Doug McLean | Common Misconceptions in Aerodynamics

well thank you for professor Martin for that introduction I'll try to live up to it I was going to say that I was happy to see so many of you decided to take a chance on a seminar was such an unusual title but then I heard that this is actually a class and that you pretty much have to be here I'd like to thank the department also for inviting me to come here one of the pluses for me for travelling anywhere these days actually believe it or not is getting to ride on an airplane I know for most people air travel is a chore but for me the actual airplane ride part of it has never gotten old yesterday for example flying from Seattle to here I had a window seat over the wing which I usually don't like because I can't see as much then but it did give me a chance to see again something that I've seen many times and that's the Sun shadow graph visualization of the shock on the upper surface of the wing I don't know how many of you have seen that but to me it's always an exciting thing to see that all of this stuff that I've seen in pressure distributions from the wind tunnel and from CFD actually happens in flight and you can actually see it with your own eyes that 737 that I wrote on yesterday actually reliably generated lift approximately equal to its weight all the way from Seattle to Detroit and lift is a subject that is still worth discussing and I'm going to get into that a bit later so as Professor Martin mentioned I've worked on a lot of different things in my professional career but throughout all of that I've had this kind of preoccupation with basic physics my undergraduate degree is in physics after all and so I've always had this interest and being able to explain things to myself in intuitive physical terms and to get things right that is not fall prey to misconceptions so that's what I picked from my topic to talk about today misconceptions in aerodynamics what I'm going to cover is a collection of erroneous ways of looking at aerodynamic flows these mostly have to do with the basic physics basically misinterpretations of the actual physics of a flow and for each of these cases I'm going to try to put my finger on what went wrong in each case and what you have to do to to set it right back when I had to send the abstract for this talk and I hadn't written the talk yet I promised I was going to identify some common threads well what I finally arrived at and in that regard isn't as much as I thought I think you'll see that the common threads are a little bit thin but I'll try to do that anyway and most of these examples are in my book although not not necessarily what the same spin is I'm going to put on them today so professor Martin's already made a shameless plug for the book it's it came out in December and it's now available at a bookseller near you so I won't belabor that any further why look at misconceptions by you might think that this is a sort of exercise in schadenfreude a-- a big word but fairly simple meaning in this case taking pleasure in chuckling at mistakes made by others and I'll have to admit that actually that is part of the fun of being an aerodynamicist but I'm going to maintain that there's a positive purpose as well and that is that if you really work through a rigorous debunking of some misconception about the physics you're almost sure to find that your own assumptions get challenged and if you work through all of that successfully it can't help but strengthen your understanding of the correct explanation when you finally get there so here's an outline of what I want to try to get at since these are mostly things having to do with misinterpretations of basic physics I'm going to take a few minutes in the beginning to actually talk about the physics that we're dealing with so we'll know what what the misconceptions are relative to and then I'm going to talk about Newton's third law and I'll actually dwell on that a bit more than I did in the book because I've become convinced lately that there are a lot of conventional explanations out there that pretty seriously abused Newton's third law lift explanations are of course with regard to finding misconceptions lifts as easy pickings setting the the misconceptions right is not quite so easy and I'll get into some of those issues another really rich vein of these things is is vorticity and the use of the biot-savart law and I'll cover a couple of examples of that we'll get into how lift impacts the motion of the atmosphere at large there are several misconceptions around in that regard and they're not necessarily just intuitive physics based they can actually there some of those actually result from misinterpretations of the mathematics I've got quite a long list here I'm proposing to also talk about boundary layer separation in 3d and some issues regarding pressure drag but as I say the list is a little long and if I if I make it through lift and momentum and 3d I can skip over the other ones if we have to in the interest of time so the basic physics this is continuum fluid mechanics I'm not talking about flight extreme altitudes or anything like that the fluid is of course not a continuous material but it flows as if it were one the velocity is a continuous vector field and that by itself tells us some pretty powerful things that constrain what the flow can and can't do their kinematic rules that have to be obeyed and so we have a lot that we can say about the flow even before we get to the dynamics the dynamics we're talking about are essentially what I call an AV ER Stokes equations or the navier-stokes equations if you went to private school and I take that turn to refer to the whole equation set not just the momentum equations some people apply it to just momentum the momentum equations essentially are enforcing Newton's second law F equals MA we use classical thermodynamics to impose a an energy balance conservation of