The physics of sailing is outlined in the first diagram, showing the equilibrium between forces. The vector-sum of forces on sail and keel is balanced by the resistance of moving the boat through water.
The speed of a typical 10-meter yacht in winds of 10 and 20 knots, as a function of its angle to the wind, is shown in the second diagram (1 knot = 1.15 mph and 1 mile = 1.6 km). As shown in the third diagram, the length of the yacht is important because the speed of the induced bow wave varies with the wave's length. It is difficult for a boat to exceed the speed of a wave whose wavelength is longer than the boat, because the boat is then attempting to climb up the wave. With sufficient power, however, a speed-boat can ride up upon its bow wave and effectively hydroplane.
Although the maximum speed of a typical yacht is less than the wind speed, high-tech catamaran yachts have reached speeds about twice that of the wind. A windsurfer narrowly beat the yachting record this year with a speed of 49 knots (56 mph). The land yacht record is 117 m.p.h. in 30 m.p.h. winds!