Resection is a method used in plane table surveying to determine the position of the survey station (where the plane table is set up) by sighting known points. Instead of plotting other objects, resection helps in finding and fixing the location of the occupied station on the map. This method is used to establish the instrument stations only to locate missing details. The characteristic feature of resection is that the point plotted on the plan is the station occupied by the plane table.
- It is used to orient the plane table correctly.
- The position of the occupied station is determined on the map by sighting two or more known points.
- It does not require direct distance measurement between the occupied station and known points.
- It is useful in situations where the distance between stations cannot be measured directly.
Types of Resection Methods:
- Simple Resection Method – Used when only two known points are available.
- Three-Point Problem – A more accurate method using three known points to determine the exact station position.
- Two-Point Problem – A special case of resection where orientation is done using two known points.
Simple Resection Method
The Simple Resection Method in plane table surveying is used to determine the position of an unknown station by sighting two known points. First, the plane table is set up at a known station, and a ray is drawn toward another known station. Then, the table is moved to the unknown station, and another ray is drawn toward the same known point. The intersection of these rays on the map gives the correct position of the unknown station. This method helps in surveying when measuring distances directly is difficult, making it useful for small areas.
Steps for Simple Resection
- Setting up the Plane Table at Station A
- The plane table is set up at station A with proper levelling, centring, and orientation.
- The table is clamped, and the point ‘d’ is marked on the map to represent station A.
- Sighting Station C from A
- The fiducial edge of the alidade is placed at point ‘a’ on the map.
- A ranging rod is placed at station C, and it is bisected using the line of sight through the alidade.
- A ray is drawn along the fiducial edge of the alidade toward C, marking ‘a’ to ‘c’’ on the map.
- Measuring Distance AC and Plotting it on the Map
- The distance AC is measured in the field and reduced to the chosen scale.
- This scaled distance is marked as ‘a’ to ‘c’’ along the ray on the map.
- Sighting Station B from A
- The fiducial edge of the alidade is again placed at point ‘a’ on the map.
- A ranging rod is placed at station B, and it is sighted through the alidade.
- A ray is drawn along the fiducial edge toward B, marking ‘a’ to ‘b‘.
- Measuring Distance AB and Plotting it on the Map
- The distance AB is measured and reduced to the chosen scale.
- This estimated distance is laid along the ray, ensuring that ‘ab’ on the map represents the distance AB in the field.
- Shifting the Plane Table to Station C
- The plane table is moved to station C for further surveying.
- Proper levelling, centring, and orientation are done.
- The point ‘c’’ on the map is now positioned approximately above station C.
- Sighting Station B from C
- The fiducial edge of the alidade is placed at point ‘b’ on the map.
- The ranging rod is placed at station B and sighted using the alidade and a new ray is drawn.
- Sighting Station A from C
- The fiducial edge of the alidade is placed at point ‘a’ on the map.
- The ranging rod is placed at station A and sighted using the alidade and a new ray is drawn.
- Determining the Correct Position of C on the Map
- The newly drawn rays from a and b are extended backward till they intersect.
- The intersection point ‘c‘ is the correct position of C.
Three Point Problem
The Three-Point Problem is a method used in plane table surveying to determine the exact position of an unknown station by sighting three well-defined points whose positions are already plotted on the map. It is a widely used method because it does not require measuring distances or setting up auxiliary stations.
Methods to Solve the Three-Point Problem:
- Bessel’s Method (Graphical Method):
- The table is oriented by trial and adjustment, ensuring the three plotted points align with their real positions in the field.
- Rays are drawn from the occupied station to the three known points, and the correct position is determined by a graphical intersection.
- Mechanical Method (Tracing Paper Method):
- A piece of tracing paper is placed over the plane table and used to transfer the three known points.
- The tracing paper is rotated until the lines sighting the three points match their actual field positions, and the correct position of the unknown station is marked.
- Trial and Error Method:
- The plane table is roughly oriented, and rays are drawn to the known points.
- Adjustments are made by slightly shifting the table until the sight lines correctly pass through the known points, determining the correct position of the occupied station.
Graphical or Bessel’s Method
The Graphical or Bessel’s Method is a technique used in plane table surveying to determine an unknown station (P) by sighting three well-defined points (A, B, C) whose positions are already plotted on the map as (a, b, c). This method involves a step-by-step adjustment of the table until it is perfectly oriented.
Steps to Solve the Three-Point Problem Using Bessel’s Method:
- Selection of Known Points:
- Identify three well-defined points (A, B, C) in the field that are already plotted on the map as (a, b, c).
- The goal is to determine the location of an unknown station P.
- First Operation:
- Place the plane table at station P and level it properly.
- Align the alidade along ca, sight point A, and clamp the table in position.
- Keeping the alidade centred at C, sight point B and draw a ray towards it.
- Second Operation:
- Now, place the alidade along ac, sight point C, and clamp the table again.
- Keeping the alidade at a, sight point B and draw another ray.
- The two rays drawn from B intersect at point d on the map.
- Final Adjustment and Orientation:
- Place the alidade along db and sight point B again.
- When this is done correctly, the table is perfectly oriented.
- Now, draw the final rays Aa, Bb, and Cc. These three lines will intersect at a common point P, which represents the correct position of station P on the map. (Fig. c)
- This position is then transferred to the ground using a U-fork and plumb bob.