Dario's Lab

Alphabet Soup

In response to numerous requests, and with the 34th America’s Cup almost upon us (short on teams but rich in technical curiosities), here is a ‘back to basics’ look at multihull foil solutions.
This post samples the main varieties of multihull foil, assuming some background sailing knowledge.

Angled Board

The simplest way to obtain a vertical component by just canting the foil lift vector.
This solution is extremely constrained in angle and span if a beam limit is to be respected when the foil is retracted. The same constraint also forces the foil exit point in the hull inboard toward the middle of the boat, moving the hull/foil junction closer to the free surface and reducing righting moment (because the centre of vertical lift moves inboard).

Every part of the foil span contributes evenly to vertical lift so, assuming enough foil angle is possible to lift the boat clear of the water, there is no stability in heave (ride height).
Tapering the foil planform and/or adding a vertical tip can help give some heave/vertical lift correlation.

Using two such foils together on a very wide platform such as Hydroptere (diagram below) can give heave stability by simply reducing immersed foil area with altitude.
But this arrangement is not practical in most classes racing ‘around the cans’.

C, J, and L Foils

C Foil: Sideforce (to windward) is unevenly vectored to generate upward lift.
Vertical component is greatest near the bottom.
By tightening the radius, more extreme lift characteristics can be obtained regardless of beam restrictions.

On the practical side, C foils are easy to install because they fit in a constant-radius foil case.

C foils are unstable in heave: as ride height increases, vertical force does not decrease significantly. Given constant thrust, if lift is greater than total weight, the boat will rise until the foil ventilates or stalls, causing a crash.

C foils are helpful in foil-assisted sailing as long as they lift less than 100% of the weight of the boat.
Vertical lift can be ‘dialed down’ (without losing sideforce) by partially raising the foil.

J Foil: Similar to C foils but maximum lift remains available when a J foil is partially retracted (shown orange).
The lower part of a J foil stays ‘canted’ until the junction radius reaches the hull.
Unlike a C foil that becomes more upright as you pull it up.

J foils are also unstable in heave so are suited to foil-assisted sailing rather than full foiling.
They potentially have less drag when sailing downwind because their draught (and hence frontal area) can be reduced when vertical lift is still beneficial but less sideforce is required.

Both C and J foils can have high induced drag when set for max lift (raked – see last diagram below) because the lift distribution along the span becomes biased toward the tip. End devices such as winglets or washout at the tip help alleviate this but cause parasitic drag at other times and add complexity to the foil case design if the foil is to be fully retractable.

Note that tightening the transition radius on a J foil progressively, gives a ‘traditional’ 90 degree or ‘open’ L foil that is also unstable in heave.

‘Acute L’ Foil: A very elegant way to automatically regulate heave for full foiling on only one (leeward) foil.
First “stumbled upon” by the ETNZ design team, this idea is a great example of how rule constraints can push innovation by forcing competitors to think laterally.

As ride height goes up, the immersed area of vertical ‘strut’ decreases (lateral area is lost).
This makes leeway increase, in turn reducing the Angle of Attack (AoA) on the ‘horizontal’ foil.

To get your head around this, imagine what would happen if you made leeway extremely large (like 90 degrees): The horizontal foil would actually start pulling down!

Under normal conditions the change in leeway is small (say 5 degrees) but the component across the boat works to reduce the AoA on the horizontal foil, moderating lift to stop a runaway leap into the air.

So: boat goes up > lateral area gets smaller > boat starts slipping sideways a bit more > horizontal foil moves toward its own low pressure field > lift decreases > boat settles > lateral area increases > leeway decreases > vertical lift grows again… And so on until an equilibrium is reached.

The higher the inboard tip relative to the outboard root/junction, the closer the coupling between ride height (through sideforce) and vertical lift.

At extreme ride heights, the acute L foil begins to work as a conventional (powerboat) V hydrofoil: When the inboard tip of the horizontal foil breaches the surface, immersed foil area is gradually reduced regardless of sideforce.
This is helpful to avoiding a crash when pulling away to a near square run in reaction to a gust.
It is a good ‘safety valve’ in situations where speed (and lift) may be high but sideforce is small.
However it should be noted that the optimum condition requires the tip to remain submerged. Drag is much lower when only the vertical is surface-piercing and leeway moderates heave.


With the basic components described above, designers have a kit of parts that can be mixed and matched to suit the particular application at hand.

The principal groups that can be seen when observing recent AC72 testing are described below in the order pictured above.

L Foil with Polyhedral: The bent inboard tip provides stability in the same way as an acute L foil. Kinking the horizontal foil reduces the junction angle between vertical strut and horizontal foil.
In a way similar to introducing a bulb or a radius, this decreases drag where interference effects are most prevalent.

The root of the horizontal is heavily influenced by the low pressure area inboard of the vertical strut so is less affected by leeway than the tip. It makes sense therefore to use the root to generate the bulk of vertical lift and exploit the tip for heave control.
The penalty is a bit more parasitic drag as there is more foil area for a given effective span.

The bent horizontal foil can also hug the hull more snugly when the foil is retracted, reducing drag when the windward hull is near the water.

Acute L with Kinked Strut: Bending the vertical strut enables some adjustment of the angle of the horizontal foil so that stability in heave can be fine-tuned.

A bend may also be necessary to stay inside the beam restriction if designers want to cant the strut inboard to get an effect similar to a C-L foil.

C-L Foil: Combines the heave stability of an acute L with some lift vectoring of the strut for lower overall drag. The cost is a shift inboard of the centre of lift which reduces righting moment.

S-L Foil: Similar objective to a C-L: more even lift sharing for lower overall drag.
But the inflection at the top moves the bottom outboard again, recovering full righting moment.

The S also fine-tunes the angle of the horizontal foil to adjust ride height and heave stability.
Often the intent is to have a deeper more upright foil for sailing upwind. At the same time as the strut becomes more upright, the tip angle decreases, giving up some heave stability. Upwind this is less critical since it is easier to maintain speed near constant by luffing up in the gusts (especially since it might not always pay to fully foil upwind. Instead an efficient foil-assisted mode may be preferred, leaving the hull to take care of heave stability).
Reducing heave stability unloads the vertical strut in sideforce because the leeward component of the horizontal foil lift goes away. So total lift-induced-drag is decreased.

The downsides are mechanical complexity at the bearings, a foil case that holds more water, and more friction when raising and lowering.
Bending the foil at the highly loaded area between hull and deck bearings is also structurally more demanding, especially on bigger boats.

And finally, a diagram showing how foil rake affects vertical lift:

Remember that heave stability is the tendency for lift to vary inversely with ride height.
For effective foiling it must be combined with pitch stability which is a bit simpler to obtain using properly sized T, + or L rudder foils.

On small boats such as the A Class, it may be possible to ‘stay on top of’ an unstable platform by actively managing weight placement and sideforce, countering in real time the continuous tendency to depart stable flight.

Like riding a unicycle this is difficult but humanly possible.
Until now this solution, though far from optimum, seems to be the best real world choice for racing around the course in the A Class, mainly due to rule constraints on foils.
The challenge for the future is getting stability with an acceptable drag penalty within the rule.

Bigger boats do not have the option of quickly shifting weight and aggressively trimming the sails, so true stability is important for safety and speed.

I hope this post has been informative for keen observers of the spectacular innovations on show in today’s multihull scene.
Remember to look critically and skeptically at the physics when assessing how effective and stable various solutions might be.
Interesting times indeed.