Contour terms and interpolation methods

Definitions

• Contour interval (CI) is the constant vertical distance between two consecutive contours, for example 1 m or 5 m. It is the same over one map.
• Horizontal equivalent (HE) is the horizontal distance between two consecutive contours. It varies with the slope of the ground: small on steep ground and large on gentle ground. $HE = \dfrac{CI}{\tan\alpha}$, where $\alpha$ is the ground slope angle.
• Index contour is every fifth contour (for example every 5th line when CI = 2 m, giving 10 m, 20 m, 30 m ...) drawn as a thicker line and labelled with its RL, so that the map can be read quickly. The other contours are called intermediate (minor) contours.

Methods of contour interpolation

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.