# center of flotation calculation and implications?

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

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### AlikSenior Member

Originally Posted by terhohalme
Eric Sponberg replies:
So the sample I posted just shows that square function works. We can discuss the physics and I agree that generally it should be cubic, but... Too many factors involved, and this is the situation when simple formula is not enough for the task and simple design ratios can be misleading.

It is interesting to look at re-powering formulas published in Russian 'Small Craft Design Handbook', 1987. They use CE - 'admiralty coefficients' based on following functions:
- cubic for displacement boats (FnV<1);
- square for semi-planning (FnV=1...3);
- 3/2 power for planning boats (FnV>3)
Not sure what statistics is behind, but seems to work if deviation from prototype is not too big. Please see attachment for details.

And now back to Crouch formula. The biggest problem with Crouch formula is: coefficient depends on boat size. Say, we have 6m and 10m power catamaran designs, that is actually same hull scaled; static load factors and DLR are about same. Coefficients are: 165 for 6m cat and 180 for 10m.

So seems there is still something to think about and to discuss...

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### AlikSenior Member

To the prevoius post, I re-read the authors' recommendations for 'admitalty coefficients' and they are:
- formula for displacement speeds P=f(v^3) - correct
- formula for semi-planning speeds P=f(v^2) - works in end of semi-planning range and early planning, say FnV=2.5...4
- formula for planning speeds P=f(v^1.5) - works for FnV>4

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### AlikSenior Member

Verification of simplified formulas

Would ask collegues to look at this file.

Green lines - simplified methods;
Red lines - series/methods for sharp chine hull shape;
Blue lines - series for round bilge shape.

Most of blue and red lines show quite goode match. The difference can be explained - say, Savitsky used to underpredict resistance at hump area.

Formally Delft and Oortmerssen series can not be used for this boat as some parameters (CP, B/T) are out of range, but those are taken as close as possible and those differences would have minor effect on resistance. Length and displacement are same in all cases.

Green lines (simplified formulas) show quite stange behavior; especially Gerr's-B method that is claimed to work in range SLR<2. I verified spreadsheets for Gerr's and Wyman's methods using samples from Gerr's paper, so hope those calculations are correct. Maybe I missed something?

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• ###### P550C_Performance_Prediction_compare.xls
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### Eric SponbergSenior Member

It is difficult to comment, Alik. I looked at the spreadsheet, and you tabulate only the results, not the equations calculating those results, so we readers cannot see if you missed something or not.

Certainly, I would expect that prediction methods that are based on model series to probably be more accurate than the simplified equations. You do not explain what Gerr-A and Gerr-B are, and I don't know what you mean by Gerr's paper--what is that reference? I have his Propeller Handbook--are those methods in there?

In my office, when I do detailed speed and power calculations, I use NavCad which is a comprehensive program that takes into account a huge variety of model series and prediction methods. You can pick and choose which method best predicts the vessel resistance for the hull form and speed at hand, and then from there add in the details of the engine and determine the propeller characteristics. Are you using NavCad, or have you developed your own software or calculation methods for the various model series that you are relying on. How is that done, the way you do it?

Eric

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### AlikSenior Member

I use Wolfson software, that is similar to NavCAD; the results are copied from there and I have no doubt in those. Most methods I used to program myself, but now rely more on commercial software (no time to play with Basic/Fortran/C++/Lisp programming anymore)

#### Attached Files:

• ###### Gerr_SHP_Formula.xls
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### AlikSenior Member

I believe that any performance prediction method should be verified prior to use. Say, if method is presented in research paper it would include results of verification and comparison with other methods. It should be at least peer–reviewed by industry professionals.

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### Eric SponbergSenior Member

OK, Gerr's Method A, as you call it, is a displacement speed formula, his original one as published in The Propeller Handbook, published in 1989. It is not meant to be used for planing craft as are shown by all the other curves in your first spreadsheet. It is not meant to be the equivalent of the Wyman or Crouch formulae.

Gerr's Method B is a newer calculation as first posted in the Masthead article from June 2008. I have never used this one. It appears to result in a much higher required horsepower, and it is clearly stated to not apply to any vessel traveling faster than a speed/length ratio of 2.0. So to include both Gerr's formulae in your graph where all the other curves are for planing hull forms is, in my opinion, not appropriate. I don't know what Dave Gerr's experience is with his Method B calculation, so I have no way to comment on its applicability. I have used his Method A with some success, as I stated in The Design Ratios document, by qualifying the coefficient to validate the formula for my Moloka'i Strait hullforms, aligning it to the model tests.

Certainly, we would like to see verification of formulae in peer-reviewed journals. This does not always happen, does it, for whatever reasons? But in fact, that is one of the reasons for this forum--with the information published here, including your spreadsheets, here is a form of verification. We can all verify these formulae in our own good time with our own projects. Eventually, we either accept them as is, accept them with modifications, or discard them.

By the way, I am here for a day or two more, and then I am off to IBEX for all of next week (International Boatbuilders Exhibition and Conference) and out of touch with internet and email. I will be seeing Dave Gerr there, by the way, as well as Don MacPherson, the author of NavCad. IBEX is in Louisville, Kentucky, this year for the first time, and I will be moderating two sessions, one on electrical propulsion options for boats of all sorts, and the other on industry standards for sportfishing boats. If any of you readers are going to be there, please introduce yourself--it would be nice to chat and meet readers of this forum face to face.

Eric

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### AlikSenior Member

I thought A and B notations come from You, or not?

