Plane Table Survey

The four methods are:

1. Radiation - rays are drawn from one station to the points to be plotted and distances are measured and scaled along them.
2. Intersection (triangulation) - a point is fixed by drawing rays to it from two stations at the ends of a plotted base line.
3. Traversing - the table is set up at successive stations of a traverse; each new station is plotted by radiation and the table is oriented by back-sighting.
4. Resection - the table station itself is located by drawing rays back from known plotted points to it (two-point and three-point problems).

Radiation method

The table is set up at one station O, from which all the points to be plotted are visible.

1. Level, centre and fix the sheet; mark the point o on the sheet for O.
2. Pivot the alidade on o and sight each station A, B, C, D in turn; draw a ray towards each.
3. Measure the distances OA, OB, OC, OD with a tape and mark them to scale along the rays to get a, b, c, d.
4. Join a, b, c, d to obtain the plan.

          b               c
           \             /
            \    ray    /
   a ------- o (table) -------- d

Suitability: small areas with open ground, where all points can be seen from one station and distances can be measured easily. It is the base of detailing by plane table.

Intersection method

Two stations A and B (the ends of a base line) are chosen so that the point P to be located is visible from both.

1. Set the table at A, orient it by compass, and plot a. Sight B and draw the ray; measure AB and plot b to scale.
2. Sight P from a and draw the ray aP (also rays to the other points).
3. Shift to B, centre b over B, and orient the table by back-sighting A along the line ba.
4. Sight P again from b and draw the ray bP. The intersection of the two rays is the plotted point p.

                 p
               / |  \
             /   |    \
           /     |      \
         a ------------- b
       (stn A)  base   (stn B)

Suitability / advantages:

• Used for locating inaccessible points (across rivers, hills, buildings, a far-away church spire, etc.) where distance cannot be measured.
• Only one linear measurement (the base line) is needed; many points can be fixed quickly.
• A third ray from another station checks the plotted point.
• Good intersection angle (about 60 to 120 degrees) is needed for accuracy.

Radiation method

The table is set up at one station O, from which all the points to be plotted are visible.

1. Level, centre and fix the sheet; mark the point o on the sheet for O.
2. Pivot the alidade on o and sight each station A, B, C, D in turn; draw a ray towards each.
3. Measure the distances OA, OB, OC, OD with a tape and mark them to scale along the rays to get a, b, c, d.
4. Join a, b, c, d to obtain the plan.

          b               c
           \             /
            \    ray    /
   a ------- o (table) -------- d

Suitability: small areas with open ground, where all points can be seen from one station and distances can be measured easily. It is the base of detailing by plane table.

Intersection method

Two stations A and B (the ends of a base line) are chosen so that the point P to be located is visible from both.

1. Set the table at A, orient it by compass, and plot a. Sight B and draw the ray; measure AB and plot b to scale.
2. Sight P from a and draw the ray aP (also rays to the other points).
3. Shift to B, centre b over B, and orient the table by back-sighting A along the line ba.
4. Sight P again from b and draw the ray bP. The intersection of the two rays is the plotted point p.

                 p
               / |  \
             /   |    \
           /     |      \
         a ------------- b
       (stn A)  base   (stn B)

Suitability / advantages:

• Used for locating inaccessible points (across rivers, hills, buildings, a far-away church spire, etc.) where distance cannot be measured.
• Only one linear measurement (the base line) is needed; many points can be fixed quickly.
• A third ray from another station checks the plotted point.
• Good intersection angle (about 60 to 120 degrees) is needed for accuracy.

Principles of plane table surveying

Principle: the table is set up so that the rays drawn on the sheet from a station point towards the objects are parallel to the corresponding lines on the ground. The plotted figure is then similar to the ground figure. This needs three things at every station:

1. Levelling - the board is kept horizontal (spirit level on the board).
2. Centring - the point on the sheet is kept vertically above the ground station (plumbing fork and plumb bob).
3. Orientation - the board is turned so that all lines on the sheet stay parallel to their ground lines (by magnetic needle or by back-sighting a previously plotted line).

Orientation by back-sighting

This is the more reliable method, because it does not depend on the magnetic needle, which is affected by local attraction.

