Tandem Keel...?

[Lew Morris]

The November 2002 issue of Sailing magazine (Perry on Design) show an option "tandem" keel offered on their 26i model.

This tandem keel is basically two keels (in line) connected by a common bulb (for lack of a better term).

I would think that the turbulance created by the forward keel would really screw up the water for the aft keel....

Can anyone enlighten me of the concept behing this design?

[MDV]

Given enough seperation, the leeway of the yacht should give smooth flow on both foils. As far as I understand it the concept is trying to obtain two high aspect ratio sections which collectively have less drag for the same amount of lift as a single section. This was the driving factor with the twin struts fixing the front wing on a F1 car, although in that case the driving factor was minimal drag for a given strength.

Check out the following site for further information.

http://www.heymanyachtdesign.com/in3a.html


Regards,

Michael

[Lew Morris]

Thanks Michael,

I should proof-read my posts... the boat in question is the ETAP 26i.

http://etap-usa.com

Unfortunately there is no further information regarding the benefits of this keel configuration on their website.

As a reference, the side elevation drawing provided in the article shows the forward and aft keels to be of the same width. The distance between the trailing edge of the forward keel, and the leading edge of the aft keel, is roughly 2/3 of the width of either keel.... the lower surface of the bulb ( in the side elevation)appears to be nearly flat. A view looking aft would have been helpful.

Thanks for your comments!

[origamiboats]

I can't offer much information, but I can offer a lead in terms of some keywords that might help your search for information. Warwick Collins is the designer of the tandem keel of cast iron used on the Hill's Bendford Badger, a junk-rigged boat featured in their book "Voyaging on a Small Income". A web search on this name may send you in the right direction.

Cheers,

Alex

[origamiboats]

I found a litte more on the Collins tandem keel at the website page for the Sadler 34 at http://www.sadlerandstarlight.co.uk/docs/sadler34.htm#tandem

A quote from that site:
Warwick Collins spent more than three years in developing his tandem keel, with tests on tank models and on full-sized boats.
Claims made for the Tandem Keel:

1. A lower centre of gravity

2. Better directional stability and resistance to broaching

3. Better damping of pitch and roll

4. Smarter tacking

5. Improved weatherliness in rough water

There is now plenty of evidence from owners and skippers that where a standard keel is replaced by a tandem keel the boat's general behaviour is much improved, and that speed made good to weather is either the same or better.

[Lew Morris]

thanks for the link.

it would appear that the "bulb" in this image, in addition to having a tandem keel, is of a "winged" configuration.

interesting stuff...

[Steve Gray]

Hello, Lew

A few years ago there was a move towards putting a slot just behind the leading edge of the fin on high-speed sailboards to help combat 'spin-out', which is the tendency of the board's tail to swing off to leeward when water turbulence or poor rider stance caused the fin to come unstuck at speed (usually a problem at about 15+Kts).

The concept was that the slot acted like the slat at the LE of an aircraft's wing (or the primary feathers on a bird's wing (or, of course, a jib in front of a main)) to assist the fluid (water or air) to stick smoothly to the higher-aspect foil surface rather than turbulate--it effectively allows the foil to maintain a better grip on the water. The keel configuration you show will obviously provide these benefits, and the bulb wing will also act as a 'tip fence' to stop water flow being diverted downwards (look at the tips of a Jumbo 400), thereby retaining even more traction (which shouldn't be confused with drag).

I reckon that the list of quoted claims can all be put down to good traction of the keel. Incidentally, on sailboards, the fashion died when it was realized that no amount (or absence) of plastic would compensate for pilot error ('heavy feet'); now we just use a longer, very high-aspect blade.

Hope this helps...

[tspeer]

Originally posted by MDV
...As far as I understand it the concept is trying to obtain two high aspect ratio sections which collectively have less drag for the same amount of lift as a single section. ...

