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Full or fin keel?

191K views 846 replies 107 participants last post by  mstern 
#1 ·
Can somebody pro/con a full vs. fin keel for a newbie (will learn to sail on said boat) and taking it thru the Caribbean? All I can seem to come up with so far is fin keel is better to the wind, and a full keel will protect your rudder.
 
#794 ·
At 2200rpm, my stern is squatted down in the water, I am using alot more fuel and gaining a 1/2kt over 2000rpm. I am going over the boats hull speed and am at it's physical limit. What you call "power sailing would not gain my more than a 1/2kt. My boat is what used to be called an auxiliary, back when engines were an auxiliary form of propulsion. Now adays it seems people use their sails for auxiliary and/or entertainment and their engines to get the boat back to the dock in time. If you need to go faster than sails will allow then maybe you should trade your boat in on a "stink pot". If a knot or too stresses you out you need to spend more time sailing...put yourself in a position where you don't have to be any where or back from anywhere at any time special.
To those of you that this does not apply, please don't be offended, because it was not directed at you. To those of you that this does apply, don't get offended either, just learn to chill.
 
#795 · (Edited)
Wolfie - I once totally ruin the salt water cooling system of a earlier boat by sailing on and off my mooring and anchoring out when cruising. Think I had zero engine hours that season. When it was time pull the boat for the winter found out mussels and other critters had taken up residence in the cooling system. Ended up having to replace most of it. Was embarressing getting towed in to be pulled. Oh well. Still, think the engine is the aid of the sails although the last few boats have been documented as oil screws. See too many folks rocking and rolling liberating hydrocarbons unneccessarily when they could leave a sail up and have a nicer ride,burn less fuel and have the pleasure of a sail up. Only time my main comes down is when I'm running in a significant breeze or singling on a day sail and too lazy to pull it up. Agree it's a problem with narrow sterns. They do tend to squat under power. Was trying to encourage more sailing. Sorry you took it differently.
 
#798 ·
Even living at the dock and not taking my boat out I still exercise my engine.

The MacGregors with enough power can get up and plane to get you back to the marina in time so you don't miss cocktail hour. As much as I dislike them, I have noticed one thing about MacGregors.....the owners do tend to use them a lot more, and that what it's all about right.
It is possible for me to get my boat over 20kts....but that would involve putting it on a container ship.
 
#803 ·
Even living at the dock and not taking my boat out I still exercise my engine.

The MacGregors with enough power can get up and plane to get you back to the marina in time so you don't miss cocktail hour. As much as I dislike them, I have noticed one thing about MacGregors.....the owners do tend to use them a lot more, and that what it's all about right.
It is possible for me to get my boat over 20kts....but that would involve putting it on a container ship.
I described my Mac 26X, Bossa Nova, as a 26-foot, sleep-aboard sailing dinghy, that can also serve as a funny-shaped travel trailer. It's a very good first boat, for someone who hasn't decided between sailing or power-boating, or who wants to take it on a camping vacation to some big lake or bay, or other sheltered waters; and I know a few people who have taken their MacGregors to the Bahamas, and had a great trip of it.

But you can only do so much with a Mac.

I don't regret putting my Mac up for sale and buying my current Bristol 29.9, even if I'm paying several times as much to keep Halcyon in a slip as I was paying to keep Bossa Nova on her trailer at the same marina.
 
#801 ·
Paulo, your last picture looks like a boat designed to beat a rating system weighted against LOA.
 
#804 ·
There are also cut away and modified keels. Much of the choice depends on your sailing preferences: fast vs comfortable (sea kindly); deep water ocean cruising (deeper keel) vs Bahamas bank or wanting to pull into shallow harbors (shoal keel); etc. As mentioned above, having the rudder be shorter than the keel and protected (hung or skeg) is import for cruising. We have a heavy boat with a 5.5’ draft. She’s not fast but she’s comfortable (aka civilized) and sea worthy. With the 5.5’ draft there are a number of hurricane holes here in the Bahamas that I can not get into and harbors that I have to wait for high tide to enter. I’m ok with these trade offs.

