Two point problem; advantages, disadvantages

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. At Q: choose an auxiliary station Q near P such that the angles PAQ and PBQ are not too small. Set up the table at Q and orient it approximately by compass or by eye. Pivot the alidade on a, sight A and draw a ray back; pivot on b, sight B and draw a ray back. The rays meet at q.
2. Pivoting on q, sight P and draw a ray. Mark p1 on it by estimating the distance QP.
3. At P: set up the table with p1 over P and orient it by back-sighting Q (alidade along p1-q). Pivot on a, sight A and draw a ray back. It cuts the line q-p1 at p.
4. Pivoting on p, sight B and draw a ray. It cuts the ray q-b (drawn in step 1) at b′. The angle between ab and ab′ is the error of orientation.
5. Place the alidade along ab′ and fix a ranging rod R far away in that line. Then place the alidade along ab and turn the table until R is bisected. The table is now correctly oriented; clamp it.
6. Pivoting on a and b, sight A and B and draw rays back. Their intersection is the true point p. Check with a third point if possible.

   A *                        * B      (ground stations)

        a ---------------- b           (plotted points)
         \               /  \
          \             /    b'  <- ray p->B meets ray q-b
           \           /
            p --------
            |   (p lies on line q-p1)
            q   (auxiliary station Q)

   angle b-a-b' = error of orientation

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 while looking at the ground.
• Little field book work; no angles need to be booked.
• Not affected by local attraction when the table is 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 or foggy weather, or in thick forest and built-up areas where intervisibility is poor.
• The table and its many accessories are heavy and awkward to carry.
• Less accurate than a theodolite survey for large areas; the accuracy depends on the quality of the drawing.
• Everything depends on the plan itself; since there are no field notes, the plan cannot be re-plotted to a different scale.
• The paper may shrink or expand with the weather.
• Plotting must be done in the field, so time is lost in bad weather, and an unskilled person may produce a poor drawing.