Drawing Cross Sections from Contours – Cross Section and Sketch Maps (Senior 6 Geography) | Ganzaa

Cross Section and Sketch Maps

Lessons

Senior 6 · Geography

Cross Section and Sketch Maps

4 lessons

Lesson 1 of 4

Drawing Cross Sections from Contours

25 min

Seeing the land side-on

Map 1 below is a topographic extract of a small area with two hills and a river. The contours already tell you which hill is higher and where the slopes are steep, but only after careful reading, because a map shows the land from directly above. A cross section turns that information on its side. Imagine cutting the ground along a straight line and looking at the cut face: that face is what a cross section draws.

Engineers draw sections to plan roads, pipelines and radio links, and geographers use them to describe relief. In the A-level examination you may be asked to draw one from a map extract, to scale, and then to label it and calculate from it. You met contours, spot heights and trigonometrical stations in S1, and grid references and scale in S2. This lesson puts them to work.

Definition

Cross section (also called a profile): a side view of the ground surface along a straight line between two points on a map, drawn to scale from the contours and spot heights that the line crosses.

The straight line on the map is the section line, named by its end points. Example: on Map 1 the section line A–B runs along northing 225, from grid reference 103225 to 159225.

Definition

Sketch section: a quick freehand drawing of the shape of the land along a line. It shows the main rises, falls and features in the right order, but does not plot every contour to an exact vertical scale.

Example: a two-minute sketch of A–B showing a long gentle climb to Hill X, a steep drop to River Z and a short climb over Hill Y.

Map 1

How to read Map 1. Each grid square is 1 km by 1 km on the ground, which is 2 cm on the original 1:50 000 sheet. The contour interval is 20 m, and the 1,600 m contour is drawn thicker. Hill X rises to a trigonometrical station at 1,671 m and Hill Y to a spot height of 1,607 m. River Z flows south between two 1,520 m contours, and a spot height of 1,508 m marks the bridge where the road crosses it. The map is illustrative: it was drawn for this lesson and is not a real place.

Drawing an accurate cross section, step by step

Find the line. Locate A and B from their grid references and join them lightly with a sharp pencil.
Lay a paper strip along A–B. Use a strip with a clean straight edge and mark A and B on it.
Tick every crossing. Wherever the edge crosses a contour, make a short tick and write the height beside it. Also tick the summits, the river, and any feature you will be asked to show (road, bridge, forest edge). Where contours are crowded, tick the thick contours first, then fill in the others one by one.
Draw the frame. On graph paper draw a horizontal base line exactly as long as A–B on the map. Choose a vertical scale (Worked example 2) and draw a vertical axis at each end, numbered in metres. Start the axis a little below the lowest height, not at zero.
Transfer the ticks. Lay the strip along the base line, A on A, and put a dot above each tick at its height.
Join the dots with one smooth freehand curve. Real slopes are rounded. A hilltop rises a little above its highest contour, and a valley floor dips below its lowest one.
Finish. Label A and B, the relief features and any other features asked for, using arrows where needed. Write a title, the horizontal scale, the vertical scale and the vertical exaggeration.

Figure 2 shows the strip for A–B. Because A–B runs due east, every distance along it is simply a difference in eastings: the 1,600 m contour on the east face of Hill X is at easting 12.94, so it lies 12.94 − 10.30 = 2.64 km from A.

Figure 2: the paper strip for A–B, with every crossing ticked.

Distance from A (km)	Height (m)	Feature
0.00	1540	A
0.50	1560
0.90	1580
1.20	1600
1.42	1620
1.60	1640
1.75	1660
1.90	1671	trig station, summit of Hill X
2.10	1660
2.32	1640
2.50	1620
2.64	1600
2.76	1580
2.86	1560
2.95	1540
3.15	1520
3.70	1508	spot height at the bridge, River Z
4.25	1520
4.40	1540
4.56	1560
4.71	1580
4.86	1600
5.00	1607	spot height, summit of Hill Y
5.17	1600
5.32	1580
5.46	1560
5.60	1540	B

Worked example 1: from the strip to the base line

Problem. On the strip, the 1,620 m contour on the east side of Hill X is 2.50 km from A. How far from the left end of the base line do you plot it, if the base line is drawn at the map's scale of 1:50 000?

