Contour interpolation and uses of contour maps

Interpolation of contours

Interpolation of contours is the process of locating the positions of contours of given values between plotted points of known RL, assuming that the ground slope between the points is uniform. The surveyed points are only a set of spot levels; the contours are drawn through them by this process.

Methods of interpolation

1. Estimation: The positions of the contours are estimated by eye between the two points. It is quick but rough.
2. Arithmetical calculation: The distance from the lower point to the contour is found by proportion:

$$x = \frac{h_c - h_1}{h_2 - h_1}\times d$$

where $h_1, h_2$ are the RLs of the two points ($h_2 > h_1$), $h_c$ is the contour value and $d$ is the plotted distance between the points. It is accurate but slow. 3. Graphical methods

• Tracing paper (transparent sheet) method: Parallel, equally spaced lines are drawn on tracing paper and numbered with contour values. The paper is turned and moved until the lines for the two end RLs pass through the two points. The points where line AB crosses the lines on the paper mark the contours. It is quick and common.
• Similar triangles method: Perpendiculars are drawn to AB at A and B, with lengths equal to the heights of the points above a convenient datum (to a scale of levels). Their tops are joined, lines parallel to AB are drawn at the contour heights, and the points where these cut the joining line are projected perpendicularly onto AB to give the contour positions.

The tracing paper method is quick, simple and accurate enough, so it is recommended for a large volume of work.

Uses of contour maps

1. To find the elevation of any point and the slope between two points from the map (without going to the field).
2. To draw the longitudinal section and cross-sections of a road, railway, canal or pipeline on paper.
3. To fix the best alignment of a road, railway or canal with a given gradient (contour gradient).
4. To find the intervisibility of two points (to decide whether a signal station can be seen from another).
5. To calculate the capacity of a reservoir, the catchment area and the volume of earthwork (from the areas enclosed by contours).
6. To select suitable sites for a dam, building, bridge, airport or water tank, and to mark the drainage lines (watershed).
7. To find the quantity of cutting and filling for levelling a site, and to plan irrigation and drainage layouts.
8. To study the general topography (hills, valleys, ridges) of a large area, and for military purposes and town planning.