PS Advisor: 12/02

Performance Equations
Although I've been a sailor for many years, there are still many sailingrelated matters (as well as non-sailing related!) of which I am ratherignorant.

One of those are the D/L and SA/D ratios frequently included in boats'specifications. Case in point are those ratios mentioned on page 21 of the October 1 issue, pertaining to the J/105. My various dictionaries define a ratio as the quotient of two numberswhich is expressed as X/Y. Maybe my calculator is confused, but it surely doesn't come up with the values expressed in subject article when dividing the D(isplacement) by the L(ength) (OA or WL), nor the S(ail) A(rea) by theD(isplacement).Please clue me in. (I really think your publication is tops; I've been reading it for15+ years.)

-Onno Boswinkel
Merrimack, NH

We received two other letters like Mr. Boswinkel's this month—enough to make us go back and check the J/105 numbers. They're OK. Must be something in the air...

We're talking about boats here. Of course it's not so simple as dividing one number by another. (Actually it's pretty simple in a couple of instances, like dividing ballast by displacement to get the ballast ratio.)

SA/D and D/L are two of the non-dimensional ratios that help give an idea of a boat's potential performance. The first has to do with horsepower, the second with the mass it has to push around. Neither takes into account nuances of hull shape, or what happens when you heel the boat over and increase waterline length, or several other performance-influencing factors. Balancing the effects of one design move against another in a structure that changes its shape in the water, depending on how it's tipped, is a great puzzle of naval architecture. Luckily, since boat designers do know a lot about creating efficient underwater shapes and putting wind power to them, these ratios end up being pretty good general indicators.

Here's a quick explanation...

For SA/D:

SA / (DSPL/64)^.66

That is, sail area in square feet, divided by the result of the displacement (in pounds) divided by 64 (the number of pounds in a cubic foot of seawater), to the two-thirds power. It obviously helps here to have a scientific calculator that lets you multiply by fractional exponents. Most of them come with "invert" buttons that you can use to select an XY function.

By the way, sail area should be figured with a 100% foretriangle; that is, with no overlapping headsail. Builders have been known to equip their boats with, say a 130% genoa, and include that extra 30% in their published SA number. For a quick and dirty idea of the 100% foretriangle area, multiply the I measurement by the J measurement and divide by 2.

For D/L:

DSPL / 2240(.01 x LWL)³

That is, displacement in pounds, divided by the number of pounds in a long ton, divided by the product of .01 times the waterline length in feet, cubed. You also have to convert feet/inches into feet/decimal feet for things to work.

For more on these and other numbers and ratios to consider visit naval architect Ted Brewer's website at www.tedbrewer.com, and follow the link to the yacht design primer.

With all the possibilities for fuzziness in how these ratios work as indicators, and without precise, agreed-upon definitions for boat types, there's plenty of room for debate—but here are some figures that can serve as guidelines:

D/L

<100 = very light racing boat
100-150 = light racing boat
150-200 = moderate racer/light cruiser
200-300 =moderate cruiser/racer
>300 = heavy cruiser

SA/D
<16 = very conservatively powered
16-18 = conservatively powered
18-24 = moderately powered
24-26 = high-powered
>26 = very high-powered