Origins Of Lift
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The Origins of Lift By Arvel Gentry January 2006 Abstract 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 twodimensional airfoils that leads to the generation of lift effects supply additional flow complications but are not December central to 1999 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 aloftThe 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 in Figure 1 Water channel photograph showing separated flowmy case being left drifting with the tidal currents when the winddies But how is this lifting force generated What is the 3 Fluid flow without viscosity Computed streamlines forfundamental explanation for the generation of lift the inviscid flow about a flat plate airfoil are shown in Figure 2 The flow is from left to right Green streamlines that actually 1 To understand the fundamentals of how lift is touch the surface are called stagnation streamlines They it is best to start with a simple twodimensional the flow that goes on the top of the airfoil from the lower surfaceairfoil This allows us to get at the real essence of the origins of flow In areas where the streamlines get closer together thelift effects are just additional complicating air speeds up and the pressure goes down Bernoullis and are not central to what really causes lift Although the Reference 1 page 226 Where the streamlines get fartherprimary purpose of this article is to help sailors understand how apart the air slows down and the pressure goes up If you rotatetheir sails work the concepts presented are exactly the same as this flow diagram 180 degrees you will see that it looks thefor conventional airfoils used on aircraft The emphasis here is same The pressure force on the top will therefore be the sameon understanding more of the details of the airflow than is taught as the pressure force on the bottom giving zero lift and zero dragto the beginning pilot The pilot has only minimal influence on This is known as DAlemberts paradox 2 p 225 A flat platethe shape of his wing control surfaces and flaps up or down airfoil is used here to illustrate this However regardless of theHowever the sailor has rather complete control of the shape of airfoil shape without viscosity the resulting lift and drag alwayshis airfoils and frequently makes use of two or more flexible sails turns out to be zero according to DAlemberts paradoxthat must be constantly shaped to work together for Sailing also sometimes requires knowledge of theairflow patterns around boats in close proximity 2 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 rapidlythe normally wellbehaved viscous boundary layer will separatefrom the surface This leaves an unsteady chaotic region thatdistorts the external flow decreasing lift and increasing drag seeFigure 1 Separation is a viscous effect Figure 2 Nonlifting flow around a flat plate Copyright C 2006 by Arvel Gentry All rights reserved 1 4 Formation of the starting vortex However air doeshave some viscosity As the wind is initially turned on or 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 393 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 The starting vortexwill eventually dissipate because of the fluids viscosity Figure 5 Lifting flow about flat plate lifting flow field and the circulation flow field are added together you get the final liftingflow streamlines shown in Figure 5 The circulation flow field is obviously the primary contributor to creating the upwash in front of the airfoil and the downwash behind the airfoil The circulation flow field causes a large amount of air to flow on the top lee side of the airfoil The same amount of air is flowing between each pair of streamlines The speed of the flow increases in areas where the Figure 3 Formation of the starting vortex streamlines get closer together such as near the leading edge of 5 The vortex theorems A set of vortex theorems by the airfoil Higher speeds mean lower pressures Where theHermann von Helmholtz and William Thomson Lord Kelvin streamlines get farther apart such as on the lower surface theplay key parts in aerodynamics 1 p523 The most important flow slows down and the pressures get higher Lower pressuresone in this situation is Thomsons circulation theorem The on top and higher pressures on the bottom mean that the of this theorem in the twodimensional airfoil case now has liftbasically means that as the starting vortex is created in the flow With the proper computer programs we can preparefield there must be another vortex equal in strength and opposite accurate streamline drawings such as shown here to help usin direction 3 p168169 understand how the air flows around our thin sails or In aerodynamics terminology this new vortex field is conventional airfoils Again the green streamlines are thecalled circulation and it surrounds the airfoil The circulation stagnation streamlines and divide the flow that goes on top leefield emerges as the starting vortex is formed This is a dynamic side from the flow on the lower windward side Note that theprocess that becomes stable when the starting vortex is swept streamline just above the airfoil passes very close to the and the flow conditions at the trailing edge have edge and then gets farther away as it nears the trailing edge Thisbecome smooth and stable This happens when the flow on both means that the flow will be the fastest right at the leading edgesides of the trailing edge have equal speeds and pressures This and then slow down as it