Splitting the area into two surfaces of the same span does not increase the aspect ratio. Aspect ratio is the span^2 / total area. If you substitute the keel dimensions into the formulae for drag to get the total drag (in pounds or newtons), as opposed to the drag coefficient, I think you'll see what I mean.

Most of the reasons given for a twin keel don't make sense to me. On a beat, the lift from the keel is dictated by the sail rig, so getting more lift from a slotted section only makes sense when the boat is tacking or if the area of the keel is reduced.

The induced drag due to lift depends on the total lift distribution over the span of the keel. If the lift distributions of the single and tandem keels are similar in shape and the depth of the two keels is the same, then the induced drag will be the same. This is true regardless of the area of the keels or how that area is distributed in the streamwise direction (this is known as the Munk stagger theorem). Likewise, the effect of winglets on the keel's induced drag should be largely independent of their location relative to the keel in the streamwise direction, so the same winglets should be comparably effective for either keel.

The tandem keel can have less skin friction drag if the total area is less than the single keel. However, the tandem keel's I've seen pictured don't seem to have markedly less area. So the profile drag should be comparable for both designs.

With comparable profile drag, induced drag, and lift coefficients, that pretty much rules out all the conventional explanations as to what makes tandem keels go. But I think there are some other factors that haven't been mentioned.

For keel sections of comparable thickness ratio, the thickness of the tandem keel is half that of the single keel. The intersection drag at the boat and bulb junctions depends on thickness squared, so it's possible the junction drag is halved in the tandem design. The tandem keel's leading edge can go right to the nose of the bulb, with the attachment line of the keel ending at the stagnation point on the bulb. This would eliminate the necklace vortex that would form at the junction of a blade attached to the middle of the bulb, and reduce junction drag even more. Of course, the aft surface on the tandem keel is still subject to forming a necklace vortex at its junction.

The pressure disturbance of a narrow fin keel is concentrated in one location, and there's a wave drag penalty for this. From a wave drag point of view, it's as though you wrapped a bump around the hull at the keel location, much like the equivalent body of revolution used to analyze transonic wave drag in air. The tandem keel may well provide a better distribution of the equivalent cross sectional area and reduce the wave drag over the single keel.

The two surfaces of the tandem keel will provide more yaw damping than a single blade. Yaw damping varies with the square of the distance between the surface and the center of gravity, so damping provided by the rudder is much more dominant than either keel. but if you didn't have a rudder, the increased damping would be significant.

The real gains may be structural rather than hydrodynamic. The twin keel will be thinner, and thus weaker than a comparable single keel with respect to sideways bending moments. However, it should be much stiffer in torsion when supporting a long, heavy bulb because the torsion loads are reacted by differential bending in the two surfaces. The tandem keel is also attached over several more floors, which would be especially valuable in a grounding situation.

Whether or not there's a net gain for a tandem keel probably depends on the details of its implementation. However, the most effective way to improve the efficiency of any keel going to weather is simply to make it deeper. There's no substitute for span.

A good figure of merit for comparing two keels is the boat's wetted aspect ratio. This is the depth-squared divided by the total wetted area, including hull, keel, bulb, wings, etc. Chances are the boat with the highest wetted aspect ratio will be the more closewinded one.

Tom
I don't understand your statement about the aspect ratio. If I have a keel of span X and area Y and I then slit the keel into 2 keels each of the same span (x) but each having an area of Y/2, wouldn't the apsect ratio of each keel be x^2/(y/2) as opposed to the original single keel of X^2/Y. Is there a reason the two keel would not be considered seperately and treated as two seperate surfaces? I would think that the increase in aspect ratio would be the best argument for the twin keel. If this argument is invalid that really puts a substancial dent in the argument for twin keels.

[tspeer]

Originally posted by Guest
...If I have a keel of span X and area Y and I then slit the keel into 2 keels each of the same span (x) but each having an area of Y/2, wouldn't the apsect ratio of each keel be x^2/(y/2) as opposed to the original single keel of X^2/Y...I would think that the increase in aspect ratio would be the best argument for the twin keel. If this argument is invalid that really puts a substancial dent in the argument for twin keels.

