I asked a while back about [how sails produce a forward force on a boat][1] and got some good answers and (I thought) a good understanding: essentially the sail produces a force that has some non-zero forward component and a lateral component. The dagger-board/keel produces a large resistance to the lateral component of the force, leaving only the forward force. Voilà, the boat moves forward. 

Today I have been trying to understand the physics behind how a [hydrofoil equipped sail boat][2] is able to function. In all the videos I have watched, the boat does not appear to have a keel. 

Further, when the boat lifts out of the water, there isn't even the hull to provide the resistance to lateral motion. **Given this, how are hydrofoils able to tack (or even sail not directly with the wind)?**

One option is that they can't and hydrofoil boats work more like wind surfing, but that doesn't seem to be the case. 

[This Wikipedia section on Catamarans][3] seems to suggest that a hydrofoil actually works as a replacement for a keel. However, looking at the design of the foil, they do not seem to have sufficient surface area to provide the same lateral resistance as a keel. 


  [1]: http://physics.stackexchange.com/questions/123672/problem-understanding-basic-sail-mechanics
  [2]: https://en.wikipedia.org/wiki/Sailing_hydrofoil
  [3]: https://en.wikipedia.org/wiki/Catamaran#Catamarans.27_peculiarities