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Two hills drawn as contour rings, one gentle and one steep Two sets of closed loops, each set nested inside itself like the rings of a tree stump, drawn as a map seen from directly above. Both sets have five rings, so both hills climb by the same amount. The set on the left has its rings spread far apart, which means a long gentle walk from one height to the next. The set on the right has the same five rings packed close together, so the very same climb happens over a much shorter distance and that hill is steep.

A Contour Line Is a Waterline

About 25 minutes

Open a walking map and it is covered in thin brown lines. They loop and swirl and never quite touch, and in places they bunch up into a thick smear.

Most people decide they are something to do with hills, and leave it there. But they are not a general impression of hilliness. Each line is a precise instruction, and there is one picture that makes all of them obvious at once.

Flood the hill

Take a hill. Pour water around it until the water stands at exactly 100 metres above sea level, and let it settle.

Now walk round the edge of that water, right where it meets the grass, and paint a line on the ground as you go. You will come back to where you started, because a waterline has to close — water cannot stop halfway round a hill.

Every point on that painted line is at exactly 100 metres. Not near it. Exactly.

Drain the water away and that painted loop is a contour line. Do it again at 110 metres and you get a smaller loop inside the first one. Again at 120, and so on up to the summit.

Water rising up a hill, and the loop its edge leaves on the map On the left a hill is drawn from the side, standing in the sea. A level surface of water can be raised up the hill. On the right the same hill is drawn from directly above, with the shoreline already marked as a closed loop round its foot. Each time the water reaches a new ten metre level, the loop that its edge traces round the hill at that height is added inside the ones already drawn. By the time the water reaches the summit the map carries a nest of loops, and the smallest loop in the middle is the top of the hill. from the side raise the water from above a loop at every level

Raise the water on the left and watch where its edge lands. The map on the right is the same hill seen from above, with the loop drawn in as the water passes it.

Nobody ever floods a real hill, of course. Surveyors measure heights instead. But the loops on the map are exactly the loops the water would make, and once you can see the water the lines stop being mysterious.

Four things that follow immediately

Almost everything a map teacher tells you about contours is just this picture, said again.

They never cross. A spot on the ground has one height. It cannot be both 100 metres and 120 metres, so two waterlines can never run over the same patch of grass.

They never stop in the middle of nowhere. A waterline goes all the way round. If a line seems to end on your map it has only run off the edge of the paper, and it is carrying on somewhere on the next sheet.

Rings inside rings mean a hill. Each loop is higher than the one outside it, so the smallest ring in the middle is the top. If the numbers count down as you go inward you are looking at a hollow instead — a crater, or a pit, and a good map marks those with little ticks pointing inwards.

And this is the useful one: close together means steep.

Why crowded lines mean a cliff

The height gap between one line and the next is fixed — 10 metres on many maps, and printed in the map's key. It is the same 10 metres everywhere on the sheet.

So the only thing that changes is how far apart the lines are drawn, and that gap is a real distance across the ground.

If two lines are far apart, you walk a long way to climb 10 metres. That is a gentle slope you would hardly notice. If they are almost touching, you climb the same 10 metres in a couple of paces. That is a scramble, or a cliff.

The same climb spread over a long walk and over a short one Two slopes are drawn from the side, one on each half of the picture, and both rise by exactly the same forty metres. The slope on the left takes a long way to do it. The slope on the right does it in a short distance and then runs flat. Dashed level lines mark every ten metres of height on both, and thin dotted lines drop from each of those marks onto a strip of map underneath. Both map strips are the same width and drawn to the same scale. On the left map the five resulting lines are spread far apart. On the right map the very same five lines are crowded almost on top of each other at one end, with empty flat ground beyond them. gentle lines far apart steep same five lines, crowded Both climb 40 metres. Only the distance is different.
The same 10 metres of climb, twice. On the left it is spread over a long walk. On the right it is not. The map shows that difference as the space between two lines.

This is why a walking map tells you how tiring a route will be before you set off. A path that stays parallel to the lines is flat. A path that crosses a lot of lines in a short distance is going to hurt.

On one part of a map the brown lines are almost touching. What is the ground doing there?

Reading a valley

One last trick, and it works every time.

Where a contour crosses a stream it always bends into a V — and the V points upstream, uphill, away from where the water is going.

That has to happen. The stream sits in the lowest ground around, so the line, which must stay at one height the whole way, has to detour inland and up the valley before it can come back down the other side. It is the waterline poking its finger up the notch.

Which means you can tell which way a stream flows on a map you have never seen, in a country you have never visited, without any arrows: find the Vs, and the water is running away from their points.