How do the Americas Cup Yachts sails work? With the vast majority of sailing boats its pretty evident how the sails work to harness the energy of the wind to propel themselves forward. However on the modern Americas cup foiling yachts i can't seem to understand how you can be going more than twice the speed of the wind. I have tried to work it out myself by looking at airplane wings as they are essentially the same as these sails but obviously if an airplane could harness the wind like these sails do then we could fly round the world with no engine at all.
Thanks.
 A: Just look at it as a wedge.
To a 0th approximation, a sail or wing through fluid is just like a knife through jello.
It can only move along a line.
A sailboat has two of those.
It has a sail cutting through the air, and it has a keel (centerboard, leeboard, hull) cutting through the water.
Neither one of those can move sideways in its fluid, so if the air moves some distance over the water, the boat has to move also.
It's just like squeezing a greased wedge.

You see, if the slant of the sail is very close to the centerline of the boat, there is no limit to how fast the boat can go, if it had no drag.
But it does have drag, which is what limits it.
Notice the boat does not have to be going directly cross-wind.
The arrow of wind can be going in any direction, as long as it is not aligned with the boat.
P.S. Aircraft are different, because they are only traveling through one fluid, not two.
A: This is not limited to hydrofoil hulls.  You can sail across the wind ("reaching") on other low-drag shapes such as windsurfers at speeds greater than the windspeed.  The fastest such craft, so far as I've heard, are iceboats -- which are sort of an ultimate "hydrofoil," in that they skate along the frozen lake surface with almost no friction at all.
Anyway, the reason this works is that it's only the virtual wind direction at the sail that matters.  On a broad reach (aka going almost perpendicular to the true wind direction),  the ice-boat will continue to gain speed so long as the true wind exerts force on the sail.  The vector diagram in MikeD's answer should  make it clear how it happens.   However, if you sail parallel to the wind, then once you reach wind speed, clearly the wind cannot provide additional force.
Now, for real fun, google around for  "DDWFTTW", or 'dead downwind faster than the wind', which can only be achived on land, and in an unobvious manner. 
