# Radically Different Yacht Keel - "Loop Keel"

Discussion in 'Sailboats' started by Bad Mac, Mar 9, 2007.

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### CeilidhNew Member

A novice's attempt at understanding....

Dear Mr. Howes and Mr. MacNaghten,

I don't know if either of you will still be following this thread, nor if you'd have the patience to wade through a novice's musings, but I've been trying to understand how the loop keel works, and would very much appreciate it if you could please tell me if I'm on the right track. (And please forgive the lack of mathematics or fluid dynamical terms in what follows -- I'm hampered by zero experience in naval architecture or aero/hydrodynamics, and thus I'm trying to understand things by (beginner's!) thought experiment and analogy.) Thanks very much in advance!

1) Why the Loop Keel has Little Drag

For the 1st thought experiment, I'll take a U.S. inland lake scow and "bend" the twin bilgeboards until they look (in front view) like your Loop Keel w/o the central bulb section: the two boards converge with depth, and (like the limbs of the Loop Keel) are angled so that when the scow's heeled at 15-20 degrees, the windward board has not yet reached vertical, and the leeward board has not yet reached horizontal. Unlike your Loop Keel, these boards don't join at their tips.

If I angle the boards so that the windward board is "lifting" me to windward, and the sub-horizontal leeward board is "diving" downwards, I'll end up with the resultant of forces you've shown on the 1st page diagram. Fair enough -- I can see how those forces serve to counteract leeway while adding to my righting moment. So far so good. Now what do I gain by connecting my two bilgeboards at their tips?....

Hmmm. I've never understood induced drag (yes, I see the equations on Wikipedia, but I haven't an intuitive understanding of what they're describing) -- but the Wikipedia pictures of tip vortices are clear enough(!). I can see how a tip vortex is produced; how the planform of the tip can influence the strength of the vortex; how there's a certain amount of energy associated with tip vortex production -- and since a board/keel/wing will produce an ever-lengthening vortex behind it as it travels, that energy has to come from the boat / plane / etc's powerplant. So it's drag. (Is that basically correct? Is that the central crux of induced drag?).

Given that, I can see how I'll have infinite-length tip vortices streaming off both my angled bilgeboards. And I can see how if I'm really unlucky, I can arrange the bilgeboard tips so that the vortices mutually reinforce each other so that they're even stronger than usual. That would be bad(!). But I can also see that as I bring the tips closer and closer to one another, at some point the production of one will inhibit the production of the other, and in the limiting case where the tips actually join, there'll be no tip vortices at all. In that situation, my twin bilgeboards are still preventing leeway and improving my righting moment, but my induced drag will plummet.

Have I got this right so far?

2) Of Toys and Smoke Rings

Moving along: my aerodynamicist (student) friends all tell me that nobody cares about Bernoulli's effect anymore (some say "it's not why airplanes fly at all!") and that "circulation theory" is the way to go these days. But none of these friends are able to explain the distinction in a way that my poor befuddled brain can understand. So I'll stick with Bernoulli's for now, and I'll use it to look at this mysterious ring vortex that you're creating without any convergence or divergence in the flow....

Ok. In my original thought experiment, I angled my two bilgeboards so that they're both "flying" away from the boat's centerline; i.e., the windward board was angled to windward, and the leeward board was angled to leeward (and thus downwards, when the boat heels). In this way each board had the angle of attack needed to generate the lift forces on your page 1 diagram. When I join the two board tips to make a loop keel, I've made a funnel, so that the flow has to converge as it passes through the loop. I think I can sort of maybe kind of see how just very possibly (have I hedged enough?) this causes wavemaking problems: for mass flux to be constant, the exit velocity out the back end of the loop has to be higher than the incoming and ambient flow velocities; there has to be a pressure head of some sort to generate that higher velocity; and that pressure head will be associated with a raised water level within the loop. Since the flow velocity presumably collapses back to ambient very quickly after it emerges from the loop / funnel, the pressure head and raised water level similarly have to collapse, and we get a wave. (Is this on the right track?)

Given that, you've eliminated the "funnel wave" by making the inlet and exit diameters of the Loop Keel identical. If I were to do that on my modified scow, I'd take away the angling on my twin bilgeboards, and I'd instead give them some cambering. This cambering would still try to "fly" the boards away from centerline -- hence the mid-chord sections of the boards would sort of bulge outwards.

[Note: from your posts and website literature, I had a devil of a time figuring out which way the flaps (on your experimental "flapped" Loop Keel) actually moved. Have I got it right? Do you move the flaps to converge the flow when you want more righting moment?]

