Module 02 · Directions
Reading notes · Module 02 · Direction, distance and time
True, magnetic and compass. Variation and deviation, and which way each sum runs.
Open the interactive chapter →The same material with the chart, the drawings and the exercises.
Three norths · topic 1
Two skippers, one heading
Two boats leave Hallow Quay together. Both point at the same tower on the point — the same tower, the same line, no argument about where they are going.
One skipper writes 204 in his log. The other writes 215.
Neither of them has made a mistake.
One of them read the number off the chart. The other read it off the compass in front of him. Eleven degrees apart, and both of them are right. They are the same direction, counted from two different norths.
The rose on the chart
Every chart carries one. The outer ring is counted from true north — the top of the paper, the meridians, the same for everybody who owns this chart.
The inner ring is counted from magnetic north, which is where a compass actually looks. The two are not the same, and the rose says by how much.
The legend says how far apart they are, when that was measured, and how fast it is moving — because it does move, and that is the next topic.
Real variation in these waters is a fraction of a degree today, and drifting east. This chart uses a bigger one on purpose, the way training charts do — so that getting the sign wrong is something you can see instead of something you can only be told about.
One heading, three norths
A direction is not a number She is pointing somewhere. That is real — you could sight along it. The number is not real: it is something you have to work out, and to work it out you have to say where you are counting from.
The first zero: true north The chart is drawn to true north, and the rose’s outer ring counts from it. Sweep from there round to her bow and you get 204. That is what you write on the chart.
The second zero sits 6° to the west The rose said 7°00′W, measured in 2020; six years on it is 6°00′W. (Bringing a rose up to date is the next topic — here we just use the answer.) Magnetic north is a different zero, so the same bow gets a different number: 210. Look at the boat: she has not moved a degree. Only the place you started counting from.
And her own compass is a third zero The iron in this boat pulls her card another 5° west again. So her compass reads 215 for the very same bow. That last five degrees belongs to this boat alone — take the card ashore and it is worth nothing.
The whole sum, written out There is no formula here. You add or you subtract, and the entire difficulty is knowing which — so it is worth seeing one done from top to bottom.
204 true. The variation is 6° west, so add it: 210 magnetic. Her deviation is 5° west, so add that too: 215 on her compass.
Going down from the chart to the compass, west is added every time. Coming back up it comes off. Getting that backwards is the mistake that costs you twice the variation — and you will meet it again by name.
Now turn her yourself Take hold of the handle on her bow and swing her. Watch the three numbers run together and never change their spacing: six degrees, then five, always — and the sum on the right is the same sum wherever you put her.
Because the bow is what moves. The norths never do.
The rose · topic 2
The rose has a date on it
Look at the middle of the rose again, at the year. 2020. That is not decoration: it is when somebody measured the angle you are about to use.
Magnetic north moves. Not much in a year — minutes of arc — but it moves every year, always, and the rose says how fast: ten minutes eastward each year.
So the number printed there is not the number you want. It is the number somebody wanted in 2020. Yours is a short sum away, and doing that sum is the whole of this topic.
It is the only number on the chart with an expiry date. Everything else — the depths, the coastline, the meridians — is as true today as the day it was printed.
Bringing the rose up to date
What the rose says, and when The legend gives you three things, and you need all three: how far apart the two norths were, when that was measured, and how fast it is moving. Start with the year.
How long ago was that? Take the rose’s year off this one. That is how many years the variation has been drifting since anybody measured it.
That many years of drift Those are the years you have to account for. Each one of them moved magnetic north a little further east.
At so many minutes a year Multiply. Sixty minutes make a degree, the same as an hour — so sixty minutes of drift is one whole degree of variation gone.
So what is it today? The drift is eastward. That is what the rose says and it does not change. What changes is what eastward does to your number: a westerly variation gets smaller, and an easterly one gets bigger.
That is why it is worth doing the sum instead of remembering a direction. Try another rose, and another: of the twenty on this button, eight of them grow.
The sign · topic 3
Which way does the west go?
You already have both numbers She is on 204 true — that is the number you would lay off on the chart. And you know the variation: the rose gave you 6°W.
So her magnetic number is six degrees away from 204. The only thing left to decide is which way.
