Gentry was the Boeing engineer who first taught sailors aerodynamics. In the Revised Edition, the authors used computer testing to show where the wind speeds up around a sail plan and where it slows down. And why and by how much? What if there are two flows — rather than one — around an airfoil like a sail, wing, keel, or rudder?
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The fundamentals of lift generation are presented with emphasis on their usefulness for understanding the flow around sails on a sailboat.
These same concepts are applicable to conventional airfoils for aircraft. Well known basic aerodynamic principles are used to illustrate the starting vortex and the formation of a circulation flow field about two-dimensional airfoils that leads to the generation of lift. Three-dimensional effects supply additional flow complications but are not central to the fundamental origins of lift. The generation of lift requires that the fluid have some viscosity.
An experiment with a fluid without viscosity has been conducted to prove this point. Without viscosity there would be no lift; birds and aircraft would not fly, and sailboats would not sail. The wind is blowing nicely as I trim my sails and movesmoothly across the water. A glider pilot searches for thermals toprolong his playtime in the air. The NASA space shuttle pilotmakes his final maneuvers to line up with the runway and flaresto make a nice landing. All of these situations have one thing incommon; they all are able to generate a force that we call lift.
Forthe sailor, lift is everything as long as the wind blows. For theglider pilot, it is almost everything but he needs help to get aloft. The shuttle pilot needs just enough lift to get back to the runwaysafely. All of these vehicles are flying, and flight depends upongenerating enough lifting force to avoid falling like a rock or, inmy case, being left drifting with the tidal currents when the winddies.
But how is this lifting force generated? What is thefundamental explanation for the generation of lift? To understand the fundamentals of how lift isgenerated, it is best to start with a simple two-dimensional airfoil. This allows us to get at the real essence of the origins oflift. Three-dimensional effects are just additional complicatingfactors and are not central to what really causes lift.
Although theprimary purpose of this article is to help sailors understand howtheir sails work, the concepts presented are exactly the same asfor conventional airfoils used on aircraft.
The emphasis here ison understanding more of the details of the airflow than is taughtto the beginning pilot. The pilot has only minimal influence onthe shape of his wing control surfaces and flaps up or down. However, the sailor has rather complete control of the shape ofhis airfoils and frequently makes use of two or more flexible sailsthat must be constantly shaped to work together for bestperformance. Sailing also sometimes requires knowledge of theairflow patterns around boats in close proximity.
Air and water are fluids that have a small amount ofviscosity. Viscosity effects are most apparent in the region of theflow very near the airfoil surfaces. We call this region theboundary layer. The boundary layer is responsible for creatingskin friction drag on a surface.
For most low speed flows, thefluid outside of the boundary layer the external flow may beviewed as inviscid zero viscosity. When the pressure in theexternal flow near the boundary layer is increasing too rapidly,the normally well-behaved viscous boundary layer will separatefrom the surface.
This leaves an unsteady chaotic region thatdistorts the external flow, decreasing lift and increasing drag see Figure 1.
Separation is a viscous effect. Figure 1. Water channel photograph showing separated flow. Fluid flow without viscosity. Computed streamlines forthe inviscid flow about a flat plate airfoil are shown in Figure 2. The flow is from left to right. Green streamlines that actuallytouch the surface are called stagnation streamlines. They dividethe flow that goes on the top of the airfoil from the lower surfaceflow.
In areas where the streamlines get closer together, theair speeds up and the pressure goes down Bernoulli's equation,[Reference 1, page ]. Where the streamlines get fartherapart, the air slows down and the pressure goes up.
If you rotatethis flow diagram degrees, you will see that it looks thesame. The pressure force on the top will, therefore, be the sameas the pressure force on the bottom giving zero lift and zero drag. A flat plateairfoil is used here to illustrate this. However, regardless of theairfoil shape, without viscosity the resulting lift and drag alwaysturns out to be zero according to D'Alembert's paradox. Figure 2. Non-lifting flow around a flat plate.
Formation of the starting vortex. However, air doeshave some viscosity! As the wind is initially turned on or airfoilmovement is started, the flow on both the upper and lowersurfaces near the trailing edge have some difficult maneuvers tomake. As soon as the boundary layer develops, it will not be ableto negotiate these maneuvers.
