A map projection is a systematic transformation of the Earth’s three-dimensional, curved surface onto a two-dimensional, flat plane. This process translates geographic coordinates (latitude and longitude) from the spherical model into planar Cartesian (x/y) coordinates used to create a map. The projection is a mathematical formula that dictates the exact position of every point on the resulting flat surface, making the Earth’s geography portable and practical for cartography.
Why Flat Maps Require Projection
The Earth is a sphere with constant curvature, while a flat map is a plane with zero curvature. Converting a curved surface into a flat one without stretching or compressing the material is a fundamental geometric challenge, often visualized by the difficulty of flattening an orange peel. Map projections are necessary because a globe is impractical for many applications, such as folding or measuring small distances. The transformation relies on complex mathematics to account for the geometric conflict. Every projection is a deliberate compromise, choosing which geometric properties to preserve and which to distort. The mathematics ensures the nature and magnitude of the distortion are known and predictable.
Classification by Physical Form
Map projections are broadly categorized into three families based on the geometric “developable surface” used to conceptualize the transfer of data from the globe. These three primary forms are the cylinder, the cone, and the plane. Each form is conceptually placed around the globe, and the Earth’s features are projected onto it before the form is unrolled or flattened.
Cylindrical Projections
The Cylindrical family is generated by wrapping a cylinder around the globe, typically touching the Earth along the equator. When unrolled, the resulting map is rectangular, with lines of latitude and longitude intersecting at right angles. This configuration is widely used for world maps because it can display the entire surface, although distortion increases significantly away from the equator.
Conical Projections
Conical projections are created by placing a cone over the globe, often tangent to a single line of latitude (the standard parallel). When flattened, the parallels appear as concentric circular arcs, and the meridians radiate outward from the apex. This form is effective for mapping mid-latitude regions with a greater east-west extent, as distortion is minimal along the standard parallel.
Azimuthal Projections
The Azimuthal, or Planar, family is formed by projecting the globe’s features onto a flat plane that touches the Earth at a single point, such as the North Pole or the equator. Distortion increases outward from this central point in a radiating pattern. Azimuthal projections are commonly used for maps focusing on a single hemisphere or for specialized mapping of polar regions.
The developable surface can be tangent, touching the globe at a single point or line, or secant, intersecting the globe along two lines. Distortion is lowest precisely along these lines of contact, where the map scale is true. Distortion systematically increases proportionally with the distance away from these lines of zero distortion.
Understanding the Four Types of Distortion
The geometric conflict between a sphere and a plane necessitates that every map projection sacrifices the accuracy of some spatial properties to preserve others. Cartographers focus on four specific properties subject to distortion when moving from three to two dimensions. No projection can perfectly preserve all four properties simultaneously, forcing a trade-off based on the map’s purpose.
Shape
The first property is Shape, preserved by a conformal projection. These projections maintain the accurate local shape and angles of small areas, meaning that coastlines appear recognizable. However, this preservation severely compromises area, leading to an extreme exaggeration of size away from the center. A well-known example is the Mercator projection, where Greenland appears much larger than its true size relative to Africa.
Area
The second property is Area, preserved by an equal-area projection. On these maps, the relative size of all geographic features is maintained. Equal-area maps are mandatory for displaying statistical data, such as population density, to prevent visual misrepresentation. The cost of preserving area is the distortion of shape, causing landmasses to appear stretched or compressed near the map’s margins.
Distance
Distance preservation defines an equidistant projection, which maintains true scale and distance measurements, but only from one or two specified central points to all other points. The distance between two random points that do not involve the center point will generally be inaccurate. These projections are useful for applications focused on travel or communication radiating from a single origin, such as mapping airline routes from a central hub.
Direction
The final property is Direction, which is accurately shown by an azimuthal projection from a central point to any other point on the map. This allows for the correct plotting of true compass bearings. The true direction property is especially useful for long-distance navigation, as it aids in following great circle routes, which represent the shortest path between two points on the globe.
Projections and Their Purpose
The selection of a map projection is a deliberate, purpose-driven choice connected to the map’s intended application. For marine and air navigation, a conformal projection like the Mercator is chosen because it preserves local angles and true compass bearings. This allows navigators to follow a rhumb line (constant compass direction) as a straight line on the map.
When the goal is to visualize and compare statistical data, such as population density, an equal-area projection is necessary. This ensures the visual representation of relative sizes is accurate, preventing misinterpretation. Specialized mapping, including planning polar air routes, also relies on the direction-preserving qualities of azimuthal projections to accurately represent the shortest path between distant points.