SPACIAL METHOD OF RESECTION

SPACIAL METHOD OF RESECTION

Sometimes, after completion of plane table traversing, it may be noticed that an important object has not been located due to oversight. If no station pers are found on the field, some special methods of resection are applied in order to establish a new station for plotting the missing object. The methods are based on:

[1]. The two-point problem, and [2] the three-point problem.

The two-point problem: In this problem, two well defined points whose positions have already been plotted on the plan are selected. Then, by perfectly bisecting this point, a new station is established at required position.  

Procedure [a] Suppose P and Q are two well-defined points whose positions are plotted on the map as p and q. It is required to locate a new station at A by perfectly bisecting P and Q.  

[b]. An auxiliary station B is selected at a suitable position. The table is set up at B and levelled and oriented by eye estimation. It is then clamped.

[c]. With the alidade touching p and q, the points P and Q are bisected, and rays are drawn. Suppose these rays intersect at b.

[d]. With the alidade centred on b, the ranging rod at A is bisected and a ray is drawn. Then, by eye estimation, a point a₁ is marked on the ray.

[e]. The table is shifted and centred on A, with a₁ just over A. It is levelled and oriented by back-sighting. With the alidade touching p, the point P is bisected, and a ray drawn. Suppose this ray intersects and line ba₁ at point a₁, as was assumed previously.

[f]. With the alidade centred on a₁, the point Q is bisected, and a ray is drawn. Suppose this ray intersects the ray bq at point q₁. The triangle pqq₁ is known as the triangle of error and is to be eliminated.

[g]. The alidade is placed along the line pq₁ and a ranging 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 saib to be perfectly oriented.

[h]. Finally, with the alidade centred on p and q, the points P and Q bisected and rays are drawn. Suppose these rays intersect at a point a. This would represent the exact position of the required station A (Fig. 14). Then the station A is marked on the ground.

The three-point problem: In this problem, three well defined points are selected whose positions have already been plotted on the plan. Then, by perfectly bisecting these three well-defined point, a new station is established at required position.  

  No auxiliary station is required in order to solve this problem. The table is directly placed at the required position. The problem may be solved by three methods: [a] the graphical or Bessel’s method, [b] the mechanical method and [c] the trial-and-error method.  

[a] The Graphical 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 new station at P.

[ii] The table is placed at the required station P and levelled. The alidade is placed along the line ac and the point A is bisected. The table is clamped. With the alidade centred on C, the point B is bisected, and ray is drawn (Fig.15.a).

[iii] 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 point d (Fig. 15.b).

[iv] 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 ray Aa, Bb and Cc are drawn. These three rays must meet a point p which is required point on the map. The point is transferred to the ground by the U-fork and plumb bob (Fig. 15.c).

[b] The Mechanical Method [i] Suppose A, B and C are three well-defined points which have been plotted as a, b and c. It is required to locate a new station at P. 

[ii] The table is placed at P and levelled. A tracing paper fixed on the map and a point p marked on it.

[iii] With the alidade centred on P, the points A, B and C are bisected, and rays are drawn. These rays may not pass through the points a, b and c as the orientation is done approximately (Fig.16.a).

[iv] Now the tracing paper unfastened and move over the map in such a way that the three rays simultaneously pass through the plotted position a, b and c. Then the point p is pricked with a pin to give an impression p on the map, p is the required point on the map. The tracing paper is then removed (Fig. 16.b).

[v] Then the alidade is centred on p and the rays are drawn towards A, B and C. These rays must pass through the points a, b and c.

[c] The Trial-and-Error 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 establish a point at P. 

[ii] The table is set up at P and levelled. Orientation is done by eye estimation.

[iii] With the alidade, rays Aa, Bb and Cc are drawn. As the orientation is approximate, the rays may not intersect at a point, but may form a small triangle the triangle of error.

[iv] To get the actual point, this triangle of error to be estimated. By repeatedly turning the table clockwise and anti-clockwise, the triangle is eliminated in such a way that the rays Aa, Bb and Cc finally meet a point p. This is the required point on the map. This point is transferred to the ground by U-fork and plumb bob (Fig. 17)

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