Guess it and you are out by twice Is it 210 or is it 198? It is tempting to shrug and pick one — it is only six degrees.
It is not. Correct the wrong way and you are not six degrees out, you are twelve: once for not adding it, and once again for taking it off. The size of the mistake is always double the correction. That is why this topic exists.
Look at where the second zero sits Magnetic north is 6° to the west of true north — that is what a westerly variation means, and it is drawn up there.
You count clockwise from your zero round to her bow. Start from a zero that is further west and you have further to go before you reach the same bow. So the magnetic number is the bigger one: 210.
The rule, once and for all Going down from the chart to the compass, west is added.
Coming up from the compass to the chart, west comes off.
And east does the opposite, because east is the other side of true north. The sign turns round and the rule does not — only which side of true north you happen to be on. There is an easterly chart waiting at the end of this example.
You have been doing this since the first example It has a name. That block is the correction ladder — the rungs are the numbers, the steps between them are the corrections, and the arrows say which way you are travelling. You have been writing it since the first example without being told what it was called.
Sailors also have a phrase: error west, compass best — when the variation is west, the compass number is the bigger one. It is worth knowing because you will hear it. But it is a reminder of the rule, not a reason for it, and you have just seen the reason.
Now swing her past north Take the handle and turn her, or press the arrow keys. Both numbers move together and stay six degrees apart, wherever you put her.
Take her round past north and watch what happens: 356 plus 6 is not 362. There is no 362 — the compass only goes round once. Take 360 off and it is 002. The third chart below starts her right there.
The other way: magnetic to chart
Now start at the other end You have been at the chart table working outward. Now do it the way you do it at sea: she is steering 210 by her compass, and you want to draw where she is going.
The chart does not care what her compass says. It wants the true number.
The same ladder, read upward Nothing new is drawn. It is the same three lines, the same two numbers, the same variation between them — you are simply starting at the bottom and climbing.
And what you added on the way down comes off on the way up: 210 − 6 = 204.
The rule, at the other end Coming up from the compass to the chart, west comes off. It is the second half of the same sentence you learned going down, and the arrow on the right is the one that is lit now.
The sign in the middle has turned round with it. Nothing else moved.
One figure, both directions That is the test of a good diagram: the same ladder does both jobs without being redrawn. Only the lit arrow and the sign change.
You may also meet CADET — compass add east true — which is this direction said as a mnemonic: coming up to true, east goes on. Same rule, and the same warning as before: it reminds you, it does not explain you.
And past north the other way Swing her again. This time watch the bottom rung go under north: 002 magnetic with 6°W is not −004. There is no such heading — add 360 and it is 356.
Down or up, the ladder is the same and so is the wrap.
The card · topic 4
The compass lies too, and differently every time
We told you her compass was 5°W out. That was only ever true on one heading — the one she was on — and it is time to say so properly.
The variation is the chart’s problem, and it is the same for every boat that sails these waters. The deviation is yours. It comes from the iron in your own boat — the engine, the anchor chain, the speakers somebody fitted last winter — and it changes with the heading, because as she swings, all that iron swings with her.
So it cannot be one number. It has to be a card: twelve rows, one every thirty degrees, measured on this boat on a day somebody spent turning her round in circles. Look at the row for 210 — there is the five degrees west you were told about.
This card belongs to Kittiwake . Take it aboard another boat and it is worth nothing. Somebody had to make it, and how that is done is waiting for you near the end of this part.
Reading the card
Twelve rows, and nothing in between There is no formula on this page and there is not going to be one. A deviation card is a list — somebody measured her, heading by heading, and wrote down what they found.
Twelve rows, one every thirty degrees. That is the whole of it.
You go in by the magnetic heading This matters more than it looks. The card is tabulated by magnetic heading — not by true, and not by what her compass says. She is on 210 magnetic, so that is the row.
Remember it. When both corrections come together it is the whole trap.
Read the row, and apply it The row says 5°W. And the rule has not changed since the last topic: going down towards the compass, west is added.
210 + 5 = 215. Which is the number the second skipper wrote in his log, back at the beginning.
Now turn her, and watch it move Take the handle and swing her, or press the arrow keys. Watch the lit row run down the card, and watch the green arrow wander while the magenta one stands still.
