Mercator: preserving angles, distorting size

Flattening Earth’s curved surface requires a projection. No global transformation preserves all areas, distances, shapes and directions simultaneously.

Mercator preserves angles locally and represents meridians and parallels as perpendicular straight lines. To achieve that relationship, parallel spacing increases towards the poles.

The grid looks simple, but scale is no longer uniform with latitude.

On Mercator, a line of constant bearing relative to north—a rhumb line—appears straight. That geometrical property is useful for representing courses.

On a sphere, the shorter great-circle arc between two points provides the shortest surface distance. Except in particular cases, it differs from the rhumb line.

A projection property is not a recommendation for selecting a sea route.

Enlargement increases northwards or southwards from the equator. In the spherical model normalised to equatorial scale, the local factor is 1/cos φ.

At latitude 60°, cos 60° = 0.5, giving a factor of 2: a small dimension appears twice as large as at equatorial scale. Physical distance has not doubled.

Real charts declare their reference scale and model; the figure shows the ideal relationship only.

The projection cannot represent the poles at a finite distance. Nor should Mercator be explained as a photograph made by a lamp at a globe’s centre: it is a mathematical transformation.

Understanding these compromises makes grid and scale legible without giving the chart capabilities its geometry cannot provide. Distance measurement uses a scale appropriate to the segment, developed in the next lesson.

Meridian spacing on the flat grid is uniform, while physical spacing on Earth decreases with latitude. Preserving local angular relationships requires enlargement in the north–south dimension too.

This explains why parallels cannot be equally spaced on Mercator. A small teaching square retains recognisable sides and angles, but its size relative to another distant square changes.

Local conformity does not remove the need to interpret every angle between distant connections. Projection acts point by point; a long line can pass through different scales.

Other projections suit different contexts, including polar regions. Projection choice responds to area and intended use.

Identifying “Mercator” supplies a specific geometrical property rather than universal superiority over other maps.