Condition: the table is at station B; the line ba (from the previous station A) is already plotted.

1. Level the table and centre b over station B.
2. Place the alidade along the line ba.
3. Turn the board until the ranging rod at A is bisected by the line of sight.
4. Clamp the board. The table is now oriented, since ba is parallel to BA.
5. Check by sighting another known point; the ray should pass through its plotted position.

   SHEET (table at B)             GROUND
   a o--------o b                 A o ........ o B
     \_ alidade on ba             (rod at A seen
       along the line)             along the line)

The board is turned about its vertical axis, with the alidade kept on the line ba, until the rod at A is bisected.

Principles of plane table surveying

Plane tabling is a graphical surveying method in which fieldwork and plotting are done together on the spot, using a drawing sheet fixed on a board (plane table), an alidade for sighting and a tripod.

Principle: the table is set up so that the rays drawn on the sheet from a station point towards the objects are parallel to the corresponding lines on the ground. The plotted figure is then similar to the ground figure. This needs three things at every station:

1. Levelling - the board is kept horizontal (spirit level on the board).
2. Centring - the point on the sheet is kept vertically above the ground station (plumbing fork and plumb bob).
3. Orientation - the board is turned so that all lines on the sheet stay parallel to their ground lines (by magnetic needle or by back-sighting a previously plotted line).

Advantages and disadvantages

Advantages

• Fieldwork and plotting are done together, so omissions and mistakes are detected on the spot.
• Contours and details can be drawn directly by looking at the ground.
• Less field book work; no angular booking is needed.
• Not affected by local attraction when oriented by back-sighting.
• Quick and economical for small and medium-scale maps.
• Inaccessible points can be plotted by intersection and resection.
• Needs less skill than theodolite surveying and the instruments are simple.

Disadvantages

• Not suitable in rainy, windy, foggy weather or in thick forest and built-up areas where intervisibility is poor.
• Instruments are heavy and many accessories must be carried; difficult to transport.
• Less accurate than a theodolite survey for large areas; accuracy depends on drawing quality.
• The whole work depends on the plan only; a plan cannot be re-drawn to a different scale from field data as there are no field notes.
• Paper may shrink or expand with weather.
• Plotting is done in the field, so the time is wasted in bad weather and an unskilled person may make a poor drawing.

Advantages

• Fieldwork and plotting are done together, so omissions and mistakes are detected on the spot.
• Contours and details can be drawn directly by looking at the ground.
• Less field book work; no angular booking is needed.
• Not affected by local attraction when oriented by back-sighting.
• Quick and economical for small and medium-scale maps.
• Inaccessible points can be plotted by intersection and resection.
• Needs less skill than theodolite surveying and the instruments are simple.

Disadvantages

• Not suitable in rainy, windy, foggy weather or in thick forest and built-up areas where intervisibility is poor.
• Instruments are heavy and many accessories must be carried; difficult to transport.
• Less accurate than a theodolite survey for large areas; accuracy depends on drawing quality.
• The whole work depends on the plan only; a plan cannot be re-drawn to a different scale from field data as there are no field notes.
• Paper may shrink or expand with weather.
• Plotting is done in the field, so the time is wasted in bad weather and an unskilled person may make a poor drawing.

Orientation is the process of putting the plane table in a fixed direction at every station, so that all the lines on the sheet are parallel to the corresponding lines on the ground. It is needed whenever the table is shifted from one station to another.

Orientation by back-sighting

This is the more reliable method, because it does not depend on the magnetic needle, which is affected by local attraction.

Condition: the table is at station B; the line ba (from the previous station A) is already plotted.

1. Level the table and centre b over station B.
2. Place the alidade along the line ba.
3. Turn the board until the ranging rod at A is bisected by the line of sight.
4. Clamp the board. The table is now oriented, since ba is parallel to BA.
5. Check by sighting another known point; the ray should pass through its plotted position.

   SHEET (table at B)             GROUND
   a o--------o b                 A o ........ o B
     \_ alidade on ba             (rod at A seen
       along the line)             along the line)

The board is turned about its vertical axis, with the alidade kept on the line ba, until the rod at A is bisected.

