I enjoyed tonight's episode of the Discovery program, Mythbusters, as I do every Sunday, but this episode was especially interesting because of a segment on a physics thought experiment called “Blow Your Own Sail”.

This is a very old thought experiment for physics students. Suppose you are in a sailboat on a day with no wind, and there is no motor onboard but there is a large fan. Can you use the fan to blow the sail and propel yourself along?

According to Newtonian physics for every action there is a reaction, which means that the force applied on the sail to move the boat forward is exactly cancelled by the forces on the fan pushing it backwards. Another way to view this is that since there are no external forces on the boat, the boat cannot move. Either way, this is a reasonable argument that predicts the boat will not move.

I happened to work out the mathematics and physics of this problem many years ago for a school project back when I was a physics undergraduate student, and so I knew the answer, but surprisingly many very skilled and experienced physicists use the false logic above to predict that the boat cannot move. They are wrong.

The problem with the logic is that it assumes that the boat is a closed and isolated system. In truth there are two sources of external forces that most people forget about.

The first and most important is the recoil of the air after hitting the sail. Air is hard to visualize, and even harder to handle in Newtonian physics, so I will give a different example to illustrate this point. Suppose you replace the fan with a cannon and replace the sail with an indestructable brick wall. When the cannon is fired, the boat moves backwards from the recoil. Then the cannon ball hits the wall and the boat's motion stops. But then the cannon ball bounces off the wall with the same momentum in the opposite direction and flies off the back of the boat. Now the system is composed of a boat and a cannon ball flying backwards from the boat – and by Newton's laws if the cannon ball is sent out the back with some momentum the boat must react by moving forward with the same momentum!

The second (and arguably negligible) effect is a Venturi force created at the front of the boat. An airplane wing works by creating a low pressure region above the wing, caused by fast moving air. In the boat and fan experiment, some air will slip around the edge of the sail and move quickly past it. This in principle creates a low pressure zone in front of the sail which sucks the boat along.

There are of course uncertainties in both of these forces. The problem with the low pressure forces is that it is very difficult to model, so as far as I know no one has actually calculated how strong the effect would be. It might have no effect at all. And with the air recoil forces, there are arguments that the air being sucked in by the fan counters the air pushed out backwards – except that the fan increases the energy and momentum of the air so it doesn't quite balance. There is also an effect of the sail being flexible and absorbing some of the momentum from the air – but this is also difficult to model since it depends on the material used. There are also problems with air being compressible, with air spilling around the edge of the sail, and with a large resistance to motion caused by the water beneath the boat.

But the Mythbuster team built it in full-scale and proved that in fact it is possible with a strong enough fan and large enough sail to actually power a boat this way. Really cool experiment!