That is the whole difference between the two corrections. The variation stays where it is whatever you do. The deviation is hers, and it changes with every degree she turns.
And the heading you want is not always on it Swing her slowly and watch the lit row jump. It does not slide: it jumps, because there is nothing in between. A card is discrete — twelve rows for three hundred and sixty degrees, and most of the time she is between two of them.
When she is, you take the nearest row. On this card the rows are never more than two degrees apart, so the nearest one is inside half a degree of the truth — which is closer than you can steer.
Both · topic 5
Both corrections, in order
Three norths again, and now you can do all of it Here they are, the three of them, for the first time since the very first example — and this time none of the numbers is handed to you. The rose gives you the variation. Her card gives you the deviation.
Two corrections, one after the other. That is the whole of this part, and you already know both halves.
The variation first. Always. Her card is tabulated by magnetic heading. So you cannot go into it until you have a magnetic heading — which means the variation has to be applied first.
204 true, variation 6°W, so 210 magnetic. And only now do you open the card.
Then the deviation, read on that magnetic heading Row 210, and it says 5°W. Add it: 215 on her own compass.
Do it in the other order and you go into the card by the wrong row. On 193 true with 11°W the card row is 210, not 180 — and those two rows are a degree apart. Some day they will be more.
The same ladder, one rung taller Nothing new has been drawn. It is the correction ladder you have been writing since the third topic, with a third rung on the bottom and a second correction between.
The arrows say the same thing they always said: going down, west is added; coming up, west comes off. Both corrections obey it, because it was never a rule about variation — it was a rule about which way you are travelling.
Now swing her, and watch both of them work Take the handle. The magenta arrow keeps its six degrees, whatever you do — the variation belongs to the chart. The green one wanders, because her deviation belongs to her and changes with every heading.
And the ladder does the sum again, wherever you put her.
Two ways to get it wrong, and they look different Forget a correction and you are out by that correction. Apply it backwards and you are out by twice it — once for not adding it, once for taking it off.
So the size of the error tells you which mistake you made. Six degrees out on this chart is a forgotten variation; twelve is a variation applied the wrong way. The screen after this one will tell you which one you just made.
Bearings · topic 6
A bearing is a direction too
You are not steering it — you are looking at it A bearing is the direction of something else from where you are: a headland, a light, a church tower. The line is real and the number is not, exactly as it was on the very first screen.
So it needs the same treatment. You take it in one north and you draw it in another.
But this compass has no deviation You take a bearing with a hand bearing compass, standing where you can see the mark — which is away from the engine, away from the anchor chain, away from her iron.
So it has no card and no deviation. What it hands you is magnetic, and there is only one correction to make.
One rung, and the same rule The ladder again, two rungs this time: magnetic at the bottom, true at the top, the variation between.
Coming up to the chart, west comes off. It has not changed since the third topic and it is not going to.
And the way back is the same line The bearing you took runs from you to the mark. To draw it on the chart you want it the other way — from the mark back to you, because the mark is the end you know the position of.
Same line, other end: add 180, or take it off. Whichever keeps you inside 000 and 360. That is all a reciprocal is.
Now swing the sight round Take the handle and move the line of sight. Both numbers follow, the variation between them never changes, and the reciprocal stays exactly opposite — because it is the same line.
Watch it cross north in both directions. There is no 400 and there is no minus twenty.
Where the card came from
Somebody had to make that card, and this is how — the thing you were promised back when the card first turned up.
Two marks ashore at Stennick line up on 032° true. The chart says so, in print. Line them up over the bow, hold her there, and you know your true heading without any instrument at all.
Now do what you have been doing all part. The variation first: 032 true with 6°W is 038 magnetic — and that is the heading a card is tabulated by. Now look down at her compass: 033.
The five degrees between them is her deviation on that heading, and it is easterly. Do it again on another line, and another, and you have a card. Take the short way — compass minus true — and you get four degrees the wrong side: that is the variation mixed in with it.
You will meet these two marks again, properly, in the next module — Where you are . They are called a transit , and there is a great deal more to say about them. Here they are just a direction you can trust.
Open the interactive chapter →The same material with the chart, the drawings and the exercises.