Going back to my scow: with these bulged, cambered bilgeboards (which are now joined at the bottom to make an unballasted Loop Keel), the entry and exit Loop diameters are now equal (which will cut the wavemaking), but the Loop diameter midway along the chord is now greater than that of the entry or exit. Hence, to maintain constant flux, the flow velocity (of the water passing through the loop) midway along the chord must be lower than ambient, and thus by the maligned-and-no-longer-believed-in-by-anybody-who's-with-it-and-cool Bernoulli's effect, there must be higher pressure within the loop. So my bilgeboards will still generate the forces shown on page 1.

Right. Now if the water flowing through the loop is slowing down relative to ambient (as argued above), then this is the source of the ring circulation that's superimposed on the general flow. And if I understand it correctly, if we go to the reference frame of the boat (or loop keel), this ring circulation looks like a doughnut, with the flow passing forward through the Loop Keel and circulating back around the outside.

[Note: in hindsight, I can see how the above must have been obvious to you hydrodynamicists, but it took me a while to figure out....]

If the above is anywhere near correct, I now have a good mental picture of what's happening! I've seen smoke rings go wafting merrily across a room with seemingly no drag or decay, and a buddy has one of those ring-vortex toys (consisting of a bucket with hole, a plastic sheet, and bungee cords) that you can use to send an invisible air doughnut rocketing along like a projectile). With your loop keel, you've eliminated tip vortices and their attendant induced drags, and you've turned an entire sailboat into a waterborne smoke ring....

3) Of Increased Inertia

The final question for this evening concerns the increased inertia (note: the above only deals with drag; the inertia is a separate issue). Initially I was stumped:

Yes, I can see how the water level inside the loop can be made higher than ambient, and I'm happy with that water (which has mass!) moving along with the boat.....but it wasn't at all clear how that gave you "good" inertia. Even now I'm not sure I understand -- so if you could please comment on what follows, I'd appreciate it! To wit:

The added water inside the loop is (as you've pointed out earlier) akin to a standing wave that travels with the boat -- but the bow, stern, and quarter wakes that accompany normal boats are also akin to standing waves that travel with the boat. Upon acceleration, all of these waves act sort of like inertia: to get the boat moving, you have to put energy into generating the waves. But the thing about the bow, stern, etc. waves is that while they're great at resisting acceleration, they're not particularly great at keeping the boat moving when you're trying to slow down: cut the power, and these associated wave systems merrily travel forward without the attached boat, and thus they don't really increase the boat's inertia or effective displacement.

So why should the water within the Loop Keel behave differently?

The best I can guess is that since the raised water level within the Loop Keel is associated with this travelling doughnut of a ring vortex (as discussed above), then the water can only surge ahead of a decelerating boat if the ring vortex itself surges ahead. But for the ring vortex to surge ahead, it has to detach itself from the Loop Keel -- and this it can't do, as detaching would mean that it's somehow pushing fluid normal to the surfaces of the Loop. Hence, since the ring vortex can't flow through the surfaces of the Loop, it has to stay centered on the loop. And if the ring vortex stays centered on the loop, then the water-level bulge will stay centered as well -- and thus the inertia of the bulge will try to resist acceleration. Ergo, the Loop Keel mimics the inertia of a heavier displacement boat.

[Note: I can see how there's an increased effective inertia in the longitudinal direction, but I can't see it for roll, pitch, or yaw. Will the Loop Keel boat still rotate about its axes like a light-displacement craft? Or do the dynamics somehow damp out rotational accelerations as well?]

Finally (for tonight), saying the Loop water-bulge stays attached and thus increases inertia is all well and good, but it'd be nice to actually understand the forces involved when a Loop Keel boat tries to decelerate. Is it because as the ring vortex tries to shift forward (relative to the boat & keel), the Loop Keel moves backwards into a convergent, forward-flowing part of the ring vortex? Or is something else actually generating the forces that inhibit deceleration?

Thank you Misters Howe and MacNaghten! If you've actually read through the above, you deserve a medal for humouring a fluids neophyte. But I find your work fascinating, and I'm doing my best to understand it. Hope your business goes well and you get lots of contracts with this keel (it's really neat!). Thanks again, and all the best!

- Ceilidh

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Hi Ceilidh,

I will try to answer your questions. I have much less technical knowledge than Jon, so this helps as I spend large amounts of time putting everything in to a non mathematical/fluid dynamics context for myself as well.