Why back-sighting is more reliable

• It depends only on the direction of a line already plotted on the sheet, and the line is sighted directly through the alidade.
• The magnetic needle (the other method) is affected by local attraction from iron, steel structures, power lines and by its own errors, so orientation by compass may be wrong by several degrees.
• A long back-sight line gives a more accurate orientation than a short one, and the result can be checked by sighting a third known point.

Plane table surveying is a graphical method of surveying in which fieldwork and plotting are done at the same time on a drawing sheet fixed on a board (plane table). A rays-and-scale plan is made directly in the field.

Intersection method

Two stations A and B (the ends of a base line) are chosen so that the point P to be located is visible from both.

1. Set the table at A, orient it by compass, and plot a. Sight B and draw the ray; measure AB and plot b to scale.
2. Sight P from a and draw the ray aP (also rays to the other points).
3. Shift to B, centre b over B, and orient the table by back-sighting A along the line ba.
4. Sight P again from b and draw the ray bP. The intersection of the two rays is the plotted point p.

                 p
               / |  \
             /   |    \
           /     |      \
         a ------------- b
       (stn A)  base   (stn B)

Advantages:

• Used for locating inaccessible points (across rivers, hills, buildings, a far-away church spire, etc.) where distance cannot be measured.
• Only one linear measurement (the base line) is needed; many points can be fixed quickly.
• A third ray from another station checks the plotted point.
• Good intersection angle (about 60 to 120 degrees) is needed for accuracy.

Reliable method of orientation

Orientation by back-sighting is the more reliable method. It is not affected by local attraction, unlike the magnetic needle.

1. At the new station B (line ba already plotted from the previous station A), level the table and centre b over B.
2. Place the alidade along the line ba.
3. Turn the board until the ranging rod at A is bisected, then clamp it.
4. The sheet is now parallel to its first position. Check by sighting a third known point; the ray must pass through its plotted position.

When intersection is preferred over radiation

So intersection is preferred when the distance to the point cannot be measured, when the points are far, when many points are to be located quickly, and when a check on the position is required.

Methods of orienting the plane table

Orientation means placing the board at a new station so that all lines on the sheet are parallel to the corresponding ground lines. There are two methods:

1. By trough compass (magnetic needle): the trough compass is placed along the magnetic meridian line drawn on the sheet at the first station, and the board is turned until the needle floats at the zero marks. Quick but affected by local attraction, so it is used only for small work or for rough orientation.
2. By back-sighting: the alidade is placed along the line joining the present station to the previously plotted station, and the board is turned until the previous station is bisected. This is the more reliable method used in traversing and in intersection.

Methods of plane table surveying

The four methods are:

1. Radiation - rays are drawn from one station to the points to be plotted and distances are measured and scaled along them.
2. Intersection (triangulation) - a point is fixed by drawing rays to it from two stations at the ends of a plotted base line.
3. Traversing - the table is set up at successive stations of a traverse; each new station is plotted by radiation and the table is oriented by back-sighting.
4. Resection - the table station itself is located by drawing rays back from known plotted points to it (two-point and three-point problems).

Salient features

Plane tabling is a graphical surveying method in which fieldwork and plotting are done together on the spot, using a drawing sheet fixed on a board (plane table), an alidade for sighting and a tripod.

Principle: the table is set up so that the rays drawn on the sheet from a station point towards the objects are parallel to the corresponding lines on the ground. The plotted figure is then similar to the ground figure. This needs three things at every station:

1. Levelling - the board is kept horizontal (spirit level on the board).
2. Centring - the point on the sheet is kept vertically above the ground station (plumbing fork and plumb bob).
3. Orientation - the board is turned so that all lines on the sheet stay parallel to their ground lines (by magnetic needle or by back-sighting a previously plotted line).

Equipment: plane table with tripod, alidade (plain or telescopic), plumbing fork with plumb bob, spirit level, trough compass, drawing sheet, pins, ranging rods, tape or chain.