It's a common misconception that induced drag depends on aspect ratio. It doesn't. Induced drag depends on span and is independent of aspect ratio if you fix the span. Here's why:

Let's assume a parabolic drag polar, typical of wings and keels when wave drag is not a factor. The drag coefficient can be written as

AR = b^2/S

CD = CDo + CL^2/(pi * AR * e)

AR = aspect ratio
b = span (depth of keel)
CD = total drag coefficient
CDo = parasite drag coefficient
CL = lift coefficient
e = efficiency factor (approx. 1.0)
pi = 3.142...
S = reference area

This makes it look like the induced drag (second term in the equation above) depends on the aspect ratio. But this is a nondimensional drag coefficient - it's been divided by the really big influences; the velocity, fluid density, and reference area.

Now take a look at what the drag really is, in pounds or newtons:

D = total drag
L = lift
rho = fluid density

D = CD * 1/2 * rho * V^2 * S
L = CL * 1/2 * rho * V^2 * S

D = CDo*1/2*rho*V^2*S
+ [L/(1/2*rho*V^2*S)]^2 / (pi*b^2/S*e) * (1/2*rho*V^2*S)

D = CDo*1/2*rho*V^2*S
+ L^2 / (1/2*rho*V^2*pi*b^2*e)

Aspect ratio has totally disappeared! The parasite drag depends on the reference area, and if you picked the wetted area as the reference area, CDo would be close to the skin friction coefficient.

The induced drag depends on span-squared, not aspect ratio, and e, which depends on the planform shape. Winglets get into the act by increasing e, and improving b when the boat heels. If you keep the span, b, the same and increase the chord, the drag goes up because you're adding wetted area to the parasite drag. The aspect ratio is going down, too, but the induced drag isn't changing (assuming e stays constant). Finally, the induced drag goes down with speed if lift is held constant. So if you have a short span (like a boardless catamaran) you can make up with speed what you're lacking in depth. This is all completely opposite of what you'd expect from looking at the drag coefficient instead of the actual drag.

Instead of thinking of aspect ratio as being a "skinny-ness" factor, think of it as the nondimensional form of span (squared). When nondimensionalizing an equation, anywhere you have a length^2 component, you divide it by reference area. So b^2 becomes b^2/S and you have aspect ratio. Long skinny glider wings have low drag because they have a lot of span for their area - this is what aspect ratio is really saying. Or because they have small area for their span, which would be another valid way of looking at it.

If you look at it in this light, then the nondimensional equation starts to make more sense. The induced drag is inversely proportional to the nondimensional span-squared (aspect ratio), just like it is in the dimensional equation. For a fixed lift, the lift coefficient drops with speed, and this accounts for the reduction in induced drag with speed. So the two approaches are consistent.

Now let's look at a tandem keel. For comparsion, I'll assume the skin friction is the same (it would actually increase somewhat because the chord Reynolds number will be lower for the tandem), and total area and span will be the same. We're just going to take a single keel and split it into two tandem surfaces.

Drag of the single keel is

D = CDo*1/2*rho*V^2*S
+ L^2 / (1/2*rho*V^2*pi*b^2*e)

Now distribute the lift between two equal sized surfaces and assume that the surfaces are independent:

L1 = L/2
S1 = S/2
D1 = CDo*1/2*rho*V^2*S1
+ L1^2 / (1/2*rho*V^2*pi*b^2*e)

D1 = CDo*1/2*rho*V^2*S/2
+ (L/2)^2 / (1/2*rho*V^2*pi*b^2*e)

D1 = (CDo*1/2*rho*V^2*S) / 2
+ L^2 / (1/2*rho*V^2*pi*b^2*e) / 4

Dtandem = 2 * D1
Dtandem = CDo*1/2*rho*V^2*S
+ L^2 / (1/2*rho*V^2*pi*b^2*e) / 2

Wow - the induced drag has been cut in half! The trouble is, the surfaces aren't independent. The wake from the forward surface affects the aft surface and, surprisingly, vice versa. The real expression for the induced drag of two surfaces is (ref 1):

Di = L1^2 / (e1*b1^2)
+ 2*(sigma/e3)*(L1/b1)*(L2/b2)
+ L2^2 / (e2*b2^2)

For two surfaces of equal span and no separation in the crossflow direction, (sigma/e3) is approximately 1.0. And the interference between the two surfaces exactly fills in the difference between the tandem wing and single wing.