Nope

The induced drag of a closed circulation system (such as one generating an equal force out the whole way around a ring) is zero because it does not generate any lift. If you superimpose incidence on the whole system and generate lift it will create vortices as it has to. You cannot generate lift without creating vortices and hence induced drag (unless you have an infinitely wide wing ie 2d flow).

The idea behind the lower induced drag is fairly simple – imagine you have 2 wings width W a large distance apart carrying a load. They will each have half of the lift of one wing width W of the same size carrying the same load. Because they have to generate half of the lift they will have one quarter of the induced drag ie. They will have the induced drag of a wing of twice the width (2W). Now as you move these two wings together their lift systems will interfere with each other and slowly reduce this benefit. Generally the closer they are the less the benefit generated.

You can also do things like put end plates on to make a box wing. This is now a closed system and the ends also generate force which helps to reduce the induced drag. However, this lift system is no longer a two dimensional problem and it has to be properly analysed. It is really easy to create a non-planar lifting system like the boxwing or the loop keel which has higher induced drag than an equivalent wing. Solving this is one of the biggest headaches and for the loop keel it needs to be done at a number of different heel angles. You then pick a fairly good general performer that will give benefits over a range of heel angles rather than optimum at one angle and bad at all the rest.

You are pretty much there apart from this section

See the bit below on circulation (it is not a localized effect) and added mass when upright.

The main difference between us and a smoke ring is that we are operating at an air/water interchange and while your smoke ring is a virtually lossless and hence no drag system, we do create some drag. This seems principally to be a surface effect as a result of having the smoke ring sitting under the boat near the water surface – it creates some wave drag.

You are correct about the way the flaps move.

I found this quite difficult to answer as a number of the questions were based on earlier questions/assumptions that were not quite right. Here is my first shot. If you have more questions or I have not explained it fully please come back with further questions.

The added mass effect is related to the dynamic righting but totally different. Take for example the yacht traveling in an upright and forward direction. By varying the angle of attack of the foils you can vary the force generated outwards by the keel. If you sum up all of the forces generated by the keel and hull you end up with a big zero, regardless of the size of the forces. The ‘added mass’ or ‘added inertia’ is directly related to the size of the forces, but if the yacht is not resisting leeway or heeled it is generating no net force and therefore has no induced drag associated with it or dynamic righting.

Now when you heel the yacht the size of the forces has an effect on the leeway angle you generate, the amount of dynamic righting and the added mass. This dynamic righting is generating lift and hence you see the heap of sea. However, if the yacht was upright you would have the same (or similar) added mass without this heap of sea. Therefore, the heap of sea should be regarded as a physical manifestation of both the added mass and dynamic righting when heeled, as you cannot separate the two, but it is not the only indication of when you have added mass – yes it makes my head hurt also.

Now to deal with your inertia point.

Most yachts have added mass generated by displacement ie as you push a body through water it tends to effect a certain amount of water around it. Obviously the blunter the body the more water it effects and the more added mass you have. You discuss this in terms of waves and we do regard these as a physical manifestation of added mass. Don’t be fooled by the larger waves that appear as you meet hull speed. These are the result of a tuning effect from the length of the hull and are not related to added mass. If you do any tests with this effect make sure you are below hull speed. Moving on - it is not just the waves that are moving with the craft but a ‘loose’ body of water. This is quite difficult to prove as you cannot turn it off and measure it – ie when you turn your boat engine off you will slow down more slowly than you should have if you had suddenly lost all your apparent water mass around the vessel, but how can you actually do that in reality? The only way we know is to do tank test runs with related types of hull shape and the same mass, then measure the acceleration/deceleration data to discover the added mass – the acceleration is normally held constant for these tests and you calculate the added mass from the force data.

The Loop Keel inertia is slightly different to the inertia from displacement, but the effect is exactly the same. We did tank test runs with the same hull shapes (and mass), but different keel and force configurations in order to measured the variation in ‘added mass’. This inertia is related to the water effected by the keel circulation system. This system runs both ahead and behind the yacht and is probably much larger than you realise – we show it as being a fairly tight loop on diagrams, but this is only to make it easier to visualize. It is also important to realise it is not actually rotating around the keel but must be regarded as a superposition of a rotating flow on the linear flow past the hull.