This is same problem again: the limitations of formula are not specified and it is claimed to be universal without input of coefficent depending on hull shape... I enclose updated file where formula A is tabulated to SLR=2.0 only.

I do no use fomula B for planning speed; in my file I use it below SLR=2.0 that should be acceptable (according to the author). SLR=2.0 corresponds to 8 kts for this boat. So formula for SLR<2.0 is expected to work; but evidently it does not. Just look at predictions by Delft, Oortmerssen, Groot, NPL - those are not planning craft methods and there is no match with formula B. (In next post I will show why it does not work).

This is true, for qualified users - I would never use any of such formulas without check. But what happens if such formula is presented to students, without verification???

I am in IBEX also, session 406

#### Attached Files:

• ###### P550C_Performance_Prediction_compare_V2.xls
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### AlikSenior Member

Those interested can play with enclosed file and make their own conclusions. Green cells are for input. When chaning numbers pls refer to limitations for Groot method on top of GROOT page.

My conclusions:

1. Gerr's formula B is only suitable for power estimate of heavy boats in range of speeds around hump of resistance.

2. Both formulas A and B can not be used in entire range of displacement speeds; they show some match only in narrow band of speeds.

3. Actually I would not use formulas A and B even for rough estimates - results are not evident and hardly predictable.

#### Attached Files:

• ###### Gerr_SHP_Formula_compare_with_GROOT.xls
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Last edited: Sep 24, 2010
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### Eric SponbergSenior Member

No, I did not use the terms Method A and Method B when describing Gerr's formulae. That must be somone else.

See you at IBEX.

Eric

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### AlikSenior Member

Sorry, my oversight, they were versions A and B, not methods A and B

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### Eric SponbergSenior Member

And sorry, I stand corrected. I did indeed refer to these equations from Gerr as "version A" and "version B." It is surprising what slips through my mind 6 months after I wrote it. I do not keep this stuff in front of me all day every day. I guess more specific references at the outset of this discussion would have helped to avoid the confusion.

So, you have made a point to review different speed prediction formulae and analysis methods. You have shown both planing formulae and displacement formulae. You have clearly shown that there is a fair amount of disparity between them, even those of a type. So, does the disparity make them invalid or not useful for estimating speed? I don't think so necessarily--they all go toward helping our understanding of power's dependence on length, displacement and speed. I think that all the formulae and calculation methods have to be taken with a grain of salt, shall we say, and it is up to the designer to determine which method is appopriate for the project at hand. There will be boats that better conform to the Newman and Groot curves, for example, and there will be other boats that will better conform to the Gerr A and B curves. All of them are valid to one degree or another depending on the design at hand, so I would not write them off entirely.

I am not totally familiar with the bases of Newman and Groot, but presumably they are based on some model testing. Fine--how valid are those models to all of boat design--they can't cover everything. So, you use the method with the best match, and the best one that you can afford. You are never going to get universal convergence on all accounts for all boats at all speeds. Certainly, the Gerr methods are not based on model testing, rather they are based on Dave Gerr's study of many boat designs and his own extensive experiences. They are more generic and simplified methods of calculation, and we do know that there are places in design where they can be used. The vast majority of design projects do not have the budgets to go into the model tank for more sophisticated analysis, and so we apply simplifications of analysis where we can. Newman and Groot (or any other method--pick a name) may be more empirical, but does that mean to say they are better? Who knows? Only the designer who is seeking to use them has to decide in the context of the design at hand.

The purpose of my discussing these formulae in The Design Ratios was to explain where they came from and what meaning they had in physics. I discussed them in the context of displacement boats and of planing boats so that should have been clear. I also had discussed speed/length ratio earlier in the series of lectures to help define the displacement regime, the semi-displacement regime, and the planing regime. So I think that was pretty clear. You have offered more definition in these contexts, certainly, and that is appreciated.

Eric

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Exactly.

Naval Architecture is not an exact science, and never shall be. There are disciplines within this field that are, such as structures and certain aspect of fluids/hydrodynamics. But a boat is more than the sum of its individual parts.

Thus, the naval architect is the master of estimation, it has been said. One uses whatever tool is available, knowing its limitations and its applicability and then “fudges” to suit the end goal. The fudging is based upon previous designs to “correct” the previous assumptions.

But, without previous data, these “curves” and “algorithms” all help, however, they are not absolutes. A designer that treats them as absolutes is not a naval architect, but a mathematician/theorist, or just simply inexperienced.

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### AlikSenior Member

In last spreadsheet I posted, please try to enter data for lighter boat and see what happens.

DeGroot is a systematic series, well described in PNA and Savitsky-Mercier paper. This method have been around for decades, it is 'naval architecture classics' and it proved to work well. See match of Groot with NPL, Delft, etc. from my spreadsheet.

I do not know how and why Gerr invents his formulas but it is clear that many of them do not work properly - both for power and for structural calculations. Unfortunately he has no background in hydrodynamics and in structural engineering, and now inventing some methods without peer-review and his 'institute' is teaching students to use those methods... this is far from naval architecture, sorry. 'This is not medicine, this is sorcery'.

This Design Ratios is great input. I am just trying to develop it further, showing the limits of formulas You mention. I will prepare detailed paper and publish it, with review of all these and other methods.

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### AlikSenior Member

This is true, but have You seen the graphs in my spreadsheet? Do You think it is normal that those simplified formulas A and B show such a huge difference with physically-based methods (I mean systematic series)? These formulas are in the books intended for students and amateur designers, and people are using them! And those simple formulas create feeling of simplicity, without expatiation of potential problems of such 'calculations'.

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