# Foiler Design

Discussion in 'Sailboats' started by tspeer, Nov 12, 2003.

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### NiklasLStudent member

Tip vortex reduction...

Interesting, great replys Speer and Wardi!

If you look at the Mig it seems as the most important lift is in the middle. Would'nt it be effective to have the vertical strut divided in two and placed at the tips of a single foil perhaps with small fairings at the intersections (outside moth rules, but with compromise...)?

-not disturbign lift in center
-eliminating tip vortex
-give a constant lift over width

/NiklasL :idea:

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### tspeerSenior Member

You don't actually eliminate the tip vortex by putting the struts out there. There's still lift on the foil and no lift outside the struts. Theres downwash behind the foil and none outside the ends. So there're still going to be trailing vortices. But the struts will move some of the vortex shedding away from the center span and reduce the induced drag.

The optimum lift distribution won't be elliptical, like it is for the isolated single element wing. But the downwash distribution will be uniform along the span, as is the case for all minimum-drag designs. The resulting lift distribution will be fuller toward the ends, and it doesn't have to go to zero at the ends because of the lift on the struts. The optimum lift on the struts will be just enough to result in zero induced velocity along the strut - in other words, just enough lift to cancel the induced velocities that would be there from the horizontal foil.

The struts are basically really big winglets. Here's what the optimum lift distribution for a wing with winglets looks like:

This graph, from Ilan Kroo's digital aerodynamics textbook, shows the starboard half of the lift distribution. The part left of the break is the main foil distribution. The rounded triangular part right of the break is the lift distribution on the winglet/strut, rotated 90 degrees to show how it essentially picks up the load from the main foil.

In principle, you can reduce the induced drag by 30% or more with struts at the tips. This would be good for a 15% improvement in maximum lift/drag ratio. (At max L/D, induced drag accounts for half the total drag)

BTW, Kroo also has a good discussion of sweep theory: http://www.desktopaero.com/appliedaero/potential3d/sweeptheory.html

In order to meet the Moth rules, you might consider a "Pi" foil that has the struts moved inboard. This is also a better arrangement for the structural loads, although it does pick up an additional two intersection corners. To meet the Moth rules, you'd have to lead both struts to the hull. An acute-angled corner is bad news from a drag standpoint, so you might want to add dihedral to the main foil so the struts intersect it at right angles. The result would be like the stern foil in this design:

But if you can get away with it structurally, the T foil is probably still the way to go.

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### NiklasLStudent member

Thanks, great liks! I will be half a year ahead of the lectures at school with this. /NiklasL

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### tspeerSenior Member

Here's another link to ponder at school, Max Munk's "Minimum Induced Drag of Aerofoils", NACA Report 121. Skip all the sextuple integrals and read the words. Most people know this report as the source of Munk's Stagger Theorem, that says if you don't change the loading of the wings, it doesn't matter whether one wing is ahead of the other one or not.

But I think it's far more important for establishing the fact that uniform downwash is the condition for minimum induced drag. In all the text books, you read that minimum induced drag is associated with the elliptical lift distribution. Uniform downwash is treated as a by-product. This is because the text books almost always use Fourier series to calculate the loading on an isolated planar wing with an arbitrary planform. It's a neat analytical solution. But it's a special case. In fact, the elliptical lift distribution and planform are by-products of the uniform downwash.

If you have any other case - like a sail rig in ground effect or the hydrofoil with struts (and surface effects) or a wing with winglets - the elliptical lift distribution isn't optimum. But the uniform downwash is. No matter how many surfaces you have, or how they are configured, you get the minimum drag when the wake leaves the trailing edge as though it were a rigid sheet. It even works for propellers (Goldstein, S., "On the Vortex Theory of Screw Propellers," Proceedings of the Royal Society of London, Series A, Vol. 123, 1929, pp. 169-269).

You can turn lifting line theory around and make it a design code instead of an analysis code, by specifying the downwash distribution and calculating the lift distribution. This spreadsheet does this for the case of a single planar foil and various surface conditions. It can be expanded to handle more than one element.

Once you've read Munk, look up Jones, Robert T., "The Spanwise Distribution Of Lift For Minimum Induced Drag Of Wings Having A Given Lift And A Given Bending Moment", NACA-TN-2249, 1950. There are lots of times when you have to take the moments into consideration too, like the heeling moment of a sailboat...

