and applications

• Standard sea navigation charts (direction)
• Other directional uses: air travel, wind direction, ocean currents
• Conformal world maps

The best use of this projection's conformal properties applies to regions near the equator such as Indonesia and parts of the Pacific Ocean.

Parameters

Desktop

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

Mercator auxiliary sphere (ArcGIS 9.3 and later)

• False Easting
• False Northing
• Central Meridian
• Standard Parallel 1
• Auxiliary Sphere Type

Note:

The Auxiliary Sphere Type parameter accepts 0 (use semimajor axis or radius of the geographic coordinate system), 1 (use semiminor axis or radius), 2 (calculate and use authalic radius), or 3 (use authalic radius and convert geodetic latitudes to authalic latitudes).

Workstation

• Longitude of Central Meridian
• Latitude of true scale
• False Easting (meters)
• False Northing (meters)