energy and the energy equation these are all concepts from classical physics where we have mathematical equations of course but there's more to it than just equations the equations actually represent some clear cause-and-effect relationships we're not in the realm where we have quantum weirdness or any of that going on this is strictly classical physics applying F equals MA to a continuous material takes a little bit of extra mathematical manipulation to deal with the acceleration of the fluid you have not just the unsteady term the DV DT but you also have to deal with a term that we call a convective acceleration forces are transmitted between parcels in the fluid by what appear to be internal stresses these are really the result of momentum transport by molecular motions relative to the continuum flow but they have the same effects as if a continuous material were under internal stresses so this is the pressure and the viscous shear stress we formulate these terms in a way that automatically satisfies Newton's third law that is the formulation automatically enforces a condition that the force exchanged between two fluid parcels across their common boundary is equal and opposite these are of course surface forces we ordinarily neglect body forces gravity for example we simply omit from the equations assuming that that's going to be balanced by a hydrostatic pressure term that we also leave out and then the interaction of the fluid with other things like a solid surface requires an extra bit of physics that is not inherent in the equations themselves and for ordinary fluids and ordinary materials the way that interaction works it's very accurately approximated by a condition of no slip and note no jump in temperature so the consequences for all of this for flows around bodies fluid flows are not a hail of bullets like Newton assume they were when he tried to calculate lift the fluid has to deform and flow around obstacles rather than fly directly into them we have forces that are transmitted only by contact between adjacent fluid parcels and we have no action at a distance taking place and we'll see later that actually this action at a distance thing has been a source of some misunderstandings so we can move on to what I call stretching the stretching of Newton's third law my first example here is from the Smithsonian website and here they're talking about rocket propulsion and they're using the example of a toy balloon that's balloon that's been inflated and then it's been released fly around the room like a compressed air rocket and so I'll read it here that the air coming out the back of the balloon is the equal and opposite reaction to the thrust well not really not not in the sense that Newton intended when he put forth the third law for every action that there is an equal and opposite reaction when Newton used those words or what translates from the Latin into those words by action and reaction he just meant force the third law actually isn't about motion at all it's only about forces exchanged by bodies another example from a NASA website about propulsion systems and this one says that all thrust is generated through some application of Newton's third law of motion well again it's true that a fluid and a body exchange equal and opposite forces across their interface but just saying that doesn't really tell you anything about how that force actually comes about it doesn't say anything about how the fluid can actually exert a force on a body generating an aerodynamic force generally requires the fluid to be accelerated somehow and acceleration and force are the domain of Newton's second law not the third law so all of these were kind of examples of this kind of general conclusion I've reached and I I don't really come down as heavily on this in the book as I wish I had that Newton's third law by itself really isn't very helpful in those situations it's obeyed of course but it doesn't really tell us anything we have these sort of generic sorts of explanations that people put forward a rocket pushes on the gas and the gas pushes back therefore we have thrust wing pushes on the air the air pushes back and therefore we have lift an explanation of this kind really doesn't tell us anything about how the fluid generates the push to understand that we really have to get into the down-and-dirty sort of details of the fluid flow field accelerations out in the field and of course as I said before the key is Newton's second law not the third law so explaining a flow field phenomenon fully and correctly requires getting into some details of a continuum flow field this phenomenon that's very spread out not that easy to understand intuitively and and so needless to say this is been a source of a lot of misconceptions and misunderstandings through the years I think the poster problem for this or the poster yeah the poster child for this problem is is aerodynamic lift physical explanations of aerodynamic lift has been a problem for the last hundred years or more and I I just love this quote from my Boeing colleague Philippe's bull art this is from an email he sent to me a few years ago and I think it really hits the nail on the head about how difficult lift is to explain it also gets in a little bit of a of a dig at its some current popular culture to terminology and that is why is it that if you design airplanes you're called an engineer but if you design rockets you get to be called a scientist it doesn't seem quite fair to me anyway explaining explaining lift is more difficult than people realize it's generated a lot of misunderstandings a lot of and resulting controversy so start off I've been involved in some online discussions in recent years of this problem where people really get into the details and and some of the arguments get pretty heated but people really do get into the details of this problem and try to work it through and then I've seen it happen several