THREE POINT PROBLEM |Civil Easy Learning

THREE POINT PROBLEM 

Three point problem is 

“Given three visible stations and their plotted  positions, to plot the station occupied by  the table with the table correctly  oriented.”  

Methods of Solution 

1. Mechanical method (Tracing paper  

method 

2. Graphical method (Bessel’s method) 

3. Trial and error method

Graphical Method (Bessel) 

Procedure – Bessel’s method 

1. A,B,C stations are three well defined  points which have been plotted as a,b,c.  

It is required to locate a station at P. 

2. The table is placed at the required station  P and levelled . The alidade is placed  along the line ca and the point A is  bisected. The table is clamped. 

3. With the alidade centred on c , the point  B is bisected and a ray is drawn.  (I Position)

4. Again the alidade is placed along the line  ac and the point C is bisected and the  table is clamped. 

5. With the alidade, touching the position a,  the point B is bisected and a ray is drawn.  Let this ray intersects the previous ray at a  point (II Position)

6. The alidade is placed along the line db, and the point B is bisected. At this position  the table is perfectly oriented. Now the  rays Aa, Bb, Ca are drawn. These rays  must meet at the point P, which is required  

point.

7. The point is transfered to the ground by   U frame or U fork. 

TRACING PAPER METHOD

Procedure – Tracing paper method 

1The table is placed at P and levelled. A  tracing paper is fixed on the map and a  point p is marked on it. 

2. With the alidade centred on P, the points  A, B, C are bisected and the rays are  drawn. The rays will not pass through the  points a,b,c. 

3. Now the tracing paper is removed and  moved over the map such a way that , the  three rays at a time pass through the  positions a, b, c.

• The point p is picked with a pin to give a  impression p on the map. p is the required  point on the map. The tracing paper is  removed. 

• Alidade is centred on p and the rays are  drawn towards A, B, C. These rays must  pass through the points a,b,c. 

TRIAL AND ERROR METHOD 

Lehmann’s method Procedure 

1. Set up the plane table at S. The station S  should be such that P,Q and R do not subtend  very acute angles at S. 

2. Orient the table approximately. 

3. Now keeping the alidade at s, draw the three  rays to P, Q and R. They will not intersect at a  point but form a triangle of error. 

4. Select a new position of s and draw again the  three rays. A new triangle of error, but smaller,  

will be formed.

Lehmann’s Rules: 

1. If S is outside the great triangle PQR, then s  

will be outside triangle of error. If S is inside  

PQR, triangle of error will be inside PQR and s  

will be inside the triangle of error. 

2. The position of s will be such that its distance  

from pP,qQ and Rr will be proportional to  

distance of S from P,Q,R. 

3. S will lie on the same side of pP,qQ and rR.

ERRORS :

1. Table not levelled. 

2. Table not oriented. 

3. Wrong placement of alidade. 

4. Inaccurate bisection of objects. 

5. Improper clamping. 

6. Lines not accurately drawn. 

7. Inaccurate scaling and plotting 

8. Expansion/contraction of paper.