Module 02 · Speed, distance and time
Reading notes · Module 02 · Direction, distance and time
An hour is a length. Open it, measure with it and walk it — then the three sums.
Open the interactive chapter →The same material with the chart, the drawings and the exercises.
Three numbers
Three numbers, and you always have two
There are only three numbers in this part.
How far you are going. How fast you are going. How long it takes.
Give a navigator any two of them and the third is not a matter of opinion. It is already decided, and the whole of this part is learning to get it out.
distance · speed · time
any two give you the third
Nothing else comes into it. No tide, no weather, no reason for the passage. Three numbers and a pair of dividers.
A knot is one mile in one hour
That is the whole definition. A boat doing one knot covers one nautical mile in one hour.
You already have the mile: it is one minute of latitude, taken off the latitude scale up the side of the chart, and a cable is a tenth of it. You measured with both in module 01 and neither has changed.
And it is always the latitude scale, up the sides — never the one along the top or the bottom. A minute of latitude is a mile anywhere on earth; a minute of longitude is a mile only at the equator, and about three quarters of one here. Distance comes off the side. You met that in module 01 and it has not changed either.
So a boat doing 5 knots covers five miles in an hour — which is to say she covers five minutes of latitude in an hour.
1 knot = one mile in one hour
= one minute of latitude in one hour
And it is never knots per hour. A knot is already a speed — the “per hour” is inside the word. Saying knots per hour is like saying miles per hour per hour.
An hour is a distance
Here is the idea the whole of this part hangs on, and it is worth stopping on.
At your speed, an hour is a length. A boat doing 5 knots covers five miles in an hour, and five miles is something you can open a pair of dividers to: five whole minutes on the latitude scale up the side.
Open them to that and you are holding one hour of your boat between the two points.
your speed, opened on the latitude scale up the side = one hour of your boat
Lay it on the chart and you can see how much of a passage an hour eats. Step it along and every step is another hour gone.
That is not a trick for the screen. It is how it is done on paper, and it is why the dividers live beside the chart and not in a drawer.
Take a length off the chart
You have opened the dividers to a length you chose. Now the other way round: a length the chart chose.
You did this in module 01 — span, carry, read — and after you had proved it, the chart started reading the scale for you. From here you do it yourself again, because in a moment this same pair of dividers is going to walk hours down a leg, and a tool you let someone else read is a tool you cannot walk with.
Speed and time to distance
The one you can see
Start with the easy one, because you can watch it happen.
You have the speed. You have the time. You want the distance.
An hour is already in your dividers. Two hours is two of them, laid end to end. There is nothing to work out: you step it and you read where you got to.
There is a line drawn across the chart. It goes nowhere in particular — it is there to be walked.
One hour forty-five is not 1.45
Two hours is two paces. One hour forty-five is one pace and three quarters of a pace. You can see it, and there is nothing to convert.
The moment you put the dividers down and reach for arithmetic, there is. Converting is the price of letting go of the dividers.
One on paper
Put the dividers down. From here the three numbers come on paper, the way they come in an exam.
And the first thing that happens is the thing that goes wrong most.
Distance and time to speed
Turn it round
The second question. You have the distance. You have the time. You want the speed.
You measured a leg and somebody tells you how long it took. How fast were you going?
With the dividers you do not divide: you open them until one pace covers the leg in the time you were given. If it took two hours, half the leg is one hour — so open to half, and read that on the latitude scale. That is your speed.
Miles in one hour is what a knot is. That is the whole of it, and it is why the scale can answer a question about speed at all.
How fast was she going?
Here is the gesture, on a passage somebody else made.
Watch what does NOT happen: nothing gets divided.
When the time is not whole hours
You have written a time as one number before. Now you have to divide by one, and that is where this goes wrong.
The difference does not look like much until you see what it costs.
Distance and speed to time
The one you will use most
The third question, and the one that comes up more than the other two together: you have the distance and the speed, and you want the time.
Step your hour down the leg and count the paces.
And here is the catch: the leg almost never runs out at the end of a pace. There is nearly always a piece left over, and that piece is a fraction of an hour.
That fraction is where this whole topic is failed — not in the stepping, which you can see, but in what gets written down afterwards.
A leg that takes less than an hour
Here is the whole of it on somebody else's passage: a leg the hour is too big for.
Watch what tells you the answer is under one, before any number appears.
Naught point something of an hour
You are holding a fraction of an hour. Three quarters of an hour is a thing you can feel. Naught point nine five is not, and that is where this goes wrong.
It goes wrong the same way every time, and it is worth seeing it happen once.
Fewer paces, less error
One more way of using the dividers, and it is the one that gets asked about.
When the leg is long you do not walk it an hour at a time.
Writing it down
The shorthand, and the 60 D Street
You have now answered all three questions, and you answered them with a pair of dividers and the latitude scale up the side of a chart.
Here is how the same three are written down.
D = S × T S = D ÷ T T = D ÷ S
with the time in hours
And here is the way most people remember which is which. Cover the one you are looking for and what is left is the sum.
Now the same three with the numbers in them. Move any two and the third follows — and watch the line underneath, which tells you whether you are multiplying or dividing, and why.
S = (60 × D) ÷ T D = (S × T) ÷ 60 T = (60 × D) ÷ S
with the time in minutes
It is the same three sums. The 60 is in there only because the time is in minutes instead of hours — nothing else. People call it the 60 D Street triangle and learn it by heart, and you will meet it in every book and on every course.
Learn it if you like. But if you ever cannot remember which way round it goes, you do not have to: open the dividers to one hour and walk it.
A formula can be remembered backwards. A pair of dividers cannot.
Through the water and over the ground
Two distances, two speeds
One more thing before you trust any of this, and it is about which numbers you are allowed to put together.
When you measure a leg on the chart, you measure a distance over the ground. The seabed does not move.
When your boat says 5 knots, that is almost always the log, and a log measures the water going past the hull: speed through the water.
chart distance → over the ground
log speed → through the water
If the water itself is moving, those are two different measurements of two different things, and dividing one by the other gives a number that means nothing.
On a still day they agree and every sum in this part is exact. With a tide running they do not.
Open the interactive chapter →The same material with the chart, the drawings and the exercises.