How Wings and Sails Work

I recently visited The Australian Museum in Sydney and saw this sign in the bird exhibit.

I had seen it before and complained without a response and it drives me nuts every time I see it. Why? Because it is wrong in almost every aspect of how a bird stays in the air.

Even on Facebook when I railed against this, expert yachtsmen, bird lovers and pilots alike still misunderstand how this all works.

So let us sort this out once and for all.

Square Rig Sails and Spinnakers (Running Downwind)

This is the simplest form of sail from a physics perspective.

The square sails get pushed by the wind.

In physics, F=ma=mdv/dt=d(mv)/dt

In other words, the force (F) generated is equal to the change of momentum (mv) that creates it. The momentum of the air is the mass of the air captured by the sail multiplied by the velocity of the air (relative to the ship).

So, for a square rig running downwind, the fastest you can ever go is the speed of the wind because, when you are travelling the same speed of the wind, the relative velocity of the air to the ship is zero. In reality, the water resistance will slow the ship down making it sail slower than the wind.

Spinnakers (the big bloated sail on the front of a yacht) work the same way.

Now, in fact, a square rig can run with the wind in front (well, off to the side and in front, at least) but to tackle the physics of this we will look at a fore and aft rig.

Fore and Aft Rigs

These are the sails we think of these days and they do not catch the wind at all, which is why they can sail very close to wind i.e. into it and can sail faster than the wind.

Often the explanation for how these work talk about Bernoulli’s Principle, which is valid, just not very intuitive. I prefer to think in terms of the Coanda Effect, which is a different way of thinking about the same thing.

The Coanda Effect describes the phenomena that flowing air likes to stick to the surface it is running along.

So in terms of our fore and aft sail, the wind runs along the leading edge and then tends to bend around with the curve of the sail.

So how does this move the boat?

Remember before that the force generated is due to the change in momentum? Well momentum is what is called a ‘vector quantity’ so as well as an amount, it also has a direction. So, even if moving along the sail does not diminish the speed of the air, via the Coanda Effect, the direction does change and this has an equal and opposite effect on the sail, effectively pulling it.

In this case, the force generated is trickier to calculate because it involves vector maths and trigonometry. For those with an interest in such things, here is a great link.

Laminar flow and turbulent flow often get mentioned in the explanation of how sails work. Again, it is easier to think about this in terms of the Coanda Effect. A laminar flow means the air travels nicely along the sail and pops out the other side, redirected. Turbulent flow happens when the viscosity of the air is insufficient to keep it running along the sail and it goes any which direction. Therefore less air makes it to the end of the sail and we are redirecting less air and generating less force.

In short though, as long as the sail can be set so the wind runs along the edge and make the boat move forward, the limit to the amount of force that can be generated is not limited by the wind’s speed, but by the momentum of the air whose direction we are changing (its mass multiplied by its speed). If we have a big sail which can redirect a lot of air, we get a lot of force. That force then accelerates the ship (Force = ship mass * acceleration) until the force of the water against the hull matches it and we reach our top speed.

A lightweight ship with a square rig running downwind can still only go as fast as the wind. A lightweight ship using a fore and aft sail can literally fly.

Plane and Bird Wings

So which is the mechanism for plane and bird wings? Plane wings are often not curved and can fly upside down. Even birds can fly upside down.

The fact is, planes and birds fly by pushing the air down (flapping in the case of birds and the air hitting the underside of the wing and flaps, redirecting it downwards in the case of planes). Even a gliding bird is flying by pushing air down off the bottom of the wing.

If you doubt this, look at a bat’s wing and try and work out how a nice laminar flow could happen across it.

In terms of our sails, planes and birds work like a square rig running downwind. Only, in this case, the plane’s engine generates the relative movement of the air and the plane, rather than relying on wind. In the case of a bird, as well as pushing down, they are pushing forward for the same effect in a very complex motion (which makes it very hard for us to replicate with machines).

It is true that high performance aircraft make use of a curved wing to optimise the efficiency of the plane, but the lift is primarily pushing the air downwards and having this change of momentum impart a force on the plane, lifting it up, not from the finer details of the curve on the wing.

When you think about it in these terms, extending the flaps to land makes sense (a larger wing, means you can push a greater mass air downwards, changing more momentum and this means you can fly slower and generate the same lift).

It also explains a plane stalling because if the lift generated off the wings and flaps does not counter gravity, the plane will sink like a stone. This is why a pilot will fly into the stall to increase velocity and try and generate the lift to pull out.

Conclusions

Boats are very clever and use a combination of being pushed by the wind and being pulled by the wind, depending on the sail used and the direction they are going. Planes and birds, however, use straight redirection of the air to generate lift.

And THAT is SCIENCE ;)