High-performance sailing

Devices that are powered by sails (such as sailboats and iceboats) can sail faster than the wind. Of course they cannot do that by using simple square sails that are set perpendicular to the wind. But they can do that by setting sails at an angle to the wind and by using the resistance of the surface on which they sail (for example the water or the ice) to maintain a course at some other angle to the wind.

Sailing perpendicular to the wind

For example, a boat can sail a course that is perpendicular to the true wind. As it accelerates, the wind as seen from the boat will increase and the wind will appear to shift forward. This is the same effect that causes rain to appear to fall at angle when seen from a moving car, and that causes your hand to be blown backwards when you stick it out of the window of a moving car.

As the wind increases in speed and shifts forward (because of the acceleration of the boat), the sails have to be trimmed in order to maintain performance. This causes the boat to further accelerate, thus causing a further increase in windspeed and a further forward windshift.

Eventually, the sails cannot be trimmed any further and an equlibrium is reached. Although the boat is sailing perpendicular to the true wind, its sails are set for a close hauled course.

The actual speed of the boat in such a situation depends on the wind speed, how close to the wind it can sail, the strength of the wind, the resistance of the surface (water or ice), and leeway (downwind drift). Normal yachts can sail at a about 45 degress off the apparent wind. High performance racing yachts at about 35 degrees. High-performance multihulls can sail at 20 degrees off the apparent wind. Iceboats can sail even closer to the apparent wind.

If hull speed is not a limiting factor, and if the strength of the wind is sufficient to overcome the surface resistance, then the speed of the boat as a multiple of the wind speed will depend only on how close it can sail to the wind. For example, assuming that surface resistance is neglible (as for an iceboat), if a boat sails at 90 degrees to the true wind, but at 45 degress to the apparent wind, then it must be sailing at the same speed as the true wind. That is, if the wind speed is V, then the boat's speed is also V. Elementary trigonometry and elementary vector operations can be used to show that, if a boat sails at 90 degrees to the true wind, but at alpha degrees to the apparent wind, and the wind speed is V, then the boat's speed must be V×cotan(alpha). The table below shows the values of this function, as a multiple of windspeed.

Alpha	Multiple of windspeed
45	1.00
40	1.19
35	1.43
30	1.73
25	2.14
20	2.75
15	3.73
10	5.67

Hull speed is not a limiting factor for an iceboat nor for high-performance multihulls. So a boat capable of sailing at 10 degrees off the apparent wind (which is the case for many iceboats) that sails at 90 degrees to the true wind will be sailing nearly 6 times faster than the wind. It can sail slightly faster, as a multiple of the windspeed, if it sails at a greater angle off the true wind.

Vector diagrams and formulas

The drawing below shows the vector operations and resulting calculations for sailing upwind. Alpha is the angle of the sails to the apparent wind. Beta is the course of the boat with respect to the true wind.

The drawing below shows the vector operations and resulting calculations for sailing downwind. Alpha is the angle of the sails to the apparent wind. Beta is the course of the boat with respect to the true wind.

Speed made good

However, most sailing is not done in order to achieve a maximum speed, but in order to go from one point to another. In most sailboat racing, the objective is to sail a certain distance directly upwind (to a point called the upwind mark), and then to return downwind, as fast as possible.

Since sailboats cannot sail directly into the wind, they must tack. This lengthens the course, thus the boat takes longer to reach the upwind mark than it would if it could have sailed directly towards it.

If a boat sails perpendicular to the wind, it will never reach the upwind mark. So, in racing, speed is not everything. What counts is the velocity made good, that is, the progress towards the upwind mark. Again, simple trignometry can be used to calculate the velocity made good. The tables below shows velocity made good, again as a multiple of windspeed, and again assuming negligeable surface resistance. The first column indicates the course as an angle off the true wind. Alpha is again the closest angle to the wind at which the boat can sail. The calculation assumes that the boat accelerates until the apparent wind is alpha degrees off the bow.

Upwind made good as multiple of windspeed	Downwind made good as multiple of windspeed
Alpha	Alpha
Course 10 15 20 25 30 35 40 45 10 20 0.94 0.32 30 1.71 0.87 0.44 0.18 40 2.21 1.25 0.77 0.47 0.27 0.12 50 2.38 1.42 0.94 0.64 0.44 0.29 0.17 0.08 60 2.21 1.37 0.94 0.68 0.50 0.37 0.27 0.18 70 1.71 1.08 0.77 0.57 0.44 0.34 0.27 0.20 80 0.94 0.61 0.44 0.34 0.27 0.21 0.17 0.14 90 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00	Course 10 15 20 25 30 35 40 45 100 1.00 0.67 0.50 0.40 0.33 0.27 0.23 0.20 110 1.94 1.32 1.00 0.81 0.67 0.58 0.50 0.44 120 2.71 1.87 1.44 1.18 1.00 0.87 0.77 0.68 130 3.21 2.25 1.77 1.47 1.27 1.12 1.00 0.91 140 3.38 2.42 1.94 1.64 1.44 1.29 1.17 1.08 150 3.21 2.37 1.94 1.68 1.50 1.37 1.27 1.18 160 2.71 2.08 1.77 1.57 1.44 1.34 1.27 1.20 170 1.94 1.61 1.44 1.34 1.27 1.21 1.17 1.14 180 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

It can be seen that a boat that can sail closer than 20 degrees to the apparent wind can make good upwind faster than the real wind. And any boat can make good downwind faster than the real wind, by not sailing dead downwind, but instead jibing(also spelled gybing) back and forth (but not as fast as the table above, which assumes that the boat can accelerate until the apparent wind is alpha degrees off the bow).

Of course real boats cannot equal those performances, although iceboats can come close to them. Indeed iceboats can make good both upwind and downwind at speeds far greater than the wind. And certain sailboats (such as the 18ft Skiff) can make good downwind at speeds faster than the wind.

It is even possible to conceive of a boat that can sail dead downwind faster than the wind. At first, this seems impossible. But consider a boat that has a very large spinnaker and that drags behind it a propeller-driven electric power generator. The spinnaker can be made suffiently large so that the boat sails nearly as fast as the wind despite the drag from the power generator. Suppose that the generated power is stored in a batteries. After a while, the boat can lower its sails and use the power from the batteries to run a propeller to advance faster than the wind. Thus, on average, the boat can sail dead downwind faster than the wind.

This scenario is highly theoretical and it would be difficult to achieve it in practice because of the high resistance of water. But a sail powered cart running on wheels, on a flat surface, has much less resistance. And indeed, a cart that ingeniously uses a propeller linked to its wheels (without batteries or electrical power generators) to sail dead downwind faster than the wind has been built and demonstrated.