I asked a while back about how sails produce a forward force on a boat 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 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 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.