Finding Your Position

Map Reading and Navigation

Course 1 · Chapter 8 · Finding Your Position: When the Plan and the Ground Disagree

Everyone is unsure of their position sooner or later. The skill is not never being lost; it is noticing early, stopping, and working out where you are before you make it worse. This chapter covers three tools: relocating by matching map to ground, resection with bearings, and building a plan that makes losing your position unlikely in the first place.

First: Stop and Think

The moment you are not sure, stop walking. Walking on in the hope that something familiar turns up is how a small error becomes a large one. Then work through these steps in order:

Stop and tell the group. Do not carry on while you work it out.
Go back to your last certain point: the last checkpoint you were sure of.
Estimate how far you have come since then, from the time walked and your pace (Chapter 6), and the direction you have been heading.
Look for features and match them to the map.
If that is not enough, take bearings (resection, below).
If you still cannot say where you are, go back to the last known point or to a handrail you can trust.

Relocation: Matching Map to Ground

Relocation means working out where you are from what you can see, without a compass. Set the map to match the ground (turn it until the map's north points to north, or until the map's features line up with the ones in front of you) and then compare.

Big features first

Hills, valleys, lakes, forests and large changes of slope are easier to match than small details.

Slope under your feet

Are you on a ridge, a spur, in a valley, on a shelf? Chapter 3's contour shapes tell you which ones the map allows.

Linear features

Paths, walls, fences, streams and power lines. Which one are you next to, and which way does it run?

Point features

A building, a sheepfold, a crag, a lone tree. Small, but each one can narrow the area a great deal.

Then narrow it down: "I am on a path (so I am on this line), the ground slopes down to my left (so I am on this side of the ridge), and I can see a stream ahead (so I am between these two points)." Each clue removes part of the map. When the clues all agree on one spot, you have relocated. If they disagree, one of them is wrong. Re-check the one you are least sure about.

Check, do not assume It is easy to see what you expect to see. Look for one more feature that should be there if your guess is right, and one that should not be. If the first is there and the second is not, you can have more confidence.

Resection: Fixing Your Position With Bearings

If you can see two or three identifiable features on the ground and the map, you can fix your position with a compass. This is resection. It is the reverse of following a bearing: instead of taking a bearing from the map and walking along it, you take a bearing on the ground and draw it back on the map.

The method

Pick two or three features that you can identify on both the ground and the map, spread well apart, ideally at about 90 degrees to each other (not nearly in the same direction).
Point the direction-of-travel arrow at the first feature and turn the housing until the needle is in the orbit: this is your field (magnetic) bearing to the feature.
Convert it to a grid bearing by subtracting the magnetic variation (Chapter 4; the sign rule depends on whether the variation is west or east, so check the map).
Find the back bearing: the direction from the feature to you, which is the grid bearing plus or minus 180 degrees.
Place the compass on the map with its edge through the feature, line up the grid lines with the orienting lines, and draw a line along the back bearing from the feature, in the direction towards you.
Repeat for the second feature. You are where the two lines cross.
With a third feature, the three lines usually make a small triangle (a "cocked hat"). Your position is inside it. The smaller the triangle, the better your readings.

Back bearings

A back bearing is the bearing in the opposite direction. Add 180 degrees if the bearing is under 180, and subtract 180 if it is 180 or over. A wrap-around with modulo handles both cases at once.

# Back bearing: the opposite direction
def back(bearing):
    return (bearing + 180) % 360

print(back(45))     # 225
print(back(300))    # 120
print(back(180))    # 0

The classic slip The bearing you measure points from you to the feature. The line you draw on the map runs from the feature to you. Forgetting to reverse the bearing puts your fix on the wrong side of the feature, which is far worse than a rough position.

Working the same thing out in code

The map method is geometry: two lines cross at a point. Using eastings and northings in metres from the grid (Chapter 2), a feature at (E, N) with back bearing b puts you at (E + t sin b, N + t cos b) for some distance t. Two features give two such lines; solving for where they meet gives your position.

import math

def resect(a, bearing_a, b, bearing_b):
    # a and b are (easting, northing) in metres
    ra = math.radians(back(bearing_a))
    rb = math.radians(back(bearing_b))
    da = (math.sin(ra), math.cos(ra))
    db = (math.sin(rb), math.cos(rb))
    det = da[0] * -db[1] + db[0] * da[1]
    rx, ry = b[0] - a[0], b[1] - a[1]
    t = (rx * -db[1] + db[0] * ry) / det
    return a[0] + t * da[0], a[1] + t * da[1]

print(resect((2800, 2300), 45, (2900, 900), 124))
# about (2004, 1504): within a few metres of (2000, 1500)

The small difference from the true position is down to rounding the bearings to whole degrees. In the field, the error is bigger: a compass is good to a degree or two at best, and a feature a kilometre away turns one degree into about 17 metres. Resection fixes your position to a small area, not a point.

