Lift (force) - Knowledge

2284:"The lift on the body is simple...it's the reaction of the solid body to the turning of a moving fluid...Now why does the fluid turn the way that it does? That's where the complexity enters in because we are dealing with a fluid. ...The cause for the flow turning is the simultaneous conservation of mass, momentum (both linear and angular), and energy by the fluid. And it's confusing for a fluid because the mass can move and redistribute itself (unlike a solid), but can only do so in ways that conserve momentum (mass times velocity) and energy (mass times velocity squared)... A change in velocity in one direction can cause a change in velocity in a perpendicular direction in a fluid, which doesn't occur in solid mechanics... So exactly describing how the flow turns is a complex problem; too complex for most people to visualize. So we make up simplified "models". And when we simplify, we leave something out. So the model is flawed. Most of the arguments about lift generation come down to people finding the flaws in the various models, and so the arguments are usually very legitimate." Tom Benson of NASA's Glenn Research Center in an interview with AlphaTrainer.Com 1999:" above. The pressure differences associated with this field die off gradually, becoming very small at large distances, but never disappearing altogether. Below the airplane, the pressure field persists as a positive pressure disturbance that reaches the ground, forming a pattern of slightly-higher-than-ambient pressure on the ground, as shown on the right. Although the pressure differences are very small far below the airplane, they are spread over a wide area and add up to a substantial force. For steady, level flight, the integrated force due to the pressure differences is equal to the total aerodynamic lift of the airplane and to the airplane's weight. According to Newton's third law, this pressure force exerted on the ground by the air is matched by an equal-and-opposite upward force exerted on the air by the ground, which offsets all of the downward force exerted on the air by the airplane. The net force due to the lift, acting on the atmosphere as a whole, is therefore zero, and thus there is no integrated accumulation of vertical momentum in the atmosphere, as was noted by Lanchester early in the development of modern aerodynamics. 882:. When an airfoil produces lift, the flow ahead of the airfoil is deflected upward, the flow above and below the airfoil is deflected downward leaving the air far behind the airfoil in the same state as the oncoming flow far ahead. The flow above the upper surface is sped up, while the flow below the airfoil is slowed down. Together with the upward deflection of air in front and the downward deflection of the air immediately behind, this establishes a net circulatory component of the flow. The downward deflection and the changes in flow speed are pronounced and extend over a wide area, as can be seen in the flow animation on the right. These differences in the direction and speed of the flow are greatest close to the airfoil and decrease gradually far above and below. All of these features of the velocity field also appear in theoretical models for lifting flows. 921:, a force causes air to accelerate in the direction of the force. Thus the vertical arrows in the accompanying pressure field diagram indicate that air above and below the airfoil is accelerated, or turned downward, and that the non-uniform pressure is thus the cause of the downward deflection of the flow visible in the flow animation. To produce this downward turning, the airfoil must have a positive angle of attack or have sufficient positive camber. Note that the downward turning of the flow over the upper surface is the result of the air being pushed downward by higher pressure above it than below it. Some explanations that refer to the "Coandă effect" suggest that viscosity plays a key role in the downward turning, but this is false. (see above under " 1975:

the fluxes of vertical momentum through the front and back are negligible, and the lift is accounted for entirely by the integrated pressure differences on the top and bottom. For a square or circle, the momentum fluxes and pressure differences account for half the lift each. For a vertical rectangle that is much taller than it is wide, the unbalanced pressure forces on the top and bottom are negligible, and lift is accounted for entirely by momentum fluxes, with a flux of upward momentum that enters the control volume through the front accounting for half the lift, and a flux of downward momentum that exits the control volume through the back accounting for the other half.

721: 1708:, a curve or line from some point on the airfoil surface out to infinite distance, and to allow a jump in the value of the potential across the cut. The jump in the potential imposes circulation in the flow equal to the potential jump and thus allows nonzero circulation to be represented. However, the potential jump is a free parameter that is not determined by the potential equation or the other boundary conditions, and the solution is thus indeterminate. A potential-flow solution exists for any value of the circulation and any value of the lift. One way to resolve this indeterminacy is to impose the 941:

depends on the air's motion. The relationship is thus a mutual, or reciprocal, interaction: Air flow changes speed or direction in response to pressure differences, and the pressure differences are sustained by the air's resistance to changing speed or direction. A pressure difference can exist only if something is there for it to push against. In aerodynamic flow, the pressure difference pushes against the air's inertia, as the air is accelerated by the pressure difference. This is why the air's mass is part of the calculation, and why lift depends on air density.