Solution. At 1:50 000, 1 cm on paper represents 50 000 cm, which is 0.5 km. So

\text{distance on paper} = \frac{2.50\ \text{km}}{0.5\ \text{km per cm}} = 5.0\ \text{cm}.

The whole base line is $\frac{5.6}{0.5} = 11.2\ \text{cm}$ long. If you lay the strip itself on the base line, you need no calculation at all: that is why the strip method is used.

Worked example 2: choosing the vertical scale

Problem. The heights along A–B run from 1,508 m (the river) to 1,671 m (the trig station). The answer booklet leaves a box 4 cm high. Choose a vertical scale.

Solution.

Pick round numbers just outside the range: a base of 1,500 m and a top of 1,680 m, a span of 180 m.
Divide by the space: $\frac{180\ \text{m}}{4\ \text{cm}} = 45\ \text{m per cm}$ .
Round up to an easy value, so the drawing still fits: 1 cm represents 50 m.
Check: $\frac{180}{50} = 3.6\ \text{cm}$ , which fits in the 4 cm box.

The summit of Hill X is then plotted $\frac{1671 - 1500}{50} = 3.42\ \text{cm}$ above the base line. Figure 3 uses this scale. The next lesson shows why this makes the land look 10 times steeper than it really is.

Worked example 3: the valley floor and the hilltop

Problem. Between 3.15 km and 4.25 km from A the section crosses no contour at all. How should the ground be drawn there?

Solution. The land on both sides is at 1,520 m, and no 1,500 m contour appears between them. So the ground there is below 1,520 m but above 1,500 m. The spot height of 1,508 m at the bridge fixes the lowest point. Draw the curve dipping gently from 1,520 m down to 1,508 m at the river and back up to 1,520 m. In the same way, the summit of Hill X lies inside the 1,660 m contour, so the curve rises above 1,660 m to the trig station's 1,671 m. Never draw a flat top at 1,660 m or a flat floor at 1,520 m.

The finished section

Figure 3: the accurate cross section A–B.

Compare Figure 3 with Map 1. On the west face of Hill X the contours are far apart low down and close together near the top, so the slope steepens as you climb. On the east face the opposite happens: the contours crowd together just above the river, so the slope is gentle near the summit and steep near the valley.

Definition

Concave, convex and uniform slopes

A concave slope curves inwards: gentle at the bottom and steep at the top. On a map its contours are widely spaced at low levels and close at high levels. Example: the west face of Hill X.
A convex slope bulges outwards: gentle at the top and steep at the bottom. Its contours are close at low levels and widely spaced at high levels. Example: the east face of Hill X.
A uniform (even) slope has contours evenly spaced, so its gradient does not change.

Drawing a sketch section

A sketch section is drawn when a question asks for "a sketch section" or when you need a quick picture of the relief to support an answer. Use only the heights of the main features: the ends, the summits and the valley floors. Plot these roughly in their correct order and at about the right heights, then join them with a curve that shows the character of each slope (concave, convex, steep or gentle). Label the main features and give a title. Leave out the vertical scale, or write "not to scale".

