# Gerr's Roll Period Recommendation

Discussion in 'Stability' started by DCockey, Jun 20, 2011.

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### DCockeySenior Member

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### AlikSenior Member

There is basic ratio called 'captains' formula' for roll period t, s:

t=c*B/(GM)^0.5

c - dimensional coefficient, depends on size an type of boat, for sailboats with fin keel c=1.7...1.8; for powerboats and ships c=0.8...0.9; for small boats - to be checked.
B - beam of hull at WL, m;
GM - metacentric height, m

So Gerr's recommedation is clearly related to GM; just divide both parts of 'captain's formula' by B and see what happens. Basically this is recommendation to have certain GM, nothing else.

Then, there is a mistake here, thanks for pointing this issue of Masthead:
Formula for roll period on p.9 bottom (claimed to be exact) is wrong.

Formula includes moment of inertia of boat Ix and hydrostatic component GM*DISPL, but should also include added moment of intertia Jx (20...40% of Ix) and roll damping factor (depends on appendages and parameters of motion). This is very significant difference - all hydrodynamic reactions in Gerr's formula are missing; as given by Gerr formula describes roll without water. Also this formula is limited to small angles of inclination. But maybe nobody in that school needs to know what added moment of interia is

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### DCockeySenior Member

Thanks for the insight.

Gerr includes a version of the "captain's formula" in his earlier article on p 9, though he doesn's use that name.
t=0.44*B(ft)/GM(ft)^0.5
It is interesting that Gerr's formula has a fixed coefficient. He says it "will provide a close estimate of roll time for any vessel of normal form". That brings up the question of what's meant by "normal form". It works out the same as what you give with c=0.8 after converting feet to meters.

So Gerr's recommendatin, using his formula, or your formula with c=0.8, and consistent units works out to GM=0.9m for t(sec)/B(m)=1.0.

Any estimate of how large the roll damping factor may be? I assume it can vary greatly between a round bottom boat with small appendages and a V=bottom sailboat with a full keel. My recollection is damping generally has a larger impact on amplitude than on period/frequency unless the damping is quite large.

But they are now accredited by RINA.

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### baeckmoHydrodynamics

A review of stability issues, also referring to the ratio (roll period)/beam, is found in the "Fishing boats of the World 3, ISBN 0 85238 043 7", by Traung, Doust and Hayes, pp 139. Also see FBW 2, 1960: "Behaviour of trawlers at sea", by W. Möckel, and "Stabilitäts- und Schwingungsversuch mit zwei Lotsenversetzbooten", Hansa no 22 1963, pp 2179.

The criteria relating to roll period are strongly linked to the damping performance, as Alik already has noted. The really interesting thing is that the vessel, with its own rolling frequency is the coupling link between the dominant wave frequency and the "tuned" response of the human balance system. Certain combinations become particularly bad. Our brains are suspended with a damping which is tuned to reduce the acceleration impacts from our "walking step frequencies". Outside this frequency domain, our sensitivity increases, i.e. the sensation from a given acceleration level will stress our brain, causing nausea and mental exhaustion.

If the roll behaviour is tuned to coincide with the damped frequencies, the human performance and endurance is remarkably increased.

The FAO was quite active regarding development of fishing and safety for fishermen in those days. Today it's more focus on killing fishing societies.......

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### dgerrSenior Member

It is regrettable when someone critiques something based on claimed expertise and is, in reality, ignorant. Alik's assertion that the roll-time formula presented in the Dec. 2007 issue of The Masthead is wrong, is egregiously and wholly incorrect.

Alik has been making a practice of finding fault with various things about Westlawn Institute for a while now on this forum. I guess it's a hobby. In any case, regarding the roll time formula, Alik is incorrect on all counts:

1) It is not a Gerr formula. I did not create it or modify it in any way.

2) This is a standard formula found in any naval architecture text and any competent naval architect should know and understand it.

3) Large-angle heel/roll is not a factor in this formula as applied. Stating otherwise indicates lack of knowledge and understanding.

4) The formula was not stated as being exact. It as a very useful approximate formula. Indeed, on the very same page, the more exact formula is given and explained, along with an explanation of why it is impractical to apply in most instances for boat design work.

5) The constant of 0.44 recommended is the correct and standard constant used for normal vessels of average form.

6) Attached is a page from "Principles of Naval Architecture - Volume 2," by the Society of Naval Architects and Marine Engineers (SNAME) that presents this formula and discusses it. It is formula 75 in the first column.

216.119.80.31/SNAMErollTimeFormula.jpg

You will note the following explanation of the use of this formula (75) on the middle of the second column of the page from "Principles of Naval Architecture" attached:

"From the above and numbers cooroborative observations, it is an accepted fact that equation (75) can be used to determine either the period of roll or the or the metacentric height, if the value of C appropriate the the particular class of ship is known, and that value of C for merchant ships of usual form is very nearly 0.44 and may be taken as such without great error."

I felt it was necessary to set the record straight on this, and I would recommend that Alik's technical comments be viewed with extreme caution in future.

I will not likely reply to the barrage of probable rebuttals to follow. The facts above speak for themselves.

Dave Gerr, Director
Westlawn Institute of Marine Technology
www.westlawn.edu

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All rules of thumb have caveats. To understand what rnage this is applicable to, you need to know what generic data was used and how they arrived at their constants and conclusions.

Rules of thumb, are just that, rough guidelines and not absolutes.

It seems this "0.44" fudge factor is used elsewhere too.

