# The "S" Number

Discussion in 'Sailboats' started by Pat Ross, Feb 13, 2011.

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### Pat RossCorinthian 41 Tri #12

In the February/March 2011 issue of Professional Boatbuilder magazine, the ROVINGS section by Dan Spurr, there was a summary of a section of The Design Ratios by Eric w. Sponberg of SPONBERG Yacht Design Inc. dealing with the S Number. The S Number is a formula that assesses relative performance of sailing yachts, giving values that range from 1 to 10
The Multihull Dynamics, Inc. website has used the term Base SpeedTM to do comparisons of performance potential. It results in a projected Best Days Run speed over a 24 hour period under racing conditions.

The article roused Cal Markwoodâ€™s curiosity, Engineering Analyst for Multihull Dynamics, Inc. He was interested in the applicability of the S# to catamaran sailboats and how it compared with Base SpeedTM as a method of evaluating performance potential.

Monohull sailors may be interested in the S formula for monohulls listed in the article.

The S Number http://www.multihulldynamics.com/news_article.asp?articleID=232

Pat Ross

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### trenaceNew Member

It is an interesting calculation but some points may be worth bringing out:

While Sponberg thought that the equation was such that the values are inherently limited to the 1-10 range, with 10 being approached only asymptotically, actually that isn't so. The equation isn't in such a form, and some boats -- e.g. the 49er and 18 foot skiffs -- exceed 10.0 at all-up sailing weight (including crew.)

It was made clear that the formula is no speed predictor: if I could summarize what Sponberg seemed to me to be trying to communicate, it simply gives a "what sort of category" analysis and further isn't really useful if comparing boats of markedly different lengths. Though it would remain true, for example, that a boat of whatever length wouldn't be racy with a low S number, or a plodding cruiser if having a high S number.

Personally I would rather look at sail area vs actual displacement (which is not what most mean by "SA/D") as well as sail area vs displacement^(2/3), and at other parameters. After having put some effort into the S number equation, to me it is more of a snapshot picture than anything else.

Combining everything into one number is a way of losing information, rather than gaining more.

Lastly, when comparing different boats using values found in a spreadsheet or on the web, unfortunately there is often no consistency in how sail area is counted. Where large genoas are counted in the sail area, but reported only as "sail area," this can skew calculations greatly. But this is true no matter the equation, of course. It is definitely true however with at least one spreadsheet with S number calculations, and so may be worth mentioning as a caution.

Last edited: Feb 21, 2011
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### Pat RossCorinthian 41 Tri #12

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### Eric SponbergSenior Member

The S-Number

The S-Number was first published on this Forum at the following thread at post #198 (scroll down):

http://www.boatdesign.net/forums/boat-design/center-flotation-calculation-implications-30857-14.html.

This was part of a discussion of The Design Ratios, which began at the beginning of this thread. The complete series of "lectures" that became The Design Ratios, which includes the S-Number, was compiled into a pdf document that you can download in its revised version here, at post #305:

http://www.boatdesign.net/forums/boat-design/center-flotation-calculation-implications-30857-21.html. It is also available on my website in the "Articles" section: http://sponbergyachtdesign.com/Articles.htm.

It is true that the S-Number is not truly asymptotic as it is possible to get numbers above 10, but those instances are pretty rare. For Multihulls, as pointed out in the article on Multihull Dynamics, it can apply pretty well if you reduce the primary coefficient from 3.972 to 1.52.

In the original thread, you can follow the discussion that ensued about S-Number, and the fact that all it is, indeed, is just a way to classify boats in order to differentiate those that might be faster sailers from those that might be slower sailers, and to add some degree of spread. When the equation is modified for multihulls, it seems to give the same kind of context. That is all that S-Number is good for. It is not a rating rule.

As pointed out, one has to be careful as to what area is included in sail area. Is it the basic triangular area or is it the actual sail area of the sails in use? The same applies with displacement--displacement varies too, as it can be lightship displacement, displacement at the design waterline, or full load displacement. So, of course, nothing is hard and fast, and one always must take the numbers in context, and when comparing boat, make sure that you are comparing the same numbers and the same ratios--apples to apples as they say.

Eric

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### Perm StressSenior Member

To Eric:

My guess some correlation between (average speed)/(length^(0.5)) and S-number should exist?

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### Eric SponbergSenior Member

Actually, I don't thnk so. To compare S-Number against speed-length ratio is essentially comparing it against length because speed is an independent variable--that is theoretically, given enough power any boat can go any speed regardless of length or displacement. The S-Number is meant to show the speed potential of any given boat design by combining it's speed producing property (sail area/displacement ratio) with its drag producing property (displacement/length ratio) into a number that has some control on its upper and lower limits.

Eric

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### Perm StressSenior Member

Than some correlation should exist.
Like average speed made good (including almost-no-wind-drifting, and only counting distance made good when beating) over the season (I'm not the first to discover it, my small experience simply confirm this) of sailboat of IOR era, i.e not readily half-planing downwind, is ~1.5*(LWL^(0.5))knots.
If S-number compare drive to drag in some generalized way, at least a correlation should exist; as length for most sailboats is still very important speed-limiting factor.

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