Axel Boldt wrote:

Hi,

I'm trying to understand how a boat can sail against the wind.
Explanations on the internet usually go like this: "The sail has an
airfoil shape, the air goes faster on one side than on the other,
creating lift by Bernouilli's principle." But I know that for flying
planes, the wing's airfoil shape is not essential (otherwise planes
couldn't fly on their back): it's the angle of attack that matters. So
I'm wondering if the same is true for sailing: would it be possible to
sail against the wind with a sail that's a rigid flat surface, not an
airfoil-shaped piece of cloth?

Thanks,
Axel

Yes, but slowly - a flat surface is not an efficient aerofoil.

A boat goes to windward by generating lift from its sail, just like an
aircraft's wing. If you understand a wing you are 3/4 of the way there.
Of course it generates drag as well; the resultant force from the sail
will be pointing a bit behind right angles to the boom (the long hard
thing usually made of wood or metal at the bottom of the sail) - in your
"flat surface" case, a bit behind right angles to the surface.

The force is angled sideways and forwards by controlling the amount the
sail is directed away from the centre line of the boat.

The forward vector of the force propels the boat forwards.

The sideways vector is absorbed by the centreboard, keel, or sometimes
just the shape of the hull, which acts as another aerofoil shape but
underwater. (It's technically a hydrofoil, but most people think of a
hydrofoil as something to lift the boat out of the water).

Of course, in absorbing the sideways force the underwater parts of the
boat create some drag.

It's much easier to understand with a boat to look at and wave your hand
over - or at least a piece of paper to scribble on!

HTH

Andy