times where someone new will join the conversation and say wait a minute why is everybody making such a complicated deal out of this lift is just a pressure difference or lift is just Newton's third law why are you making it so complicated well we're making it complicated because these explanations are simply inadequate they don't explain much of anything the most popular explanations get into a little more detail and they tend to fall into one of two categories the Bernoulli based explanations and the explanations based on downward turning of the flow so I'll go into those a little bit to show what their shortcomings are and the Bernoulli based explanations we say that faster flow over the upper surface results in lower pressure and therefore you have lifts so you need to have that higher speed over the upper surface to get where you want to go you can't use the lower pressure as the reason for the higher speed because that seems like it's roundabout so you have to come up with a reason for the faster flow and two main approaches to that the longer path length and equal transit time which is really bad and the stream tube pinching and conservation of mass which is not quite as bad but still not good the longer path length and equal transit time first the transit time isn't reason tree aliy well-defined in a viscous flow we have a no slip condition or we assume a no slip condition at the surface so if you look at fluid parcels traversing the airfoil closer and closer to the surface the transit time goes to infinity the closer you look even if you want to look at a potential flow if you have an airfoil with a rounded leading edge and a stagnation point you have the same problem the closer you look to the surface the larger the transit time is okay you can get around that problem you can gloss it over by saying well I'm going to follow fluid parcels that traverse the airfoil a little ways off say outside the viscous boundary layer so let's say we get around it that way the typical difference in path length between the two surfaces is typically an order of magnitude roughly an order of magnitude too small to explain the actual observed lift so the if you take the path difference in equal transit time as a theory of sorts the theory misses the mark pretty badly and the problem is that the equal transit time assumption is simply wrong if you look at these fluid parcels that start together on on the attachment stream line they finish permanently shifted from each other that is the parcel what traverse the upper surface gets there in a short significantly shorter time stream tube pinching starts with the statement that the stream tubes that pass over the upper surface are pinched more than those that pass over the lower surface therefore the velocity is higher through conservation of mass and therefore with Bernoulli we have lower pressure now we have lift the common problem with all of this is that the pinching is just assumed or it's justified by pointing you to some smoke flow visualization pictures or CFD or something but I haven't come across one that really explains why the stream tubes pinch at all let alone why they pinch more over the upper surface than they do over the lower surface I go through a little exercise in the book where I show that there are kinematically possible flow patterns that don't have any pinching at all so if you want to explain why pinching happens you have to get into the dynamics which this kind of explanation typically doesn't do and my final complaint about this is that mass conservation really isn't a very direct physical reason for any acceleration to happen in the flow field Newton's second law says that an acceleration requires a force so if something accelerates and you want to explain to me why tell me what the force is these explanations don't do that so common fault of these Bernoulli based explanations is that they they don't use the real direct reason for the higher speed which is the lower pressure because they want to explain the lower pressure so they end up going to indirect reasons like stream tube pinching or incorrect reasons like equal transit time and implying that the causation between speed and pressure is a one-way street that is that the speed results in lower pressure is a misconception so the downward turning based explanations you just say that the flow passing by the airfoil gets deflected downward through a combination of airfoil shape and angle of attack turning the air downward is an acceleration and to produce an acceleration you have to exert a force so you say the airfoil must push it down on the air now that's a Newton's second law thing and then of course with Newton's third law you say the air has to push up on the airfoil and you have lift some of these explanations point out that the downward turning action is contributed to significantly by the fact that the air over the upper surface follows the convex surface and actually gets directed downward as it goes over the F part of the airfoil and then they suppose that in order for air to follow a convex curve there has to be something like a kowambe effect or some viscous effect involved okay most of these things deal only with the interaction that takes place at the airfoil surface that is the airfoil pushed on the air and the air pushed back they don't satisfactorily explain how downward turning gets imparted to a lot more flow than the airfoil actually touched and the fact is that viscosity and the cuando effect are not needed flows follow convex surfaces just fine without either of those effects I've also seen it put forward sometimes that actually only a 3d wing turns the flow downward with all that downwash between between the trailing vortices and that in a 2d airfoil flow there really isn't any net downward turning because the vertical velocities involved go to zero at large distances from the airfoil so you get far enough away from