As all the sailboat cruising and boat buying books would say, there are always trade-off when aquiring a boat.

Julia
S/V Esprit
Mariner 39 (NH built, cruising version)
 
#809 · (Edited)
"I believe they can design them in an effective way otherwise they would not be using them."

What a novel thought. I wonder how many design features have been tried over the years that have proven less than effective but initiated with that same optimism? The "split keel" has been around for quite a long time.

Maybe in time it will join some other "breakthrough" keels like theScheel keel, Reijo Salminen wing keel, eliptical planform keels, to name three.
 
#810 · (Edited)
"I believe they can design them in an effective way otherwise they would not be using them."

What a novel thought. I wonder how many design features have been tried over the years that have proven less than effective but initiated with that same optimism? The "split keel" has been around for quite a long time.

....
Sorry, I guess I was not been clear:). They are around as you say for a long time, from the time CFD studies were not the norm to study keel, hull and rudder efficiency, but things were done by try and error, experience and a good eye.

They survived till today were they are designed not by trial and error but by seeing their comparative performance with other types of keels in CFD studies. If they are still used by major NAs it is because they are a valid alternative to other options, specially in what regards low draft options.

For instance, Mortain&Mavrikios, the designers of the line of Harmony, Etap, Lockwind, Passoa, Nautitech Feeling and some Dufour said about tandem keels regarding their use on the Harmony:

"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.mortain-mavrikios.com/MMC Brochure.pdf

And Etap said some years ago regarding the use of tandem Keels on the Etap 30i:

"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. "


Tandem keels are also used by J&J yacht design in several Bavarias.

http://greenlinehybrid.com/J-and-J-design

Regards

Paulo
 
#811 ·
Don't see anything about CFD Paulo. How are you certain CFD was used? Can you provide a CFD study that has been published? I'd like to see that for my own education. I wouldn't make the automatic assumption that CFD is being used for every new keel you see from a major design office.

I understand the theory behind the tandem keel. As I said it is far from a new keel geometry. I don't doubt that it works, to some degree. But the real appeal may be more for marketing. Seems like you bought it.
 
#812 ·
I don't know of any major NA cabinet that does not use CFD in what regards hull, keel and rudder design.

I am not defending tandem keels against other solutions for swallow draft. I am only saying that it is still a contemporary solution in a sense that it continues to be a valuable option.

Personally I think that the best contemporary solution for a shallow draft are swinging keels. Those are the only ones that manage the miracle of offering a similar tracking upwind, a slightly lower weight for the same RM at the cost of a slightly bigger draft without having a big intrusion on the interior habitability. The only real problem is that they increase the boat price and need some maintenance.

Regards

Paulo
 
#813 · (Edited)
Paulo:
I'll have to defer to your superior knowledge in the area of yacht design and yacht design offices. I have not been at this very long. You obviosly have far more depth and bredth to your design office experience than I have. I can only hope to one day have as much knowledge of yacht design as you think you have.

Here are a couple of small projects of mine. I'd love to see some of yours.

I am in full agreement with you that swing keels are the optimal solution for shoal draft. I am very lucky in that I live where the water is very deep so shoal draft is not a concern of mine. Although I have designed one or two boats where draft was a major consideration.
 

Attachments

#814 ·
I don'y understand your attitude. I am not a yacht designer and I never have pretended to be. That does not make less true that today all major NA cabinets use CFD in what regards designing hulls, keels or rudders. Many advertise so on their web sites and others even publish some computer prints of the studies. It is only a complex computer program that accesses the efficiency of what has been drawn and contributes to improve the design.

Regards

Paulo
 
#820 ·
Paulo those are lovely photos you downloaded from the internet. I'm not sure what they have to do with the tandem keel though. I see no mention of the tandem keel in any of that downloaded material.

I have no issue with CFD at all. It's a wonderful tool when used correctly. My original question had to do with why was Paulo so certain CFD had been used to design those tandem keels?
 
