10 minute read
max ebb: in theory
"Weight to leeward!" shouted the skipper. The race had started in a pleasantly warm northerly breeze, but as often happens with light northerlies in early spring, it had faded by the second windward leg. "More leeward weight!" he repeated. "I need more heel angle!" We all slid our feet over the leeward rail, leaning out against the bare lifeline wire. "Why are we doing this?" asked the novice crew sitting just astern of me. "Don't the sails and fi ns work better when they're vertical, so they can project more of their area to the fl ow?" Lee Helm had brought one of her engineering grad student friends along for the race. He was not a sailor, but knew enough about hydrodynamics to be dangerous. "We're using gravity to keep the sail full," I answered. "There's not enough wind pressure to keep the sails in the proper shape, so heeling the boat helps. What little wind there is will fi nd something resembling the right shape in the sails." "That's true, but it's, like, mostly for helm balance," Lee corrected me from her perch forward on the rail. "Gotta heel enough to put some weather helm on the boat, 'cause the keel and rudder are more effi cient if they both lift in the same direction. Induced drag is minimized if the spanwise lift loading is distributed evenly on each foil." "Good point," said the new sailor, who seemed to fully comprehend the point Lee was making. "If heel were zero," Lee continued, now directing her explanation at me, "the boat would not have any weather helm, the rudder might have to push to leeward
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to hold course, and the keel would have to do all the work resisting side force." "Isn't helm balance controlled more by mast rake?" I asked. "The range of adjustment for mast rake is, like, only 10 or 20 centimeters," said Lee. "But heel angle moves the rig side to side by meters. The books show helm balance as being all about side force, but there's a forward thrust force from the sails too. Heel moves the thrust from side to side, so heel angle has a big effect on steering force. Changing heel angle is, like, the quickest way to adjust helm balance." Meanwhile the wind had started to come back. "Too much heel!" called the skipper. "Let's move a couple of bodies to windward!" This was a welcome development. I stayed on the leeward rail while Lee and her friend moved to the high side. I expected to join them on the windward rail as soon as the wind came up just a little more, but instead it held at around eight knots. A larger and faster boat was starting to gain on us from astern, threatening to roll over us to windward. "Let's move to centerline," Lee suggested quietly, gesturing that I should come off the rail while she moved down to the boat's centerline. "Get right under the boom," she instructed. "If we do this right we can seal the root loss from the mainsail, and point higher." The three of us, in our PFDs and foulies, fi lled up the air space nicely between the front half of the boom and cabin top. "That should give you, like, another degree of pointing," Lee called back to the afterguard. "Good, we're trying to pinch up to give that boat on our stern some bad air and hold them off," replied the tactician. "But, like, don't sit on their face," Lee advised. "That will make them tack, and we want to stay in safe leeward position where we're lifted a little in their upwash. We're going faster with them on our windward quarter than if they weren't there." It was subtle, but it seemed to work. With our bodies blocking the air flow under the boom, we were pointing high enough to hold even with the oncoming threat, and stay in the advantageous safe leeward position. "I'm never happy," announced the skipper, "unless I'm pointing higher than all the boats around me!" "A pincher," Lee whispered. "But on this kind
of boat it's the fastest way up the wind." "This is cool," observed the new crew. "We're probably cutting the induced drag from the mainsail in half by suppressing the root vortex." "I can see how our body position prevents some power loss," I said. "But how does it reduce drag?" "Induced drag." said Lee. "It's the unfavorable change in the direction of the lift vector, induced by the vortices at either end of an airfoil." The engineering student was eager to explain, so he found a mostly blank page in the tide book in his pocket and started to draw a diagram of a wing in cross section." "Draw a sail instead," suggested Lee. Circular arc, no thickness, like our jib. And by the way, sailors usually show the boat from the starboard side, air going right to left. Not like airplane convention, with the air going left to right." The engineer scratched out his airfoil sketch and drew an arc, with lines representing the fl ow of air around the section of the sail. "In theory," he said, "with no friction, no viscosity and no boundary layer, and with infi nite acceleration around corners not allowed, the fl ow is symmetrical. What fl ows in is a mirror image of what fl ows out." "But what makes the fl ow turn upward before it even gets to the sail?" I asked, after looking closely at his drawing. "How does it know?" "The air doesn't know anything," Lee interjected. "It's just fl owing from high pressure toward low pressure." "Right," said her friend. "The low pressure is on the top of the foil, high pressure underneath, and the upwash is caused by air