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### WardiSenior Member

Makes sense for lifting foils, but for a sail it seems important to depower from the top down as the breeze increases, due to the greater heeling moment up higher.

Does this mean it is more efficient to flatten the whole sail all at once, rather than have a full sail down low and a twisted flat sail up top?

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### tspeerSenior Member

That's where the Jones paper comes in! It turns out that minimum drag for given heeling moment occurs when the induced velocity distribution varies linearly over the span. You can get this by shaping the planform, or twist, or both.

If there's no constraint on heeling moment, here's what the optimum span loads look like:

If there's absolutely no gap between the sail and the surface, you get the half-ellipse that people expect. But if there's even a small gap, then the optimum loading looks a whole lot like a full ellipse that gets a bit egg-shaped as you close off the gap. There's a big hit to the induced drag due to the gap, too.

You've got a good point about having to balance the drag vs the heeling moments. Here's the design tradeoff for the minimum drag loadings shown above:

The circled point at the bottom corresponds to the sealed half-ellipse case that's the best you can possibly do for a given span. As you open up the gap, you see the drag shoot up to half again greater than the theoretical best. For very large gaps, the drag would approach twice the minimum and the center of effort would be very high because you've lifted the rig way up into the air.

If you try to recover the drag by making the rig taller, the center of effort goes up. Each of the points in this carpet plot correspond to a different design, optimized for that combination of span and gap. The lines running up and to the left correspond to anchoring the foot and stretching the mast. The drag goes down, but the center of effort goes up.

So let's say you adopted the Jones approach, and tapered the loading so the induced velocity distribution was a maximum at the foot and tapered to zero at the head. This is what the spanloads would look like:

If you use a linear twist, you can get each spanwise station to have the same lift coefficient and the planform shape will look just like the span loading. These sure look a lot like sailboard rigs to me! Which isn't surprisng, because the sailboard were able to evolve without any artificial constraints due to rating rules, etc.

Here's what the design tradeoffs look like for these rigs:

At comparable spans and gaps at the foot, these planforms have more drag than the previous ones. But here are the design trades for the two laid over top of each other:

For any given heeling moment, the more tapered planform allows you to increase the span enough to reduce the drag without exceeding the design heeling moment. Or you can reduce the height of the center of effort without taking a drag penalty by making the rig both more tapered and a little higher.

In principle, there's no end to how much you can apply this principle. If you taper the induced velocities more and more, you start to produce negative lift at the head of the sail. And you can drive the center of effort right down to zero. The negative lift at the head balances the greater lift in the body of the rig, leading to a net gain with no heeling moment at all! The performance is terrible for a given size of mast, but if you make the rig really tall...

Obviously you're not going to get this with typical a soft sail - it can only be done with a highly twisted rigid rig or perhaps a gaff vanged to leeward. Personally, I think the planforms with the induced velocity driven to zero at the head are the practical limit.

All this is based on simple theory and a uniform wind. But the trends and conclusions are still good when you consider the wind gradient. And the optimum span loadings are good for both cat rigs and for other rigs when you add together the contributions for all the sails.

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### tspeerSenior Member

Getting back to the original subject of this thread, hydrofoils, here are the matching minimum drag spanloads and design trades for vertical hydrofoils (struts, rudders, etc) operating at high speed (infinite Froude number):

For reference, the curve on the left is the same one from the zero gap minimum sail rig case in the previous post. The line in the middle assumes no surface interference at all. At very low speeds (zero Froude number), the water surface acts like a solid boundary, and you get the curve at the left. At intermediate Froude numbers, the characteristics are nonlinear, and the drag doesn't necessarily fall in between the two extremes for the surface condition.

Also note that increasing the gap between the free surface and the foil decreases the drag for the high speed case.

Finally, for a horizontal foil (no end plates, etc), the optimum planform is pretty much elliptical no matter what depth it's running:

But the induced drag doubles as the foil is designed at the surface compared to deeply submerged:

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### WardiSenior Member

Self Righting Rigs

Hello Tom,
It is intriguing to consider that for very tall rigs, it may be possible for the top to be inverted and provide sufficient negative heeling moment (positive righting moment) to balance the heeling moment from the rest of the rig lower down. Presumably if the rig is tall enough, or if a small sail or foil is set on the tip of a very tall mast, even above the sail, then we can have lots of righting moment with relatively little drag.

This means we could in effect have a self righting rig! The big question is if it would be efficient??