#821 · (Edited)
Bob, I don't know if the several modern tandem keels designed recently by some major NAs where designed used CFD, a speed prediction program or tank testing.

... I wouldn't make the automatic assumption that CFD is being used for every new keel you see from a major design office....
Not all NA are using yet CFD or based speed prediction complex programs but big NA offices are (in general terms) and some smaller ones too. Those images that I downloaded from the internet were from the sites of two Naval Design offices : Ker and Berret/Racoupeau.

But I would find hard to believe major NAs making statements like these ones without knowing about what they are talking about:

"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"
Mortain/Mavrikios

"The tandem keel is an alternative to the twin keel, it increases lift while reducing drag "
Defline

Both have recently worked and used tandem keels on their sailboats designs. Do you think they don't know what they are talking about?

Both firms are well respected and credible, we are not talking about a boat manufacturer making publicity, they work with several different types of keels. I don't think they are making these statements without knowledge. Sure, there are several ways of testing to acquire that knowledge, from tank testing to testing in real size, but CFD or a based speed prediction complex program is the more inexpensive way.

Regards

Paulo
 
#823 ·
Paulo,

I would like to comment that very often it sounds like you and I are disagreeing with each other when in fact, we seem to have similar opinions. ;)
I suggest that this conversation is one of those cases.

For example, we agree that many of the larger yacht design firms do employ CFD. We seem to agree that the use of CFD is not always the case. It sounds like we agree that the forms of CFD that are used vary from extremely sophisticated versions, capable of reasonably fine grained analysis, to pretty course versions which are good at evaluating general data trends but not providing highly accurate quantitative data.

I should also note that I am very aprpeciative of your posts which talk about the broad range of 'experimental' or 'non-traditional' design taking place in Europe. I use the terms 'experimental' or 'non-traditional' only in reference to what is happening in the U.S. which, for better or worse, tends to be more conservative.

Where we sometimes go off the rails is in how we interpret what we read. For example: "Digital tools enable us to optimise hull shapes, sail plans, appendages such as keels, and rudders for example, and to predict their performance based on outdoor conditions such as the wind, its strength, the direction its blowing from and the state of the sea. All of our yachts systematically undergo these simulation steps to guarantee optimized performance and handling. Structure is high on the agenda too, using finite element method (FEM) calculations. This equipment is systematically incorporated into our design procedure, for all of our creations."

I think that statement is one that all of us come to general agreement on. But that statement does not describe the specific digital tools being used, and does not specify CFD. So while CFD may be used, it does not necessarily mean that Berret/Racoupeu does use CFD, or how they use CFD, or whether they analyze their keels and rudders using CFD.

This is similar to the two Mortain/Mavrikios statements:

"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"

"The tandem keel is an alternative to the twin keel, it increases lift while reducing drag "

I think that we could agree that there is a possibility that these statements could be true. But where you and I, and perhaps Bob might not agree is the pieces of those statements which are missing.

If we look at the first statement, my interpretation is that it says two things, a that cast-iron tandem keels can offer almost as much stability as a deeper lead keel with a bulb, and that cast-iron tandem keels can point as high (i.e. close winded) as a deeper lead keel with a bulb. Properly designed, both may be true. And it does not take CFD to prove that statement to be true.

What that statement does not say is that cast-iron tandem keels designed to offer the same stability and pointing ability offer the same VMG as a deeper lead keel with a bulb.

And my sense is that the cast-iron tandem keels offering the same stability and apparent wind angle, cannot offer the same VMG, because by its very nature being cast iron, and shallower, the volume of the tandem keel needs to be greater than the volume of the deeper straight fin with bulb, and therefore there is more wetted surface, and therefore there is more drag, and therefore there is less speed for a given sail area, even if there is equal stability to carry that sail area.

The second statement can be viewed similarly. To me that statement says that properly designed a tandem keel offers greater lift relative to drag as compared to a twin keel. It does not take CFD to find agreement in that statement.