the airfoil there hasn't been any downward turning well that's only true when you look at the at the velocities locally yes they do go to zero at large distances but the distribution of vertical velocities also gets much more spread out and the integrated effect that is the integrated fluxes of momentum are actually constant and don't go to zero so in an integrated sense there is actually downward turning in 2d if you look at a control volume like this with two vertical faces you find that with an airfoil circulation around it there are fluxes ahead of the airfoil and behind that is a flux of upwash ahead of the airfoil a flux of downwash behind that account for half the lift each and then you can say well the airfoil is is what impart of the difference between those two and that accounts for all of the lift and this is a result we're going to see later also applies in 3d okay having two explanations Bernoulli based on downward turning base that sounds so different has really been a problem for a lot of people how can the same phenomenon be explained by two such different sounding things and you you get some people who say that only one or the other can be right you've got other people to say that both are right and they're just equivalent ways of looking at the same thing and which one you prefer is just a matter of taste actually each one of these is partly right but incomplete and my position is that a complete explanation Lee needs to look at both the bernoulli explanation deals with the speed of the flow outside the boundary layer with the surface pressure so that's all very near-field stuff the Newton explanation deals with the flow direction over a much deeper swath of the flow and is more sort of far field stuff these are not contradictory they're really complementary aspects of the same phenomenon one single phenomenon and I don't think it's really fair to say that they're equivalent ways of looking at the same thing they're ways of looking at separate parts of the same thing so to get it right as I said I think a correct complete explanation really needs to have elements of both the Bernoulli approach in the downward turning approach but it also needs to emphasize some other things that are either glossed over or completely neglected in the in the conventional explanations for one thing I think we need to put a lot more emphasis on the fact that the fluid is flowing as a continuous material and that therefore the velocity and the pressure are affected over a very wide area around the airfoil so we have of course the downward turning and and that being imparted to a deep swath of flow we also have the pressure disturbance spread out well into the field the pressure difference between the upper surface and the lower surface is not confined just to a region very close to this to the surface it's spread out over quite an area the flow field we have the sort of diffuse cloud of low pressure over the upper surface diffuse cloud of higher pressure over under the lower surface and these clouds of pressure difference of course involve gradients in both directions we have significant pressure gradients in both the stream-wise end to cross flow directions so we really have to be talking about both a Bernoulli and a Newton approach to explaining this or Newton in a vector sense the other way to look at it would be we're talking about trying to explain the interaction between the velocity field and the pressure field it's embodied in the Euler equations this is really more an oil or explanation of lift that I think we have to go to another one the cause and effect relationship between velocity field and the pressure field is not a one-way street it's a reciprocal or mutual interaction of course we have the pressure field being the direct cause of all the accelerations in the field at least outside the boundary layer this is Newton's second law and this is the little bit more difficult part to to grasp intuitively and to explain but the pressure field is sustained by the fluids inertia and the acceleration so this this piece of it because it's harder to grasp intuitively is kind of the weak link it's the part that in the explanation that I have in my book is the part I'm least satisfied with it's the weak link mathematically speaking we can say of course that the pressure rises as part of the solution to a set of field PDEs with multiple variables physically speaking we know that motion around an obstacle is non uniform it requires a non uniform pressure field a pressure pressure gradient can exist only if something pushes back and that's a statement that you won't see any in any fluids book and I've had I've had people push back on me on this one but it really is just a consequence of Newton's third law if a pressure gradient exists it's exerting a net course on any fluid parcel that'sthat's submerged in it and Newton's third law says that that push that net force on fluid parcel has to be opposed by some equal and opposite reaction that pushback is provided by the inertia of the fluid and the fact that it's being accelerated okay in any of you read the book and look at how I go through this in the book I'd appreciate it if you'd give me feedback on how to strengthen that part of the explanation because as I say I think that's its weakest link right now so I've gone through a quick outline of what I think are the ingredients in explaining lift the actual embodiment of this in a and an explanation is in the book and I urge you to look at that ok another rich vein of misunderstanding is the vorticity field and the biot-savart law the biot-savart law is of course just a mathematical equation it's essentially a bit of a vector calculus it doesn't have any physics in it just arises from the fact that the velocity field is a continuous vector field if we look at the vorticity vector Omega which is just the curl of the velocity we can use this integral formula to