approaches the trailing edge Theis known as the Kutta condition The circulation flow field is slowing down of the flow means the pressure is in strength to the staring vortex and rotating in a clockwise Remember that in real flow with viscosity too rapid of andirection opposite to the starting vortex as shown by the increase in pressure tends to make the boundary layer plot in Figure 4 Much of our sail shaping efforts are devoted to decreasing flow Aerodynamics theory tells us that the airfoil lift is equal to separation on our sailsthe overall strength of the circulation flow field The circulation Note the distance between the two streamlines on each sideflow field is the strongest near the surface of the airfoil and of the green stagnation streamline right at the trailing edge indecreases at farther distances from the airfoil When the non Figure 5 The streamlines are equally spaced This means we have equal speeds and pressures on both sides at the trailing edge so no new starting vortex will be formed The Kutta condition has been satisfied At this stage in our analysis we have ignored the sharp turn around the leading edge of the simple flat plate airfoil In the case of a sail we would bend the leading edge of the airfoil down into the flow in order to avoid flow separation For an airfoil on an airplane we would give the airfoil some thickness with a round leading edge and possibly give the airfoil some overall curvature camber The streamlines shown in Figures 2 4 and 5 were calculated using conformal as devised originally by Joukowski 4 p46 The calculations and display of streamlines in these figures were accomplished using Boeings Aero Grid and Paneling System AGPS see 5 6 Figures similar to 2 and 5 above may be found in a number of other Figure 4 Circulation flow field references 7 p174 3 p174 2 6 The flow field around an airfoil is the combination oftwo flow fields The flow field without lift shown in Figure 2and 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 the speed of the bicycle The same analogy appliesto the sailor as he motors at an angle to the true wind The newwind that he actually feels on his face is called the apparentwind He only feels one wind but he knows that it is acombination of the true wind and the boatspeed wind Figure 6 Figure 6 Apparent wind vectors Figure 8 Bathtub experiment showing circulation field Whidden and Michael Levitt 9 In this experiment a thin airfoil representing a sail is slowly pulled through a two inch layer of Figure 7 Circulation vector at a point in the flow field water in a bathtub see Figure 8 The airfoil should always be touching the bottom of the tub Pepper sprinkled on the water The twodimensional airfoil as discussed above also feels surface helps visualize the movement of the waterthe combination of two winds the nonlifting inviscid flow field At the start of movement we will see the formation of theplus the circulation flow field caused by the starting vortex as starting vortex near the right end of the tub It will be rotating in ashown in Figure 7 direction Halfway down the tub we can However the merging of two different flow fields is more observe how some of the water is adjusting to flow on the topcomplicated than the simple boat apparent wind problem Both side of the airfoil As we near the left end of the tub we quicklythe zerolift speed vectors and the circulation vectors vary in remove the airfoil from the water What we see left near the endspeeds and direction all over the flow fields around the airfoil of the tub is a circulation of flow in a clockwise direction This isThe example shown in Figure 7 is for a point on a streamline as it the circulation flow field It is realswings up toward the airfoil In this example the circulation In this experiment it is important to use a thin curved airfoilvector has only a small effect on the final speed vector but the at a relatively small angle of attack about 5 to 10 degrees Letflow direction is changed significantly by the circulation vector the water settle down with no movement before starting theat that point as it redirects the air to flow up and over the airfoil experiment Try to keep the speed of the airfoil constant from theAt a different location such as on top of the airfoil the circulation start until the end where it is quickly lifted out of the water Thevector would point in the aft direction and added to the non airfoil should still be moving as you lift it out of the water Eachlifting flow field gives a much higher final local wind speed The test run should take about 5 seconds A number of tests may becirculation flow field effects get smaller as you get farther away required so you can concentrate on a key part of the experimentfrom the airfoil as noted previously each time the starting vortex the upwash in front of the airfoil When the sails are raised and generating lift the actual the downwash behind the airfoil and the circulation flow fieldmeasured wind at the masthead that we loosely call the apparent You will have to wait between tests in order to let all waterwind is further complicated by the flow field movement stoparound the sails bound vortex and trailing vortex systems This experiment can be done with a conventional thick 7 The bathtub experiment The concept of circulation at airfoil to illustrate the starting vortex and the upwash flowfirst seems like mathematical trickery However the circulation However the view of the circulation itself will not be very goodflow field is real and there is an