# Fin area

Discussion in 'Boat Design' started by ivor Bittle, Mar 10, 2009.

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### ivor BittleJunior Member

Suppose that I joined a course of instruction on the design of racing yachts. How might the instructor suggest that the area of the keel could be found?

Ivor Bittle

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A shape, be it flat ie 2D like a sail, or voluminous ie 3D like a hull will generate forces when inclined to the flow of a medium. The magnitude of the force is principally determined by the area and angle to the flow. The 3D shape can be
treated as a 2D shape (in the view that is being considered) since the forces are always in-plane.

So, something like a yacht is subjected to air forces on the sails and water forces owing to the shape of the hull. As such the transverse couple produced by these air and water forces is reacted to by the hydrostatic righting moment to keep the yatch in a stable equilibrium.

Work out the force, from a given area (you have to start with something). If unbalanced, use the force of one to establish the other and reverse engineer to find the area of the other.

I don't specialise in yacht design, so a yacht designer may give a better explanation.

But the above assumes some knowledge of naval architecture and physics. So unless you have some understanding of the basic principals, it wont help you much in your understanding.

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### daiquiriEngineering and Design

Since you have joined a course of instruction on the design of racing yachts, the best way to discover how will the instructor suggest that the area of the keel could be found is to attend the course and wait for him to suggest what he is supposed to suggest.
...Imho.

But, to be honest, I didn't quite get the question. If you are supposed to instruct others on how to design racing yachts, then it is more than understated that you already have the necessary knowledge on these topics. If, on the other hand, you are there to learn how to design yachts, then my first phrase applies. Imho (always).

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daiquiri

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### amolitorJunior Member

Given a drawing or other specification for a keel, how does one determine its area? (this is geometry, and you're primarily interested in the 2D area of the side-view of the thing)

Or:

How does one determine the appropriate area for the keel, given the specifications or design of the rest of the boat?

For a rough measure, you make the area of the entire lateral plane, keel+rudder+underbody a percentage of sail area. There's some rules of thumb here, depending on what sort of boat you're doing, but 8% is probably a good starting point.

For more detail, you can look at some boats that are similar to what you're trying to draw, and make incremental changes to their properties based on what you're trying to achieve relative to what those boats actually achieved.

In theory you can perform the sorts of analysis that Ad Hoc suggests, but I'm not sure how productive that's going to be, boats are crazy-dynamic systems.

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### TcubedBoat Designer

Ivor Bittle,

I for one think your question is worthy of a serious response so i will outline my methods here for what it's worth.

I am suspicious of rules of thumb in general, unless we are talking about some very specific well established class of boats, especially something as facile as underwater lateral surface area must be x% of sail area... So from first principles;

The side force that the underwater shape must counter will be ;

Righting moment (@ H angle of heel) / Vertical separation between CLR & CE.
This is actually complicated by the fact that the spanwise load (both keel & sails) distribution is rarely ideal for sailboats and by wind and water shear, but we'll take it as a starting point for this numerically derived estimate.

Then we will look at the worst likely combination of conditions we're likely to expect the boat to perform in.

Finally we will moderate that estimate of necessary area by our other priorities.

So for example, for a moderate displ. sailboat that has 12 M LWL , 15 T disp, limited to 2.5 M draft, with a hull that draws 1 M , a CE to CLR approx 9 M, and a righting arm @ 5 deg, 15 deg, 25 deg of 0.3 M, 0.45 M, 0.6 M;

(please do not attack my choice of numbers, they are just plucked out of spur of the moment estimates of what might be reasonable enough just to illustrate the example)

Taking 1 N = 0.1 kg - Side force at 5, 15, 25 deg is

5 000 N , 7 500 N , 10 000 N

We will assume the limiter at low wind speeds is V/W , not sail area, so we'll take the 15 deg in 4 knots of wind and 2 knots ( approx 1 M/s) boat speed which gives , using the standard eqn of lift and a conservative max lift coeff to start with of 0.8, given that we are not sure of reynolds number (chord) nor aspect ratio yet;

7 500 = 0.5 * 1010 * 0.8 * 1^2 * S

So S = 18.5 M^2

Now we have about 1.5 M to play with between the bottom of the hull and the bottom of the keel so the avg chord would have to be 12 M. Now we observe there are a number of corrections to be made such as a keel this long becomes much wider at the ends due to rocker, the boat if it can sport enough sail area to heel 15 deg in 4 knots of wind will probably be going near the V/W =1 zone so one quarter as much keel would be needed, also a keel with an aspect ratio as low as this should never be operated at such a high Coeff of lift as 0.8 etc , My point is merely to illustrate the process of achieveing a workable minimum.

