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BeginnerGrades 6–725 min4 / 28

Plans of an area, azimuth and contour lines

Learn to read and draw a plan of an area, find directions, work out azimuths and back azimuths, read heights from contour lines, find the relative height of a hill and build an A–B relief profile.

Check yourself
In this lesson you will learn
  • Tell a plan from a map, recognise the four kinds of map symbols and draw a simple sketch plan
  • Find directions and calculate an azimuth and a back azimuth
  • Use contour lines to find the absolute height of points, the contour interval and the relative height of a hill
  • Build a relief profile along a line A–B and choose the correct profile in a DİM-style task

At an orienteering race near Gabala, Murad is handed a card: “From the spring, walk 400 m on an azimuth of 60°, then go round the hill along the 150 m contour line.” A runner with a compass and a plan finishes in minutes; one without them gets lost in the forest. In this lesson you will learn how the ground is drawn on paper and how to read directions, distances and relief on a plan.

The plan of an area and map symbols

Definition
Plan of an area

A detailed drawing of a small area (a yard, a park, a village) at a very large scale — usually 1 : 5000 or larger — using map symbols. Because the area is small, the Earth’s curvature is ignored, there is no degree grid, and north is shown by an arrow.

Plans, maps and globes are compared in the lesson “Maps and scale”; here we learn the “language” of a plan. A plan uses four kinds of symbols:

  • Scale (area) symbols — objects whose area is drawn to scale: a forest, an orchard, a lake, a field. You can measure their outline on the plan and work out the area.
  • Non-scale (point) symbols — objects too small to draw to scale: a well, a spring, a single tree, a windmill. The plan shows where they are, not how big they are.
  • Linear symbols — objects whose length is to scale but whose width is not: a road, a river, a fence, a power line.
  • Explanatory symbols — give extra information: the direction of a river’s flow (an arrow), the kind of trees in a forest, the length of a bridge, the depth of a well.

Drawing a plan in the field is called surveying. At school we make a sketch (eye) survey: directions are measured with a compass and distances in steps. In the polar method the observer stands at one point and measures the azimuth and distance to every object; in the route method the observer walks along a path and records the azimuth and the distance at every turn.

  1. 1
    Measure your step

    Pace a 10 m distance several times and find your average step length (usually 0.6–0.75 m).

  2. 2
    Choose a scale

    The whole route must fit on the sheet, e.g. 1 : 2000 (1 cm to 20 m).

  3. 3
    Measure each leg

    Count your steps to the next turn and take the azimuth with the compass; convert the distance to metres, then to centimetres on the plan.

  4. 4
    Draw and add symbols

    Draw the north arrow, draw each leg on its azimuth and add the objects along the way with symbols.

Example: distance in steps

Elvin’s average step is 0.6 m. He took 350 steps from the school to the spring.
1) How many metres is that?
2) How many cm is this distance on a plan at 1 : 3000?
3) On the same plan the spring is 4.5 cm from the bridge. How many steps will Elvin take?

Show solution
1) 350 · 0.6 = 210 m.
2) 1 : 3000 → 1 cm to 30 m (drop two zeros); 210 ÷ 30 = 7 cm.
3) 4.5 · 30 = 135 m; 135 ÷ 0.6 = 225 steps.

Directions and orientation

There are four main directions — north, south, east and west — and four intermediate ones: north-east, south-east, south-west and north-west. Working out your position relative to these directions is called orientation. There are four main ways to do it:

  • With a compass: one end of the magnetic needle always points north. Hold the compass level and, when the needle settles, turn the dial so that 0° (N) is under its north end.
  • By the Sun: north of the Tropic of Cancer, including Azerbaijan, the Sun is due south at local noon, and the shadows of upright objects point north.
  • By the Pole Star: Polaris, in the Little Bear (Ursa Minor), always appears in the north. You find it on the line through the two end stars of the Big Dipper’s “bowl”, about five times their separation away.
  • By local signs: snow melts sooner on south-facing slopes; moss and lichen usually grow on the north side of trees and rocks; anthills are usually built on the south side of a tree. These signs only help — always check several of them.

Azimuth and back azimuth

Definition
Azimuth

The angle between the direction to north and the direction to an object, measured clockwise. An azimuth runs from 0° to 360° and is measured with a compass.

