The Physics of Sqiling Bryond
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The physics of sqiling BryonD. Anderson Sqilsond keels,like oirplone wings, exploit Bernoulli's principle. Aerodynomicond hydrodynomicinsighis help designeri creqte fosterioilboots. BryonAnderson is on experimentolnucleor physicist ond,choirmon of the physicsdeportment ot KentSlote University in Kent,Ohio. He is olsoon ovocotionolsoilor who lecfuresond wrifesobout the intersectionbehyeen physics ond soiling. In addition to the recreational pleasure sailing af- side and lower on the downwind side. fords, it involves some interesting physics.Sailing starts with For downwind sailing, with the sail oriented perpen- the force of the wind on the sails.Analyzing that interaction dicular to the wind directiory the pressure increase on the up- yields some results not commonly known to non-sailors. It wind side is greater than the pressure decrease on the down- turns ou! for example, that downwind is not the fastestdi- wind side. As one turns the boat more and more into the rection for sailing. And there are aerodynamic issues.Sails direction from which the wind is coming, those differences and keels work by providing "lift" from the fluid passing reverse, so that with the wind perpendicular to the motion of around them. So optimizing keel and wing shapesinvolves the boat, the pressure decrease on the downwind side is wing theory. greater than the pressure increase on the upwind side. For a The resistance experienced by a moving sailboat in- boat sailing almost directly into the wind, the pressure de- cludes the effects of waves, eddiei, and turb-ulencein the crease on the downwind side is much greater than the in- water, and of the vortices produced in air by the sails.To re- crease on the upwind side. duce resistanceeffectively by optimizing hulls, keels, and Experimenting with what can be done, a beginner finds sails, one has to understand its various components. some surprising results. Sailors know well that the fastest point of sail (the boat's direction of motion with respect to the Wind power wind direction) is not directly downwind. Sailboats move Moving air has kinetic energy that cary through its interac- fastest when the boat is moving with the wind coming tion with the sails,be used to propel a sailboat.Like airplane "abeam" (from the side). That's easily understood: When a wings, sails exploit Bernoulli's principle. An airplane wing is sailboat is moving directly downwind, it can never move designed to causethe air moving over its top to move faster faster than the wind because, at the wind speed, the sails than the air moving along its undersurface.That results in would feel no wind. In fact, a boat going downwind can lower pressure above the wing than below it. The pressure never attain the wind speed because there's always some re- difference generatesthe lift provided by the wing. sistance to its motion through the water. There is much discussionof whether the pressurediffer- But when the boat is moving perpendicular to the wind, encearises entirely from the Bemoulli effector partly from the the boat's speed doesn't decrease the force of the wind on the wing's impact and redirection of the air. Classicwing theory sails. One sets the sails at about 45o to the direction of mo- attributesall the lift to the Bemoulli effectand ascribesthe dif- tion-and to the wind. The boat's equilibrium speed is de- ferencein wind speedsabove and below the wing to the wing's termined by the roughly constant force of the wind in the asymmetric cross-sectionalshape, which causedthe path on sails and the resistance against the boat's motion through the top to be longer. But it's well known that an updown sym-, water. If the resistance can be made small, the velocity can be metrical wing can provide lift simply by moving through the large. That's seen most dramatically for sail iceboats, which air with an upward tilf called the angle of attack. Thery de- skate on the ice with very little resistance. They can glide spite the wing's symmetry,the wind still experiencesa longer along at speeds in excess of 150 kmlh with the wind abeam path and thus greater speed over the top of the wing than at speeds of only 50 km/h! Of course sailboats plowing under its bottom. A NASA websitehas an excellentdiscussion through the water experience much more resistance. of the various contributions to lift by an airplane wing.l It dis- Nonetheless, some specially constructed sailboats have at- putes the conventionalsimple version of wing theory and em- tained speeds of more than twice the wind speed. phasizes that lift is produced by the tuming of the fluid flow. The caseis similar for sailboats.A sail is almost always Keels curved and presentedto