calculate at least one part of the of the velocity field so here's the situation we calculate the velocity at some point x XYZ by in ik by doing a volume integral over the entire space surrounding it basically the volume integral of Omega cross R over R cubed this is the form that's valid for vorticity distributed throughout a volume there are a lot of situations where the vorticity is fairly concentrated like in vortex sheets or vortex filaments and there are forms idealized forms of the formula that apply to those situations where you assume that those concentrations are very thin you can reduce the triple integral to a single integral for a vortex filament okay the difficulty arises here because here we have a formula that's very useful for computation and for theorizing about wings and so on but the vorticity vector is the input the velocity is the output and it leads to the idea that the vorticity is somehow causing the velocity to do stuff elsewhere and the analogy with electromagnetics doesn't help essentially in electromagnetics we have the same formula at least in the steady state where the electric current here is the input and the magnetic field there is the output and that really is caused and called induction and that really is a physical action at a distance kind of cause-and-effect relationship and so we carry that thinking over into aerodynamics and we even say that the vorticity induces the velocity of course this is wrong it's implying that the vorticity is causing things remotely which it's not doing okay the example a first example I'd like to use where this is when people astray is dragged due to lift and 3d here's a cartoon of the flow field that a wing causes it as it lifting wing as it passes through the atmosphere we have this jet this is illustrated in terms of velocity vectors in a cross plane so we have this general pattern of circulation around the wingtips downwash between the tips this pattern gets pretty well-established at the station of the wing itself and then it tends to persist over very long distances downstream from there it's associated with a shedding of a vortex sheet from the trailing edge of the wing and a rolling up of that vortex sheet into discrete vortex cores downstream and that's the part that really leads people astray because it's really convenient and a lot of the theories make use of this it's really convenient to look at that vorticity distribution and use it through biot-savart to calculate what this flow field does and that's what we do in a lot of the theory and it leads people to think that this flow field is a result of that vorticity that gets shed whereas the reality is that the vorticity is there kind of a trace of what's happening it's not a cause so people get the idea that this flow field is caused by the vorticity distribution this downwash across the span of the wing of course results in a tilting back of the lift vector and results in what we call drag due to lift and so we end up even calling it induced drag which is I think a misnomer and people get the idea that induced drag is caused by the wake for tissa T and that leads further to the idea you know people with inventive minds get going with this and they think well if I could just eliminate some of that vorticity catch it right after it was shed so that it doesn't get into the far field I can reduce the amount of the vorticity that I have to integrate over in biot-savart I can decrease the downwash at the wing and I can reduce the induced drag so the vortex sheets that come from the trailing edge and the resulting rolled-up vortex cores are relatively compact structures and this further leads people to think that a device that would eliminate that vorticity doesn't have to be very big it can just operate on a little bit of the flow and I can have a big effect on the flow that's what for biot-savart tells me I should be able to do so I there are numerous inventions that have been proposed to accomplish this and when I wrote the book I was going to use drawings from a lot of patents to illustrate it but of course I would have to get permission from the inventors to use those drawings and the first one I contacted for some reason was reluctant to give me permission to use it in a book that was going to say this invention was worthless so I made a generic cartoon there aren't actually any devices that look exactly like this but this is sort of the basic idea on which they all operate the idea is you you try to catch some of that vertical flow before it gets into the far field and eliminate the vorticity from it so here's one way you could do that according to the thinking of inventors of this sort of thing you have the sort of thing that looks like a fan cow it captures a stream of fairly not a very large stream tube this is a plan view of the wingtip you capture a stream tube that contains a lot of the shed vorticity because it is very heavily weighted toward the wingtip you capture it into this device and put it through a flow straightener and take the vorticity out of it and now you've greatly reduced the strength of the trailing vortices and you integrate over no trailing vortex instead of a lot of trailing vortex and you get almost no induced drag problem is it doesn't work there are two levels of how you should look at why it doesn't work the first is the causation thing that I've already talked about right vorticity doesn't cause velocities to happen elsewhere so you shouldn't be able to control velocity way out there say Way and board on the wing by tinkering with the vorticity over here but of course this raises the question you know if you could eliminate the vorticity from that stream tube and biot-savart is true which it is why isn't the whole flow field changed as a result the problem is with this word if in actuality you can't actually eliminate the net vorticity it's it's a matter of kinematics actually to eliminate it you'd