How do hydrofoils tack without a keel

Question

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.

Answer 1

The lift providing foil is mounted at the bottom of what is effectively a dagger. The foil and the part of the dagger that's not been lifted out of the water, together with the rudder itself provide enough drag to prevent downwind drift. It's possible that at maximum lift, the foiled dinghies experience a bit more drift but that they make up for this in speed. Some designs may also have a dagger extension below the foil, to further reduce drift.

Most (decent) windsurf boards have daggers too (even retractable ones, like in traditional racing dinghies).

Some catamarans have daggers but others have twin, sharp hulls that provide deceptively much resistance to downwind drag because although they don't penetrate deeply into the water their length combined with that shallow depth provides comparable surface area to a traditional dagger.

A few extra considerations re. the need for a dagger:

We can distinguish three main courses:

1. Close to the wind:

A decent dinghy can sail a course close to the wind of about 45 degrees. It is almost sailing in the opposite direction of the wind. This is generally the slowest course and one where most dagger is needed. Racers will have the dagger pushed in to the lowest position.

2. Half wind:

At an angle of 90 degrees speed is generally highest and less dagger is needed. Racers will typically push the dagger in about half way down. This is also the course where a foiled dinghy will experience most lift.

3. Wind from behind:

With the wind from behind there is no need for dagger, as drift coincides with the direction of sailing. Racers will lift the dagger to its highest position. Speed is typically between both courses mentioned above.

Answer 2

As the comments suggest, the hydrofoils are the keel, in the sense that they (and the rudder itself) generate significant "lift" based on their angle of attack under the water's surface. Perhaps an analogy will help: shorter windsurfing boards (under about 2 meters IIRC) have no keel/daggerboard, just the small skeg at the rear - where a rudder would be on a boat. Windsurfers point (sail upwind) with a combination of pressure on the windward rail and tilting the board so as to change the skeg's angle of attack.