DirectionAzimuthBack azimuth
North0° (360°)180°
North-east45°225°
East90°270°
South-east135°315°
South180°0°
South-west225°45°
West270°90°
North-west315°135°
Azimuths of the main and intermediate directions. The back azimuth always points the opposite way.
A(back) = A ± 180°
where:
  • Aforward azimuth — the direction from point A to point B
  • A(back)back azimuth — the direction from B back to A
  • ±+180° if A < 180°, −180° if A ≥ 180°

The way back is exactly opposite to the way there, so the two directions differ by 180°; the answer must stay between 0° and 360°.

NN60°240°ABForward azimuth A → B: 60°Back azimuth B → A: 240°
An azimuth is always measured from north at the point where you stand.
Example: back azimuth

Find the back azimuth: 1) 70°; 2) 300°; 3) 180°.
4) A hiker walked from the camp to a cave on an azimuth of 215°. On what azimuth should he return, and in which direction from the camp is the cave?

Show solution
1) 70° < 180° → 70° + 180° = 250°.
2) 300° ≥ 180° → 300° − 180° = 120°.
3) 180° − 180° = 0° — the opposite of south is north.
4) 215° − 180° = 35°. An azimuth of 215° lies between 180° (south) and 270° (west), so the cave is south-west of the camp and the way back leads north-east.
Example: reconstruct the route

A hiker leaves the camp and walks 2 km on an azimuth of 0°, then 3 km on 90°, then 2 km on 180°. On what azimuth and how far must he walk to get back to the camp?

Show solution
Sketch it: 2 km north, 3 km east, 2 km south.
The north and south legs cancel out: 2 − 2 = 0. The hiker is exactly 3 km east of the camp.
He must go west: 3 km on an azimuth of 270° (90° + 180° = 270°).
DİM-style task: azimuth and direction

On a plan, the azimuth from the spring to the school is 135°. Find the azimuth from the school to the spring and the direction of the spring as seen from the school.
A) 315°, north-west
B) 225°, south-west
C) 45°, north-east
D) 315°, south-east
E) 135°, north-west

Show solution
Back azimuth: 135° + 180° = 315°.
315° is north-west (see the table), so the spring lies north-west of the school.
Check: the school was south-east (135°) of the spring — the opposite side is north-west.
Correct answer: A. (Option D has the right azimuth but the wrong direction.)

Contour lines, contour interval and isobaths

Absolute and relative height are explained in the lesson “Landforms: mountains and plains”. The most exact way to show relief on a plan or a topographic map is with contour lines. Imagine a hill being flooded by water that rises 10 m at a time: every “mark” the water leaves on the slope is a contour line. Seen from above, these marks look like closed curves lying one inside another.

Definition
Contour line (isohypse)

A closed curve on a plan or map joining points of the same absolute height.

Definition
Contour interval

The difference in height between two neighbouring contour lines. It is the same everywhere on one plan (for example 5 m or 10 m) and is usually printed under the plan.

Definition
Isobath

A line joining points of the same depth on the floor of a sea, lake or ocean. On physical maps depth is also shown by darker shades of blue.

  • The closer the contour lines, the steeper the slope; where they are far apart, the slope is gentle.
  • A short tick on a contour line — a slope tick (bergstrich) — points downhill: outwards on a hill, inwards in a hollow.
  • Height labels on contour lines are written with their tops facing uphill.
  • If heights increase towards the centre it is a hill; if they decrease it is a hollow. Contour lines never cross each other.
H = H₁ + h · a / bH = H₁ + h · a / b
where:
  • Habsolute height of the point, m
  • H₁height of the contour just below the point, m
  • hcontour interval, m
  • adistance from the point to the lower contour
  • bdistance between the two contours (along the same straight line)

The slope between two contours is taken as even. A point exactly halfway has H = H₁ + h / 2.

H(rel) = H(summit) − H(foot); H(foot) = H(inner) − (n − 1) · h
where:
  • H(summit)absolute height of the summit (usually written as a number)
  • H(foot)height of the outermost (lowest) contour
  • H(inner)height of the innermost contour
  • nnumber of closed contours that show the hill

n contours have n − 1 gaps between them. If the summit has no number, it is higher than the innermost contour but lower than one contour interval above it.

Example: a point between contours

On a plan the contour interval is 5 m.
1) Point A is exactly halfway between the 110 m and 115 m contours.
2) Point B lies on the 2 cm gap between these contours, 0.4 cm from the 110 m contour.
3) Point C lies on the 115 m contour.
Find the absolute heights of the points and the height of C relative to B.

