Bessel’s Graphical Solution of Three-Point Problem in Plane-Table Surveying—Limitation and Alternative Solutions

Abstract

The orientation of a plane table at a new station is carried out with the help of three well-defined visible points available on the ground along with their corresponding plot on the plan using Bessel’s graphical solution. There are seven regions (R1–R7) in and around the area bounded by the three well-defined ground points and the plane table may be stationed in any one of them for orientation. While carrying out such field work, a completely opposite orientation was obtained for the plane-table station in reference to the ground points and corresponding plotted plan points for some of the regions, hinting at possible limitation of the method. This paper makes an effort to understand and analyze the limitation of Bessel’s graphical solution. The orientations were carried out on an AutoCAD worksheet and cross checked through field works. It was observed that the position of the plane table station and the third point used to draw the ray in reference to the line joining the first two points used for sight...