# center of flotation calculation and implications?

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

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### sorenfdkYacht Designer

Thank you Eric!

Even though I've been designing yachts for 20 years now, there was new stuff to learn! For some reason, Telltales is hard to find here in Denmark!
If anyone knows how to get TSpeer to write a similar series on basic aero-and hydrodynamics, I'd love to hear about it

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### terhohalmeBEng Boat Technology

Don't know if this is a good explanation:

When the boat is planning, the resistance is from skin friction and lifting the boat. If you increase the speed, lifting force stays (boat weight don't chance), but trim angle and skin area decrease. The power is still speed times resistance, and the resistance is proportional to speed squared times skin area, but now the skin area is reduced. This leads to relation: power is nearly proportional to speed squared.

Or not?

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### Eric SponbergSenior Member

Not. Force, although related to displacement, is still changing with trim and wetted area. Force is still proportional to speed squared. And power, which appears in the Crouch equation, is still proportional to speed cubed. There is no way around those definitions.

Eric

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### terhohalmeBEng Boat Technology

Anyway, it looks like in planing mode the resistance of the boat stays almost constant inside the operating area (when Fn = 1 to 2).

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Eric: I join the rest of the respondents who thank you sincerely for the generous sharing of knowledge. The time and enegy that you have expended will not buy so much as a cup of coffee, but it has certainly earned the admiration and appreciation of a substantial number of readers.

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### Eric SponbergSenior Member

Many thanks to all for your compliments. The Design Ratios document is almost ready to post.

I got a rare chance to go play today, going down to Mt. Dora to ride in the new Saetta 19 speedboat which I helped to design. My clients are custom airplane builders, and they want to enter the kit boat business with this mahogany barrelback design. I designed the planing bottom. You can see running video on Facebook here:

So I went down to Mt. Dora today to shoot some video of the boat for the Sunnyland Antique and Classic Boat festival for this weekend, and we are in the hanger at the airplane shop (Kimball Enterprises), and Kevin Kimball says he has a replica Gold Cup winner in the next hanger, Palm Beach Garden (or something like that, not the original name). I said, that's interesting, because Baby Bootlegger was the 1924 and 1925 Gold Cup winner and we were just talking about that boat on the Internet this last weekend. Who should show up but this boat's owner, Mark Mason, who was the very individual who restored Baby Bootlegger 25-30 years ago. How ironic. This was the first I had ever met him. So we had a nice visit. I asked if he still owned Baby Bootlegger, and he said No, someone in Michigan bought it a few years ago, who wanted it more than Mark wanted to keep it. This current replica that Mason had is the third copy of that particular boat that he had built, and this one in Turkey, no less.

In all, it was a very pleasant and serendipitous afternoon. I will be at the Sunnyland show this weekend, Friday and Saturday, if anyone is in Florida this weekend. Stop by the Saetta booth to say hello. I have another client there as well--Wooden Boathouse. They have their sailing sneak boats there, for which I designed the free-standing, rotating, half-wishbone Cypress rigs. If you want to try sailing one of these boats, they should have one in the water. The boat show is in Tavares, FL, northwest of Orlando, Thursday through Sunday. Always a wonderful show.

Eric

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### LandlubberSenior Member

Thanks again mate, ya blood is worth bottling, I look forward to seeing the pdf files of this whole lot, I will be a great reference tool for the future, for many of us here.

Thank you and kind regards, John

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### Brian@BNESenior Member

Having only discovered this thread today I find myself fortunate to coincide with 'end of class' - of course its going to take me quite a while to digest! And I might still ask 'dumb questions' in the future

As an amateur but enthusiastic 'boatie' I'm still way down the learning curve, but I want to add my voice to the chorus of 'thank you very much Eric', and also to other contributors.

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### Eric SponbergSenior Member

The Design Ratios

To all,

As promised, I attach the complete collection of The Design Ratios as has appeared on this thread. Also, again, see the two spreadsheets that we talked about, one for S# and the other for Bruce Number and the Catamaran Study. Also included are the Original S# Telltales magazine article, and the original Cruising World article on Ted Brewer's Motion Comfort Ratio, MCR.