There are a number of observations that can be made at this point;

The lighter the boat, the smaller the righting moment (even if the righting arm is the same) thus less lateral surface is required. Also the greater the heeling arm the lesser the side force the keel must resist.

Also at 25 deg and beyond the lift eqn must take into account loss of keel lift due to heel angle.

Canoe body hulls cannot be considered as contributing a significant sideforce.

Rudders certainly are part of the lateral plane that contributes lift, in fact , almost always for monohulls the rudder contributes more per area (weather helm or rudder at higher Cl ) Care must be taken not to overlad the rudder for the resistance this causes or in extreme cases stall (spinout) .

Certain hulls do contribute significantly to lateral resistance but this is a complex area that i will not enter in this brief post. One needs a fair amount of hydrodynamic understanding to be able to estimate how much lateral resistance one can apportion to a given hull.

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### amolitorJunior Member

I think I did say "rough" measure, didn't I? Yes, yes, there it is. I see it.

Interestingly, if you take your 18.5 M^2 keel as 8 percent of the sail area, you wind up with about 230 M^2 of sail. 7500 newtons of side force at your 15 degrees of heel comes up with 32.6 newtons per M^2 which is probably within a factor of 2 or 3 of the right answer for a 4 knot breeze.

Cool, huh?

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### amolitorJunior Member

That was kind of snotty, maybe. Sorry. Anyways, let me qualify my 'rules of thumb' with this:

8% as a starting point, actual values people use vary from about 3.5% to about 10% (foils only) depending on things like, as TCubed has pointed out, foil efficiency and righting moment.

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### TcubedBoat Designer

Sorry i missed the 'rough' part.

However you must admit given the huge range of values that one can observe of lateral underwater lifting surface/sail area in different sailboats i do not like , in general, the fractional approach.

if it were 230 M^2 and 7500 N then

7500 = 0.5 * 0.625 * 230 * Cl * 2^2

Gives a Cl of 26 something so in fact it would need about ten times this amount of sail which would be impossible without increasing the heeling arm, which in turn would decrease the sail area. Given those righting moments it seems the above righting arms are too large, i did say they were spur of the moment numbers..

My point on underwater lateral lifting surface/ sail area;
Look at a Thames measurement racing boat and then compare to Dutch seagoing scow (just to stay within the same time period) with leeboards, and you'll see just how varied the amounts can be. The 'feel' of the two boats will of course be quite distinct too.

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### TcubedBoat Designer

Crossed posts - above

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### TcubedBoat Designer

Furthermore the process needs to be rounded out by another approach;

That of calculating aerodynamic side force given sail area, Cl, and W, and using this as a basis.

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### ivor BittleJunior Member

I am grateful to those who have replied to my question. I have a web site in which I write about things that interest me and I am interested in sailing boats even though I have never sailed. I am an engineer and, despite my junior status in this esteemed forum, I am 81 years old. I am no slouch when it comes to engineering and physics and, if you care to go to my site you will see that I am writing a textbook on fluids for graduate engineers. It is there for anyone to read at no cost.

A coherent body of knowledge about fluid flow in pipes and channels and nozzles and so on has been created for engineers to use and it started out in a series of uncoordinated experiments many of which made no progress at the time that they appeared because they were for some specialised application but some became used extensively because they were more general. Such an ad hoc process generates far more data than can be handled and on the late 19th and early 20th centuries people, who were really in the same mould as the natural philosophers like Newton and Hooke, started to look for some underlying principles that would permit co-ordination of new experimental data and sort out the useful things in the existing data. They were Reynolds, Rayleigh, Mach and several others. We know that they were successful.

Their work revolutionised the storage, retrieval and use of experimental data and, perhaps more significantly, showed what should be done when experimenting to produce data that can add seamlessly to existing data. It relies heavily on the use on non-dimensional groups like Reynolds’ number. The only major engineering application involving fluids to have developed since this restructuring took place is, of course, aerodynamics. It has never had a wholly experimental stage of any significance.

