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How wings generate lift

  1. Jan 21, 2006 #1


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    One of my pet peaves is how many web sites and books use "hump" theory to explain lift: "the hump on top of a wing makes the air travel further to catch up to the air below and faster moving air has less pressure". For example, older versions of Microsoft Encarta used "hump" theory, until the 2002 and later versions. You can still find a lot of web sites that still refer to "hump" theory.

    I work with a group of programmers / engineers and I remember a co-worker with an instrument rating that believed in hump theory, as well as other co-workers, and it took a bit of convincing to get them to change their beliefs.

    It's a two step process.

    Step 1, explain how pressure differential is how air exerts it's weight inside a container. For example, putting 80 cubic feet of air into a scuba tank increases weight by 6 pounds, and it's the pressure difference versus alititude within the container that causes the net downwards force exactly equal to the weight of the air inside the container.

    Step 2. Replace 1 pound of air with 1 pound model aircraft. It's a closed system, so as long as the center of mass isn't accelerating vertically, the total weight of the system never changes, regardless of what the model is doing, as long as the center of mass of the model has no vertical component of acceleration. If the model is flying within the container, then it has to increase the pressure differential by just enough to create a net downwards force within the container equal to the models weight. Therefore the model lifting surfaces are air pumps creating a downwards flow of air that results in the net increase in pressure differential within the container.

    There's a third step to explain how a lighter than air balloon works inside a container:

    Step 3 - If the model is a helium baloon, then as the balloon is inflated within the container, it increases the pressure within the container, which increases the pressure differential, just like adding more air which would add more weight and increase the pressure within a container. If the balloon is hovering,then the net increase exactly compensates for the weight of the balloon. If the balloon is pushing against the top, the net increase in downforce due to pressure equals the weight of the model balloon plus the upwards force the balloon exerts on the top of the container. If the balloon is pushing against the bottom, net increase in downforce due to pressure equals the weight of the model balloon minus the downwards force the balloon exerts on the bottom of the container.
  2. jcsd
  3. Jan 22, 2006 #2
    The explanations of aerodynamic lift are often called the Bernoulli and Newtonian viewpoints. IMO they are both accurate, but describe the behavior from different perspectives. The problem comes from certain elaborations which people sometimes add.

    E.g, the Bernoulli explanation simply says pressure above the wing is lower and the wing is "sucked" upward. By contrast the Newtonian explanation says the wing deflects air downward, resulting in upward force via action/reaction.

    Certain elaborations on these are misleading or incorrect, such as the air must travel faster over the curved upper surface, hence that causes the lower pressure (it doesn't). Or that a curved upper surface wing at zero angle of attack doesn't displace air downward (it does).

    Pressure measurements clearly show a curved wing has lower pressure above it. However the curved wing also displaces air downward, even if at zero angle of attack.

    That air is displaced downward (even with a curved wing) is easily seen by a hovering helicopter. The main rotor blade is a curved wing just like an airplane. In fact it's called "rotary wing". Yet air is displaced downward equal in mass to the helicopter weight. The helicopter doesn't hover solely due to lower pressure above the rotating wing "sucking" it upward.

    It's true a flat wing (e.g, balsa wing glider) can fly. It's also true a curved upper surface wing can fly upside down. However a curved wing is far more efficient.

    The best way to reconcile these two viewpoints is they are both correct but describe different viewpoints. The curved upper surface does lower pressure above the wing, and this is one mechanism by which air is deflected downward. The plane (or helicopter) cannot fly without downward air deflection, but the efficiency of this is greatly enhanced by the curved upper surface wing.
  4. Jan 22, 2006 #3


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    My point isn't about Bernoulli vs Newtonian physics, it's specifically regarding "hump" theory. According to "Hump" theory, lift occurs with no downwards acceleration of air.

    I've found a typical example of "hump theory" on this web page, not only in the section decribing lift, but also in the nice picture provided where the air flow directly behind the wing is purely horizontal:


    A co-woker / pilot with instrument license, is an engineer, but also believed in hump theory apparently because the pilot school either taught hump theory or didn't explain how Bernoulli's equations apply to wing generating lift very well. The co-worked did have enough physics background that my closed container example, provided a bullet-proof argument that wings accelerate (deflect) air downwards.

    Microsoft Encarta used hump theory to explain lift until around 2002. Now it just states air is deflected downwards and avoids the details.