Figure 9 of Ref. 4 (http://aero.stanford.edu/Reports/MultOp/multop9.gif) shows the relative drag of two surfaces of various sizes. For equal span, the total drag is greater than that of a single surface, and two equally sized surfaces is about as bad a choice as you can make.

As you say, I think this does put quite a dent into the arguement for twin keels.

However, this isn't the whole picture, either. A twin keel with a rudder is actually a 3-surface configuration. And with the right choice of parameters, it is possible to get a net savings in the trimmed drag (http://aero.stanford.edu/Reports/MultOp/multop13.gif). But it's not a slam-dunk.


References
1. Rokhasaz, K, and Selberg, B. P., "Comparison of vortex lattice and Prandtl-Munk Results for Optimized Three-Surface Aircraft", AIAA-86-2695, Oct., 1986.

2. Kendall, Eric R., "The Theoretical Minimum Induced Drag of Three-Surface Airplanes in Trim", AIAA Journal of Aircraft, Vol. 22, No. 10, October 1985, pp. 847 - 854.

3. Feistel, T. W., "Interdependence of Paramters Important to the Design of Subsonic Canard-Configured Aircraft", SAE 850865, SAE Aerospace Technology Conference & Exposition SP-757 Advanced Aerospace Aerodynamics, Oct. 1988.

4. Kroo, Ilan, "Design and Analysis of Optimally-Loaded Lifting Systems", AIAA 84-2507, Oct. 1984. http://aero.stanford.edu/Reports/MultOp/multop.html

An interactive java applet that will calculate the trimmed drag of tandem wings can be found at
http://www.desktopaero.com/appliedaero/configuration/canardcalc.html. You will have to adjust the static margin (sm) to control the loading on the two surfaces. e = 1 means the drag is the same as a single elliptically loaded wing of the same span.

[Steve Gray]

Tom, you certainly know how to deliver a nuke to make a point. I consider myself fortunate that I can get a mental grasp on the basic idea--it must be great to actually understand the workings as well. The detailed math intimidates me a bit, so I tend to rely on analogies to get the picture.

I accept that the slot between the keel sections doesn't equate to a higher aspect ratio, and that high aspect is defined by a contiguous longitudinal section so that the whole leading edge and chord work as a whole; I guess that part of what your last evidence shows is that, in the case of the tandem keel and aspect ratio, one plus one doesn't equal two.

So, do you have any comment/instruction concerning the view I posted earlier about the effect of the slot in maintaining a good flow over the foils? Your detail responses seem to be focussed a lot on 'drag', but isn't this significantly affected by any turbulence caused by poor adhesion of the fluid's progress over the surface? And is there a relationship between induced drag and the 'grip/traction' that I mentioned (which is something that you can feel very acutely when moving at 20+kt on a sailboard--those long narrow fins make such a positive difference)?

Sorry, Tom, you're obviously being pumped for free lessons here.

Stv

[tspeer]

Originally posted by Steve Gray
...I accept that the slot between the keel sections doesn't equate to a higher aspect ratio, and that high aspect is defined by a contiguous longitudinal section so that the whole leading edge and chord work as a whole

No, what I was saying is the aspect ratio is the span-squared divided by the total reference area. The reference area is whatever you want to define it as - it's typically the planform area for a keel. It doesn't matter if the area is divided up into two narrower surfaces or is one surface.

