THE BEST A-CUP EVER "Totally. But think of what happens to a soft sail at very low angles of attack. I mean, you can't push out against the pressure difference with a soft membrane, and that's what most of the front part of an airfoil has to do. I think the team that gets its act together with the rigid wing is the one that will have the faster machine." "But I'm not convinced that bigger is faster when we're talking multihulls," said the cat racer. "Look at all the windsurfers breaking speed records." "The scaling still favors the big boats," said the cruising cat owner. "Think of it this way: Compare two cats, one twice as big as the other. The displacement of each hull is proportional to length times hull beam times hull draft. So if each one of those dimensions doubles, then displacement becomes eight times as big. And the distance between the hulls also doubles, so with one hull just out of the water, the leverage against heeling is 16 times bigger for the cat that's twice as big." "Scale factor to the fourth power," inter jected Lee. "Heeling force goes up, too," I reminded them. "Sail area is proportional to mast height times boom length," continued the owner of the big cat, "and each of these doubles when size doubles, so you have four times as much sail area, And the center is twice as high up, so you have eight times as much heeling leverage." "Scale factor to the third power," said Lee. "So the big cat has 16 times as much stability but only 8 times as much heeling. It can handle twice as much wind." "Um, 41% more wind," corrected Lee. "Square root of two, because wind pressure is proportional to wind speed squared. But, like, you're right, the big boat has an advantage. They can spend some of that extra stability margin in the design phase, with a bigger rig. Also, that's why big cats have an easier time passing the capsize screening formulas that compare heeling moment to righting moment, like for the Pacific Cup multihull division." "Except that with these giant multihulls, they might not be limited by stability," suggested the catamaran racer. GILLES MARTIN-RAGET / BMW ORACLE RACING
might cost it the match if wind conditions are shifty. The Oracle tri will dominate when the wind is strong enough for it to be foil-borne. Lee Helm, a naval architecture grad student with more technical chops than all the other pundits put together, was keeping uncharacteristically quiet on the issue. She was busy enjoying a free lunch from the snack tray that had been sent up from the kitchen. "Not enough info at this time," she insisted. "No predictions till I, like, see some numbers. But speaking of 1988, I did some research and found a paper by Burt Rutan, that aerospace guy who builds private-sector spacecraft. He also built the wing sail for Conner's defending cat. It's, like, counterintuitive, but the solid wing sail turned out to be lighter, more reliable and easier to trim than the soft sail rigs they tested." "That does sound backwards," I said.
"What if both boats are so wide that they just don't come up against stability as a limiting factor? At some point, I think the structural considerations limit the design, and I think a good small cat can be faster than a non-optimized big cat, and both of these monsters are too new to be anywhere near optimized." "Big still has an advantage," asserted Lee. "Think Reynolds number. Big foils work more efficiently than small ones." "Reynolds number?" asked the cruiser as he sat down with another drink. "What's that?" "It's just a non-dimensional index for comparing the importance of inertial forces to viscous forces acting on an object moving through a fluid," Lee explained, as if this were so simple it should be obvious to anyone. "It's proportional to length of the object times speed. If the Reynolds number is, like, very high, foils behave closer to the ideal frictionless condition, and work more efficiently. For boats operating at very low angles of attack, with very high lift-drag ratios required, bigger is going to be way faster than smaller." "How can length times speed be nondimensional?" asked the cat racer. "Good catch," said Lee. "It's really length times speed divided by kinematic viscosity." "Kinematic viscosity? What's that?" asked the cruiser. "Viscosity divided by density," said Lee. "Viscosity is the shear stress produced by a velocity gradient in the fluid. It's how much shearing force is in the fluid when there's a unit velocity gradient." The cat racer was the only one still following Lee, but she pressed on. "Force is mass times acceleration, or mass-length per time squared. You wanna do this in English or metric?" "I'll take English units, thank you," the cruiser answered as if this were a quiz show. "Cool. For shearing stress in the fluid, we need force per area, or pounds per foot squared. A pound is a mass times an acceleration, or a slug-ft/sec², so for shear stress we have slug-ft/sec²/ft², which simplifies to slug/(ft-sec²). Now divide by velocity gradient, ft/sec/ft, which is the same as 1/sec. You get slug/(ft-sec), and this is the dimension of a unit of viscosity. For kinematic viscosity, divide viscosity by density. Density is mass per volume or slug/ft³, so we get (slug/(ft-sec))/(slug/ft³). Anyone have the answer?" The cat sailor was writing on his napkin with a marking pen. It took him a minute to catch up, but according to August, 2009 •
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The August 2009 issue of the West's premier sailing and marine magazine.