the wind at an angle of attack. It was recognized centuries ago that a sailboat needs The situation is shown schematicallyin figure 1a. The something to help it move in the direction in which it's wind moving around the "upper," or downwind, side of pointed rather than just drifting downwind. The answer was the sail is forced to take the longer path. So the presenceof the keel. Until the development of modem wing theory it the surrounding moving air makes it move faster than was thought that one needed a long, deep keel to prevent the air passing along the "lower," or upwind, side of the side-slipping. But now it's understood that a keel, like a sail, sail. Measurementsconfirm that relative to the air pressure works by providing sideways lift as the water flows around far from the sail, the pressure is higher on the upwind it, as shown in figure 1a. A keel must be symmetrical for 38 February2008 PhysicsToday @ 2008 American Instituteof Physics,5-0031-9228-0802-020-6 "# Fsail F.1.ngF.,t.ng Figurel. Forceson o movingsoilboqt. (q) Soilond keelproduce horizontol "|ift" forcesdue to pressuredifferences from differentwind'ond woter speeos, respectively,on oppositesurfoces. (b) The vector sum of lift forcesfrom soil ond keelforces determines the boot'sdirection of motion(ossuming there's no rudder).When boot speedond courseore constont,the net lift forceis pre- ciselybolonced by thevelocity-dependent drog forceon the boot os it plows throughwoter ond oir. the sailboat to move to either side of the wind. with respect to the hull and the bulk of water farther away. A keel works only if the motion of the boat is not exactly The shear means that van der Waals couplings between water in the direction in which it's pointed. The boat must be mov- molecules are being broken. That costs energy and createsthe ing somewhat sideways. In that "crabbing" motion, the keel resistive force, which becomes stronger as the boat's speed moves through the water with an angle of attack. Just as for increases.The energy dissipation also increaseswith the total the sails in the wind, that causes the water on the "high" area of wetted surface. (more downstream) side of the keel to move faster and cre- Although the effect is called frictiorral resistance,it's im- ate a lower pressure. Again, the net lift force on the keel is portant to realize that the resistive force in water is basically due to the combination of that decreasedpressure on the high different from the frictional force between solid surfaces side and increased pressure on the other (low) side. rubbed together. To reduce ordinary friction, one can polish In figure 1b, the keel lift thus generated points almost in or lubricate the sliding surfaces. That makes surface bumps the opposite direction from the lift provided by the sails. The smaller, and it substitutes the shearing of fluid lubricant mol- two vectors can be resolved into components along and per- ecules for shearing of the more tightly bound molecules on pendicular to the boat's direction of motion. For a saiiboat the solid surfaces. moving in equilibrium-that is, at constant speed in a fixed For a boat moving through water, however, polishing the direction-the transverse lift components from sail and keel hull doesn't eliminate the shearing of the molecules of water, cancel each other. The componeni of the driving force from which is already a fluid. The resistive force cannot be reduced the sails in the direction of motion is the force that is actually significantly except by reducing the wetted surface. It does moving the boat forward. For equilibrium motion, that force help to have a smooth surface, but that's primarily to reduce is balanced by the opposing component of the keel lift plus turbulence. the total resistive force. The generation of turbulence is a general phenomenon Wing theory, developed over the past 100years for flight, in the flow of fluids. At sufficiently low speeds, fluid flow is indicates that the most efficient wing is long and narrow. Vor- laminar. At higher speeds, turbulence begins. Its onset has to tices produced at the wing tip cost energy. A long, narrow do with the shearing of the molecules in the fluid. When the wing maximizes the ratio of lift to vortex dissipation, thus shearing reaches a critical rate, the fluid can no longer re- providing the best performance for a given wing surface area. spond with a continuous dynamic equilibrium in the flow That also applies to sailboat sails and keels. and the result is turbulence. Its onset is ouantifiecl in terms It is now recognized that the most efficient keels are nar- of the Reynolds nrrmber row from front to back and deep. Such a keel can have much R: (Lu)l(p.lp), (1) less surface area than the old long keels.