Unhappily the mathematicians in our midst got too excited at the arrival of these non dimensional groups and went back and re-worked the earlier methods in terms of Mach number and Froude number and so on and, not being engineers, often threw away the baby with the bath water. It is particularly true for hydraulic turbines where what was discarded is much more useful to an engineer than what replaced it.

I am not the only engineer who thinks that the sailing boat and its design methods is still wholly empirical and nothing comparable to the revolution in engineering thinking of 100 years ago has taken place.

I started to think about this 20 years ago now and I have been moving steadily towards a better understanding of the whole problem.

My web site was inadvertently deleted last December and as it created an opportunity to upload it again I have been updating the section on sailing although it is not yet complete. I can calculate the area of a fin from engineering data without any bother but, as there are very successful racing yachts, there must be methods used by yacht designers to size fins. I started this thread because I wanted to be certain that I did not throw the baby out with the bath water. The question was framed in this way because it would tell me the accepted methods for designers to think about both the sailing rig and the fin.

Ivor Bittle

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### daiquiriEngineering and Design

Mr. Bittle, your age and engineering competence could not be inferred from the initial post. So my apologies for the lack of respect for your age in my first reply.

Now, I'm very puzzled by the following two parts of your last post:
I don't agree that aerodynemics hasn't had any significant experimental stage. Aerodynamics is a branch of a general fluid dynamics science. It has common roots with hydraulics and hydrodynamics, so all the first experiments with pipe flows are to be considered propedeutic to aerodynamics as much as they were to hydraulics. The first aerodynamics experiments done with some scientific rigour can be traced back to the work of Benjamin Robins in mid-1700's. Then there was a significant (though still rudimental) work done by Sir. George Cayley and by Wright Brothers, who have performed experiments on wing sections for their gliders and airplanes.
The real difference has come with the invention of wind tunnel by Francis Herbert Wenham, which was followed by a whole new series of experiments done worldwide. That's when the aerodynamics has started to take lead over other branches of fluid dynamics, thanks also to the great interest of armies around the world for flying machines.
The aerodynamic theories are the consequence of this experimental work, so what you said about the lack of experimental stage is not correct.
This part puzzles me because, the way I understand it, you seem to be contrary to empirical methods based on non-dimensional coefficients. The discovery of flow similarity was one of major break-throughs in fluid dynamics. It has allowed a sistematic research of aero/hydrodynamic phenomena in a precisely aimed range of flight (or flow) conditions, enabling scientists to distinguish the important aspects of fluid flow from the less important ones and formulate and validate new thories and mathematical models which we use today in our ordinary engineering work.

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### ivor BittleJunior Member

Daiquiri,
I am used to people underestimating me because I like to let my website speak for me and most do not or cannot read it. I am not offended.

If you can find time to read my article on “Making sense of aerofoils” on my website I think that you will see that I am not anti-empiricism.

Rayleigh made sure that testing in the British national research centre for aeronautics included values of Reynolds number with its test data before the Wright brothers showed the world how to control an aeroplane. The Wrights’ wing section simply disappeared.

I am not at all sure that aerodynamics has taken the lead. Friction in pipes is complete because the Moody diagram gives engineers all they need to design pipes. In fact I think that aerodynamics of wings is over. We have all we need to design aeroplanes. All we see now is application of what is known. There is nothing new.

I seem to be alone in thinking that it would be advantageous if we all knew how to construct an empirical science. Then we would not have mathematicians interfering in matters that do not concern them. They forget that what looks new and exciting to them might be seen as a backward step by an engineer who actually has to produce something useful.

Whilst you are on my web site go to the last paragraph of chapter 4 in my textbook. Half the viewers of this forum will see nothing wrong with the diagram there. It is the result of someone who knows no physics trying to explain the action of sails. What is sad is that not only did the author of this diagram think that it was correct but so did the editor of the Encyclopaedia in which it appears. It ranks with the nonsensical explanation of the shape of the shock wave from a bullet given in all the textbooks. I found an animation of this misleading diagram on the net and FIVE more scientists had given it maximum marks!

Ivor Bittle

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Mr. Bittle,