Interpret relief from contour lines, calculate gradient, and draw and describe a cross-section

What this dot point is asking

SEAB wants you to read the shape of the land, its relief, from contour lines, to identify common landforms from their contour patterns, to calculate the gradient of a slope, and to draw and describe a cross-section. The central insight is that contours turn the three-dimensional shape of the land into a flat map, and once you can decode them you can describe hills, valleys and slopes and even work out how steep the ground is.

The answer

Reading height and slope from contours

A contour line joins points of equal height above sea level. Every line is labelled with its height, and the difference in height between neighbouring lines is the contour interval (for example, $20\ \text{m}$). Two rules unlock relief:

• Spacing shows steepness. Contours close together mean the land rises sharply over a short distance, so the slope is steep. Contours far apart mean a gentle slope.
• Pattern shows the landform. Concentric rings rising to a central high point show a hill or summit; contours forming a V that points uphill show a valley with a river; evenly spaced parallel contours show a uniform slope.

Calculating gradient

The gradient measures steepness as the vertical rise over the horizontal distance. It is usually given as a ratio $1:n$:

Work it out in three steps:

1. Find the vertical rise: the height of the higher point minus the height of the lower point (read from the contours).
2. Find the horizontal distance on the ground, using the scale.
3. Express the ratio and reduce it: a rise of $100\ \text{m}$ over $2000\ \text{m}$ is $100:2000 = 1:20$.

A gradient of $1:20$ means the land rises $1\ \text{m}$ for every $20\ \text{m}$ travelled horizontally; the smaller the second number, the steeper the slope.

Drawing a cross-section

A cross-section is a side view of the land along a line drawn on the map. To draw one:

1. Lay the straight edge of a strip of paper along the line between the two points.
2. Mark where each contour crosses the edge and write its height.
3. Draw a horizontal axis the same length as the line and a vertical axis for height.
4. Transfer each contour mark to the horizontal axis and plot it at the right height.
5. Join the points with a smooth curve.

The result shows the profile: where the land rises and falls, how steep each slope is, and where valleys and ridges sit.

Examples in context

Example 1. Bukit Timah Hill, Singapore. As Singapore's highest natural point at about $164\ \text{m}$, Bukit Timah appears on a topographic map as a tight cluster of concentric contours, with the closely packed lines on its flanks showing the steep wooded slopes that make the summit trail a climb. A cross-section across the hill would show a clear peak rising from the surrounding lowland, illustrating how contour spacing and pattern together describe a steep, isolated summit.

Example 2. Reading slope for hiking and construction. Trail planners and engineers use gradient to judge whether a path or road is walkable or buildable. A footpath at $1:10$ is a hard climb, while a wheelchair ramp must be far gentler, often around $1:12$ or less. Reading contour spacing on a survey map lets planners route a path along gentler ground where contours are spread out, avoiding the steepest, most tightly contoured slopes, which is exactly the skill a cross-section makes visible.

Try this

Q1. State what a contour line shows and what the contour interval means. [2 marks]

• Cue. A contour line joins points of equal height above sea level; the contour interval is the fixed difference in height between one contour line and the next.

Q2. A slope rises $80\ \text{m}$ over a horizontal distance of $1600\ \text{m}$. Calculate the gradient as a ratio. [2 marks]

• Cue. Gradient is rise over run: $80:1600 = 1:20$, so the land rises $1\ \text{m}$ for every $20\ \text{m}$ horizontally.

Q3. Explain how you can tell from a map which of two slopes is steeper. [2 marks]

• Cue. Compare the contour spacing: the slope whose contours are closer together has a greater height change over the same horizontal distance, so it is the steeper of the two.