# The roll acceleration: What´s the best for crossing oceans?

Discussion in 'Stability' started by Antonio Alcalá, Dec 18, 2007.

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### Patrick BLOSSELa Terre entière.

Hello to all,

With all respect indeed for Ted BREWER's "tongue-in-cheek" (according to his own word) genuine and significant Confort Ratio, and taking into account that his "ratio will vary from 5.0 for a light daysailer to the high 60s for a super heavy vessel, such as a Collin Archer ketch."; I wonder if one nondimensional ratio wouldn't be more "standard" (as most are: Froude number, Capsize screening number, Sail area / displacement for example).

To remain as sharp as his clever purpose is, i.e. considering "adding a beam factor", the following initial ratio, issued from http://www.tedbrewer.com/yachtdesign.html
CR [lb/ft^(7/3)] = Disp/(2/3*(7/10*LWL+3/10*LOA)*Beam^(4/3)) [lb, ft]

could suspend its dimension as follows
CR1 [non dimensional] = (DSV^(7/9))/((2/3*(7/10*LWL+ 3/10*LOA)*BWL^(4/3))) [ft^3 or m^3 and ft or m]
Where DiSplacement in Volume DSV [ft^3 or m^3] replaces Disp in mass [lb], that leads to an odd dimension.

or lighter expressed, without emphasize on beam factor nor on lengths
CR2 [non dimensional] = (DSV^(2/3))/(2/3*LWL*BWL) [ft^3 or m^3 and ft or m]

Consequently, above nondimensional experimental ratios if applied to my own 35 footer leads on second hand to CR1=0.15 or
CR2=0.18 [non dimensional] (or CR1=15 and CR2=18 if prettily amplified by hundred), to be compared with CR=21 [lbs/ft^(7/3)] on initial hand.

Non dimensional CR1 and CR2 both remain perfectly equals using imperial or international units [ft^3 or m^3 and ft or m], as Froude number does as well, thus allowing a contribution towards Ted BREWER's prayer: "And please don't ask me what the Metric equivalents are!"

Because I don't have the amount of data available, on a third hand, I have no idea of the results applied to Antonio's comprehensive list presented earlier in this thread.

Fair winds and smooth seas to all.

Patrick

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### drshaddockDesign Engineer

Try this calculator

I put together a little Excel spreadsheet to play with the MCR as well as the CSF (and threw in the D/L ratio while I was at it). I'm attaching it so anyone else who wants to play can do so as well. I used Ted Brewer's original formula (MCR=Displ/.65((.7LWL + .3LOA)*B-1.33333)). This works if displacement is in pounds and linear dimensions are in feet--my apologies to the real world, which is metric. You can tell by changing just one item at a time that the Brewer formula, tongue in cheek or sticking out, does indeed give credit for narrow hulls and tends to punish long overhangs. TeddyDiver was concerned about strange results with his own formula for plumb bows or negative overhangs; I don't see problems with the original formula for plumb bows or negative overhangs--although it would be pretty hard to have a LWL longer than the LOA...

I particularly like the Capsize Screening Formula, developed by the tech committee of the CCA, and was intrigued by Brewer's example from his primer on yacht design: "...a 12 meter yacht of 60,000 lbs displacement and 12 foot beam will have a CSF Number of 1.23, so would be considered very safe from capsize. A contemporary light displacement yacht, such as a Beneteau 311 (7716 lbs, 10'7" beam) has a CSF number of 2.14. Based on the formula, while a fine coastal cruiser, such a yacht may not be the best choice for ocean passages. " I created the simple spreadsheet attached just to check this out for myself, and was curious what the MCR might be of a 12-metre yacht. Taking a stab at a typical 12 meter yacht was tricky because the formula in the 12-metre rule had changed several times, but hypothesizing a typical 70 ft LOA and 55 ft LWL for that 60,000 lbs displacement and 12 foot beam, we get an MCR of 57, which would make my stomach happy.