Why must all of the fluid in the circulation system be bound to the keel? This is a difficult one to explain, but try this - imagine a wing flying along generating lift. It does this by imposing a circulation on the air around the wing. This means that the air ahead of the wing is ‘lifted’ and has an upwards component as it approaches the wing and the air behind the wing a downwards component, which is larger. The overall effect of these is to divert air downwards so that the momentum change of the air being driven downwards equals the force required to keep the aircraft up. This force is felt on the wing, but is not generated by any one particular bit of air, but is a result of the sum of all of the different bits of air changing direction. The fact that this air is a long way away from the wing does not make its contribution to the lift any less important or real than the bits close in. You then can make the connection that if the bits of air are not bound to the wing then how can they be contributing to the generation of lift on the wing?? The contra argument that you can move the wing and the bits of air would be unaffected would mean that lift would vary wildly if you moved the wing – it would move out of its own lift/circulation system and suddenly stop generating lift!! We know this does not happen which implies that the lift system must move with the wing. The same also applies to the loop keel.

I think that is one way of looking a it, but I will see if Jon can confirm this point.

I do know that if you take incidence slowly off of the foils to reduce apparent mass you then end up with your foil operating in the original circulation system which will tend to generate forwards lift ie you have reduced the mass of the body and the conservation of momentum means that you can get some of this back as extra speed. We have not done any tests of changing incidence while doing tank test runs so this is still theoretical and very hard to do on the water in the Lasers.

James

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### TheToyDogNew Member

This "canting" or "rotating" loop sounds like it would limit the "sweep-back" of the loop. The "semi-circular" top of the loop looks like it would have to be vertically aligned and then only the lower portions could be swept back. Looks good in fore/aft projection but in profile it could look a bit uglier. would the "dog-leg" where the sweep-back joins the semi-circle introduce any strange effects?

I'm also a little wary of the bulb projection forward of its loop attachment points - wouldn't this make it susceptible to snagging stray lines, cables, nets etc? Would it upset things if the loop were positioned further forward with the bulb trailing aft of the loop to discourage snagging?

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Yes it does limit sweepback and you would have to make a decision between sweep back and how far you wanted to rotate the keel. There no particular problems with having the dogleg from a hydrodynamic point of view.

The bulb is not meant to be swept forward, but it is sometimes the only way you can retrofit it to a boat. In the picture you have seen the bulb was only swept forward to keep it in the correct place relative to the fin keel for test purposes (we needed the same CG etc..). If you designed the boat from scratch you can have the bulb sweeping aft supported under a nice beamy stern with nothing protruding from the bulb to snag ropes etc.. on.

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### scoobyNew Member

To go quite a ways back to the discussion of the looped keel behaving as if it had twice the area of a fin keel. I'm not sure if you guys have figured it out, but a similar phenomenon occurs in wind tunnel testing of airfoils, at least at the wind tunnel at my university.

Basically, the foil section sticks through the bottom of the wind tunnel and into the test section. This means that there is only one tip vortex and the tunnel floor is effectively acting as a mirror plane. Thus, when calculating the aspect ratio for the foil section, you have to multiply the tested span by two in order to get an aspect ratio relevant for a finite wing in a free stream.

While I can't claim to grasp all the theory of the loop keel, it sounds as though a similar, though reversed, process is occurring with the elimination of the tip vortex of a fin keel. Certainly, without the induced flow from the tip vortex, the loop keel should enjoy an improved effective angle of attack for a given geometric angle of attack, compared to a fin keel.

I'd love to know if you have determined the cause of the improved performance and whether it is related to the tip vortex (or lack thereof).

Cheers

Silas

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Jon (Howes) is probably the best person to answer, but as he is away I will have a go!

The apparent area effect is unrelated to tip vortices.

TIP VORTEX and INDUCED DRAG
With any wing you cannot create lift without generating a tip vortex, hence your point about the wind tunnel testing being correct. If the wing is not generating lift there is no shed vorticity and no induced drag. This is true for any closed system generating lift outwards with no net lift. We have had interesting arguments with people that cannot accept that this produces a lossless system similar to a smoke ring. With the loop keel there is a loss which is associated with creating this system on an interface (air/water) and there is a wave drag penalty. If you were to create the same system in a single medium there would be no loss unless you created some net lift.

Induced drag of a wing is related to the efficiency of the wing, not the shape of the wing or number of wing tips.