be violating some kinematic laws you can't eliminate the net vorticity locally without changing that global flow field first I go back look at this device or go back even further and look at this pattern right if you haven't first changed this global flow pattern then there's still circulation around the region where you're taking out that vorticity the circulation is still there you can eliminate all the vorticity from the stream tube that goes through the device but it's a kinematic requirement that matching vorticity is going to get generated on the in the external boundary layers on this device and that you haven't eliminated the net vorticity you've just kind of Moo moved it around me but you've eliminated it from a central core it's reestablished itself in an annual or tube around that core and it's still there okay so conclusion if you want to reduce induced drag you have to you have to do something to that large spread out global flow field which means you have to do something about the force field that produced it which is the pressure field and to do that you've got to change the span-wise distribution of lift on the wing and some major way if you want to have a major impact on induced drag okay another one having to do with induced drag and this one also has to do with propellers this is from a 1984 AI double a meeting paper analyzing the effect of mounting a propeller at a wingtip for purposes of reducing induced drag so this is a drawing that illustrates only the effect of the propeller here on the left side presumably the propeller on the right side would produce the same effect they'd add together and you'd get double so a propeller slipstream as a as a stream tube in which the flow is all swirling it's all rotating in one direction consistent with the direction of rotation of the propeller and it's kind of intuitively obvious that a stream tube with lots of swirl and it also must have net vorticity in it net axial vorticity how could it not so the author of this paper used a solid body rotation model for the for the velocity distribution of the propeller slipstream and that's not a very good one but it's not outrageous either it's a lot of the pioneers who develop theories of propeller flows actually used that model so a solid body rotation has a net vorticity to it if it has a net vorticity in the stream tube then there has to be velocity induced outside that stream tube looking like this so you get up wash if you've got the right propeller rotation direction you've got up wash induced across the whole span of this wing and a reduction in induced drag the problem with this is that the assumption of nonzero circulation and a propeller slipstream violates Stokes's theorem you can't do that and to see that you're going to have to follow my pointer here imagine a closed contour encircling this this whole propulsion stream - the whole propeller slipstream somewhere downstream of the station of the propeller and then attach a capping surface to that closed contour so the capping surface is like a balloon it's been blown out and and bulges out ahead of the propeller everywhere so the only vorticity in this flow field is in is in the slipstream but I've put a capping surface out here that doesn't cut any of that in other words there's zero flux of vorticity through that capping surface now Stokes's theorem says if there's no flux of vorticity through a capping surface and the circulation around the closed contour that bounds that surface has to be zero a propeller slipstream cannot produce any net circulation so this paper ended with a little summary of a wind tunnel test that was done to evaluate this idea it said that there was a drag reduction observed but it was considerably smaller than what this model predicted so that's good just to justify the idea that this swirling stream to behind a propeller can actually have zero net circulation I've plotted some velocity results from Mark trellis Q prop code these are circumference circumferentially averaged for an optimally loaded propeller on and on but here's the circumferential velocity you can see it is indeed all in one direction the the axial vorticity and a slender stream tube like this is dominated by this term here that 1 over R partial with respect to R term and I've plotted that here and I've waited it by R so that you can eyeball integrate it it's an axisymmetric integration after all and I think you can see that yeah the the integral there is zero as Stokes's theorem says it has to be okay let's move on I'm kind of getting close to running out of time here let's talk about the atmosphere at large and the manifestations of rift in that atmosphere the first part of this I'd like to talk about is what I call at refs plane slice that is a slice of that mysterion the airplane is generating lift L it spent time T flying through that slice so it imparted mechanical impulse LT to that slice and you'd think well there has to be a change in momentum there had better be some downward momentum in this slice corresponding to LT proportional to L anyway so the classical approach to this and this is done in several of the classical books is to use the vorticity distribution the weight and the bound vertex on the wing and biot-savart and infer what the velocity field is and do the integrals so the classical argument is well if I wait long enough the airplane it's far away and I can neglect any contribution from the bound vortex at the wing all I have to integrate over is the trailing vortex pair and this is done in several the classical books Thwaites this book is one of them and if you do that under grill like this this is the integral of the vertical velocity W and you integrate vertically first and then span-wise you get this answer it's proportional to L it's exactly what everybody expected and so nobody questioned it and they published it in their books now I my Boeing colleague Larry Wigton is