I have noticed that A-class cats set their rigs up so that the top section inverts in a strong breeze, sailboards are heading this way also.
I have also noticed that in strong breezes, if I under rotate my wing mast and use heaps of fuff tension, this not only lets the top of the rig fall to leeward to depower, but also allows the top couple of battens to invert slightly, but with a very fair inverse curve due to the under rotated wing section. In the stronger gusts, the load comes off the rig, heeling is reduced and the boat really takes off!! Feels great and goes fast!

Most sailors and classes recognise the benefit of flattening the top of the sail and twisting to depower. At the same time we have been aware that too much twist or backwinding will slow the boat, hence we have not taken this any further.

I am not aware of anyone purposely trying to harness this self righting effect!

If we follow this idea further, it should be possible to purposely design a rig to dynamically produce this effect as the breeze increases.

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### TaSSie_deVilResident Boataholic

Just quietly speaking of A-Cats...

Just had a quick squiz through the A-class cat rules.... It turns out this it is clearly stated in the rules that A-cats are permitted to have hydrofoils. Any ideas as to how this can be practically applied to these already-insanely-quick superboats? Anyone up for getting a flying A-Cat under development?

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### John ilettSenior Member

I thought that the A's outlawed foils a couple of years ago.

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### TaSSie_deVilResident Boataholic

Check out http://www.usaca.info/rules.html, rule 8. If that isn't explicit enough, I don't know what is. These are the rules as currently endorsed by the ISAF.

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### TaSSie_deVilResident Boataholic

Whoops. It helps if I take more than just a quick look... rule 10 reverses and denies rule 8. Oh well, if only they were allowed!!

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### alansAlan

Boogie

Sorry about the delayed response, Somehow the boat design system had dropped me from the forum, I have been otherwise occupied and it was not until I signed up again today that I realized I had missed a lot of traffic.

To answer your questions; kooee is only a paper design, unfortunately realization is beyond my capacity but I would be delighted, as would most of us, to work with a suitably heeled sponsor.

Kooee would be fitted with aircraft type controlâ€”joystick through to elevators and ailerons, height holding and heel angle control would be slightly easier than piloting a light aircraft. Holding height with an man in the loop to an accuracy of about plus minus 10 inches at possible 50 knots plus sounds like a big call but in actual fact no more difficult that steering a car to the same accuracy provided you have the right gearing in the steering box, no linkage slack, good tyres, the correct camber and caster; read control linkage, correct foils, dynamic stability. And donâ€™t forget this is how we achieved success with the 14 foot skiff nearly four years ago http://home.kooee.com.au/zach/hydroImages/p1.jpg

My data comes from many sources Hoerner, Marchaj, Larsson; reverse engineering current high performers such as Yellow Pages and land/Ice yacht performances. In addition Internet provides several sites which yield validation opportunities. One of the significant aspects of performance estimation of high speed sailing machines is that they are cat rigged and operate at relatively low angles of attack. This simplifies the analysis issue many fold.

Regards,
alans

http://home.kooee.com.au/zach/hydrofoil.htm

14. ### Doug LordGuest

David Luggs I14

Alans, did you work with David Lugg on the I14? Great job and a true advance being the first doublehanded monohull development class foiler ever; too bad the 14's outlawed it.
Were you satisfied with the extension tiller(rotation) control of the rudder foil only? Seems that control of a flap on the main foil like on John Iletts system and the Rave might have been a good idea as well.
Any good stories on that development project?
What is David up to these days?

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### alansAlan

We chose to use active control as it is simply necessary if you wish to control height with deep running foils. Deep running foils were not outside the int 14 rule at the time, surface piercing foils were. The control surface/s could have been on the main foil or on the rudder foil or both. We decided on the rudder foil as it was the easiest way to link the control surface to the skippers hand and be available on both tacks. We also considered automatic height control such as Rave to be outside the rules. A flap on the main foil will enable you to lift out at lower speeds and that would be an advantage but it would have a large tiring hinge moment were as the elevator on the rudder foil only has significant hinge moments at liftout.

For automatic control the main foil flap is almost certainly the best choice and putting the trailling wand well forward helps significantly.

David can tell some great stories about his attempts to foil prior to my involvement e.g coming to the surface to see the skiff airborne inverted and almost above his head.

David has stuck to the 14 for the moment but itches to get back foiling.

One can only wonder what would have happened if the int 14 ***. had embraced foils. A very difficult one for the class.

alans

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