I assume we are in agreement that when you look at the drag of any foil and bulb keel, there are a number of drag inducing elements. Wetted surface certainly is the big one at slower speeds. But as speeds increase, induced drag becomes more significant. And in that equation if we assume equal foil lengths and both keel types operating in undisturbed water, the bulbs on both acting effectively as end plates, then we can assume for the moment that for equal lift, the foils generate equal drag.

But there would be very different amounts of drag for the bulbs. The twin keel would have two smaller bulbs than the tandem, and the properties of those two bulbes mean that the tandem keel has two leading edges, two trailing edges, and more surface area, (since proportion of internal volume to surface area increases with size).

And if tandem keels could have inherently less drag for an equal lift, then its possible to partially use some of that difference to increase the lift on the tandem keel so that it offers more lift for less drag.

In other words, without CFD its pretty easy to see that this claim could be true. On the other hand, there was an assumption that the downstream keel foil of the tandem keel produces the same lift as the twin keels, and it is here that this statement may go off the rails. I do not believe that to always be the case, and it would be next to impossible to make that kind of universal statement since the reality of this is so dependent on the specific design, and conditions.

What that statement cannot address are issues that cannot be defined in broad terms and for which we have no tools to adequately evaluate universally. For example, one advantage of a twin keel is that as it heels, the leeward keel becomes more perpendicular to the side force, and in flat water, the windward one reduces drag as it is lifted out of the water. that should offer some advantages to the tandem keel.

But in waves, the collisions of the waves with the windward foil would offer a large non-steady state drag which will vary with wave size, steepness and frequency, and which could return the drag advatage to the immersed tandem keel.

It is for those types of reasons that perhaps I sometimes view these kinds of designer statements with perhaps more skepticism than your comments appear to reflect.(And while I don't want to speak for Bob, I speculate that he may also come at this with a similar and definitely far more experienced based skepticism.)

Respectfully,
Jeff
 
#825 ·
Paulo,

I would like to comment that very often it sounds like you and I are disagreeing with each other when in fact, we seem to have similar opinions. ;)
I suggest that this conversation is one of those cases.

....
Where we sometimes go off the rails is in how we interpret what we read. For example: "Digital tools enable us to optimise hull shapes, sail plans, appendages such as keels, and rudders for example, and to predict their performance based on outdoor conditions such as the wind, its strength, the direction its blowing from and the state of the sea. All of our yachts systematically undergo these simulation steps to guarantee optimized performance and handling. Structure is high on the agenda too, using finite element method (FEM) calculations. This equipment is systematically incorporated into our design procedure, for all of our creations."

I think that statement is one that all of us come to general agreement on. But that statement does not describe the specific digital tools being used, and does not specify CFD. So while CFD may be used, it does not necessarily mean that Berret/Racoupeu does use CFD, or how they use CFD, or whether they analyze their keels and rudders using CFD.
Jeff, on their site there are several pictures of keels (and not from racing boats) going through CFD analyses. That seems to indicate that they use it on all their boats as they state on the site. I do not want to make this a discussion but if you look on the sites of European main NA offices many state that they are using CFD or high quality prediction speed programs that are based on CFD. Some don't say that explicitly on their sites but that does not mean they are not using it. In fact it its a lot less expensive to use that than tank testing.

This is similar to the two Mortain/Mavrikios statements:

"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"

"The tandem keel is an alternative to the twin keel, it increases lift while reducing drag "

I think that we could agree that there is a possibility that these statements could be true. But where you and I, and perhaps Bob might not agree is the pieces of those statements which are missing.

If we look at the first statement, my interpretation is that it says two things, a that cast-iron tandem keels can offer almost as much stability as a deeper lead keel with a bulb, and that cast-iron tandem keels can point as high (i.e. close winded) as a deeper lead keel with a bulb. Properly designed, both may be true. And it does not take CFD to prove that statement to be true.

What that statement does not say is that cast-iron tandem keels designed to offer the same stability and pointing ability offer the same VMG as a deeper lead keel with a bulb.

