Drawing a cross-section

Draw a profile from a 1:24,000 map with a vertical scale of 1:200 and the hills look 120 times taller than they would at true scale.

A slice through the land

A topographic profile, or cross-section, is what you would see if you sliced the land along a line and looked at the cut from the side. It turns the bird’s-eye view of a contour map into a side view, so you can see at once where a route climbs, where it drops and how high it gets. Geologists draw profiles to show rock layers, engineers to plan roads and tunnels, and hikers to see where the hard part of a day will be.

Five steps on paper

First, draw the line of section on the map and label its ends A and B. Second, lay the straight edge of a strip of paper along the line and make a tick wherever a contour crosses it, writing the height beside each tick. Mark the streams, summits and the two ends too. Third, draw a graph whose horizontal axis is as long as the line A-B and whose vertical axis is marked in heights, with the same spacing as the contour interval. Fourth, move the paper strip to the bottom of the graph and, above each tick, plot a dot at its height. Fifth, join the dots with a smooth curve, not with straight segments.

Two details make a profile honest. Summits and valley floors are not exactly on contour lines. If a hilltop is inside the 180 metre ring but there is no 200 metre ring, the curve should rise above 180 and stay below 200 at that point. And the ends of the profile usually fall between contours too, so their heights are estimates. Laboratory manuals for earth science students list these same points in their checklists for a complete profile.

Vertical exaggeration

If the vertical axis used the same scale as the map, most profiles would look almost flat, because hills are small compared with the distances between them. So the vertical axis is usually stretched. The stretch is called vertical exaggeration, and it is the vertical scale divided by the horizontal scale. A profile drawn from a 1:24,000 map with a vertical scale of 1:200 has a vertical exaggeration of 24,000 ÷ 200 = 120. That is extreme: a gentle hill would look like a spike. A profile with an exaggeration should always say so, for example VE ×10.

Try it in the scene. The Height slider changes the exaggeration of the 3D model from 1 to 5 times. At 1, the mountain range looks surprisingly low; that is its true shape. The cross-section under the controls fits its height to the box, so its exaggeration changes when you move A or B, and the number is printed in its corner. Make the line short and the VE drops; make it cross the whole map and the VE rises.