    Regarding Bernoulli versus Netwonian, both work fine, but all too often Bernolli based explanations ignore two facts: that most of the change in air flow is vertical, and that a wing changes the total energy of the air.

    From the Newtonian perspective, it's real simple, as a wing passes through the air, it accelerates the air. The total force is equal to the mass of each affected air molecule times it's average rate of acceleration ((integral of accelration versus time) / time). Basically, total force is mass times acceleration. This is broken down into two components by definition, lift is the component perpendicular to the direction of travel and drag is the component in the direction of travel.

    Bernoulli principle is all about conservation of energy, which for aerodynamic purposes, is the sum of pressure and kinetic energies (temperature effects are usually ignored). If the total energy of a mass of air is constant, then an increase in kinetic energy results in a decrease in pressure, and vice versa. A frame of reference is required for the kinetic energy component. The two obvious choices for frame of reference are the air itself or the wing.

    The issue with typical Bernoulli approaches can be described here. The assumption is that the wing is generating positive lift.

    Using an wing based reference, the air flowing over the top of a wing is flowing faster than the air below, so the air above has more kinetic energy than the air below and therfore has less pressure.

    Using an air based reference, the air above a lift is moving slower than the air below. Oops, this is just the opposite of the wing based reference case.

    This apparent conflict is due to 2 bad assumptions which are corrected here:

    1. Most of the change in kinetic energy of the air is due to vertical flow, not horizontal flow (assuming there's more lift than drag). The relative horizontal speed between air and wing is much higher than the vertical speed, but it's the change in speeds that matters (not the actual realtive speeds), and the the vertical component of change in speed is much larger than the horizontal component of change in speed.

    2. A wing peforms work on the air, changing the total energy of the air, so the energy isn't constant. With either air or wing reference, the component of of change in kinetic energy perpendicular to direction (lift) is the same. For the drag component, kinetic energy is reduced relative to the wing, but increased relative to air.
  5. Jan 22, 2006 #4


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    So given good explanations of lift and drag, how do you create an algorithm to predict lift and drag for a given air foil, wing size, and air speed? Apparently no-one done this yet. One of the issues is that laminar air flow detaches too easily from a wing, so you need turbulent air flow. Some hand launched (actually thrown like a discus with a lot of initial yaw correction at the point of release) glider models use "turbulators" on the upper wing surface to force turbulent air flow to improve glide ratios on them.

    Turbulent air flow is difficult to model. There are expensive programs that do a pretty good job in predicting an approximate amount of lift and track, but you end up needing actual testing to see if an air foil peforms as desired.

    For classic civilian aircraft, which basically haven't in decades, this isn't an issue. Also wing effiency is often sacrificed to simply the manufacturing process which is why you see nearly flat bottom air foils used on most civlian aircraft. There's a NACA airfoil that is cambered on top and bottom that could replace the wing on a Cessna 182, but even though it's more efficient, it's too expensive to manufacture.

    Other than NASA, probably the most effort in airfoild design goes into gliders, since improving lift to drag ratios is an important goal. Some high end cross country gliders have glide ratios around 60:1 at over 60 knots. You have to be careful with such gliders as the range between best glide ratio speed and never exceed speed isn't that large and even a mild dive can get you into trouble. Spoilers and flaps have to be deployed when descending to avoid excessive speeds. Radio control models go one step further by rasing both ailerons at the same time (this is called "crow" mode). Usually only the larger scale rc gliders have spoilers. Since the flaps at 90 degrees down and up ailerons provide sufficient braking for contest like models. A high end 3 meter wingspan rc glider gets around 20:1 glide ratio at around 20mph, but the relative speed range is large, never exceed speed is probably arond 140mph to 150mph (in some contests, the launch speeds peak out at around 100mph to 120mph), and the glide ratio at 40mph to 50mph is descent enough to bring a model back up wind after thermaling downwind for quite a while.
  6. Jan 22, 2006 #5


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    This is my preferred explantion of lift. It's known that most of the downwards acceleration of air for a typical wing occurs above the wing and not below. This is due to what I call the "void / circulation theory".

    Using a bus traveling along a highway as an example, when the bus passes through the air, the air separates and flow around the bus, but as the bus passes by, the air has to accelerate inwards and forwards to fill in the void left by the bus that has now passed by. The result is a significant low pressure area behind the bus. In addition, that low pressure area behind the bus ends up drawing some of the air away from the front of the bus, reducing the pressure at the front of the bus. The final result is that you end up with a slight increase in pressure at the front of the bus, but much larger decrease in pressure at the rear of the bus.

