However, one still cannot sail against to the wind purely by tacking the sail. To do this, one needs to not just harness the power of the wind, but also that of the water beneath the sailboat, thus exploiting (barely) the third available dimension. By combining the use of a sail in the air with the use of sails in the water - better known as keels, rudders, and hydrofoils - one can now sail in certain directions against the wind, and at certain speeds. In most sailboats, one relies primarily on the keel, which lets one sail against the wind but not directly opposite it. But if one tacks the rudder or other hydrofoils as well as the sail, then in fact one can (in principle) sail in arbitrary directions (including those directly opposite to v_0), and in arbitrary speeds (even those much larger than |v_0|), although it is quite difficult to actually achieve this in practice. It may seem odd that the water, which we are assuming to be calm (i.e. traveling at zero velocity) can be used to increase the range of available velocities and speeds for the sailboat, but we shall see shortly why this is the case.

Sailing into the wind, or faster than the wind « What’s new