Actually, the best parameter for comparing two keels would be the wetted aspect ratio, which is the depth^2/total wetted area. The wetted area would include both sides of the keel, the bulb, wings, and the bottom of the boat.

...So, do you have any comment/instruction concerning the view I posted earlier about the effect of the slot in maintaining a good flow over the foils? Your detail responses seem to be focussed a lot on 'drag', but isn't this significantly affected by any turbulence caused by poor adhesion of the fluid's progress over the surface?

What strikes me most about the keel in the picture is that it's SHORT. I'd bet a single fin twice its depth would beat the pants off it going to windward. But obviously, there were other considerations driving the design of that keel than windward performance.

By "poor adhesion" I take it you are talking about separated flow, such as when the keel stalls. I think a clean fin keel with a well designed section would perform as well. The section design would take into account the speed range and size of the keel, as well as how heavily it was loaded. The section would also have to have enough thickness for the required strength and ballast.

A slotted section can have a higher maximum lift than a single element. But it's not so much that there's a slot there, but rather the way the two sections are designed to benefit from their mutual interference. It has to do with altering the pressure distribution on each piece to control the development of the boundary layer along each surface. It's hard to get the right benefit from two symmetrical sections that are lined up in the same plane like they are with a tandem keel.

And is there a relationship between induced drag and the 'grip/traction' that I mentioned (which is something that you can feel very acutely when moving at 20+kt on a sailboard--those long narrow fins make such a positive difference)?...

I'm not sure what you mean by this. I'm not a board sailor, and I don't know what the conditions are on the fin of a sailboard.

Tom

Just one more question. How far would the keels have to be staggered in order for them to be considered as individual surfaces.

[tspeer]

The factor sigma in the formulae above is factor that handles that. See http://www.desktopaero.com/appliedaero/configuration/multiplesurfaces.html for some typical values. For the tandem keel, the interference is cut in half when the surfaces are roughly 20% of the span apart in the crossflow direction.

BTW, this whole discussion also applies to two-masted rigs. Cat schooners are generally not as efficient as a single rig, so why wouldn't people expect the same thing to apply to keels?

Many thanks so far for the insightful comments on tandem keels. I have been searching the net for some information, but found little except Sadler and Etap yachts home pages.

The Etap product brochure gives a technical drawing about the tandem keel, showing a really big wing/ bulb at the bottom, which brings the center of gravity down.

From all material I have read and understood on this keel,
the claims are:
-reduced draft
-same range of stability as deep keel
-same pointing ability a deep keel

The principle involves, that

- the center of gravity is kept low although the draft is reduced

-the bulb/ wing is really big and works as a fence/ endplate (dont know the right expression in English), thereby creating an almost 2D- flow with little vortex around the keel "tip"/ endplate.

-the "window"/ slot between the keels is claimed to be carefully designed based on towing tank experiments. The slot widens towards the upper side of the keel. This is supposed to encourage the fluid passing between the tandem keels to have an upward component, thus counteracting the downward flow on the pressure side and the associated tip vortex.

If all this was true, an ingenius way of reducing draft without penalty was found. For the cruising sailor this would mean a breakthrough, avoiding all the problems associated with lifting keels.

In spite of all the insightful comments of tspeer, a comparison of the collins keel with a double wing configuartion or a shooner rig apears unjust, as there is much more control over the flow with the short distance of the foils and the big endplate - similar to the controlled flow in a turbine.

But where are the hard facts? Does anybody know about reports/ proceedings about the Collins keel? Are there test reports with the same hull design, but different keel configurations?
And who is or was Mr. Warwick Collins., if not present in the net.?
Detlef

[tspeer]

Originally posted by Guest
...
-the bulb/ wing is really big and works as a fence/ endplate (dont know the right expression in English), thereby creating an almost 2D- flow with little vortex around the keel "tip"/ endplate. ...


