# center of flotation calculation and implications?

Discussion in 'Boat Design' started by capt vimes, Jan 7, 2010.

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### capt vimesSenior Member

hi!

i just try to understand all the different ratios and calculations regarding a yacht design and i am a little puzzled with this 'center of flotation' and its implication on the balance, stability and performance of a monohull sailing yacht...

in larsson & eliasson 'principles of yacht design' this CF is not dealt with at all - it is mentioned but not what it actually means for the design... the calculation of its position is completely negelected...
but since this book describes the principles by designing an example yacht (40 ft monohull fin keeled sloop) and all the different parameters are listed, i at least realised that while the LCB is 3,5% LWL aft midships the LCF is 6-6,5% LWL aft midships depending on the laod...

what i understand is the principle explanation of the CF:
how is balance/stability compromised or enhanced if the CF is moved further aft or closer to the CB?
what are the performance implications?

thank's for any help enabling a noob to comprehend this complexity about the one thing we all love so much - woma....
darn - i mean boats...

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### Eric SponbergSenior Member

Capt. Vimes,

Your quote is correct, the CF is the center of the flotation waterplane area. Another way to think of it is, you know that by Archimedes principle a floating body displaces a volume of the liquid whose weight is equal to that of the body itself. So you have a boat floating in the sea, and now imagine that you bring a weight on board that is enough to sink the boat 1 centimeter. The weight that you have brought on is equal in weight to a volume of seawater that is the area of the boat's waterplane times 1 cm thick. The center of that volume of water is located at the CF. Now, imagine, if you will, that when you set that added weight down on the deck, you placed it directly and vertically over the CF. The trim and heel of the boat would not change, but the boat would sink straight down that 1 cm. The weight acts down through its own center of gravity and the added volume of seawater acts in exactly the opposite direction through the CF and through the CG of the weight you added. However, if you set the weight down on the deck at some other location other than over the CF, the boat would trim and heel such that now, the whole submerged volume of the boat at the deeper draft will be equal to the total weight of the boat plus the added weight, and that the center of buoyancy (CB) will be directly under the final center of gravity (CG).

Now, the weight that you brought on board does not have to be that to have a similar effect. Forces acting on the boat have the same effect, such as sailing forces from the rig. These forces do not act at the CF, but elsewhere. They push the boat over and down like an eccentrically placed weight. In order to perform properly, the boat has to balance against those outside forces, and the only way to do that is by virtue of its own hull shape and weight, and by the effectiveness of the keel and rudder. The hull portion--its shape and weight--is a huge factor. If not well shaped, then the boat may heel or trim at odd or weird angles that will affect how much lift comes from the hull itself or the appendages. A boat an unusual angles of trim and heel will generate more a lot more drag that if it is closer to upright. This, of course, affects performance. Generally, the least amount of hydrodynamic drag occurs when a vessel is upright. Drag always increases as the boat trims and heels. This is why you like to minimize heel and trim while underway, and the best way to do that is with a properly shaped boat.

We have very fine examples of this in many round-the-world racers. For example, look at the Vendee Globe fleet (open class designs)--generally these boats are very wide shallow boats and they rocket downwind and off the wind like the blazes. In these conditions, the boat stays more upright than if it is sailing to windward. When sailing to windward, however, these boats are very poor performers, and this is due primarily to their hull shape which is very side aft. As the boats heel over, the CF moves aft quite a far distance. This has the effect of raising the stern, and likewise, pushing down the bow into the sea and away from the wind. That is not the direction you want to go. This can put an adverse angle of attack on the keel. And this is why wide shallow boats are poor performers to windward. The Vendee Globe and other round-the-world racers gravitate to these hull shapes because usually these races are off-the-wind races. The exceptions are the races that have multiple stops, such as the Around Alone (formerly the BOC) and the Portimao Global Ocean Race. When you have to come back into port at mulitple stops, you come from pure maritime wind and weather to a mix of maritime and continental weather. Frequently, you have headwinds near the ends of the legs. To get through those headwinds, you need a boat with good windward ability. This is why narrower boats fare better in such races.

So the solution is, in order to have a more balanced boat, you want the CF to move very little as the boat heels over. Check the position of the LCF at zero degrees heel, and then check it again at 15 or 20 degrees heel. They should be very close in position to each other fore and aft. That way, as the boat heels over, it will have nearly zero tendency to raise the stern and push down the bow. The angle of attack on the keel and rudder are better, and windward ability is very favorable.

Take this one step further, like Capt.Nat Herreshoff of Bristol, RI, did in the late 19th century. Many of his designs showed that the CF moved forward as the boat heeled over. This had the effect of raising the bow up and to windward--precisely the direction you want to go--and which enhanced the angle of attack on the appendages and increased lift. The Nat Herreshoff boats were great performers, as everyone knows. Many of his lessons were forgotten in the latter 20th century.