Working at a station

1. Fix the paper on the board and place the tripod; mount the board and make it roughly level by eye.
2. Level the board with the spirit level placed in two directions at right angles, adjusting the tripod legs.
3. Centre the table over the ground station with the plumbing fork and plumb bob, so the sheet point is vertically above the ground point.
4. Orient the board by trough compass (first station) or by back-sighting a plotted line (later stations).
5. Sighting and plotting: pivot the alidade at the plotted point, sight the object through the sight vane and draw a ray along its fiducial edge. Measure the distance and plot to scale (radiation) or fix the point by two rays (intersection).
6. Shift to the next station, re-centre, re-orient, and repeat. Close the traverse by checking the plotted position of the first station.

Basic geometrical idea

   Ground:  O ----- A          Sheet:   o ----- a
             \                           \
               B                            b
   Triangle OAB is similar to triangle oab: each ray
   on the sheet is parallel to its ground line and
   drawn to a constant scale.

Intersection is the method in which a point is located by drawing rays to it from two known plotted stations. Resection is the method in which the table station itself is located on the sheet by drawing rays back from known plotted points to the station.

 INTERSECTION              RESECTION
   p (to be found)       a     b     c  (known)
   /\                     \    |    /
  /  \                     \   |   /
 a----b  (known)             \  |  /
                              p (to be found)

In intersection the unknown is where the rays meet forward, while in resection the unknown is where the rays meet backward from known points.

Resection is the plane table method of locating the table station P on the sheet, by sighting known plotted points A, B and C from it and drawing the rays backward from the plotted points a, b, c. The problem is called the two-point problem when only two points are available and the three-point problem when three are available.

Methods of resection

1. Orientation by back-sighting (when the station is on a line to a plotted point): the table is oriented by the line, and a ray from another point cuts the line at p.
2. Two-point problem with an auxiliary station Q.
3. Three-point problem, solved by (a) the mechanical (tracing paper) method, (b) the graphical method (Bessel's), (c) the trial and error method (Lehmann's).

Trial and error method

1. Set the table at P, level it and orient it by eye or compass as accurately as possible.
2. Pivoting on a, b, c, sight A, B, C and draw the three rays back. If the orientation is wrong they form a small triangle of error.
3. Estimate the position of P (the point p) inside or near the triangle by the rules below, and re-orient the board by placing the alidade on p-a and sighting A.
4. Repeat until the triangle of error reduces to a point. The point is then the position of P.

Lehmann's rules for locating p:

1. The true point lies on the same side of all three rays, that is, to the right of all of them or to the left of all of them, when looking from the station towards the object.
2. The distance of the true point from each ray is proportional to the distance of the object (station) from the table. So the point is nearest to the ray of the nearest object and farthest from the ray of the farthest object.

     ray a        ray b
         \      /
          \____/
          /\  /\   <- small triangle
         /  \/  \     of error
      ray c

Two point resection

Statement: to locate the table position P on the sheet when two well-defined points A and B (already plotted as a and b) are visible from P, but P is not on the line AB. An auxiliary station Q is used, chosen so that Q is visible from P, A and B are also visible from Q, and Q is on the other side of AB (or near the line PQ approx. in the same direction).

Procedure (Tracing method / two point problem)

1. Station P (first set-up): set up the table at P and orient it approximately by eye or compass. Pivot the alidade on a and sight A, draw a ray back; pivot on b, sight B, draw a ray back. The rays intersect at p1, an approximate position of P. From p1 sight Q and draw ray p1-q1; measure PQ and mark q1 to scale.
2. Station Q: move to Q and centre q1 over Q. Orient the board by back-sighting P along the line q1-p1. Pivot on a, sight A and draw a ray; pivot on b, sight B and draw a ray. These intersect at q2. Join q2 to p1 and produce it.
3. Back at P: place the alidade along the line q2-p1, and turn the table until Q is bisected. Now the board is correctly oriented.
4. Pivot at a and b again to sight A and B and draw the rays; their intersection is the true point p. Check with a third point C.

   A *                       * B
      \                    /
       \    a ----- b    /
        \      \  /     /
         \      p1      /
                |
                Q  (auxiliary station)

The method gives a good result when P and Q are chosen so that PQ is not nearly in line with AB.

Two point problem

The two point problem is the resection method of plane tabling in which the table station P is located on the sheet using only two known stations A and B (plotted as a and b), with the help of an auxiliary station Q. It is used when only two plotted points are visible from the table position.