    Using a flat board at a small angle of attack as a wing, you have a similar situation. The air stream is divided at the front of the wing, but due to the low pressure area above the wing the seperation point is lowered a bit drawing away some of the air from below the center of the leading edge of the wing. This circulation reduces the amount of pressure change both above and below the wing, but the flow beneath the wing is affected more by this than the flow above the wing. There is also significant circulation around the wing tips, and some circulation at the trailing edge.

    After the initial separtation of airflow at the leading edge, the air already has some downwards component in it's velocity, so it needs less acceleration to get pushed out of the way of the bottom of the wing.

    Above the wing, you have a slighty upwards air flow that now has to change direction more in order to avoid separating from the wing and creating a void (nature abhors vacuums), but it simply can't change direction quickly enough due to momentum. The result is that air from even higher above (and a bit behind the leading edge of) the wing is drawn into the proccess and accelerated downwards.

    Continuing with a narrow airfoil design, to improve the effeciency of this flat board wing, all but the leading edge of the wing can be cambered downwards so that it's shape follows the natural path of the air as it's accelerated downwards, maintaining the rate of downwards acceleration for a longer time as the wing passes through the air. The leading edge needs to be cambered downwards as well to improve lift versus drag ratio, but this is a bit trickier to understand. Lowering the leading edge downwards to the natural seperation point of the airfoil would make sense, but the leading edge can be lowered beyond this point and still improve efficiency. I'm not sure if such air foils are intented to create a vortice below the wing, or if it's just more effiecient to slow down the air flow (relative to the wing) before it speeds back up as it accelerates towards the low pressure area above, but generally highly cambered narrow airfoils only work at relatively low air speeds.

    The next step is to thicken the wing so that the upper and lower surfaces can have different curves. The most obivous thing to do is to take a tear drop like form, which is a low drag form, and camber it a bit.

    Since it's cheaper and easier to build a flat bottom wing, these are popular, but the reality is that there is always a cambered (top and bottom curved surfaces) airfoil that will have better effeciency across a wider range of air speeds than any flat bottom air foil.

    Sometimes it's desired that inverted flight be just as efficient as normal flight, such as an aerobatic plane, or a model radio control aerobatic helicopter (I'm not aware of any full scale heli that can fly inverted). In these cases a symmetrical airfoil is used, with mirror image curves above and below, but there is still the goal of maximimizing lift versus drag at the targeted air speed range.
  7. Jan 22, 2006 #6


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    I see a lot of references that in the study of aerodynamics, that seem to imply lift can be accurately calculated on a wing given a size, air foil, air speed, and AOA (called polars), but I know that the guys that actually make air foils end up doing a lot of actual testing to confirm the properties of an air foil. Regarding air foils designed for gilders, the main parameters are a basic air foil shape, a thickness (thickness relative to wing chord), and a camber (number of degrees of curve in the center line of the wing). These guys are the experts, and actually do the work so I trust their information more so than I do most of the web sites I find.

    Some links with reference to a lot of the air foil designers:



    I fly radio control gliders so I recognize a few of these names since they make air foils for both full scale and models, but since there are more models than full-scale gliders, I assume most of the work is for high end contest models. The HQ airfoils by Dr. Helmut Quabeck are one example; he also makes actual rc contest gliders (most of this time is spent making the wing molds used to manufacture hollow modled composite wings). Selig / Donnivan teamed up to create the SD series of air foils, SD7037 is a popular air foil for rc gliders. Michael Selig / Ashok Gopalarathnam teamed up later to create the SA series of air foils. Rolf Girsberg made the RG airfoils, RG15 and the faster RG14.

    A link to airfoils:

    http://www.gliders.dk/choosing_airfoils.htm [Broken]

    Software links:




    A link to a generalized description of lift.

    http://www.aa.washington.edu/faculty/eberhardt/lift.htm [Broken]

    I like this one because it explains that although lift is often calculated from high speed circulation around a wing, that this circulation model may not actaully match reality, although it's good for estimating lift and drag, and continues on to provide a descent explanation. Another good feature is a least one description of air movement relative to the air as opposed to relative to the wing along with a diagram is included at this site.