And my sense is that the cast-iron tandem keels offering the same stability and apparent wind angle, cannot offer the same VMG, because by its very nature being cast iron, and shallower, the volume of the tandem keel needs to be greater than the volume of the deeper straight fin with bulb, and therefore there is more wetted surface, and therefore there is more drag, and therefore there is less speed for a given sail area, even if there is equal stability to carry that sail area.
In fact it says the opposite. The word "almost" implies they are less performant than deep draft bulbed keels but that is not the point. Both designers are not defending or sugesting tandem keels as an absolute performance keel but as the better performance in what regards a shallow fixed keel options, or one of the best options regarding that.

Defline compares the performance of shallow tandem keels with the performance of twin keels implying that they are both the most efficient options in what regards swallow draft keels.

Both are not as performant as deep bulbed keels and they have to be heavier to produce the same RM. There are an interesting detailed comparison made by Marc Lombard using one of those programs I was talking about, between the performance of both keels (twin keel and deep keel) on the same boat (a RM) with different wind speeds and wind angles that can give a very approximated idea of the differences.

The second statement can be viewed similarly. To me that statement says that properly designed a tandem keel offers greater lift relative to drag as compared to a twin keel. It does not take CFD to find agreement in that statement.
...
In other words, without CFD its pretty easy to see that this claim could be true. On the other hand, there was an assumption that the downstream keel foil of the tandem keel produces the same lift as the twin keels, and it is here that this statement may go off the rails. I do not believe that to always be the case, and it would be next to impossible to make that kind of universal statement since the reality of this is so dependent on the specific design, and conditions.
...
It is for those types of reasons that perhaps I sometimes view these kinds of designer statements with perhaps more skepticism than your comments appear to reflect.
Jeff, what make the use of CFD and high end based speed prediction programs is that while they are hugely expensive if you use them often they are much less expensive than tank testing with very close results. If an office designs a significant number of boats such a program is a very efficient, easy to use toll that can give very valuable help in what regards hull, keel and ruder design options/efficiency and that's why it is widely used by major NA offices.

Regarding the use of CFD or high end speed program analyses on the design of those keels it seems probable that they have used that but if not I don't believe they had done the design without a lot of studies and tests. That is a keel that only works well if properly designed and the design is more complex than the one of a normal bulbed keel.

Mortain-Mavrikios had used them in several designs and they designed them also for Etap that says:

"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.


So it seems a lot of testing, computer or not was going on.

Regarding Defline, that is one of the most talented new generation French NA and puts performance very high in what regards cruising boat design I know a bit more. I know that he uses a very high end prediction speed program as a toll to help to design his boats and I know also that before using a tandem keel on a 43 foot fast performance cruiser he had done not only computer speed testing but live testing replacing the keel of a First and tested the performance before and after.

This is the Defline 43, a fast voyage boat. The boat was tested by a French magazine and they said that with 10K of wind the speeds were not far from the wind speed. Not bad for a boat with a shallow keel;)

[/QUOTE]





You can see the care with weight distribuition with the engine over the ballast.

Regards

Paulo
 
#824 ·
I asked a very simple question of Paulo when he claimed the tandem keels were designed using CFD studies. "How do you know that CFD was used to design those tandem keels?"
Getting a succinct answer was anything but easy.

My point was this:
The tandem keel (if we are going to call it that) Has been around for about 20 years now. It was tried on an AC boat with some success but other AC boats did not use it. There's probably a very good reason for that. In my consultations and work with Laurie Davidson and his AC effort I was exposed to some experimental AC design ideas. Most, the "hula" for example, were abandoned along with the tandem keel and the forward rudder. And certainly by any criteria the AC boats had restricted draft. It was a rule. One of the things they found with the tandem keel is the distance between fins was critical. The aft fin is operating in the "bad air" of the forward fin, i.e. turbulence off the forward fin and an increased angle of attack. Think about racing and trying to sail straight up the stern of the boat ahead. It NEVER works. So in order to get some clean flow of water with a reasonable angle of attack on the aft fin the two fins have to be separated. The basic rule, as I recall, for the aft fin to have "clean water" was 7 times the tip chord of the fin. You can clearly see that in the photo Paulo posted of the AC tandem keel.