837:", there are two main popular explanations: one based on downward deflection of the flow (Newton's laws), and one based on pressure differences accompanied by changes in flow speed (Bernoulli's principle). Either of these, by itself, correctly identifies some aspects of the lifting flow but leaves other important aspects of the phenomenon unexplained. A more comprehensive explanation involves both downward deflection and pressure differences (including changes in flow speed associated with the pressure differences), and requires looking at the flow in more detail. 2990:"The airfoil of the airplane wing, according to the textbook explanation that is more or less standard in the United States, has a special shape with more curvature on top than on the bottom; consequently, the air must travel farther over the top surface than over the bottom surface. Because the air must make the trip over the top and bottom surfaces in the same elapsed time ..., the velocity over the top surface will be greater than over the bottom. According to Bernoulli's theorem, this velocity difference produces a pressure difference which is lift." 2703:"The pressure reaches its minimum value around 5 to 15% chord after the leading edge. As a result, about half of the lift is generated in the first 1/4 chord region of the airfoil. Looking at all three angles of attack, we observe a similar pressure change after the leading edge. Additionally, in all three cases, the upper surface contributes more lift than the lower surface. As a result, it is critical to maintain a clean and rigid surface on the top of the wing. This is why most airplanes are cleared of any objects on the top of the wing." 381: 1603:

boundary layer next to the airfoil surface, at least over the aft portion of the airfoil. Predicting lift by solving the NS equations in their raw form would require the calculations to resolve the details of the turbulence, down to the smallest eddy. This is not yet possible, even on the most powerful computer. So in principle the NS equations provide a complete and very accurate theory of lift, but practical prediction of lift requires that the effects of turbulence be modeled in the RANS equations rather than computed directly.

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the pressure distributions around the airfoil sections change accordingly in the spanwise direction. Pressure distributions in planes perpendicular to the flight direction tend to look like the illustration at right. This spanwise-varying pressure distribution is sustained by a mutual interaction with the velocity field. Flow below the wing is accelerated outboard, flow outboard of the tips is accelerated upward, and flow above the wing is accelerated inboard, which results in the flow pattern illustrated at right.

1988: 3294:"A concept...uses a symmetrical convergent-divergent channel, like a longitudinal section of a Venturi tube, as the starting point . . when such a device is put in a flow, the static pressure in the tube decreases. When the upper half of the tube is removed, a geometry resembling the airfoil is left, and suction is still maintained on top of it. Of course, this explanation is flawed too, because the geometry change affects the whole flowfield and there is no physics involved in the description." Jaakko Hoffren 1730: 898: 304: 3395:"This classic explanation is based on the difference of streaming velocities caused by the airfoil. There remains, however, a question: How does the airfoil cause the difference in streaming velocities? Some books don't give any answer, while others just stress the picture of the streamlines, saying the airfoil reduces the separations of the streamlines at the upper side. They do not say how the airfoil manages to do this. Thus this is not a sufficient answer." Klaus Weltner 3231:"As stream tube A flows toward the airfoil, it senses the upper portion of the airfoil as an obstruction, and stream tube A must move out of the way of this obstruction. In so doing, stream tube A is squashed to a smaller cross-sectional area as it flows over the nose of the airfoil. In turn, because of mass continuity (ρ AV = constant), the velocity of the flow in the stream tube must increase in the region where the stream tube is being squashed." J. D. Anderson (2008), 1885: 1689: 110: 591: 1844: 1791: 275: 1712:, which is that, of all the possible solutions, the physically reasonable solution is the one in which the flow leaves the trailing edge smoothly. The streamline sketches illustrate one flow pattern with zero lift, in which the flow goes around the trailing edge and leaves the upper surface ahead of the trailing edge, and another flow pattern with positive lift, in which the flow leaves smoothly at the trailing edge in accordance with the Kutta condition. 442:

explain how flat plates, symmetric airfoils, sailboat sails, or conventional airfoils flying upside down can generate lift, and attempts to calculate lift based on the amount of constriction or obstruction do not predict experimental results. Another flaw is that conservation of mass is not a satisfying physical reason why the flow would speed up. Effectively explaining the acceleration of an object requires identifying the force that accelerates it.