#### Attached Files:

• ###### Boat index calculator.xls
File size:
29 KB
Views:
520
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### TeddyDiverGollywobbler

It's funny when just playing with numbers fails to see the obvious. Silly me..
MCR however doesn't actually count (=penalize) long overhangs although (again my opinion) it should.
Nice worksheet anyway. Thanks

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### Antonio AlcaláOcean Yachtmaster

Hummm. Amazing. Really,really, interesting.
But could you create a formula for calculating the roll acceleration and its relation with the MSI?

Are you able to let know us a table with the MCR-Roll acceleration-MSI with some popular sailboats models?

It could be terrific!!

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### drshaddockDesign Engineer

I guess it depends on how you work with overhangs in the formula. Let's say you set up a hypothetical bluewater sailboat--say 40 ft LOA, 30 ft LWL, 13 ft beam, and 24,000 lbs displacement. This gives a reasonable MCR of 36.6 (oops, I should have formatted the MCR cell to show at least one decimal place; my apologies; feel free to unprotect the sheet and fix it!). So if we keep everything the same but cut the LOA to 32, because you have less non-submerged weight on the ends to hobbyhorse, the MCR climbs to 39.5. But if you left the LOA at 40 ft and lengthened the LWL to 38, the MCR would drop to 31.3. So why would a longer, effectively narrower boat be less comfortable? Well, if the weight and beam stay the same but the LWL increases, we would have to surmise that this boat is not going to have as much beam in the water--she's still going to displace 375 cubic feet no matter what; it's just distributed differently. I guess we could say we're moving from a nicely balanced setup to a more extreme waterline--while the longer but narrower immersion profile is going to cut down on pitching, it's going to have aggravated roll.

Overhangs are an interesting proposition--on one hand, extra weight suspended out over the waterline adds that hobbyhorsing factor, but on the other, when you've got waves breaking under the bow or stern, you've got some reserve buoyancy that comes into play and can cut down on your movement. It's all a compromise... I guess the same considerations hold true for flare in the topsides--flare gives reserve buoyancy, adding some extra stability, but only until you reach a point somewhere around the vanishing angle of stability and capsize--the slope of the angles around that point would be a lot steeper than they would be with either vertical topsides or tumblehome, wouldn't they? :?:

I mentioned in an earlier post that the MCR formula 'sort of' considered BWL--can't remember what words I used--and it's this concept to which I was referring. All other things being equal, the displacement and LOA and LWL kind of establish what your BWL will be. And if you play with the spreadsheet and change just one factor at a time, it's interesting to see how the MCR is affected, and think about why it works that way. I scratch my head a bit when I see some of the results, but the more I think it over, the more sense it makes...

Hope this helps--even if it means that it just helps someone else set me straight on how I'm thinking about all this!

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### Patrick BLOSSELa Terre entière.

Hello,

I proceeded with some more data, thanks to drshaddock's following file, that I completed with my own Romanée's.

Thus I offer you the results View attachment Boat index calculator.xls for relevant discussion about nondimensional CR, introducing DSV (DiSplacement in Volume in ft^3 or m^3) and a compared calculation between IMPerial and International System Units.

Thanks to all.

Kindly.

Patrick

Last edited: Feb 25, 2008
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### TeddyDiverGollywobbler

In this I have a bit different opinion. When the breaking waves are getting big enough making them a problem, they tend to break over the bow or stern.

In the most ultimate conditions I once were, breaking waves were so steep that with 6'' bow overhang couldn't make more than 2 knots without making a nose dive.

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### drshaddockDesign Engineer

Teddy, it's hard to imagine any boat being comfortable when waves are breaking over the bow or stern. I'm only trying to say that if a boat has a larger volume above the waterline than it does AT the waterline--by having overhangs, by having flared topsides, or both--it's less likely to pitch as much (or make a nose dive). The reserve buoyancy provided by the extra percentage of volume above the DWL helps keep the bow, or stern, up. I agree that waves breaking over the deck will cause difficulties; I just think they'll be less on a 'flared' boat than they will on one with vertical topsides, plumb bow, vertical or reversed transom...