The flow will separate from thesurface and form the starting vortex as shown in the sketches inFigure 3 [1, p ]. The external flow and the boundary layer willquickly adjust, and as stable flow is established, the startingvortex will be swept downstream. The same phenomena willalso occur on a curved airfoil representing a sail and on aconventional airfoil such as used on aircraft. Figure 3. The vortex theorems.
A set of vortex theorems byHermann von Helmholtz and William Thomson Lord Kelvin play key parts in aerodynamics [1, p]. Theapplication of this theorem in the two-dimensional airfoil casebasically means that as the starting vortex is created in the flowfield, there must be another vortex equal in strength and oppositein direction [3, p].
The circulationfield emerges as the starting vortex is formed. This is a dynamicprocess that becomes stable when the starting vortex is sweptdownstream and the flow conditions at the trailing edge havebecome smooth and stable. This happens when the flow on bothsides of the trailing edge have equal speeds and pressures.
Thisis known as the Kutta condition. The circulation flow field isequal in strength to the staring vortex and rotating in a clockwisedirection opposite to the starting vortex as shown by thestreamline plot in Figure 4. Figure 4. Circulation flow field. Aerodynamics theory tells us that the airfoil lift is equal tothe overall strength of the circulation flow field. The circulationflow field is the strongest near the surface of the airfoil anddecreases at farther distances from the airfoil.
When the non-lifting flow field and the circulation flow field are addedtogether, you get the final lifting-flow streamlines shown inFigure 5. The circulation flow field is obviously the primarycontributor to creating the upwash in front of the airfoil and thedownwash behind the airfoil. The circulation flow field causes alarge amount of air to flow on the top lee side of the airfoil.
Figure 5. Lifting flow about flat plate. The same amount of air is flowing between each pair of streamlines. The speed of the flow increases in areas where thestreamlines get closer together such as near the leading edge ofthe airfoil. Higher speeds mean lower pressures. Where thestreamlines get farther apart such as on the lower surface, theflow slows down and the pressures get higher.
Lower pressureson top and higher pressures on the bottom mean that the airfoilnow has lift. With the proper computer programs, we can prepareaccurate streamline drawings such as shown here to help usunderstand how the air flows around our thin sails orconventional airfoils.
Again, the green streamlines are thestagnation streamlines and divide the flow that goes on top leeside from the flow on the lower windward side. Note that thestreamline just above the airfoil passes very close to the leadingedge and then gets farther away as it nears the trailing edge. Thismeans that the flow will be the fastest right at the leading edgeand then slow down as it approaches the trailing edge. Theslowing down of the flow means the pressure is increasing.
Remember that in real flow with viscosity, too rapid of anincrease in pressure tends to make the boundary layer separate. Much of our sail shaping efforts are devoted to decreasing flowseparation on our sails. Note the distance between the two streamlines on each sideof the green stagnation streamline right at the trailing edge inFigure 5. The streamlines are equally spaced. This means wehave equal speeds and pressures on both sides at the trailing edgeso no new starting vortex will be formed.
The Kutta conditionhas been satisfied. At this stage in our analysis, we have ignored the sharp turnaround the leading edge of the simple flat plate airfoil. In the caseof a sail, we would bend the leading edge of the airfoil down intothe flow in order to avoid flow separation. For an airfoil on anairplane, we would give the airfoil some thickness with a roundleading edge and possibly give the airfoil some overall curvature camber.
The streamlines shown in Figures 2, 4, and 5 werecalculated using conformal transformations as devisedoriginally by Joukowski [4, p46]. The flow field around an airfoil is the combination oftwo flow fields : The flow field without lift shown in Figure 2,and the circulation field about the airfoil. This concept is at firstdifficult to understand but a simple analogy might help. If youride a bicycle in a crosswind, you feel only one wind on yourface, the vector combination of the true wind plus a wind vectorrepresenting the speed of the bicycle.
The same analogy appliesto the sailor as he motors at an angle to the true wind. He only feels one wind, but he knows that it is acombination of the true wind and the boatspeed wind Figure 6. Figure 6.
Arvel Gentry was a research specialist in transonic, supersonicand hypersonic vehicle aerodynamics at the McDonnell-Douglas company. He was also a successful ocean racing skipper and an amateur photographer. His seaborne pusruits included racing his own boats very successfully primarily in Southern California , plus he had extensive crewing experience on longer ocean racing yachts. He has authored numerous magazine articles on sailing aerodynamics and sailboat performance.