fl owing downhill along the pressure gradient as it approaches." "The pressure difference is from Bernoulli?" I asked. "Forget Bernoulli," he said. "That just confuses things. Elementary texts try to teach Bernoulli in one-dimension and then apply it to two- and threedimensional problems where it doesn't make any sense. And besides, this is a thin airfoil. Think centrifugal force. We assumed no viscosity or friction, but this idealized fl ow still has mass and pressure and elasticity. So when the sail bends the air fl ow, centrifugal force tends to pull the fl ow away from the sail on the leeward side, reducing the pressure. Centrifugal force pushes the air into the sail on the windward side, increasing the pressure. That's really all you need to know to understand the ideal fl ow pattern around a sail or an airfoil." "That's easier to understand than Bernoulli," I agreed. "Except for one thing," the engineering student said. "Induced drag." I had a feeling the confusing part was
coming up next. "Remember, it's the low pressure and high pressure differential on the two sides of the sail that causes the upwash angle as the air approaches, and the symmetrical fl attening out of the downwash angle as the fl ow exits." "And like, upwash doesn't really mean up," Lee added to clarify," because we're mixing up airfoils and sails. Upwash is up for a wing; it's a bending of the fl ow to leeward for a sail, as in the diagram." "The lift force in this idealized symmetrical fl ow," continued the student, "has to be straight up because of symmetry. There's no drag, and lift-drag ratio is infi nity." "That would be wonderful if we could actually achieve it," I said. "For high-aspect-ratio wings, we come very close," he said. "Think of gliders with 50-to-1 glide ratios. But look at what happens near the bottom of the sail. Air spills under the boom from high pressure to low pressure, equalizing the two sides. So now, approaching air doesn't bend up to the low-pressure side, and you have to change the angle of attack or trim in to prevent luffi ng, and now the angle of the lift vector is tipped back. Suddenly there's drag. This new drag source, caused by the rearward inclination of the lift vector due to tip or root losses, is called induced drag." "And we're minimizing it right now by putting our bodies between the sail and the deck," Lee pointed out. Meanwhile we had moved to a position directly ahead of the larger boat, slowing them down enough with our backwind so that they were no longer a threat. "Notice the boost we got when we were in the safe leeward position, ahead and to leeward?" said Lee. "The upwash into their rig was a small lift for us. And now our downwash is giving them a header." As predicted, they tacked away rather
than breathe our bad air any longer. We assessed the likely wind shifts, and tacked a few minutes later. But the wind was still building, and soon we were all back on the windward rail and unable to play more games with induced drag and pointing angle. "It really is a shame that there's frictional resistance in actual air and water," I said. "The lee bow effect in practice isn't nearly as big as in that diagram. Think how high we'd be able to point, in theory, with infi nite lift-drag ratios." "In theory," said Lee, "there's no difference between theory and practice. But in practice, there is."
max ebb
The 12-step program for pointing high: 1) Use only deck-sweeping jibs. Don't allow any air to spill under the foot of your headsails. Applies to all size jibs. Sheet trim has a very big effect on twist with deck-sweeping jibs, so a mechanism for controlling lead angle under load is also important. 2) Use the thinnest diameter bare wire lifelines that are legal, to minimize parasitic drag. If you need padding, put it into your PFD instead of the lifelines. 3) Minimize diameter and number of lacing lines between the wires. You need just enough to keep sails on board, but no more.
4) Run all unused halyards to the masthead on light messenger lines. This also protects them from sun damage between races. 5) Never allow your crew to hang a coiled sheet or afterguy from the lifelines. That's an air brake! 6) Store the horseshoe life ring and other overboard gear horizontally, out of the breeze, or lying fl at at the back of the cockpit sole if there's an open stern. 7) Use mast rake and mainsail design to get the boom really, really low. Low booms spill less air underneath, and in the right wind conditions, the crew can more effectively seal the air leak with their bodies. On a small boat, it might even be safer if the boom hits crew on the shoulder instead of on the head. 8) Rig the most powerful backstay tensioner in your fl eet. On most boats, you'll need a very tight forestay and good mast bend control to make the sails fl at enough to point high. If you ever have to use all your strength to get the backstay tension you want, then the tackle is not powerful enough. 9) No stand-up cocktail parties. On big boats, keep the bodies low and out of the breeze. 10) On boats with multiple sets of spreaders and parallel shrouds, tape the shrouds together where possible to reduce wind resistance. A compact bundle usually causes less air drag than separated rods or wires. 11) Keep the keel and rudder perfectly smooth. 12) If your class rules or racing association allow it, remove the stern pulpit and any other deck hardware that increases air drag.
