Adjustment Computations, 6th Edition

APPENDIX FMAP PROJECTION COORDINATE SYSTEMS

F.1 INTRODUCTION

Most local surveyors are well-served by using map projections such as the State Plane Coordinate System. These two-dimensional grid systems allow surveyors to perform accurate computations over large regions of land using plane surveying computations. They are the basis for the adjustments discussed in Chapters 14 through 16.

Map projections provide a 1-to-1 mathematical relationship with points on the ellipsoid and those on the mapping surface. There are an infinite number of map projections. Most map projections are defined by a series of mathematical transformations used to convert a point's geodetic coordinates of latitude, φ, and longitude, λ, to NE (y, x) grid coordinates. Some map projections preserve the shape of objects (conformal), others areas, directions, or distances of lines. However since the Earth is ellipsoidal in shape and a mapping surface is a plane, all map projections introduce some form of distortion to observations. For example, distances and areas are distorted in a conformal map projection.

Often, to reduce the size of these distortions, the developable surface is made secant to the ellipsoid and the width of the mapping zone is limited in distance. For instance, when the National Geodetic Survey originally designed the state plane coordinate system during the 1930s, the zone widths were limited to 158 mi so that precision between the ellipsoid distance and the grid distance were no worse ...