COMMON MAP PROJECTIONS Equal Area Projections Property of equal area commands high priority on most maps used as small scale general reference maps and for instruction Choice of equal area projection depends on these two considerations: Size of the region to be mapped Distribution of the angular deformation (shape considerations)

COMMON MAP PROJECTIONS Equal Area Figure 5.B.4 A few of the many equivalent world map projections. (A) cylindrical equal-area with standard parallels at 30° N and S latitude; (B) sinusoidal projection; and (C) Mollweide’s projection. The black lines are values of 2Ω. From Robinson, Sixth Edition, page 72

COMMON MAP PROJECTIONS Equal Area Albers’ Conic projection with two standard parallels Any two small circles, reasonably close together are used Low distortion, especially along parallels Resembles earth’s graticule – curved parallels, converging meridians Best for mid-latitude areas with greater east-west extension than north-south Standard for many US Government base maps, including Census Bureau

COMMON MAP PROJECTIONS Equal Area – Albers’ From Robinson, Sixth Edition, page 81

COMMON MAP PROJECTIONS Equal Area Lambert’s Azimuthal as well as equivalent Distortion symmetrical around a single point Point can be located anywhere on globe Good for areas that have nearly equal east-west vs. north-south extension, such as some individual states

COMMON MAP PROJECTIONS Equal Area Cylindrical Two standard parallels which may ‘coincide’ at the equator, but otherwise must be “homolatitudes” Distortion arranged parallel to standard small circles When parallels are chosen at 30°, this projection provides the least overall mean angular distortion of any equal area world projection

COMMON MAP PROJECTIONS Equal Area Sinusoidal Conventionally has straight central meridian and equator; no angular distortion along either Illusion of proper spacing useful when latitudinal relations are important Particularly suitable, when properly centered, for maps of less-than-world areas - - - South America

COMMON MAP PROJECTIONS Equal Area - Sinusoidal From Robinson, Sixth Edition, page 68

COMMON MAP PROJECTIONS Equal Area Mollweid’s Appears more realistic than sinusoidal North-south decreased in high latitudes and increased in mid-latitudes East-west scale increased in high latitudes and decreased in mid-latitudes Two areas of least distortion are in the mid-latitudes, so projection is most useful for those areas

COMMON MAP PROJECTIONS Equal Area Goode’s Homolosine Combines equatorial section of sinusoidal and poleward sections of Mollweid’s Must be constructed from the same area scale (ie. reference globe) Sinusoidal and Mollweid’s have one parallel of identical length along which they may be joined Usually used in interrupted form Popular in the United States

COMMON MAP PROJECTIONS Equal Area – Goode’s Homolosine From Robinson, Sixth Edition, page 81

COMMON MAP PROJECTIONS Azimuthal Projections (preserve direction) Projected on a plane that centered anywhere on the reference globe Line perpendicular to plane passes through center of globe Distortion is symmetrical around the center point; peripheral distortion is extreme All great circles passing through the central point show as straight lines with the correct azimuth

COMMON MAP PROJECTIONS Azimuthal Azimuthal Equidistant Has linear scale, uniform along radiating straight lines through center Movement toward or away from a center point is well demonstrated Works well for mapping radio impulses or seismic waves

COMMON MAP PROJECTIONS Azimuthal Equidistant From Robinson, Sixth Edition, page 85

COMMON MAP PROJECTIONS Azimuthal Orthographic Looks something like a perspective view of the globe from a distance Distortion is less visually obvious than on other azimuthal projections Useful for illustrations which portray the globe as a sphere

COMMON MAP PROJECTIONS Azimuthal Gnomic All great circle arcs are straight lines everywhere on the projection Useful primarily for marine navigation

COMMON MAP PROJECTIONS Azimuthal Stereographic Lambert’s Equal Area Azimuthal Equidistant Orthographic Gnomic From Robinson, Sixth Edition, page 84

COMMON MAP PROJECTIONS Special Purpose Map Projections Plane chart/equidistant cylindrical/PlateCarrée/ equirectangular Oldest and simplest map projection Used for navigation before Mercator Good for city maps and base maps of small areas Simple conic Uses two standard parallels equidistant from equator No great distortion of angles or areas Often used in atlases for mid-latitude areas

COMMON MAP PROJECTIONS Equidistant Cylindrical/Plane Chart Special Purpose Equidistant Cylindrical/Plane Chart From Robinson, Sixth Edition, page 86

COMMON MAP PROJECTIONS Special Purpose – Simple Conic From Robinson, Sixth Edition, page 87

COMMON MAP PROJECTIONS Special Purpose Map Projections, cont. Polyconic – not conformal or equal area Used by the U.S. for topo sheets until 1950’s – can fit topos together in one direction or another, but not all Robinson’s – not conformal or equal area Commissioned in 1961 by Rand McNally to show uninterrupted world maps at all scales Minimizes the appearance of shape and area distortion

COMMON MAP PROJECTIONS Special Purpose - Polyconic The distribution of scale factors on a polyconic projection in the vacinity of 40° latitude. N-S SF values away from the central meridian are approximate. Note that the section of the projection which is used for a standard 7.5-minute quadrangle map would be 1/8 degree E-W and N-S along the central meridian. From Robinson, Sixth Edition, page 88, 89

COMMON MAP PROJECTIONS Special Purpose Map Projections, cont. Space Oblique Mercator Projection Projection used for satellite imagery Essentially conformal (shape/angle) Groundtrack of satellite represents central line with scale factor ~ 1.0 Groundtrack is not true great circle, but slightly curved due to rotation of earth

COMMON MAP PROJECTIONS Special Purpose Space Oblique Mercator Robinson’s