Keeping the CF in a more or less constant position as the boat heels over is easier to do with narrower hull designs. As hulls tend to get wider, CF always moves aft more easily and affects performance in an adverse way.

I think one of the great hoaxes (maybe fallacies is a better word) of modern yacht design is the concept of "powerful stern sections" which became a ubiquitous description of boats in the 1980s, and is still seen today. "Powerful stern sections" implies wider body aft, wider waterplane aft. Certainly, such wider shapes give more room in the cockpit and aft cabins, and they cruise downwind and off the wind OK, but they have a deleterious effect on performance to windward.

I hope that helps. Class dismissed!

Eric

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Well done Eric.

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### LandlubberSenior Member

Thanks Eric, that is a great explanation, and well worth us having some sort of wiki to keep it in....

if you ever feel inclined(yep it was intended)...could you do an explanation of all the other NA abreviations,Cp, CB, LWL, D/L, A/B S/L ratios, etc etc in such simple yet elaborate explanations...maybe one a week so that we can compile them for when people ask us such questuions that are sometimes hard for mere earthlings to describe

that is the best description I have ever read. Once again, ta. John

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### capt vimesSenior Member

wow...
i did not expect a reply like this... thank you very much, eric!

i knew that boats with broad sterns perform good downwind and less to windward but i actually did not know exactly the why...
thank's again, eric, for enlighting me stoopid noob...
i appreciate it!

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### capt vimesSenior Member

since eric mentioned the open ocean racers and there flat, beamy design in regard to the CF... i have another question:

on the latest VO70 racers competing in the VOR last year i noticed that most of those - probably all of them - had a hard chine from almost amidships to the transom a little way above the waterline...
if a boat with a hard chine like this heels the hull becomes V shaped to the aft and thus reducing the waterplane area in that part... this should then move the CF forward or at least not too far aft...

could that be possible or the reason why the latest VO70s had such a design?

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### HJSMember

Balance in all situations

The Swedish E-class canoe is an example of how it is possible to create a boat with planing lines that is balanced in all positions. The chine along the freeboard contributes to stability both transverse and longitudinal. In addition, the boat is drier upwind.

js

www.sassdesign.net

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### PARYacht Designer/Builder

The chine you're seeing appear on these boats isn't to appreciably affect initial stability, but to provide a crisp edge for the "flow" to release from, when she's up and scooting along.

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### Eric SponbergSenior Member

As PAR says, the chine is for hydrodynamic reasons rather than stability reasons. Think planing powerboats--they have chines to help lift the hull up on plane so that it is no longer in displacement mode--this is planing sailing.

I have been using planing chines in my designs for years. In my design Project Amazon (an early open class 60), I incorporated full-length lifting strakes from stem to stern. See photo. I designed the boat in 1995-96, and it was built in 1996-97 for the 1998 Around Alone race. The strakes worked very well.

Another design in which I have incorporated a chine was in Bagatelle, a 44' lightweight racer. See rendering attached.

If you have seen any videos of the VO70s, they are truly amazing in their blazing speed.

Eric

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### HJSMember

Dynamic stability

I have used this configuration in at least forty years. And I am convinced that a boat with a hard chine has more dynamic stability than a round bilged boat.

js

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### capt vimesSenior Member

so all of that is just to increase their planing abilitys?

oh yea.. i have seen them - not live unfortunately but even the videos are immensly impressive...

and i know that ericson 4 has demolished the existing 24 hrs mile record early in the race 2008(? i think it was)... with making more than 600 nm a day with an average speed well above 25 ktns...
extraordinary machines!

but they seem to do quite well upwind also...

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### capt vimesSenior Member

i must confess that i never sailed a hard chined boat....
but what i heard from fellow skippers is that they are more gentle when it comes to rolling and pitching...
and i am convinced that it is that way - trusting and knowing my sources...

but what about the performance impacts?
a badly designed or wrongly placed chine might impact speed by inducing drag considerably, isn't it?

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### capt vimesSenior Member

ha - looking at your amazon design i recalled 'bagatelle'.... you mentioned it but i am bad with names and the strakes gave me the clue...
http://www.sponbergyachtdesign.com/BagatellePlan.htm
found it while browsing the internet for stock plans... amazing ship!
unfortunately not the thing for my intended purpose...

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### HJSMember

Chine hight and beam

You are absolutely right. The chine must be placed at the right height, in the vicinity of the water surface when the boat leans. Thanks to the rounded rear the buttocks can be slightly straighter in the aft-section, whereby the boat may be have slightly smaller wave aft. It is easy when you knew what you are doing, but can be badly wrong if you don't know how it works.

js

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### rwatsonSenior Member

What sort of craft do you have in mind, may we ask ?

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