It's not that easy to get rid of the induced drag. There is still some vorticity shed at the junction and additional vortices shed at the tips of the wings. It's a misconception that the trailing vortices come just from the fluid spilling around the tip. In fact, the vorticity is shed continuously along the span, with a greater concentration at the tip.

Wings don't get rid of the trailing vortices, they just move them laterally away from the rest of the keel so that they don't have as great an effect. But for the same addition of wetted area, you can get a greater gain by making the wing an extension of the keel than you can by mounting the same surface as a wing.

Wings only make sense if there is some constraint on the depth of the keel. The constraint could come from rating rules, or from the need to sail in shoal waters, or even for easier carriage on a trailer. Wings may also be a more productive way of packaging the volume of ballast. But for pure hydrodynamic efficiency, go for span every time.

... But where are the hard facts? Does anybody know about reports/ proceedings about the Collins keel? Are there test reports with the same hull design, but different keel configurations?...

Exactly. There are lots of claims made for various keel configurations, but the explanations usually sound like one of Kipling's "Just-So Stories".

It's always interesting to ask, "So, may I see your data?" If you get a lot of mumbling and handwaving and statements like, "Well, it's all due to the collateral thermal end-plate effect, and you really can't compare it with a conventional configuration," then I'd be inclined to walk away. And if he claims to have discovered some revolutionary new physics then I'd not walk away, I'd run.

But if he says, "Here are some estimates of a comparable conventional configuration compared with published test data so you can see how well the estimation technique works, here are the estimates of the new configuration showing the improved performance, and here are our test data on the new keel validating the predicted performance," then I'd be inclined to plunk my money down. It's perfectly reasonable to expect a minimum of two out of these three.

[Fco.Lopez]

If tandem keel really works spectacular...

All of IACC yachts will have one... ;)

I don't like the tandem keel posted on page 1... i think for these boat, will work better a semi-long keel...

[SailDesign]

THe Collins keel seems to work really well. tRodger Martin and I put one on a 43' cruiser/racer (Quadrille) for a client who wanted low draft and high performance. There was no appreciable down-side to the thing, unless you like being bounced around on the mooring ;-)
Performance was just right, and it had the added benefit that at launching time one of the yard crew rode it down "Dr. Strangelove" style
Steve

[yipster]

"Dr. Strangelove" style
sitting backward on the bow waving a cowboy head? :D

[SailDesign]

Yipster - sitting between the two foils, on the bulb, waving a baseball hat
;-)

[Tohbi]

well, i'm dizzy from trying [unsuccessfully] to figure out the numbers, but i seem to remember an america's cup 12 meter that had twin keels. wasn't the designer or owner named blackaller, or something similar?

it seems that boat pointed high but the widely separated keels caused some handling problems. america's cup rules only allowed for two underwater appendages so the keels had to act as rudders, as well.

how about a trim tab on an existing keel design? how efficient is that addition?

[Fco.Lopez]

Originally posted by Tohbi


how about a trim tab on an existing keel design? how efficient is that addition?

Good question...!!!

Somebody sailed a boat with trim tab? Or design, build...

:cool:

[Stephen Ditmore]

If anyone would like to comment on my keel idea, check it out at
http://boatdesign.net/forums/showthread.php?threadid=2425&pagenumber=2

BTW the first tandem keel I'm aware of was on a boat designed by Art Paine, identical twin brother of Chuck Paine and built in the late 1960s (or perhaps 1970) to compete with the Soling and the Etchells to be the new 3 man olympic keelboat. Art built the boat with the assistance of a young fella named Eric Goetz, but they didn't have it ready in time for the competition (Eric's been lothe to miss a deadline since!).

[SuperPiper]

Recently posted on "Hull Is Slower Without The Keel":

I sail a micro-cruiser. It is a Sandpiper 565, 18'6" LOA with a 15'0" LWL. This little boat has 300 lbs of lead ballast in a keel that raises vertically into the cabin table. When completely retracted, the bottom of the keel is flush with the bottom of the hull.