    I'd be more inclined to believe all this stuff if the diagrams on forces on a wing generating lift were more consistent between the various web sites of aerodynamic experts, and if there wasn't a requirement for so much wind tunnel testing to confirm the properties of air foils. It's sort of like differential equations, you learn all sort of tricks to solve semi-simple equations, only to find that in the real world, most situations are complicated enough that you end up using numerical integration because the equations can't be resolved directly. A common example is ballistics, which is basically just aerodynamic and gravity, in the earliest days of computers, they fired motors, measured the results, and used computers to interpolate the in-between values (curve fittin) to generate angle versus distance tables.
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  8. Jan 22, 2006 #7


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    That bothers me a bit, too. This theory generates a lot of bad diagrams associated with the Bernoulii point of view. The bad diagrams show a wing that is generating lift without showing air being deflected downwards. It's probably mostly an oversight rather than an explicit theory (though one ocasionally finds it explicitly spelled out incorrectly).

    Ideally, diagrams would actually be correct for all three theories of lift, but they rarely are. Drawing the wingtip vortices on a diagram to illustrate the "circulation theory" would probably be hard to do, but it would be very nice if people illustrating wings generating lift would pay attention to the fact that they must displace air downwards when drawing their diagrams.
  9. Jan 22, 2006 #8


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    Personally, I think that the diagrams using the wing as the reference point in general are miss-leading as well, since you see a mostly horizontal flow, and not change in flow.

    I prefer diagrams and explantaions that use the air as a reference with the wing passing through. When using the air as a reference, the flow lines directly corrsepond to the accelerations that responsible for the aerodynamic reaction force (due to the acceleration) on an aircraft. You'd also see that most of the flow is downwards (lift) and a little bit forwards (drag).

    With most wing based reference flow diagrams, there's nothing obvious to inidcate that the air flow across the wing is accelerating and not constant. These diagrams may seem imply that the difference in horizontal flow is responsible for lift as opposed to downwards acceleration of air. One good execption to this are diagrams or pictures made from wind tunnels using timed pulses of multilple smoke streams, which let you see the changes in speed.

    The key facts here are that pressure isn't going to change unless there are associated accelerations, since pressure differentials cause accelerations of air; that most of that acceleration is directed downwards; and for a normal wing at a resonable AOA, most of that downwards acceleration occurs above a wing. This means that the pressure decreases more above a wing than it increases below the wing, which in turn means that more air is accelerated towards the low pressure area above the wing than accelerated away from the high pressure area below the wing. Unimpeded, air flows from all directions towards low pressure areas, and away in all directions from high pressure areas, but any flow from below the wing to above the wing is blocked by the presence of the wing (except for circulation around the edges), and the result is a net downwards acceleration (and some forwards).

    What I'd like to see is an explanation by an expert explaining the aerodynamics of a bus as well as a wing, using the same princples, since it's pretty obvious that after a bus passes by, it's dragging a lot of air with it (net forwards acceleration).
    Last edited: Jan 22, 2006
  10. May 25, 2006 #9
    wing lift theory

    Hi, just had to upset the flow over that upper surface by sticking in my oar and dredging up a much loved subjectof mine, wing lift theory.
    I consider the so called upper surface of a wing to be a trailing surface because it is never horizontal to the flight direction. If this condition creates a reduction in pressure enough to lift a jumbo then my brains should get sucked out my ears when I ride my motorcycle close behind a bus but strangely this does not even cause them to pop.
    Action and reaction from the lower surface gives us lift, the trailing upper surface has to be shaped such to allow the air to curve gently and not induce drag by having it accelerate round a sharp corner, try drawing a wing with this in mind and when you streamline the trailing back side or 'upper surface' as its called you will end up with the classic section of a wing.
    Flat plate wings generate good lift but due to the nature of the shape of the upper surface a nasty curl over develops right behind the wings L.E. This is not a problem at low AOA but as soon as we increase it the wing suddenly flips out. This horrid corner causes such a disturbance to the air that it robs all the energy from the wing and it is the consequent loss of speed which actualy causes the stall. Draw that wing section again and try to smooth it out. Now we see that the upper surface is shaped so the door does not close with a bang.
    I think I am tired argueing against myself with these ideas so I thought I may try this forum.

