The physics of sailing
From Physclips:
Mechanics with animations and film.
Joe Wolfe
School of Physics, The University of New South Wales.
- How can a boat sail upwind?
- How can boats sail faster than the wind?
- Why are eighteen foot skiffs always sailing upwind?
We introduce the physics of sailing to answer these and some other
questions. But first:
A puzzle.
A river runs straight from West to East at 10 knots. A 10 mile race
is held: the boats sail downstream, from West to East. The first
heat is held in the morning, when there is no wind. The second heat
is held in the afternoon, when there is a 10 knot wind from the West.
In which heat are the faster times recorded?
(Answer below.)
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| Sailing downwind (parallel to the wind, like the
boat at left) is easy to understand: the wind blows into the sails
and pushes against them. The wind is faster than the boat so
the air is decelerated by the sails. The sails push backwards
against the wind, so the wind pushes forward on the sails. But for
a boat with normal sails, the catch is that, downwind, you can only
ever sail more slowly than the wind. Which is usually boring, even
with a spinnaker.
You know this force: In a strong wind, it is easier to walk,
run or bicycle with the wind pushing on your back. Usually,
the wind pushes you in the direction it is going.
Sailing directly upwind (exactly anti-parallel
to the wind, like the boat at right) is also easy to understand:
it's impossible. You just sit there with your sails flapping.
This is also usually boring.
But boats can sail at say 40° to the wind and, by tacking
(alternate lines on either side of the wind direction) they
can go where they like. So let's think about....
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| An experiment. Here is what my left hand looks
like as I bicycle, signalling a left turn. If my hand is flat and horizontal,
I just feel the drag force of the wind acting backwards. But if I tilt
my hand up a little at the front, I feel lift force as well: the force
on my hand is both upwards and backwards. The arrows show the wind
speed relative to me. To get past my hand, the wind is deflected down,
and this pushes my hand up (as well as back).
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Sailing close to the wind uses the shape of the sails to generate
lift. To flow around the sails, the wind has to deviate in direction,
as shown by the arrows for initial velocity vi and
final velocity vf, which are given with respect
to the boat. The change of velocity dv is in the direction shown.
The acceleration aa of the air is dv/dt,
so the force Fa that sails exert on the air is
in the same direction. (Newton's first and second laws: F =
ma.) The force Fw that the wind exerts on
the sails is in the opposite direction. (There is also a Bernoulli
effect, which contributes in a secondary way.)
Note that nowhere in this argument did we need to say that
the wind was faster than the boat.
Now this force is mainly sideways on the boat, and it gets
more and more sideways as you get closer to the wind. However,
part of the force is forward: the direction we want to go.
So...
Why doesn't the boat drift sideways? Well it does a
little, but when it does, the keel, a large nearly flat
area under the boat, has to push a lot of water sideways. The
water resists this, and exerts the sideways force Fk on
the keel.
This cancels the sideways component of Fw.
As to the forwards component: it accelerates the boat until
the drag force Fd holding it back is big
enough so that
So a boat can sail close to the wind: typically 45°, although
many high performance boats go closer than that.
A little digression: the sideways components
of wind and water on the boat make the boat heel (tilt) away
from the wind, as is shown in the diagram below. These two
horizontal components have equal size but opposite direction:
as forces they cancel, but they make a torque tending to rotate
the boat clockwise. This is cancelled by another pair of forces.
The buoyancy and the weight are also equal and opposite, and
they make a torque in the opposite direction. As the boat heels
to starboard, the lead on the bottom of the keel, which has
a substantial fraction of the weight, moves to port and exerts
an anticlockwise torque. These two torques cancel.
So now back to our question:
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How can boats sail faster than the wind? Lots of boats can---especially
the eighteen footer skiffs on Sydney
Harbour. Ask a sailor how, and he'll say "These boats are so fast that they
make their own wind", which is actually true. Ask a physicist, and she'll
say that it's just a question of vectors and relative velocities.
Downwind (diagram at left) is easy. If the wind is 10 kt, and the boat makes
6 kt in the same direction, then the crew feels a wind of 4 kt coming over
the stern of the boat. The true wind vw equals the speed
of the boat vb plus the relative wind vr.
The equation vw = vb + vr tells
us the problem: as the boat speed approaches the wind speed, the relative
wind drops towards zero and so there is no force on the sail. So you can't
go faster than the wind. When the wind is at an angle, we have to add the
arrows representing these velocities (vector addition). Upwind (right), exactly
the same equation holds: vw = vb + vr.
The faster that the boat goes, the greater the relative wind, the more force
there is on the sails, so the greater the force dragging the boat forwards.
So the boat accelerates until the drag from the water balances the forward
component of the force from the sails.
 
| Why are eighteen footers always sailing upwind?
In a fast boat, there's no point going straight downwind: you
can never go faster than the wind. So you travel at an angle. But
if your boat is fast enough, then the relative wind always seems
to be coming mainly from ahead of you, as these arrows show. So
the eighteen footers never set ordinary spinnakers: they have asymmetrical
sails that they can set even when they are travelling at small
angles to the apparent wind.
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Links
The School of Physics and other schools
from the University of New South
Wales provided educational material for the Volvo Ocean Race,
whence this page. Details at Science
Outreach Centre news and Activities
for students and teachers.
Answer to puzzle. The faster heat is the one with no
wind. When the wind and the water both move W to E at
10 kt, the boats drift down the river at 10 kt, with their
sails hanging limp. In the heat with no wind (as measured on
the land), a drifting boat has a headwind of 10 kt. You can
tack into that.
Of course, you don't get something for nothing. In the heat
with wind, the river does very little work on the boat. In
the heat without wind, it exerts much greater force on the
boat, in particular on the keel or centreboard. Much of that
work goes into disturbing the air downwind of the boat's sails.
Tricky? The man in the photo at right did a lot of sailing
on rivers: he would have known that.
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