experiment that can be performed with the thick airfoil because of the inrush of water to fill theto visualize this whole process This is described in one of my volume space when the thick airfoil is removed To do thetechnical sailing papers A Review of Modern Sail Theory 8 experiment correctly use a thin rectangular piece of metal or partand also in the book The Art and Science of Sails by Tom of a milk carton for the airfoil 3 8 The generation of lift The resulting circulation flow a tube The superfluid was pulled throughfield causes some of the fluid that would normally go below the vertically A normal fluid would have spun theairfoil to be redirected to flow on the top side This is most wings like a tiny propeller but the out in front of the airfoil where the circulation vector is refused to cause twisting Instead it slipped frictionlessly past In their search for lighterin an upward direction Some of the fluid in front of the airfoil and lighter airfoils the experimenters finallystarts changing direction so that it will pass on the top side to the killed some local flies or so they claimed andlee side of a sail In aerodynamics we call this upwash the investigation became known as the flieswings On the top side of the airfoil the circulation vectors are in experimentthe same direction as the free stream direction therefore causing A quantum liquid may be pushing the definitionthe flow to speed up This increase in speed means lower of a real fluid a bit but I have thought thatpressures according to Bernoullis equation On the bottom this experiment might help illustrate the factside of the airfoil the circulation vector is opposite the general that a fluids friction properties are responsible for the generation of lift Without frictionflow direction so the fluid tends to be slowed down resulting in there would be no Kutta condition at the pressure The difference in pressure forces between edge of airfoils and therefore no drag and nothe top and bottom sides of an airfoil are what gives us lift lift Birds could not fly airplanes would not The concept of circulation not only helps explain how and fly and sailboats would not sailwhy the fluid flows about an airfoil as it does but it turns out tobe a key concept in correctly explaining the slot effect between From Russell J Donnellythe jib and the mainsail With two sails each airfoil has its own Sent Saturday November 06 1999 443 PMcirculation flow field The two circulations appose each other in To ArvelGentry Subject RE Quantum Fluidsthe slot between the sails and add to each other in the region to leeof the jib More air is caused to flow on the lee side of the jib You are right You might consult my bookAlso each airfoil has its own Kutta condition The flow at the Experimental Superfluidity for atrailing edge of the mainsail nears free stream conditions This is discussion of some of these matterscalled the dumping velocity The trailing edge of the jib I obtained Russell Donnellys book 11 and also studiedhowever is under the influence of the flow around the mainsail other references on superfluidity One very enjoyable book wasand therefore does not return to near free stream conditions Its by EL Reflections on Liquid Helium 12 ItKutta condition is satisfied at a higher dumping velocity thus was interesting that the introduction in this book was by nonereducing the possibility of flow separation This means that the other than the same Russell J Donnelly from the University offlow on the jib is improved by the presence of the mainsail The Oregonjib helps the mainsail by reducing the peak suction pressure near It can be argued that the formation of the starting vortex atthe mast so the sail will not stall These effects were first properly the sharp trailing edge of an airfoil is a result of the very highunderstood by visualizing the respective circulation flow fields velocities that would be necessary to flow around the airfoil andFor more details see The Aerodynamics of Sail Interaction 13 not due to viscosity However even an airfoil with a thick and 9 effects With our simple two rounded trailing edge to avoid the high local velocities still has adimensional airfoils if you draw flow streamlines starting way starting vortex and generates lift under the definite influence ofout in front of the airfoil and also extend them way downstream viscosity and flow separation In the case of objects with bluntyou would find that at the extremes they are at about the same trailing edges the resulting separated flow region may belevel The circulation flow field causes some of the fluid to flow thought of as a rough extension of the original airfoil and aup and around the airfoil and then return to the same condition starting vortex will be formed and circulation developed Thedownstream With wings the circulation and aerodynamic lift forces and most other contributors to the forceslift changes along the span and wing tip effects cause another set and moments on aircraft and other bodies moving through fluidsof vortex systems that greatly complicate the picture and creates do not exist in the absence of vortices McGrawHilla trailing downwash flow field Gliders have very long wings in Encyclopedia of Science Technology Onlineorder to minimize the 3D effects However 3D effects are not 11 Other theories Note that in this entire discussion I havecentral to understanding the basic origins of lift not once mentioned anything about 1 the air having farther to 10 Physical proof If the fluid has no viscosity our go on the