Cylindrical projection
The term "cylindrical projection" is used to refer to any projection in which the ruled surface used to draw the map is a cylinder. In which the meridians are mapped to equally spaced vertical lines and circles of latitude (parallels) are mapped to horizontal lines (or, mutatis mutandis, more generally, radial lines from a fixed point are mapped to equally spaced parallel lines and concentric circles around it are mapped to perpendicular lines). Cylindrical projections are commonly used for world maps, regions bordering the equator, and regions that are predominantly north-south in extent.[1]
The mapping of meridians to vertical lines can be visualized by imagining a cylinder (of which the axis coincides with the Earth's axis of rotation) wrapped around the Earth and then projecting onto the cylinder, and subsequently unfolding the cylinder.
Types of Cylindrical Projections
By the geometry of their construction, cylindrical projections stretch distances east-west. The amount of stretch is given by the secant of the latitude as a multiple of the equator's scale. The various cylindrical projections are distinguished from each other solely by their north-south stretching (where latitude is given by φ):
- North-south stretching is equal to the east-west stretching (secant φ): The east-west scale matches the north-south scale: conformal cylindrical or Mercator; this distorts areas excessively in high latitudes (see also transverse Mercator).
- North-south stretching growing rapidly with latitude, even faster than east-west stretching (secant² φ: The cylindric perspective (= central cylindrical) projection; unsuitable because distortion is even worse than in the Mercator projection.
- North-south stretching grows with latitude, but less quickly than the east-west stretching: such as the Miller cylindrical projection (secant[4φ/5]).
- North-south distances neither stretched nor compressed (1): equidistant cylindrical or plate carrée.
- North-south compression precisely the reciprocal of east-west stretching (cosine φ): equal-area cylindrical (with many named specializations such as Gall-Peters projection or Gall orthographic, Behrmann, and Lambert cylindrical equal-area). This divides north-south distances by a factor equal to the secant of the latitude, preserving area but heavily distorting shapes.
In the first case (Mercator), the east-west scale always equals the north-south scale. In the second case (central cylindrical), the north-south scale exceeds the east-west scale everywhere away from the equator. Each remaining case has a pair of identical latitudes of opposite sign (or else the equator) at which the east-west scale matches the north-south-scale.
Cylindrical projections map the whole Earth as a finite rectangle, except in the first two cases, where the rectangle stretches infinitely tall while retaining constant width. This causes a distortion in the northern and southern parts of the map, making it appear as if the area of the land in those regions is larger than it actually is. For this reason, while cylindrical map projections are useful in mapping comparisons at similar latitudes, they should not be used for comparing things at different latitudes as they would not be projected on the same scale and thus provide inaccurate information.
