Contour interpolation, method for large work

Contour interpolation is the process of locating the positions of contours of required values between two plotted points of known RL. It assumes the ground slope is uniform between the two points.

Methods of interpolation

1. Estimation: The positions of 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 equidistant lines are drawn on tracing paper and numbered with the contour values. The paper is turned and moved until the lines for the two end RLs pass through the two points. The crossing of line AB with the lines of the paper marks the contours. It is quick and common.
• Perpendiculars (similar triangles) method: At A and B, perpendiculars to AB are drawn with lengths proportional to their heights above a convenient datum (to a scale of levels), and their ends A' and B' are joined. Lines parallel to AB are drawn at the contour levels; where they cut A'B', perpendiculars dropped back to AB give the contour points.

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

Application of the tracing paper method for a large area

1. Plot all spot levels on the sheet, with their RLs written beside each point.
2. For CI = 1 m (say), draw equally spaced parallel lines on tracing paper (or use a ruled transparent sheet) and number them with consecutive levels (50, 51, 52, ... 60).
3. To interpolate between A (RL 52.4) and B (RL 57.8), place the paper so that the line for 52.4 passes through A (estimate between lines 52 and 53) and the line 57.8 passes through B.
4. Prick the points where AB crosses the lines 53, 54, 55, 56, 57 on the sheet.
5. Repeat for all pairs of neighbouring points, then join the equal values by smooth curves and thicken every fifth contour.