Taking Bearings

Map Reading and Navigation

Course 1 · Chapter 5 · Taking Bearings: From Map to Ground and Back

Chapter 4 explained what a bearing is. This chapter uses one. You will learn to take a bearing from the map and carry it onto the ground, to follow it without wandering off line, and to do the reverse: take a bearing from a landmark you can see and turn it into a line on the map.

Map Bearing to Field Bearing

This is the everyday job: you are at point A, you want to reach point B, and you cannot simply see it. The compass is used first as a protractor on the map, then as a direction finder on the ground.

Join the two points. Lay the long edge of the compass baseplate along the line from A to B, with the direction-of-travel arrow pointing towards B. The map is not turned; you only need the edge of the plate.
Set the housing to grid north. Turn the rotating housing until the orienting lines inside it run parallel to the map's vertical grid lines, and the orienting arrow points to the top of the map (grid north).
Read the grid bearing at the index line.
Convert to a field (magnetic) bearing. With the variation west of grid north, add it; if east, subtract it (Chapter 4). Turn the housing to the new figure. (Or set the declination scale in advance, if your compass has one.)
Take the compass off the map, hold it level in front of you, and turn your whole body until the red end of the needle sits inside the orienting arrow ("red in the shed"). The direction-of-travel arrow now points at B.
Pick a mark. Look along the arrow to a clear feature on that line and walk to it.

Turn yourself, not the housing Once the bearing is set, never touch the housing again until you have arrived. The only thing that turns is you. A common beginner mistake is to twist the housing until the needle looks right, which just resets the bearing to whatever way you happen to be facing.

import math

# Grid bearing between two points given as (easting, northing) in metres
def grid_bearing(e1, n1, e2, n2):
    return math.degrees(math.atan2(e2 - e1, n2 - n1)) % 360

print(round(grid_bearing(450, 200, 600, 350)))   # 45
print(round(grid_bearing(300, 300, 300, 100)))   # 180

The function takes the east-west difference first and the north-south difference second, because a bearing is measured from north, not from east as in school geometry. The final % 360 turns a negative angle into its positive equivalent.

Following a Bearing

Holding the compass out and walking while staring at it is the worst way to follow a bearing: the needle swings, you wander, and you trip. Use the compass to choose a mark, then put it away and walk to the mark.

Pick a mark on the line

A rock, a tree, a gatepost, a patch of different grass: anything distinct and in line with the arrow. Walk to it by the easiest ground, not necessarily the straight line.

Keep legs short

An error of 2 degrees is about 35 m sideways per kilometre. Short legs reset the error each time you reach a mark.

Leapfrogging

In poor visibility, send a companion ahead to the edge of visibility and direct them onto your line with the compass. Walk up to them, then repeat.

Going around obstacles

Offset at right angles by a counted number of paces, pass the obstacle, then return by the same number of paces on the other side.

Sideways error	Over 500 m	Over 1,000 m
1 degree	about 9 m	about 17 m
2 degrees	about 17 m	about 35 m
5 degrees	about 44 m	about 87 m

Field Bearing to Map Bearing

The reverse job: you can see a landmark, perhaps a distinctive summit or a tower, and want to draw the line to it on the map.

Point the direction-of-travel arrow at the landmark.
Turn the housing until the red end of the needle is in the orienting arrow. Read the magnetic bearing.
Convert to grid: with variation west, subtract it; if east, add it.
With the housing set to the grid bearing, put a corner of the baseplate on the landmark on the map and pivot the whole compass until the orienting lines are parallel to the grid lines and the arrow points to the top of the map.
The plate edge now lies along the line between the landmark and the point you stand on. But you are looking towards the landmark, so you lie on the opposite side. To draw the line from the landmark back to yourself, use the back bearing (add or subtract 180).

# Variation 2 degrees west of grid north
def magnetic_to_grid(mag, variation_w):
    return (mag - variation_w) % 360

def back_bearing(bearing):
    return (bearing + 180) % 360

grid = magnetic_to_grid(128, 2)
print(grid)                  # 126
print(back_bearing(grid))    # 306

One bearing gives a line, two give a position A single bearing only tells you that you are somewhere along a line. Taking bearings on two or three landmarks, and drawing each line, gives the point where they cross: your position. Chapter 8 develops this properly (resection).

Common Mistakes

Mistake	Fix
Turning the map or the baseplate edge the wrong way round	The direction-of-travel arrow must point from start to destination
Orienting lines not parallel to the grid lines	Check along several grid lines, with the arrow pointing to the top of the map
Forgetting the variation (or applying it backwards)	Grid to magnetic and magnetic to grid use opposite signs
Twisting the housing while walking	Turn your body, never the housing
Using the forward bearing when you needed the back bearing	Ask: am I drawing a line from the landmark to me, or from me to it?
Long legs with no marks	Break the walk into legs that end at features you can see

Challenges

Exercise 1

The variation is 2 degrees west of grid north. Eastings and northings are in metres. Find the grid bearing, the magnetic bearing and the distance for each leg: (a) (450, 200) to (600, 350); (b) (300, 300) to (300, 100); (c) (700, 250) to (500, 450); (d) (100, 500) to (400, 100).

→ Solution

Exercise 2

With the same variation, you sight a landmark and read 128 degrees on the compass. (a) What grid bearing do you draw on the map? (b) What is the back bearing, in grid, from the landmark to you? (c) If you drift 3 degrees off a bearing over 800 m, how far off line are you? And 5 degrees over 500 m? (d) Why does walking in short legs to marks reduce the problem?

→ Solution

Exercise 3

Write a short program or spreadsheet that takes two points (easting, northing) and prints the grid bearing, distance and magnetic bearing for a given westerly variation, and a second function that returns the sideways drift for a given angle error and distance. Test it with the legs from Exercise 1 and the figures from Exercise 2.

→ Solution

Quick Reference

Map to ground: edge along the route, orient to grid north, read, add variation (west), body turns "red in the shed"
Ground to map: sight, red in the arrow, read, subtract variation (west), draw the line
Back bearing: plus or minus 180, to draw the line from the landmark to you
Walking: pick marks on the line, keep legs short, never twist the housing
Drift: about 17 m per degree per kilometre

Coming next Chapter 6 adds distance and time: measuring a route on the map, counting paces on the ground, and estimating how long a walk will take.