Ellipsoid
A mathematical surface (an ellipse rotated around the earth's polar axis) which provides a convenient model of the size and shape of the earth. The ellipsoid is chosen to best meet the needs of a particular geodetic datum system design. (Figure 5).

Datum
A mathematically defined reference surface used to represent the size and shape of the earth. A horizontal datum is defined by its ellipsoid, latitude and longitude orientation, and a physical origin. The two most commonly used horizontal datums in Wisconsin are the North American Datum of 1927 (NAD 27) and the North American Datum of 1983 (NAD 83).

Geoid
An undulating surface represented by extending the earth's mean sea level through the land areas. The geoid is a theoretical surface perpendicular at every point to the direction of gravity (Figure 5).

Geoidal separation
The perpendicular distance between the geoid and the reference ellipsoid, at a point (c to g on Figure 5). A negative geoidal separation indicates that the geoid is below the ellipsoid. In Wisconsin, the geoid separation is roughly 30 meters and is a negative value.

Projection
The method used to transform and portray the curved surface of the earth as a flat (map) surface. Although there are theoretically an infinite number of possible projections, a relatively small number are commonly used. Different projection systems have differing amounts and patterns of distortion.

Coordinate Systems --

geographic system: The network of curved lines (latitude and longitude) representing the earth's spherical surface. These coordinates are measured in angular values of degrees, minutes, and seconds, and are based on the equator and an arbitrary location of a prime meridian as the origin location.

rectangular system: A network of two sets of straight parallel lines intersecting at right angles and superimposed on a map projection. The origin (zero point) is located based upon the area covered on the earth. Coordinate values are usually expressed in feet or meters.

Standard Line (standard parallel)
A defined line in a map projection along which the scale of the ellipsoid and the map projection plane are equal . It is a line of no distortion (along which the scale factor is equal to 1.0). Many map projections have two standard lines. For example, in Lambert projections, the north latitude and the south latitude (sometimes called the first and second standard parallels, respectively) are lines of latitude where the scale factor is equal to 1.0 on the ellipsoid.

Central meridian
Central line of origin though the area of interest, used in many rectangular coordinate systems to orient the coordinate grid.

Actual origin, false origin
The actual point of origin (zero point) for the coordinate system, as distinguished from a false origin (Figure 6). The actual origin is the true geodetic origin of the system, but it may be assigned arbitrary coordinate values, to eliminate negative coordinates in the system. (This is done using false eastings and/or northings ---see next entry). The false origin is an assumed point, typically to the west and south of the projection area, which has a coordinate value of 0,0.

False easting, false northing
A numerical constant used to eliminate negative coordinates in a system, or to change the coordinates to more convenient values. The false easting and/or northing values are assigned to the true origin of the projection system (Figure 6).

Design elevation
The elevation of the map projection surface. Regional coordinate systems are usually designed at mean sea level, however the design elevation of a local coordinate system typically represents the median elevation in the area (Figure10).

Scale factor
A ratio, at a given point, of projection (grid) distance (e to f on Figure5) to ellipsoid distance (c to d on Figure 5). Because the transformation of the ellipsoid to a flat surface creates distortions, the scale factor on a map varies from place to place. A value larger then one (e.g., 1.0001) means the scale at a given point is larger than actual (or "scale greater than true.") A smaller value (e.g., 0.9999) means the scale is less then true (Figure 3).

Ground to grid ratio
This statistic expresses the difference between distances calculated on the grid surface (e to f on Figure 5) and distances measured on the ground (a to b on Figure 5). Small ratios (e.g., 1:500,000) indicate less difference, while larger ratios (e.g., 1:5,000) indicate more difference. Converting a ground distance to a grid distance requires the combination of two factors: the scale factor (see above) and the elevation factor, which relates ground distance to ellipsoid distances.

Units of measure (Linear)
Rectangular coordinate systems may use meters, international foot, or the U.S. Survey Foot as the unit of measurement. (Most surveying and mapping work at the local level is based on the U.S. Survey Foot.) When a conversion from one of these units to the other is performed, it is important to ascertain which standard foot (U.S. Survey or international) is involved.

The international (S.I.) foot, based upon a redefinition of the meter in 1959, is equivalent to 0.3048 meter. The U.S. Survey Foot, upon which many years of land tenure information and legislation are based, retained the 1893 definition of 1200/3937 meter*. In Wisconsin, Chapter 236 of State Statutes requires use of the U.S. Survey Foot with the State Plane Coordinate System, for certain purposes. The Wisconsin County Coordinate System also uses the U.S. Survey Foot.

* For conversion of meters to U.S. Survey Foot, multiply the meters by 3.28083333333 (to 12 significant figures). For conversion of meters to international feet, multiply the meters by 3.28083989501 (to 12 significant figures). Return to Top

References and Suggested Readings