But in the new, tandem keels the two fins are squeezed together with barely one chord length separating the two fins. With the two fins this close together I can't See how the aft fin can have any clean flow over it. It has to be operating in turbulence and with an increased angle of attack, i.e. increased drag. And, unlike a sail, you cannot trim this fin. You cannot change the angle of attack.

So if these new "compacted" tandem keels are working as well as the promotional material claims, then I would like to learn more about them.

Paulo said the tandem keels were the product of CFD studies but he was assuming that. I'd like to know if they were and I'd sure like to see the evidence so I can learn something. I am always looking for ways to reduce draft while preserving windward ability.

"Breakthrough" keels come along regularly. The Scheel keel was an attempt as was the Reijo Salminen wing keel to name two. Both worked, sort of and mostly because they lowered the VCG. But they are clunky keels and not good for boat speed. If the tandem keel preserves stability and windward ability on an equal level with a keel of reasonably deep draft then I would like to know more about it.

I am not going to buy into every piece of promotional material I read from any designer or any builder, even if I do read it on the internet.

I am waiting this morning for a new custom design client. He wants a variation of the 62 SLIVER project I have going now. Undoubtedly the question of draft will come up. I need to be prepared to present him with workable, efficient options. Talking the talk won't work for me. I have to be be ready to walk the walk.

Right now I believe I'll go walk my dogs.
 
#826 ·
Feel some level of responsibility for this back and forth given I was the first to mention a 20+ yr. old tandem keel design. Having said that and noting how much useful information I have gained from Jeff and Bob and how little from this distraction concerning CFD let's please agree CFD exists - it it used by some NAs and my Aunt Tilly - as with all technologies it continues to be devloped and doesn't answer all possible questions to be asked. Please move on and continue to educate me and the others following this thread.
 
#830 · (Edited)
....

Morelli and Melvin, designers for two of the big AC cats does not use CFD.
If you say so, but on the design team EMIRATES TEAM NZ DESIGN TEAM, and on Morelli and Melvin design team for EMIRATES TEAM NZ they have specialists in VPP and CFD and I don't believe they are there only for the ride. The same with Luna Rossa design team, in what regards CFD and VPP specialists and all the other teams for that matter.

http://www.sail-world.com/multimedia/EMIRATES TEAM NZ DESIGN TEAM1.pdf

http://www.morrellimelvin.com/emiratesteamnz/team.html

http://luna-rossa-challenge-2013.americascup.com/en/team#design

Regards

Paulo
 
#831 ·
Paulo:
I would be extremely surprised if someone working with any of the AC cat teams did not do some CFD. But given the seat of the pants revisions to the designs it appears they should have done more. Because M&M did not do the CFD does not mean that someone else didn't do it.

My comment about M&M was made because Jody Culbertson who does my 3D rendering work has also been working with M&M on a cat project (not AC). We discused this today, this morning. He asked M&M about doing some CFD work on another project he was involved in and Gino told him they did not use it. They use VPP's. This is not first hand information. But it is second hand. I did not read it on the internet.

The horse is really still now. Doesn't look good. Probably playing possum.
 
#832 ·
My comment about M&M was made because Jody Culbertson who does my 3D rendering work has also been working with M&M on a cat project (not AC). We discused this today, this morning. He asked M&M about doing some CFD work on another project he was involved in and Gino told him they did not use it. They use VPP's. This is not first hand information. But it is second hand. I did not read it on the internet.

The horse is really still now. Doesn't look good. Probably playing possum.
Bob, I was not doubting. M&M have a specialist in VPP in their design team but then VPP is strongly based on CFD. They are very complex program with its roots in it. Some work directly with CFD, some use programs that are based on. Both are very powerful computer analytic tools that can predict how a boat will behave and can help boat design. On AC teams they have both, CFD and VPP specialists.

Regards

Paulo
 
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