    Look forward to any relevant posts. Regards
  11. May 25, 2006 #10


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    Max take off weight of a 747-400 is 800,000 lbs, wing area is 838,800 in^2. Less than 1psi in pressure differential is required for flight. A bus at 70mph would probably produce much less of a pressure differential. A F22 max weight is 62,000 lbs, wing area is 120,672 in^2, not much more than .5 psi pressure differential. A Duo-Discus glider, max weight 1653lbs, wing area 25420 in^2, .065 psi pressure differential. Radio control models range from 4 oz / ft^2 (small gliders) to 30 oz / ft^2 (fast models) = .00174 -> .013 psi.

    I agree with this, basically a wing introduces a downwards and forwards moving void as it passes by a volume of air at the upper surface, and deflects air downwards and forwards from below. However, as previously mentioned, the low pressure above the wing draws air flow away from below the wing, lowering the seperation point, and reducing the air flow below a wing. At smaller angles of attack, most of the downwards acceleration of air occurs above a wing, even in the case of a flat board. At higher angles of attack, the deflection of air below a wing becomes more significant.
    Last edited: May 25, 2006
  12. May 25, 2006 #11
    wing lift theory

    What is the pressure reduction in PSI if one climbs to 1,000 feet ASL?

    Why does a photograph taken from one aircraft to another in level flight clearly show a nose high attitude of both compared to the horizon?

    Why does an aircraft require such high AOA to get airborne?

    Why do aircraft not smash into the runway on landing because of the venturie effect if the lower surface was indeed at negative AOA?

    Ever tried taking some thick cake mix and flying a knife through it?
    Lift remains the same I think even if a great big cavity forms above the so called top surface. Ground effect can be felt by flying the knife almost against the side. It's path is greased by a supporting film of cake mix and the AOA can be reduced but the lift remains. The efficiency goes up because the AOA required to sustain flight in ground effect is less and that parasitic trailing upper surface is levelled off.

    Your thoughts please oh learned one. Regards Bruce
  13. May 26, 2006 #12


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    The wing loading / pressure differential remains the same at all reasonable altitudes, until an aircraft is so high that the pull of gravity is reduced significantly.

    Don't need a photo, if an commercial airliner has a fairly full load, it's going to fly nose up enough to notice this as a passenger. It turns out that nose up at high altitude is more efficient with airliner with a heavy load by design. Apparently they get some additional lift from the body of the aircraft. Otherwise, the wings could be mounted with more built-in AOA to keep the fuselage level. On the other hand, a glider is normally slightly nose down most of the time, even if it's climbing because of an updraft.

    Mostly because an aircraft is heaviest at take off due to the weight of fuel, and the airspeed is relatively slow, and also it depends on how much the the leading and trailing edges are extended and camber increased. With some commercial airliners this almost doubles the coefficient of lift versus AOA, but with the cost of added drag. As the airliner picks up speed, the camber is reduces and the edges retracted back into the wing.

    Aircraft with swept back wings or delta wings will have a higher AOA because these wings can operate at higher AOA.

    At take off, aircraft are pitched up quite a bit in order to gain altitude quickly. This provides more safety margin in the case of an engine failure, and also reduces the noise to areas below the flight path.

    Because a wing is doing work on the air. It's increasing the pressure (and overall energy) of the air below the wing which causes the air to move outwards from under the aircraft in all directions. AOA and drag are reduced when in ground effects, for the same amount of lift.

    Also, go back to my original post about the model aircraft flying inside a closed box. The model increases pressure below it and reduces pressure above it. The increase in pressure differential within the box will create a net force differential that exactly equals the weight of the model, assuming that the model doesn't have any vertical component of acceleration. In an open unrestricted area, a wing accelerates air downwards, but in a closed or semi-closed area, like in the case of ground effects, a wing creates a pressure differential. As previously posted, it doesn't take a lot of pressure increase to keep a 747 in the air, less than 1psi, so even if a 747 flies over you at low altitude, you won't get crushed from the pressure, although I would recommend not getting sucked into the intake of one of those engines.

    Venturi like effect could be an issue if an high wing aircraft were to fly close to the roof of a large square tunnel, because of the low pressure area above the wings, that is drawing air inwards and accelerating it.

    A solid traveling through another solid is not the same as a solid traveling through a gas or a liquid. The solid isn't free to move to fill in voids. In the case of a cake, air would fill in the void.

    I hope this helps, information from the true experts can be found in the links I've posted prevoiusly.
    Last edited: May 26, 2006
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