a mathematician by training and he was going through this classical theory back in the 1980s and Larry's the kind of guy who doesn't just take something for granted he goes and he does all different derivations himself so he repeated the integration but he changed the order of integration and he got zero now if I did that I would just assume I made a mistake and I'd go on but Larry isn't like that if you get a different value for a double integral when you change the order of integration that says the integral doesn't exist and in fact Larry applied other tests of integrity and sure enough that functions not integral the function W just doesn't die off fast enough at large distance for the integral to exist so Larry said well alright no airplanes that were flown for an infinite length of time so I'll take the expression for trailing vortices of finite length that integral exists the values independent of the order and the answer is zero so the flow field associated with this trailing vortex pair doesn't contain any net downward momentum so where is the downward momentum that you'd think has to be there so Larry went back and reevaluated the assumptions that you can ignore the bound vortex he did those integrals and he found well there's an integral of upwash ahead of the airplane corresponding to half the left and there's an integral of downwash behind the airplane corresponding to the other half and this is exactly the same result that applied in in 2d that we all saw before and it's just a simple matter of doing doing the integrals to show that this applies whether the flow is 2d or 3d let's move on and look at momentum accumulated in the atmosphere seems like if an airplane has been in the air for time T lifting with lift L there should be downward momentum in the atmosphere equal to Lt so Larry set that problem up you model the vortex system as a rectangular loop a bound vortex two trailing vortices a starting vortex the atmosphere is infinite the integral doesn't exist the the downward momentum in the atmosphere is indeterminate well Larry said well okay nobody's ever flown in an infinite atmosphere there's always a ground plane so you put the ground plane and you do it for a semi infinite atmosphere and the integral exists the answer is zero there is no down momentum accumulated in the atmosphere well that results consistent with a classical picture from parental and teachings book that shows the pressure being reacted as an overpressure on the ground if you had it both as an overpressure on the ground and as momentum in the atmosphere that would be double bookkeeping it's also consistent with conservation of mass as Lanchester pointed out in his 1907 book so this is the figure from pram limitations you get this sort of bell-shaped distribution of overpressure on the ground plane and actually this is just kind of a special case of some control volume analysis that you can do for what I call pancake control volumes that is control volumes that are small vertically compared to their horizontal extent for that kind of control volume if you do the free air case where the ground plane is far away compared with any dimension of the box you get an overpressure on the on the below the airplane corresponding to half the lift you get a deficit above the airplane that accounts for the other half if you put the ground plane at the bottom of the box this is getting it's essentially the parental and teaching situation it doubles the disturbance on the ground plane and it corresponds to half the lift the disturbance above the airplane doesn't go away in this case locally but the integral does and it it's surprising it looks a little bit like it does in the free air case in the center but remember this is an axisymmetric integration and what happens far away matters a lot and there is a slight positive pressure distribution at large radius that actually drives this integral to zero okay I think I've just about talked myself out of time here I was going to talk about the problem with using the zero C F criterion for deciding where separation happens in 3d and proposing that you can't use a local criterion like this in 3d flows it only works in 2d and I was going to talk about it through looking at flow patterns like this the conclusion is that finding separation and 3d actually requires looking at the global flow pattern there is no single local criterion you can apply you actually have to look at the goal at a map of the global global flow pattern and and look at what's happening there and I talked about a region of origin concept and how separation is a line of near discontinuity in the region of origin of the skin friction lines if you want to get a more detailed description of that idea you'll have to look in the book and with that I'm going to open it up for questions because I've used up all the time thank you Aviation is the largest manufacturing export of the United States and generates about 3% of the world's GDP so it's economically important and since now I work

Channel: University of Michigan Engineering

Views: 474,759

Keywords: Umich, AERO, Aerodynamics (Field Of Study), doug mclean, boeing technical fellow, understanding aerodynamics, University Of Michigan (College/University), physics, misconceptions, aerodynamics, lecture on demand, lectures on demand

Id: QKCK4lJLQHU

Length: 48min 25sec (2905 seconds)

Published: Mon Oct 21 2013

Reddit Comments

[u/setheory]

I love this video! I bought his book!

I'm a non-engineer, math major/physics teacher with a strong interest in aerodynamics! I'm finding it challenging, but very interesting. As i self-teach myself more about aerodynamics I can see how many misconceptions, and false paths, and even multiple ways to view things exist in the field.

Also do a search for McLean's paper on wingtip devices, another fantastic read! I really wonder what he'd think of Prandtl wing "bell curve" lift distributions.