top side of an airfoil or 2 Newtons laws of motion oraerodynamic theories indicate that we would have no lift and no 3 about getting lift by deflecting the air downwarddrag But is there any physical proof of that Yes There is a fluid In the first case there is nothing in aerodynamics requiringwith zero viscosity supercooled helium 10 I really got the top and bottom flows having to reach the trailing edge at theexcited when I learned of this for I had been saying for years that same time This idea is a completely erroneous explanation forwithout viscosity we would have no lift I did some research to lift The flow on top gets to the trailing edge long before the flowlearn more then contacted an expert in superfluid helium at the on the bottom because of the circulation flow of Oregon to get final verification As for Newton his laws are included within theTo Prof Russell J Donnelly aerodynamic theories discussedSent Thursday November 04 1999 1014 AM And on the deflecting the air downward idea that is aSubject Quantum Fluids effect In our 2D case the circulation flow I am a retired Boeing aerodynamics engineer I am field causes the air out in front of the airfoil to be directed for information on an experiment performeda number of years ago at Caltech called the around the airfoil and then back down to about the same level asflieswings experiment I learned of this in the it started out in front Yet due to viscous effects and resultingbook GENIUS the Life and Science of Richard circulation lift is generated Yes we cant fly with a twoFeynman by James Gleick page 302 dimensional wing and therefore are influenced by three In this experiment Tiny wings airfoils were dimensional effects caused by a complex trailing vortex systemattached to a thin quartz fiber hanging down through We can reduce these 3D effects by using very long wings such as 4on gliders or the around the world aircraft design by Bert RuttanOn an infinitely long wing the 3D effects are gone and we are back to looking at twodimensional If we can reduce the 3D effects then deflecting 1 Krishnamurty Karamcheti Principles of Idealfluidthe air downward is not essential to the origins of lift Aerodynamics 12 Multielement airfoils My first technical paper on of sails was published in 1971 The Aerodynamics 2 Richard Von Mises Theory of Flightof Sail Interaction 13 The primary objective of that paper wasfor the first time to properly describe how two sails the jib and 3 L Prandtl OG Tietjens Applied Hydro andthe main worked together It used circulation concepts to how the circulation flow fields about multiple sailsinteract causing even more air to flow on the lee side of the jib 4 Frederick O Smetana Introductory Aerodynamics andwhile at the same time helping prevent the mainsail from Hydrodynamics of Wings and Bodies A The old slot effect theory was dead That paper also Approachmade it clear that the old theories as to how slats and slots on theleading edge of aircraft wings worked were also wrong 5 DK Snepp RC Pomeroy A Geometry System for In 1974 AMO Smith the famous aerodynamicist at Aerodynamic Design AIAA Paper 872902 Sept 1987Douglas Aircraft and my boss at the time published his WrightBrothers Lecture HighLift Aerodynamics 14 AMOs paper 6 Arvel E Gentry Requirements for a 63 and subsequent sections describes how previous Programming Language for CFD Applications fromtheories were wrong They also provided more detail as to how Proceedings Software Systems for Surface Modeling andcirculation fields are important in properly understanding multi Grid Generation Workshop NASA Langley Research Centerelement airfoils and therefore how our sails work AMOs paper April 2832 1992is also in the book Legacy of a Gentle Genius The Life of AMOSmith edited by Tuncer Cebeci 15 7 L Prandtl OG Tietjens Fundamentals of Hydro and However old ideas are slow to die A recent book on how fly 16 contains a very old and incorrect explanationfor how slots and slats work The highpressure air below the 8 Arvel Gentry A Review of Modern Sail Theorywing is drawn up through the slot and flows over the top of the Proceedings of the 11th AIAA Symposium on thewing This energizes the boundary on top of the wing of Sailing September 12 1981 the authors of that book which includes a college professor have not seen AMOs 1974 many of these old incorrect slot effect 9 Tom Whidden Michael Levitt The Art and Science ofexplanations also still appear in the sailing literature when Sails Chapter 5discussing the flow about the jib and the mainsail combination 13 Conclusion Fluid viscosity is the fundamental reason 10 James Gleick Genius The Life and Science of Richardwhy birds and airplanes can fly and why sailboats are able to sail FeynmanFluid viscosity causes the formation of the starting vortex whichleads to the creation of the circulation flow field Understanding 11 EL Reflections on Liquid Heliumthe of the flow about our sails and keels isimportant in adjusting the airfoil shapes for maximum 12 Russell J Donnelly Experimental 13 Arvel Gentry The Aerodynamics of Sail Interaction Proceedings of the 3rd AIAA Symposium on the of Sailing November 20 1971 Redondo Beach California 14 AMO Smith Wright Brothers Lecture HighLift Aerodynamics AIAA Paper No 74939 AIAA 6th Aircraft Design Flight Test and Operations Meeting Los Angeles California August 1214 1974 15 Tuncer Cebeci Legacy of a Gentle Genius The Life of AMO Smith 16 David F Anderson Scott Eberhardt Understanding Flight 5
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