Sailing faster than the wind blows

A sailboat can actually sail faster than the wind blows. Twice as fast, or even more.

When I first heard about it, a long time ago, I thought it was a rubbish. But I kept hearing the same thing so I started looking for the right answer. And I found many answers but wasn’t able to understand because the language was full of sailing terms (and I am not a sailor). So I started thinking about it mayself, but it didn’t hit me until I learned that a wind turbine wheel can rotate faster than the wind blows if its blades are inclined enough. Then it was obvious.

To make faster than wing sailing possible, the wind must not come straight from behind. Instead, the wind must blow from side (relative to the sailing direction of the boat). The other important thing is that the keel and the rudder must keep the boat strongly at its path no matter the wind is trying to divert the boat sidewise. The keel and the rudder must keep the boat as if it is on rails (it of course means that the boat must be already moving fast because the keel and the rudder are effective only then).

Let us start from the beginning... The sail is a wing. As the wind blows over it, the high pressure region is formed at one side and the low pressure region is formed at the opposite side of the sail. This causes the lift (force, thrust) to be formed perpendicular to the sail. On the other hand, as the wind slides through the sail, it creates some drag that is parallel to the sail surface. The resultant force is a vector sum of these two forces. As you can see, the wind doesn't simply try to blow the sail (a wing) away in the direction it is blowing, instead it creates force that is somewhat "off-course". In fact, as we are able to produce a sail that has much smaller drag than the lift, the force is more like perpendicular to the sail than directed in the wind direciton.

A wind is blowing over a sail and creates the high pressure region (below) and the low pressure region (above). The lift and the drag forces are shown using red vectors, and the resultant force is the blue vector. The drag force is very small in modern sails.

First assume that our boat is not moving – it is firmly anchored. Now note that in most cases we can adjust the sail so that the force produced by the wind has at least a small component in the forward direction (we only can't do it if the wind is blowing too much from front - say, under 30 degrees). This is depicted on the picture below.

On a sailboat, in most cases we can adjust (angle) the sail so that the wind produces a force that has at least a small component in the front direction. We only can't do it if the wind is blowing dircetly or almost directly from the front (the case E). (Turbulences are not shown on this picture).

In the A case (wind directly from the rear) all the force produced by the wind is aimed into the front direction of the boat (all the force is pushing the boat). In cases B-D only a part of the force is aimed into the front direction while the other component is trying to move the boat aside. Please note that in the D case, only a small component of the force is available for the forward movement meaning that the boat would have to have a very low friction to maintain its speed in the D case.

If the boat was moving, the keel and the rudder would not allow shifting it aside (in cases B-D) and so only the front-aimed component of the force matters (the component that is pushing the boat forward).

Second, assume now that our boat is moving. Now the boat has its own speed and we can calculate the speed of the wind that the boat “feels” as equal to vector difference of the wind speed and the boat speed. We have several examples depicted on the picture below.

Blue vectors represent boat speed, while green vectors represent wind speed. The red vector is the wind speed that is “felt” by the boat. In the case 1 the wind is moving in the same direction as the boat and is faster than the boat. The wind speed that is “felt” by the boat is represented by a small red vector pointing forward – meaning that the boat feels some small wind directly from behind (hopefully this will be enough to maintain its speed).

In the case 2 the wind is also moving in the same direction as the boat, but the boat is faster. As you can see the boat will “feel” a small wind directly from the front. We know already that this wind cannot make any useful force (case E) and the boat will not be able to maintain its speed and will slow down.

In the case 3 we have wind perpendicular to the movement of the boat. In this case, wind is moving faster than the ship (by absolute value). The resultant vector that represent the wind “felt” by the boat will come from an angle, slightly from front. We know (from case D) that it is still possible to position the sail so that this wind causes some useful force in forward direction. Hopefully this will be enough to maintain the speed. In fact, if our boat is really good (has small friction) this force will be enough to speed up the boat further.

In the case 4 we have the same situation as in the case 3, but now the boat moves faster than the wind (by absolute value). Still it is possible to position the sail so that the “felt” wind causes useful force in the forward direction. Obviously this force will be smaller than in the case 3, but if we really have a racing class sailboat, it will be enough.

So we see that the boat can move faster than the wind. But in this case it is able to use only a small portion of force provided by the wind. It means that the boat must have very low drag when speeding through the water. Also it must not roll over, because the side force gets very high.

Danijel Gorupec, 2006