Finally, since it is good to back up all important information, these files are all included now in the Articles section of my website, which you can access here:

http://www.sponbergyachtdesign.com/Articles.htm

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Thanks for all the effort,Eric! Big help to me......

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### MikeJohnsSenior Member

I just read the opening post and eric’s reply. Sorry if this is a bit tardy.

You have lumped together the centre of waterplane area and the centre of buoyancy one being the geometric centre of the waterline plane the other of the immersed volume. Which is a bit misleading, eg adding mass over the CoF would trim most vessels

The C of Floatation ( centre of waterplane area) is generally the point around which the vessel will trim particularly dynamically. As well as the CoG CoB moment, the position of the CoG relative to the CoF creates a dynamic moment in heave and in wave encounter.

As to problems relating to CF location that vimes was asking about:
The light weight wedge shaped hulls can have a problematic dynamic moment from the CoF and CoG couple. At times the CoF can be well aft of the CoG and the CoB is not encouraged to shift fwd much because of the slim forward sections plumb stem and lack of reserve buoyancy fwd.
In wave encounter analysis there are two things happening: the Centre of the Water Plane shifts and the COB rushes off fwd to restore trim. But COB can run out of volume on a slim bowed hull because there just isn’t the immersed volume fwd to develop a healthy restoring arm. Then to make matters worse the CoF CoG may temporarily and dynamically resists the already inadequate restoring force from the CoB CoG arm.

The dynamic moment CoF to CoG can be illustrated for example in a drop test.

If you were designing for seaworthiness it would be better to have CoF shifting close to the CoB when you analyse longitudinal trim with the vessel running into a wavefront. Trim the vessel bow down by different angles at a constant D and look at what the CoB and CoF do.

I suspect this is the crux of the articles Vimes was referring to in the opening post.
Any thoughts anyone

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### ancient kayakeraka Terry Haines

If I have understood that correctly, it implies the bottom profile should be similarly curved aft and forward. More curvature (rocker) forward would move the CoG/CoB aft relative to the CoF resulting in more lift to an oncoming wave. Garveys rule the waves? The same thing can be achieved with topsides flare.

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### LyndonJSenior Member

Not the section shape alone but normally people ignore the centre of floatation plane , but in more extreme forms it's necessary to consider the
the relation of the trimmed floatation plane along with the shifted centre of buoyancy all relative to the fixed centre of gravity.

baeckmo another NA was talking of this in another thread too:

http://www.boatdesign.net/forums/design-software/cfd-solid-models-31978.html#post352696

Which might help understand what that is all about.

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### AlikSenior Member

Though I do not fully trust those simplified formulas they are useful tool for ballpark estimates. Did You notice that coefficient in Crouch formula depends on boat size? It is confirmed by statistics and by tests of scaled-up versions of same hulls.

I am writhing this because I recently read interesting paper by M.Peters in PBB magazine. He is using coefficient in Crouch-type formulas to evaluate the efficiency of design. It does not seem to be fair comparison because of size dependence of such coefficients.

There is good paper by J.Robinson where similar formula used by Wolfson Unit is studied in detail, and in that formula the coefficient depends on length.

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### Eric SponbergSenior Member

Hi Alik,

Yes, if you read through the last chapter in The Design Ratios, you'll see my explanations for Crouch's formula and the fact that the coefficients actually vary with speed and boat type. You'll also see that I conclude that Crouch's formula does not necessarily agree with common physics because it uses a square root factor of horsepower and displacement, whereas it would be more appropriate to use a cube root of horsepower and displacement to more closely align with physical principles. I conclude that Wyman's formula is probably a better formula. That one too is fully discussed in the chapter.

Yes, I just got through studying Mike Peters two articles in the latest issues of Professional Boatbuilder. I am also studying his data in relation to Wyman's Formula. I have met Mike a number of times and think he is a very talented and down-to-earth individual--a great designer.

The speed formulas are actually very reliable and they do lend themselves to good predictions and comparisons between different designs.

Eric

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