Consider the following examples for a Bi-plane:

i. Both wings are almost touching. In this case the wing will have virtually the same induced drag as a single wing, but double the surface area - Bad Idea!

ii. Both wings are a long way apart and have no effect on each other. In this case each wing will carry half of the load and have a quarter of the induced drag. There are two wings so the overall result is half the induced drag of the single wing. This is the same result that you would get for a single wing of double the span. For a number of other reasons such as tip losses and junction drag the single wing of double the span is always better if you can afford the space required.

iii. The two wings are somewhere between these two extremes - in this case you get a benefit over a single wing in terms of induced drag, but there is an area penalty. Generally two wings (properly optimised) will always give a benefit, but never as much as increasing the span by the same amount.

With the loop keel, the fact that the wings are joined is irrelevant, it is the reduction in induced drag that is important. The joining of the tips is there purely to create a closed loop system.

Another way to look at this problem is to consider it from an energy perspective. For a plane to generate lift the wing must divert a certain mass of air downwards. The momentum (velocity) change of this mass of air equals the lift generated by the wing. However, the energy (induced drag) put into the air is equal to the velocity change squared. This means that if you can increase the mass of air effected then you disproportionately reduce the energy required to keep you aloft. The best way to increase the mass of air effected is to increase the wing span, but if you are limited in span you can also do this by using a non-planar wing.

APPARENT AREA
This is something that only came out of tank testing and we are still not sure of the reasons behind it. You see the effect because the loop keels are much harder to stall than their area should suggest (even allowing for the swept configuration). In fact, while the two tests boat have the same wetted keel area, the test results suggest that the loop behaves as though it has double the area of the fin keel.

We have put this down to the fact that there is an entrained flow of water through the loop, although we are not 100% sure. There is very little research in this area and we have not been able to find anything to properly explain this effect.

This apparent area effect does not have a particular 'racing' performance benefit unless you use it to reduce the chord of the loop keel. We have avoided this for structural reasons and because it is not fully understood. The larger effective area does translate in to better seakeeping - lack of stall, sailing upwind at low speeds etc.. as it is much harder to overload the keel.

Last edited: Jan 7, 2008
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### kenJSenior Member

A comment was made a few pages ago about applicability to the cruising market. With the loop keel extending beyond the max beam it will be hard to dock side to. Special bumpers would need to be carried or mooring restricted to a stern to Med Moor. Both would put crimps in many cruisers style.

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Without finding the exact comment we have always kept the loop keel inside the maximum beam of the boat for the reasons you mention. The only circumstances you would go outside the beam is if you wanted to develop a high performance racer.

Apart from the rotating version we had looked at an extreme fixed version of the loop keel. Imagine something equivalent to a single catamaran hull will a loop keel extending out 10 or 15 times the beam to either side, but with normal keel draft - it will look like a very wide squashed loop keel. We thought you would probably need to connect the outer most part of the keel directly to the rigging to keep the loads sensible.

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### kenJSenior Member

My comment was based on the pictures in the first couple posts. I'm glad as the design progressed you took the beam into consideration. Good luck in your continued progress, it is an interesting concept.

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### TeddyDiverGollywobbler

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### gonzoSenior Member

Reinventions of the wheel seem to always create some monstrous complicated apparatus. If a fin keel is weak, a wider base will solve it with less drag than two "wings".

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### ZedSenior Member

Sensational! About time the status quo was given a nudge, especially if it can be done with no moving parts... KISS, love it. Hope it goes better than these canting things, keels that swing don't inspire my trust, not at sea, maybe thats just me.

The above vid embedded -->

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### peterAustraliaSenior Member

hi

Interesting idea. I know the designers do not create credit for the joined V shape keel, but a little background.

A fellow called Sir Lawrence Hargrave, an early aviation pioneer that did work with wing cross sections and box kites and also attempted a steam powered aeroplane (before wright brothers, but not enough power to take off) built his own 30ft boat.

here is a little more about the fellow
http://www.ctie.monash.edu.au/hargrave/hargrave.html

That boat was unusual in that it was a large sharpie, with three identical standing lugsails, all inline. three in a row. But the keel had a weight below and had two fins supporting it, one from each side. I have seen a sketch of this boat in a book about Mr Hargrave, Obviously it did not catch on, but an interesting idea none the less. His boat dates from about the year 1900.

Mr Hargrave keels were straight, and as his sharpie hull was flat, the shape made my his two joined keels below the waterline was a triangle.

Just interesting background knowledge. You mention others have tried if before, I assume with straight fins.

One idea might to to combine the twin co-joined boards/keel structure with a bipod mast and a lateen sail. The bi-pod supports that lateen sail and distributes the stress directly into the keels.

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