Recently, while sailing straight downwind wing-on-wing, the keel was cranked up to reduce wetted surface and to reduce drag. To our amazement, the boat speed appeared to decrease! So the experiment was repeated a 2nd time and the result was inconclusive. But, the speed did not increase as expected.

The experiment was later repeated by a different boat using its outboard motor. Again, there was no detectable change in speed.

The boat speed was being measured using GPS with resolution to 0.1 knot. The sailing experiment was conducted at about 2.8 - 3.1 knots. The motoring experiment was conducted at 4.7 - 4.8 knots. Hull speed is estimated at 5.3 - 5.7 knots.

Is there an explanation why withdrawing the keel should not increase the boat speed? Especially while travelling below hull speed? Does the keel somehow change the boat's wave-making ability to give the illusion of a longer boat? Does the appendage sticking out the bottom of the hull somehow mimic the winglet on a bulb keel? Does it provide less drag despite its increased wetted and frontal areas?


It's a common misconception that induced drag depends on aspect ratio. It doesn't. Induced drag depends on span and is independent of aspect ratio if you fix the span. Here's why:

Let's assume a parabolic drag polar, typical of wings and keels when wave drag is not a factor. The drag coefficient can be written as

AR = b^2/S

CD = CDo + CL^2/(pi * AR * e)

AR = aspect ratio
b = span (depth of keel)
CD = total drag coefficient
CDo = parasite drag coefficient
CL = lift coefficient
e = efficiency factor (approx. 1.0)
pi = 3.142...
S = reference area

This makes it look like the induced drag (second term in the equation above) depends on the aspect ratio. But this is a nondimensional drag coefficient - it's been divided by the really big influences; the velocity, fluid density, and reference area.

Now take a look at what the drag really is, in pounds or newtons:

D = total drag
L = lift
rho = fluid density

D = CD * 1/2 * rho * V^2 * S
L = CL * 1/2 * rho * V^2 * S

D = CDo*1/2*rho*V^2*S
+ [L/(1/2*rho*V^2*S)]^2 / (pi*b^2/S*e) * (1/2*rho*V^2*S)

D = CDo*1/2*rho*V^2*S
+ L^2 / (1/2*rho*V^2*pi*b^2*e)

Aspect ratio has totally disappeared! The parasite drag depends on the reference area, and if you picked the wetted area as the reference area, CDo would be close to the skin friction coefficient.

The induced drag depends on span-squared, not aspect ratio, and e, which depends on the planform shape. Winglets get into the act by increasing e, and improving b when the boat heels. If you keep the span, b, the same and increase the chord, the drag goes up because you're adding wetted area to the parasite drag. The aspect ratio is going down, too, but the induced drag isn't changing (assuming e stays constant). Finally, the induced drag goes down with speed if lift is held constant. So if you have a short span (like a boardless catamaran) you can make up with speed what you're lacking in depth. This is all completely opposite of what you'd expect from looking at the drag coefficient instead of the actual drag.

Instead of thinking of aspect ratio as being a "skinny-ness" factor, think of it as the nondimensional form of span (squared). When nondimensionalizing an equation, anywhere you have a length^2 component, you divide it by reference area. So b^2 becomes b^2/S and you have aspect ratio. Long skinny glider wings have low drag because they have a lot of span for their area - this is what aspect ratio is really saying. Or because they have small area for their span, which would be another valid way of looking at it.

If you look at it in this light, then the nondimensional equation starts to make more sense. The induced drag is inversely proportional to the nondimensional span-squared (aspect ratio), just like it is in the dimensional equation. For a fixed lift, the lift coefficient drops with speed, and this accounts for the reduction in induced drag with speed. So the two approaches are consistent.




This old post by Tom Speer may include some revelation about my retracting keel. Tom's logic held the span constant. In my Sandpiper example, the span and the area are both changing - each countering the advantage of the other. Reducing the span causes a marginal increase in drag but reducing the wetted area causes a marginal decrease in drag.