Choosing features for a good fix

Choice	Why
Features about 90 degrees apart	The lines cross cleanly. Two features in nearly the same direction give lines that overlap, and a long, vague crossing.
Features close to you	A small angular error matters less over a short distance.
Features you are certain about	A wrong feature gives a wrong fix with no warning. A third bearing exposes it.
Sharp, distinct features	A summit or a building is a point; a broad hillside is not.

If you are on a linear feature

If you know you are on a path, stream or ridge but not where along it, one bearing is enough. Take a bearing to a known feature, draw the back bearing from it, and your position is where that line crosses the path.

Handrails and Catching Features

The best way to cope with losing your position is to plan so that it matters less. Two ideas from Chapter 7's legs help here.

Handrail

A linear feature you can follow, such as a wall, a stream, a fence or a path, that runs roughly the way you want to go. Keep it beside you and it keeps you on line.

Catching feature

A large feature beyond your target that you cannot walk past without noticing: a road, a stream across your line, a wall. It tells you that you have overshot.

Attack point

An easy-to-find feature near a hard-to-find target. Navigate to the attack point first, then take a short, careful leg to the target.

Aiming off

Deliberately aiming to one side of a target on a linear feature, so you know which way to turn when you reach it.

A catching feature is most useful with a limit: decide beforehand how far you should have walked, by time or by paces, and what to do if you reach that distance and have found nothing. This is simply Chapter 6's pacing and timing used as a safety net.

# Pacing limit for a leg
def paces(metres, per_100m):
    return round(metres / 100 * per_100m)

leg = 800
print(paces(leg, 60))              # 480 expected
print(paces(leg * 1.2, 60))        # 576: stop and think by here

Put It Together

Suppose you have been walking along a bearing in mist for twenty minutes and a wall that should have appeared has not. Stop. Compare your elapsed time and pace with the leg length. If you are still within the expected distance, you may simply be slow; if you are past the limit, you have probably veered off or miscounted. Go back to your last certain point, or if you can see anything identifiable, take bearings. Use the nearest handrail to get back on a line you trust, rather than guessing a new one.

Common Mistakes

Mistake	Fix
Walking on while unsure	Stop at once and return to the last certain point if needed
Forgetting the back bearing	Bearings from you to the feature must be reversed before drawing
Skipping the variation conversion	Field bearings must be changed to grid bearings before use on the map
Two features in nearly the same direction	Choose features about 90 degrees apart
Fitting the map to a guess	Look for something that should and should not be there to test the guess
No limit on a leg	Set a pace or time limit, and decide what you will do at it

Challenges

Exercise 1

Write a function back(bearing) that returns the back bearing, and use it to print the back bearing for each of these grid bearings: 45, 124, 300, 180, 0 and 359. Explain in one line why the modulo operator works for both small and large bearings.

→ Solution

Exercise 2

Feature A is at easting 2800, northing 2300 (metres, local grid) and Feature B is at 2900, 900. You measure grid bearings of 45 degrees to A and 124 degrees to B. Write a program that finds your position by resection and prints it to the nearest 10 m. Then show what happens to the answer if the bearing to B is wrong by 5 degrees (129 instead of 124).

→ Solution

Exercise 3

A leg is 900 m long and you walk 62 double paces per 100 m. A road (a catching feature) crosses your line 300 m beyond the target. Write a program that prints (a) the expected number of paces to the target, (b) the number of paces at which you should stop and think if you have not reached it (120% of the leg), and (c) the number of paces at which you would reach the road. Is the 120% limit before the road?

→ Solution

Quick Reference

When unsure: stop, go back to your last certain point, estimate distance, match features
Relocation: match big features first, then slope, then linear and point features; test your guess
Resection: bearing to feature, convert to grid, reverse it, draw from the feature; position is where the lines cross
Back bearing: add or subtract 180 degrees (or (b + 180) % 360)
Good fixes: features about 90 degrees apart, close, certain, and three if possible
Handrails and catching features: follow a line, stop at a feature you cannot miss, and set a pace or time limit

Coming next Chapter 9 covers poor visibility and darkness: how the techniques change, what the safety margins are, and when the right decision is to turn back.