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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.

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    $\begingroup$ I think it's just that your intuition is failing you - the hydrofoil does provide enough resistance. It's all relative anyways; all sailing craft slip downwind a little bit. Maybe hydrofoil craft do it more than others - not sure, but the hydrofoil support provides the resistance that a keel or centerboard would normally provide. $\endgroup$ – Brionius Sep 9 '15 at 16:23
  • $\begingroup$ If I had to take a stab at it I would suggest that the analysis should start with understanding the role of the sail as a wing, i.e. it seems that with the correct angle the wind may be able to provide both the propulsive force and the component that is required for tacking. And with this wave of a giant foam hand in the light morning breeze I declare my complete ignorance of all things aerodynamic (with or without surface effects) and leave it to someone who actually understands the Naviere-Stokes equation and its solutions to tell you what's really going on. $\endgroup$ – CuriousOne Sep 9 '15 at 16:48
  • $\begingroup$ Alternatively, if plan A does not lead to fruition, my plan B would be to analyze the role of the hydrofoil strut as a wing/rudder. There are certainly hydrofoil designs that have steerable strut surfaces very similar to plane rudder designs. $\endgroup$ – CuriousOne Sep 9 '15 at 16:52
  • $\begingroup$ @CuriousOne your intuition is incorrect: wind can only blow on the sail. Without a keel or similar restraining force, dead-downwind is the only way you can go. $\endgroup$ – Carl Witthoft Sep 9 '15 at 17:13
  • $\begingroup$ @CarlWitthoft: I was more trying to say that I simply don't have a working intuition for these kinds of things, in which case I like to resort to not ruling out effects that I don't understand clearly. Thanks for clarifying that it's plan B, then. $\endgroup$ – CuriousOne Sep 9 '15 at 17:35
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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.

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  • $\begingroup$ "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. " This is completely wrong. The drag that the foil & rudder create is in the direction of motion through the water, and is always detrimental. The force that's needed is at right angles to this & is easily obtained by angling the foil laterally (assuming the foil is not perfectly horizontal). $\endgroup$ – D. Halsey Apr 3 '18 at 0:28
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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.

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