Two points problem of plane table
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This document describes methods for solving two point and three point problems in plane table surveying. The two point problem involves bisecting the lines between two known points P and Q to locate a new point A. An auxiliary point B is used to orient the plane table. The three point problem can be solved graphically by bisecting lines between three known points A, B, and C to find their intersection at the new point P, or through a trial and error process of adjusting orientation to eliminate errors until the lines intersect at the precise point.
Two points problem of plane table
- 1. TITLE: TWO POINT PROBLEM AND THREE POINT PROBLEM IN PLANE TABLE SURVEYING GROUP MEMBERS SHAKIR AHMED CU-139-2018 ISHAQ AFRIDI CU-133-2018 HILAL ROME CU-130-2018 SYED BILAL CU-136-2018 HASHIM ZAFAR CU-127-2018
- 2. The Two Point Problem • Suppose P and Q are two well-defined points whose positions are plotted on map as p and q. It is required to locate a new station at A by perfectly bisecting P and Q • An auxiliary station B is selected at a suitable position. The table is set up at B, and leveled and oriented by eye estimation. It is then clamped. • With the alidade touching p and q, the points P and Q are bisected and rays are drawn. Suppose these rays intersect at b
- 3. The Two Point Problem • With the alidade centered on a1 the point Q is bisected and a ray is drawn. Suppose this ray intersects the ray bq at a point q1. The triangle pqq1 is known as the triangle of error, and is to be eliminated. • The alidade is placed along the line pq1 and a ranging rod R is fixed at some distance from the table. Then, the alidade is placed along the line pq and the table is turned to bisect R. At this position the table is said to be perfectly oriented. • Finally, with the alidade centered on p and q, the points P and Q are bisected and rays are drawn. Suppose these rays intersect at a point a. This would represent the exact position of the required station A. Then the station A is marked on theground.
- 5. The Three Point Problem The graphical method or Bessel’s method • (i) suppose A,B, and C are three well-defined points which have been plotted as a, b and c. Now it is required to locate a station at P. • (ii) The table is placed at the required station P and leveled. The alidade is placed along the line ca and the point A is bisected. The table is clamped. With the alidade in centre on C, the point B is bisected and rays is drawn
- 6. The Three Point Problem • Again the alidade is placed along the line ac and the point C is bisected and the table is clamped. With the alidade touching a, the point B is bisected and a ray is drawn. Suppose this ray intersects the previous ray at a point d • The alidade is placed along db and the point B is bisected. At this position the table is said to be perfectly oriented. Now the rays Aa, Bb and Cc are drawn. These three rays must meet at a point p which is the required point on the map. This point is transferred to the ground by U-fork and plumb bob.
- 8. The Three Point ProblemThe method of Trial and error • Suppose a, B and C are the three well-defined points which have been plotted as a, b and c on the map. Now it is required to establish a station at P. • The table is set up at P and leveled. Orientation is done by eye estimation • With the alidade, rays Aa, Bb and Cc are drawn. As the orientation is approximately, the rays may not intersect at a point, but may form a small triangle the triangle of error. • To get the actual point, this triangle of error is to be eliminated. By repeatedly turning the table clockwise or anticlockwise. The triangle is eliminated in such a way that the rays Aa, Bb and Cc finally meet at a point p. This is the required point on the map. This point is transferred to the ground by U-fork and plumb bob.