Show solution
1) H(A) = 110 + 5 ÷ 2 = 112.5 m.
2) H(B) = 110 + 5 · 0.4 ÷ 2 = 110 + 1 = 111 m.
3) H(C) = 115 m; C is 115 − 111 = 4 m higher than B.
Example: relative height of a hill

A hill is shown by 4 closed contours with a contour interval of 5 m. The innermost contour is labelled 85, and the summit is 87.6 m high.
1) Find the height of the foot of the hill (the outermost contour).
2) What is the relative height of the hill?
3) How would the answer change if the contour interval were 10 m?

Show solution
1) 4 contours → 3 gaps: H(foot) = 85 − 3 · 5 = 70 m.
2) H(rel) = 87.6 − 70 = 17.6 m.
3) H(foot) = 85 − 3 · 10 = 55 m; the relative height would be 87.6 − 55 = 32.6 m. Always check the contour interval.
Example: isobaths

1) The surface of a mountain lake is at 1450 m, and the deepest isobath in the lake is 60 m. What is the absolute height of the deepest point of the lake?
2) The level of the Caspian Sea is about −28 m and its greatest depth is about 1025 m. How far below ocean level is its deepest point?

Show solution
1) Depth is measured down from the surface: 1450 − 60 = 1390 m.
2) −28 − 1025 = −1053 m, that is, about 1053 m below ocean level.

The relief profile: building and choosing it

A relief profile is a vertical cross-section of the ground along a chosen line A–B: it shows how steep the slopes are and where the tops and hollows lie. Drawing a profile is a graphic method of map analysis, and DİM usually asks you to pick the right profile out of five.

  1. 1
    Draw the line A–B

    Join points A and B on the plan with a straight line.

  2. 2
    Mark the crossings

    Lay a paper strip along A–B, mark every place where the line crosses a contour and write its height. Estimate the heights of A and B from the nearest contours too.

  3. 3
    Draw the axes

    The horizontal axis is the length of A–B (at the plan’s scale). Mark heights on the vertical axis in steps of the contour interval; the vertical scale is made larger, otherwise the relief looks too flat.

  4. 4
    Join the points

    From each crossing go up to its height and join the points with a smooth line. Between two neighbouring crossings of the same height the line bends either up (a hill) or down (a hollow).

  5. 5
    Check

    Where the contours are crowded the profile must be steep; where they are sparse it must be gentle.

AB136100110120130NContour interval: 10 m100110120130H, mABgentle slopesteep slope
The foot of the hill is the 100 m contour, so its relative height is 136 − 100 = 36 m.
DİM-style task: choose the profile

The contour interval is 10 m. The line A–B runs from west to east and crosses, in order, the 100, 110, 120, 130, 130, 120, 110 and 100 m contours. The summit lies inside the 130 m contour, and the contours on the east side are closer together than on the west side. Which statement about the profile is true?
A) The profile starts at 130 m and ends at 100 m
B) The highest point is 130 m and the profile runs flat there
C) In the middle there is a point higher than 130 m, and the east slope is steeper than the west slope
D) In the middle there is a hollow lower than 120 m
E) The west slope is steeper than the east slope

Show solution
The crossings rise from 100 to 130 m and then fall from 130 to 100 m: A–B goes over a hill, and A and B are both below 100 m (A is wrong).
Between the two 130 m crossings lies the summit, so the height there is above 130 m (B and D are wrong).
The contours are crowded in the east → the east slope is steeper (E is wrong).
Correct answer: C. The diagram above shows exactly this kind of profile.
Check yourself
  1. 1.The back azimuth of a direction with an azimuth of 45° is °.
  2. 2.The azimuth of due west is °.
  3. 3.A hill is shown by 6 closed contours; there are gaps between them.
  4. 4.A line joining points of equal depth is called an .

Key points

  • A plan shows a small area at a very large scale: there is no degree grid and north is shown by an arrow; symbols are scale, non-scale, linear and explanatory.
  • An azimuth is measured clockwise from north, 0°–360°: east 90°, south 180°, west 270°.
  • Back azimuth = A ± 180°: add to an azimuth below 180°, subtract from a larger one.
  • A contour line (isohypse) joins points of equal height, an isobath points of equal depth; crowded contours mean a steep slope.
  • Relative height of a hill = summit − foot (the outermost contour); n contours span n − 1 contour intervals.
  • A profile is built from the crossings of the line A–B with the contours; pick the right profile by its start and end heights, the position of the top and the steep side.

Check yourself

12 questions. Every correct answer earns XP.

1 / 12
How is an azimuth measured?