Technical » The S Number

Release Date: 2/13/2011

The S Number

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, with sub-ranges of these values assigned to Racing Machines (5-10), Racer-Cruisers (3-5), Cruisers (2-3) and Lead Sleds (1-2). Mr. Sponberg applied this to monohull sailboats. The equation is:

 

S# = 3.972 x 10^[-DLR/526 + 0.691 x (log(SAD)-1)^0.8]

 

DLR in the formula is Displacement-Length Ratio and

SAD is Sail Area/Displacement Ratio.

 

DLR =(+Disp)/((0.01)*Lwl)^3 for monohulls and trimarans

 

DLR =(+Disp/2)/((0.01)*Lwl)^3 for catamarans

 

SAD =+SA/(Disp*2240/64)^0.667

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(Lwl is design waterline length in feet, SA is upwind sail area (or mainsail plus 100% foretriangle) in feet squared, displacement is in pounds.)

 

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. It uses sail area, waterline length and displacement in the equation :

 

Base Speed = 1.7*(Lwl^0.5)*(SA^0.352)/((Disp*2240)^0.253)

 

(Lwl is design waterline length in feet, SA is sail area in feet squared displacement is in long tons.)

 

 

It resulted from curve fitting actual race results for 89 boats, both monohulls and multihulls. It is used in Europe and other locations for handicapping multihull races. It was developed by Richard Boehmer of Great Britain, who emphasized that Simple equations like Base Speed provide speeds that are best used for relative comparisons. Sponberg makes a similar statement for S#.

 

The article roused my curiosity as to the applicability of the S# to catamaran sailboats and how it compared with Base Speed as a method of evaluating performance potential.

 

The article stated that the values of S# ranged from 1 to 10 because of the logarithmic nature of the formula. The first thing I discovered when I computed S# values for the boats in the MDI database was that many of them resulted in values greater than 10. Examination of the formula shows that, while one term is logarithmic, the other is not and the limit of 10 must have been imposed by the choice of 3.972 as a scaling constant to make the answers fit a range of 1 to 10. The boat that drove the scaling is Alinghi, a 110 foot long ocean racing catamaran, the highest performing boat in the database.

 

I calculated a constant of 1.52 to make my largest S# value equal 10 and plotted the values as shown below. The chart is marked with the various S# categories and appear logical from what I know about the boats. So it could be concluded that the S# can be used to illustrate the relative performance potential of catamarans as it is for monohulls.

Comparing the value of S# and Base Speed as indicators of relative performance potential, I was initially turned off by the fact that S# is just a number. Without comparing its value for one boat against another, it has little meaning. Base Speed, on the other hand, is an estimate of average speed over a 24 hour period under race conditions.

However, when S# is plotted against Base Speed, its significance becomes apparent as follows. Whereas Base Speed indicates how fast a boat can go, it doesnt give any indication of the type of boat. S# gives both, but as just a number. So, the fastest boats with lower S# are big, fast cruisers and racing cruisers (think Gunboat 90). The fast boats with very high S# are indeed racers.

Comments are welcome multihull.analysis@comcast.net

Calvin H. Markwood

Engineering Analyst

Multihull Dynamics, Inc.