How can an ice boat go faster than the wind speed?

Question

I had this question in college, and I know it has something to do with vectors, but I can't remember how to solve this problem.

Answer 1

Because of the TOTAL force acting on the large area of the sail.

Answer 2

It's hard to explain this with vectors if I can't draw you a diagram, so you'll have to manage with the following:

First, understand that most sails work by redirecting the wind, much like how a curved pipe redirects the flow of the water. This creates a resultant force on the sail which is at a angle from the direction of the wind.

Next, understand that force accelerates mass, as per F = ma, so that as long as force is present, the mass will continue to accelerate indefinitely, unless other factors such as friction or wind resistance limits it.

If an ice boat is travelling at a angle relative to the wind, such as the cross direction to the wind, regardless of how fast it is going, to the sails and people on the ice boat, the wind will always be blowing on them; it will never feel like still air.

Most of the time, it's possible to orient the sails such that the resultant force from the wind can be decomposed into 2 orthogonal force vectors, one in the direction of the ice boat, one cross it.

Therefore, if done right, so long wind is present, there will always be a force vector in the direction of the ice boat driving it forward, and its speed is independent of the wind speed, limited only by friction and air resistance.

Addendum: Stan the Rocker's explanation of wind vectors, B, W, and A is correct only in that the apparent wind vector A is the vector sum of B and W. However, it's not true that A is always larger than W. For example, even if the boat was going at the same speed as the wind, but at 60 degrees from the direction of the wind, the apparent wind speed is the same as the real wind speed. There is no connection between the apparent wind speed and ultimate boat speed. On a perfectly frictionless ice, there is no theoretical limit to how fast an iceboat can go, regardless of real wind speed.

Answer 3

It has to do with actual wind, apparent wind, and boat speed. As you move forward, you encounter wind in your face. This wind is travelling at your boat speed (vector B). The actual wind which is driving your sails is coming at an angle between 45 to 90 degrees off your bow (vector W). The apparent wind (sum of vectors B and W) is now what you feel (vector A).

By vector addition, vector B + vector W = vector A

The magnitude of vector A will be greater than vector W.

This only explains how the apparent wind is faster than the actual wind. What happens next is that the sails are adjusted for the apparent wind. The apparent wind, being faster than the actual wind, provides a greater aerodynamic driving force on the sails. This is what makes it possible to travel faster than the actual wind speed.

Answer 4

The boat's direction of travel is a result as 2 forces or 2 vectors
1st the same direction as the wind
2nd at an oblique angle created by the steering mechanism


Vectors can be additive,
The boats speed will be the resulting speed of the two vectors , which will be much faster than the wind speed.

Theoretically , as the direction or travel approaches 90 degrees from the wind speed,
you will continue increasing velocity..