Procedure

1. Station P (first set-up): set up the table at P and orient it approximately by eye or compass. Pivot the alidade on a and sight A, draw a ray back; pivot on b, sight B, draw a ray back. The rays intersect at p1, an approximate position of P. From p1 sight Q and draw ray p1-q1; measure PQ and mark q1 to scale.
2. Station Q: move to Q and centre q1 over Q. Orient the board by back-sighting P along the line q1-p1. Pivot on a, sight A and draw a ray; pivot on b, sight B and draw a ray. These intersect at q2. Join q2 to p1 and produce it.
3. Back at P: place the alidade along the line q2-p1, and turn the table until Q is bisected. Now the board is correctly oriented.
4. Pivot at a and b again to sight A and B and draw the rays; their intersection is the true point p. Check with a third point C.

   A *                       * B
      \                    /
       \    a ----- b    /
        \      \  /     /
         \      p1      /
                |
                Q  (auxiliary station)

Advantages and disadvantages of plane table survey

Advantages

• Fieldwork and plotting are done together, so omissions and mistakes are detected on the spot.
• Contours and details can be drawn directly by looking at the ground.
• Less field book work; no angular booking is needed.
• Not affected by local attraction when oriented by back-sighting.
• Quick and economical for small and medium-scale maps.
• Inaccessible points can be plotted by intersection and resection.
• Needs less skill than theodolite surveying and the instruments are simple.

Disadvantages

• Not suitable in rainy, windy, foggy weather or in thick forest and built-up areas where intervisibility is poor.
• Instruments are heavy and many accessories must be carried; difficult to transport.
• Less accurate than a theodolite survey for large areas; accuracy depends on drawing quality.
• The whole work depends on the plan only; a plan cannot be re-drawn to a different scale from field data as there are no field notes.
• Paper may shrink or expand with weather.
• Plotting is done in the field, so the time is wasted in bad weather and an unskilled person may make a poor drawing.

Three-point problem: given three well-defined points A, B and C that are plotted on the sheet as a, b, c, locate on the sheet the station P at which the table is set up, from which A, B, C are all visible. It is the resection method of plane tabling. Three solutions are used:

1. Mechanical method (tracing paper method, Bessel's)
2. Graphical method (with the help of the principle of the circle through three points)
3. Trial and error method (Lehmann's method)

Mechanical (tracing paper) method

1. Fix a tracing paper over the drawing sheet. Mark a point p on it for the station P.
2. Set up the table at P, level it, and orient roughly with compass.
3. With the alidade centred on p, sight A, B and C and draw rays on the tracing paper.
4. Loosen the tracing paper and move it until the three rays pass through a, b and c at the same time.
5. Prick the point p through to the drawing sheet. This gives the position of P.
6. Orient the table by placing the alidade along the line p-a and turning the board until A is bisected. Check by sighting B and C.

      a         b         c      (on sheet)
       \        |        /
        \       |       /
         \      |      /
            rays from p (tracing paper)

Trial and error (Lehmann's) method

1. Set the table at P, level it and orient it by eye or compass as accurately as possible.
2. Pivoting on a, b, c, sight A, B, C and draw the three rays back. If the orientation is wrong they form a small triangle of error.
3. Estimate the position of P (the point p) inside or near the triangle by the rules below, and re-orient the board by placing the alidade on p-a and sighting A.
4. Repeat until the triangle of error reduces to a point. The point is then the position of P.

Lehmann's rules for locating p:

1. The true point lies on the same side of all three rays, that is, to the right of all of them or to the left of all of them, when looking from the station towards the object.
2. The distance of the true point from each ray is proportional to the distance of the object (station) from the table. So the point is nearest to the ray of the nearest object and farthest from the ray of the farthest object.

     ray a        ray b
         \      /
          \____/
          /\  /\   <- small triangle
         /  \/  \     of error
      ray c

Strong and weak positions

• The position is well fixed when P is inside the triangle abc, or outside it but well away from the circle through a, b, c.
• If P lies on or very near the circle through a, b, c (the "dangerous circle"), the rays meet at many points and the problem has no definite solution. Then another set of points should be chosen.