Join Date: Jun 2005
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Can't tell you the math, but it is possible for some low-drag sailboats (like light displacement planing hulls when planing, catamarans, iceboats, and some wheeled land "boats" to sail faster than the true (but not apparent) wind.
They do this by using their speed too pull the apparent wind forward, which also increases its strength by a factor (vector) almost equal to the boat's own speed. So, an iceboat beam-reaching on smooth ice in a 10-knot true wind may end up close-reaching or close hauled doing about 20 knots in an apparent wind of close to 30 knots. It's said that iceboats can go at 3 to 7 times the true wind speed, by ''creating" their own wind this way. In water, catamarans, windsurfers, and some planing dinghys can do the same, though not nearly as fast as an iceboat.
Mathematically, it's basically a vector problem, but I don't know the lift and drag coefficient factors you'd use to turn it into a windspeed/direction-boatspeed diagram, sometimes called a "polar" diagram.