So, ain't that cool ?

[Vega]

Harmony is a French big prduction sailboat manufacturer directed and owned by Mr Poncin, the man that was for many years the Director of Dufour yachts (that he has sold to the Italians some years ago). The Harmony are on the rise and that in a country that is the home of Beneteau, Jeanneau and Dufour (that made boats for the same market segment) is quite an accomplishment, considering that Harmony has no tradition and is a completely new company.

One of the most distinctive features of the Harmony is the tandem Keel that is offered as an option. The Tandem is the keel choice for cruisers and has proven very well.

Harmonies are designed by Mavrikios and Mortain and they say about the tandem keels on the Harmonys:

“Those looking for small draughts will be delighted to know that cast-iron tandem keels …offer almost the same sail stiffness and the same ability to go close winded as lead keels with far deeper bulbs”.

http://www.harmony-yachts.com/public/harmony/html/upload/doc/45dd6cca323db20P%20Harmony.pdf

http://www.eurobateaux.com/accueilpy.htm

http://www.mortain-mavrikios.com/

They also do them for the Etaps.

Etap says about them:

"After thorough investigation and numerous tests, ETAP Yachting N.V. is pleased to introduce its ETAP tandem keel. The most important advantages of this keel are the excellent sailing qualities at a considerably reduced draft. This new design is the result of a co-operation with the architects' bureau Mortain-Mavrikios.

The two most important features to reduce drift, are the size of the lateral plan and its efficiency. The efficiency is defined by the proportion between the depth of the keel and the length. Also a wing section is a classic aid to improve the efficiency.

For a strong reduction of the draft neither a wing keel or a bulb keel were sufficient. The solution was found in placing two shorter keels behind one another, linked by a wing-bulb profile : the ETAP tandem keel.

The ETAP tandem keel gives a better aspect ratio, thus generating more lift.
In addition to increased stability, the wing-bulb also provides better hydrodynamic characteristics. "

http://www.etapyachting.com/index.php?pageID=37

[Paul Scott]

n+1 > n just turned into EMO's bad dream? Say it ain't so! Must be those pesky details Tom's mentioning. I must admit, though, when those slotted windsurfer skegs spun out, they REALLY spun out. Usually when goofyfooting on the starboard tack. Yikes.

Exit, stage L, right ankle (and L hemisphere) throbbing,

Paul

[naval ark]

Is there an explanation why withdrawing the keel should not increase the boat speed? Especially while travelling below hull speed?

This old post by Tom Speer may include some revelation about my retracting keel. Tom's logic held the span constant. In my Sandpiper example, the span and the area are both changing - each countering the advantage of the other. Reducing the span causes a marginal increase in drag but reducing the wetted area causes a marginal decrease in drag.



Yes, of course the presence of an appendage alters the hull-generated wave pattern, whether this is in a positive or negative manner depends on the length/speed and number of wave crests between bow and stern.

Might I suggest that your initial findings are a little on the crude side, but as you found out, in most cases the difference in viscous resistance between centerboard down/retracted is marginal when compared to the wetted surface and wave-making capacity of the hull.

Tspeer makes some very good points, and he is entirely correct, but two and three surface interactions can be very difficult to predict - possibly for the reason that obvious definitions in the aerospace industry become muddied rather quickly when applied to sailing yachts. For example, in the above example the aspect ratio term drops out entirely because he is defining AR as b^2 over S, where S is the total keel area (more accurately could be total underwater planform area). This is valid for closely spaced foils but if stagger increases to around 3 or 4 (distance normalized against chord length) then considering the foils separately and each having their own AR (b^2/S) would be valid. This is what the America's Cup yachts were doing, although they were hampered by the two movable appendage rule, which is something a tandem can really use to advantage...

[SuperPiper]

Naval Ark:

Great explanation. Even I comprehend. Yes, the wetted surface of the keel is only a fraction of the hull's wetted surface. And it is the hull that is making waves.

Thanks for the insight.