	Accurate cross section	Sketch section
Points plotted	Every contour crossing, summit and spot height	Main features only
Scales	Horizontal and vertical scales stated; vertical exaggeration given	Not to scale, or approximate
Tools	Paper strip, graph paper, sharp pencil	Freehand
Use	Measurements: gradient, intervisibility, heights	A quick picture of the relief

Warning

Common mistakes

Joining the dots with a ruler. Straight segments make the land look like a staircase of ramps. Draw one smooth freehand curve.
Reversing the section. A must be at the left of the base line, as the question names it. Mark A on the strip before you move it.
Flat hilltops and valley floors. Ground inside the highest contour is higher than that contour; ground between two equal contours with no lower one is lower than them.
Starting the vertical axis at 0 m. On a map of land near 1,500 m this leaves most of the graph empty and the relief flattened into a thin line.
No labels. An unlabelled section earns few marks. Title, both scales, A and B, and the features asked for.

Tip

Exam technique. Before ticking the strip, write the value of every thick contour along the line on the map itself. Then, if two contours sit close together, you can tell whether the next one is higher or lower by counting from the nearest thick contour. A river between two equal contours is always lower than both of them.

Earth Science Classroom: "Topo Maps – How To Draw A Cross Sectional Profile". Watch how the edge of a strip of paper is used to carry each contour crossing from the map to the graph, then compare it with the seven steps above. The method works the same way whatever the units of the contours.

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Practice

Practice (use Map 1, Figure 2 and Figure 3)

Give the six-figure grid reference of the trig station on Hill X.
How long is A–B on the ground, and how long is it on the original 1:50 000 map?
How far from A does the section cross the 1,600 m contour for the second time?
How many times does A–B cross the 1,560 m contour? Name the slopes where it does.
What is the lowest point on the section, and what feature is there?
A pupil uses a vertical scale of 1 cm to 25 m with a base line at 1,500 m. How high above the base line should she plot the summit of Hill Y?
Without drawing, decide which point is higher: 1.0 km or 4.9 km from A. Give your reason from the map.
Use the spacing of the contours on the east face of Hill X to show that the slope is convex.

Show answersHide answers

Easting 12.2 gives 122; northing 22.5 gives 225. Answer: 122225.
From easting 10.3 to 15.9: $15.9 - 10.3 = 5.6\ \text{km}$ . On the map: $\frac{560\,000\ \text{cm}}{50\,000} = 11.2\ \text{cm}$ .
At 2.64 km from A (easting 12.94), on the east face of Hill X.
Four times: the west and east faces of Hill X (0.50 km and 2.86 km) and the west and east faces of Hill Y (4.56 km and 5.46 km).
1,508 m, the spot height at the road bridge over River Z, 3.70 km from A.
$\frac{1607 - 1500}{25} = \frac{107}{25} = 4.28\ \text{cm}$ .
4.9 km is higher. It lies between the 1,600 m contour (4.86 km) and the 1,607 m summit of Hill Y, so it is above 1,600 m. The point at 1.0 km lies between the 1,580 m (0.90 km) and 1,600 m (1.20 km) contours, so it is below 1,600 m.
Near the top, the 1,660 m and 1,640 m contours are $2.32 - 2.10 = 0.22\ \text{km}$ apart; near the bottom, the 1,560 m and 1,540 m contours are only $2.95 - 2.86 = 0.09\ \text{km}$ apart. The same 20 m drop happens over a shorter distance lower down, so the slope steepens downhill: it is convex.

Summary

A cross section is the ground's profile along a straight line, built from every contour crossing with a paper strip.
Choose a vertical scale that fits the space; start the axis just below the lowest height.
Draw one smooth curve; summits rise above the top contour and valley floors dip below the lowest one.
A sketch section shows only the main features, not to scale.

Sources and credits

Written by Ganzaa. Map 1, the paper strip, the cross section and all exercises were drawn and written by Ganzaa for this lesson; the map shows an invented area.

Video: "Topo Maps – How To Draw A Cross Sectional Profile", Earth Science Classroom, embedded from YouTube.

1Seeing the land side-on

2Map 1

3Drawing an accurate cross section, step by step

4The finished section

5Drawing a sketch section

Seeing the land side-on

Map 1

Drawing an accurate cross section, step by step

The finished section

Drawing a sketch section