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Abstract

Two- and three-dimensional coordinate systems are fundamental to most quantitative mapping applications. The Geodetic, Universal Transverse Mercator (UTM),and State Plane systems have traditional roles in various science, surveying, and government agency engineering applications. The coordinates of three-dimensional Geodetic system are latitude, longitude, and height above ellipsoid (HAE).Because of its ability to cope with the intrinsically three dimensional character of the earth's surface, the Geodetic system is capable of supporting precise relative positioning and very high accuracy computations of distance between any two positions on or near the earth's surface. The two-dimensional UTMand State Plane systems are extremely useful for the local horizontal positioning and scaling required for paper maps of county-size land areas. In the two plane systems, horizontal distance computation is a very straightforward application of the distance formula (analytic geometry) based on the Pythagorean theorem. Although precision line- and geodesic- distance formulas based on geodetic coordinates are more complex, useful horizontal distance estimates are easily derived from the latitudes and longitudes of two positions. This paper examines this premise for Arkansas. The approach to estimating horizontal distances utilizes an application of the distance formula in conjunction with an assumed constant distance/unit latitude of 30.8 m (arc sec)" 1.Alinear regression equation is used to represent distance/unit longitude as a function of latitude in Arkansas. The approximation math is extremely simple, and the process as a whole is equivalent to a portable coordinate projection.

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