In the "Procedures Manual - Dynamic Stability Analysis for U.S. Navay Small Craft" Published Sept. 1982 also quote 0.44 as their fudge factor.

But it does state that "...A value of 0.44 is used unless another value has been determined by model or, preferably, full scale tests or has been estimated from other sources of information.."

There is also another interesting paper "The Hydrodynamic Lift Effect on the Stability and on Banking Angle of the Fast Crafts" by Prof. Simeone. He concluded that these 'estimates' are very much influenced by forward speed and showed big differnces between "slow" speed and "high" speed behaviour and of course influenced by the deadrise angle.

Rolling is a complex bevahiour of a boat espeically when there is a forcing function...thus rules of thumb, as a guideline are good. But don't treat them as exact absolutes, nor across a wide range of differening vessel types/speeds.

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### AlikSenior Member

That is good reference and well known, but it is clear that I was talking about another formula from Masthead (formula itself is on page 8, explained on page 9):

Roll period=2*Pi*((Slr)/(GM*Displ))^0.5

In this formula (claimed to be exact), two important components are missing - added moment of inertia and damping factor.

Yes, they do.

I would take any of Dave's statements on subjects related to hydrodynamics with great caution. I believe he heeds to submit his writings for peer-review prior to publication, otherwise such mistakes will happen again.

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### AlikSenior Member

This '0.44 formula' well known and is correct; it is just a modification of the one I posted above.

For damping, there are different mathematical models so numerical values of factor depend on model applied. Yes, it can be significant depending on how big the appendages are, chines, etc. I will try to find and post some pre-calculated samples showing the effect later.

Both Ix and damping are hydrodynamical forces, the first one is of inertial nature (shows change of kinetic energy of water involved in motions) and second one is non-inertial.

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Well, if you wish to be pedantic, you must state that the formulae you’re suggesting is based upon a linear model of simple harmonic motion and is an unforced in equilibrium equation. This is also far from reality..thus how 'exact' is exact?

To go “exact” is terribly complex….and the differences are not always significant anyway, save for the extra several hundred pages of complex equations of motion and changes in added mass with each change of CoF initially into large angles…and so on.

Naval architects use rules of thumb for quick guidance, they may not be exact. But only mathematicians are concerns with absolutes and exact values. For a naval architect, if the rule of thumb describes a nice “trend” reasonably well...that’s good enough. Just take note of the caveats of said rule, as you can’t compare apples with oranges.

All that I would add to that article is that D.Gerr could say it is a very good and ‘easy’ simple approximation to provide a guideline to non-naval architects and that it is not applicable for every vessel, other than that, I don’t see any problem with it.

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### AlikSenior Member

'Exact' is the word used in Masthead. To be closer to reality, at least those components should be present. The formula as it is published describes the behaviour of ship in air.

Sometimes treating complex things in easy way helps for better understanding, unless it becomes profanation.

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### DCockeySenior Member

Not quite in air because it includes the hydrostatic term.

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### AlikSenior Member

Concur. I meant hydrodynamic reactions are missing; yes hydrostatic is present.

There is method of defining Jx for ship models, by oscillations in air, using modification of this formula with pendulum length instead of GM.

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### AlikSenior Member

Regarding coefficient 'c' (dimensional!) in captain's formula:

0.75-0.85 - passenger ships
0.70-0.82 - cargo ships
0.76-0.80 - trawlers
0.78-0.82 - fishing boats

Note: this data is from old book and might be obsolete for new types of craft.

I used to check 'c' values during sea trials by free roll test (heel and release, or let crew run from side to side). It is easy in low-damping case - for round-bilge craft with moderate B/T and almost no appendages. But for some modern V-type powerboats with high B/T the decay is high and this method of defining 'c' does not really work.

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### Mat-CSenior Member

Alik,
I won't pretend to fully comprehend either side of the argument here, nor do I question your (or Gerr's) knowledge on the subject.
You've been kind enough to help me with information on a number of occaisions, so I hope you will accept this in the manner that it is intended....
But your obvious gripe with anything and everything that comes from Gerr, or has anything to do with Westlawn borders on fanatacism and is almost offensive. I'm certainly sure that all of the former and current Westlawn students who spend time here would feel agrieved by the tone of your remarks. You can belittle the school as much as you like, but their results speak for themselves, with any number of very highly regarded designers practicing out in "the field".
Certainly, if there are errors or omissions, point them out... but please, consider more carefully the manner in which you present them. I'm sure that if you had done so in a more respectful manner in the past, then both Gerr and the Westlawn alumni would appreciate rather then resent your input.

Once again - please don't take this thew wrong way... And I might also add that I have no connection with Westlawn or Dave Gerr.

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### AlikSenior Member

Mat, pls note that it was not me who started discussing personalities; I am only discussing technical issues. If one has right to publish some data/paper/book, believe others have the right to discuss its content.

Problem is that some colleagues start treating those simple formulas as dogma, referencing them during discussion on forum. And this is how the issue arises if those formulas are correct or not. Pls note that I am not creating any threads specially intended to discuss Gerr's formulas! So what should we do in this situation - walk away and let amateurs/builders/designers play with those pitfalls, or point a problem? OK I can leave it; my presence on this forum can be terminated.

There is no doubt that school in question has taught a lot of great designers (also some of our staff have taken the course). In this connection, having evident mistakes/omissions on regular basis in their publications is a regret. Such publications are always peer-reviewed in all academic institutions and specialist editions...

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