Map Projections

• Problem: Project a sphere onto a flat surface.

• Scale

• Alternative projection methods

• Distortions

• Terminology of map projections

Maps - Resource A

Properties of the Globe Grid

• All meridians are of equal length; each is one-half the length of the equator.

• All meridians converge at the poles and are true north-south lines.

• All lines of latitude (parallels) are parallel to the equator and to each other.

• Parallels decrease in length as one nears the poles.

• Meridians and parallels intersect at right angles.

• The scale on the surface of the globe is the same in every direction.

Map Projections - Resource A

Geometrical (Perspective) Projections

• Graticule transferred to geometric shape and then the shape is cut and flattened.

• Developable surfaces

Map Projections - Resource A

Projection Classes

• Cylindrical

• Conic

• Planar (Azimuthal)

• Oval or Elliptical

Map Projections - Resource A

Map Projections - Resource A

Orthographic

• light source at infinity

Gnomonic

• light source at center

Stereographic

• light source at antipode.

Map Projections - Resource A

Mathematical Projections

• Emphasize and preserve elements of globe grid that perspective projections cannot.

Map Distortions of the Globe Grid Properties

• Equal Area (equivalent) - Preserves proportionate size but distorts shape.

• Shape (conformal) - Preserves true shape and directionality for small areas.

• Only maps for small areas can preserve both conformality and equivalence.

Map Distortions of the Globe Grid Properties (cont.)

• Distance (equidistant) - Correctly represent true great arc distances for one or two points on map. Distances between other points are distorted.

• Direction (azimuthal) - Preserve directionality radiating from one central point.

Gnomonic projection centered on Washington, DC. Great circle arcs are straight lines.

Map Projections - Resource A

Gnomonic

Examples Equal area sinusoidal

Azimuthal equidistant

Mercator (conformal)

Map Projections - Resource A

Examples Miller (cylindrical)

Albers equal area (conic)

Azimuthal Equidistant (planar)

Robinson Projection (oval)

Map Projections - Resource A