However, in waves that aren't breaking over the ends but are high enough to approach the decks, or are square or steep, the 'flared' boat is going to pound more, and in that aspect it's going to have LESS comfort and more noise--in my humble opinion.

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### drshaddockDesign Engineer

Your calculations are interesting work. I notice that the Catalina 27 row has an inconsistent formula--if you copy the formula from the row above or below it, you'll see a more rational result. The others all seem to correlate quite nicely with the MCR column, and show a little different look at motion comfort.

I do wish that we could provide a quick and easy solution to roll-axis acceleration comparisons, but the figures we have available for the boats--for example, the things shown on this spreadsheet, which originally came from SailCalculatorPro--don't have information about draft, CG or CB, air draft, or sail center of effort. I think accurate figures for those as well as weight of the mast(s) and sail(s) would be needed to predict a roll index--but maybe I'm being too narrow-minded and exact. Maybe we could all work out a way to infer a ballpark figure for draft, mast weight, mast height, and so forth to generate a roll index. Any ideas?

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### TeddyDiverGollywobbler

And more ballast should give greater stabilisizing inertia, and less pitch aswell less volume above the waterline. There are pros and cons in both ways.
So shouldt adjustable ballast tanks make the difference...

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### Patrick BLOSSELa Terre entière.

Dear drshaddock,

Your were perfectly accurate: the file is now up-to-date and the Catalina 27 shows her proper formula (*) obviously more comfortable.
(*) Concerning my Romanée, reducing her BOA (3.50m) by 12% makes me obtain her own real BWL (3.10m), so I did for the complete list.

The essential of such minor contribution thus remains for nondimensional formulas, strictly the same using IS (m and m^3) or US (ft and ft^3) units with respect for original purposes.

Thanks.

Fair winds to all.

Patrick

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### Antonio AlcaláOcean Yachtmaster

And i ask myself...who has any information about the MCR in the new models of x-yatchs and the first 45 and 50 of beneteau?
Maybe it could be interesting compare the numbers of new racer sailboats ( the lowest MCR) with the ancients models...Does anybody got any data?

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### Antonio AlcaláOcean Yachtmaster

Does anybody information about the "Vilm 34". It seems to be a great example about how crossing oceans in a small sailboat!!!

http://www.vilm.de/?pageID=63

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### David RobertsNexus

Getting back to the OP, I believe that roll accelerations are not of as much interest as roll period. For one thing, we do have research into how roll periods relate to seasickness, but AFAIK nothing on roll accelerations. We know that 10-11 seconds seems to be the magic number which one should avoid.

Dave Gerr believes that roll period should be some function of waterline beam; around 1 to 1.1 * WLB. My planing powerboats are faster, coming in around .5 to .7 * WLB. There are other factors in planing powerboat design which might be more important for success than roll period.

Roll period, of course can be calculated from GM (metacentric height), or simply measured at the dock, with one's foot for small boats, and with a crew running from side to side for larger craft, roll period being pretty much independent of amplitude.

If one is designing, then one will calculate GM as a matter of course. If one is buying, then a simple measurement of roll period will suffice, and from it GM can be calculated, if it is of interest.

Brewer's ratio is interesting, but it won't tell you GM, while your foot and a tape measure will.

To calculate roll period from GM:
(0.44*beam-in-feet)/GM^0.5
The constant of .44 comes again from Dave Gerr. Research tells me it will vary will boat type and size, but this will suffice for the boats in which we are interested.

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### LyndonJSenior Member

David

I think we are refering to ocean crossing displacment boats here , not planing power boats.

Your suggested period is in what units ? If its in feet its not sensible for a ballasted sailboat but it is closer if it's in meters. 4 seconds is usually accepted as comfortable and a good target for a ballasted sailboat.
Roll period calculation requires the radius of gyration (k) without that the formula isclose to useless except for comparing boats with the same k .

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