3267:"The problem with the 'Venturi' theory is that it attempts to provide us with the velocity based on an incorrect assumption (the constriction of the flow produces the velocity field). We can calculate a velocity based on this assumption, and use Bernoulli's equation to compute the pressure, and perform the pressure-area calculation and the answer we get does not agree with the lift that we measure for a given airfoil." NASA Glenn Research Center 3423:"There is nothing wrong with the Bernoulli principle, or with the statement that the air goes faster over the top of the wing. But, as the above discussion suggests, our understanding is not complete with this explanation. The problem is that we are missing a vital piece when we apply Bernoulli's principle. We can calculate the pressures around the wing if we know the speed of the air over and under the wing, but how do we determine the speed?" 40: 945:

turning of the flow and changes in flow speed according to Bernoulli's principle. The pressure differences and the changes in flow direction and speed sustain each other in a mutual interaction. The pressure differences follow naturally from Newton's second law and from the fact that flow along the surface follows the predominantly downward-sloping contours of the airfoil. And the fact that the air has mass is crucial to the interaction.

1827: 3244:"The theory is based on the idea that the airfoil upper surface is shaped to act as a nozzle which accelerates the flow. Such a nozzle configuration is called a Venturi nozzle and it can be analyzed classically. Considering the conservation of mass, the mass flowing past any point in the nozzle is a constant; the mass flow rate of a Venturi nozzle is a constant... For a constant density, decreasing the area increases the velocity." 2195:"Most of the texts present the Bernoulli formula without derivation, but also with very little explanation. When applied to the lift of an airfoil, the explanation and diagrams are almost always wrong. At least for an introductory course, lift on an airfoil should be explained simply in terms of Newton's Third Law, with the thrust up being equal to the time rate of change of momentum of the air downwards." Cliff Swartz et al. 1867:(a vector-calculus relation) can be used to calculate the velocity perturbation anywhere in the field, caused by the lift on the wing. Approximate theories for the lift distribution and lift-induced drag of three-dimensional wings are based on such analysis applied to the wing's horseshoe vortex system. In these theories, the bound vorticity is usually idealized and assumed to reside at the camber surface inside the wing. 627: 1783: 2514:"Essentially, due to the presence of the wing (its shape and inclination to the incoming flow, the so-called angle of attack), the flow is given a downward deflection. It is Newton's third law at work here, with the flow then exerting a reaction force on the wing in an upward direction, thus generating lift." Vassilis Spathopoulos – Flight Physics for Beginners: Simple Examples of Applying Newton's Laws 402:

small to explain the observed speed difference. This is because the assumption of equal transit time is wrong when applied to a body generating lift. There is no physical principle that requires equal transit time in all situations and experimental results confirm that for a body generating lift the transit times are not equal. In fact, the air moving past the top of an airfoil generating lift moves

825:, a lift force is generated by a spinning cylinder in a freestream. Here the mechanical rotation acts on the boundary layer, causing it to separate at different locations on the two sides of the cylinder. The asymmetric separation changes the effective shape of the cylinder as far as the flow is concerned such that the cylinder acts like a lifting airfoil with circulation in the outer flow. 2471:"When air flows over and under an airfoil inclined at a small angle to its direction, the air is turned from its course. Now, when a body is moving in a uniform speed in a straight line, it requires force to alter either its direction or speed. Therefore, the sails exert a force on the wind and, since action and reaction are equal and opposite, the wind exerts a force on the sails." In: 3556:"You can argue that the main lift comes from the fact that the wing is angled slightly upward so that air striking the underside of the wing is forced downward. The Newton's 3rd law reaction force upward on the wing provides the lift. Increasing the angle of attack can increase the lift, but it also increases drag so that you have to provide more thrust with the aircraft engines" 1682:, a method based on the theory of functions of a complex variable. In the early 20th century, before computers were available, conformal mapping was used to generate solutions to the incompressible potential-flow equation for a class of idealized airfoil shapes, providing some of the first practical theoretical predictions of the pressure distribution on a lifting airfoil. 3587:"If we enlarge the angle of attack we enlarge the deflection of the airstream by the airfoil. This results in the enlargement of the vertical component of the velocity of the airstream... we may expect that the lifting force depends linearly on the angle of attack. This dependency is in complete agreement with the results of experiments..." Klaus Weltner 258:, which are based on established laws of physics and represent the flow accurately, but which require solving partial differential equations. And there are physical explanations without math, which are less rigorous. Correctly explaining lift in these qualitative terms is difficult because the cause-and-effect relationships involved are subtle. A 740:. At angles of attack above the stall, lift is significantly reduced, though it does not drop to zero. The maximum lift that can be achieved before stall, in terms of the lift coefficient, is generally less than 1.5 for single-element airfoils and can be more than 3.0 for airfoils with high-lift slotted flaps and leading-edge devices deployed. 365:

the flow following the upper surface simply reflects an absence of boundary-layer separation, thus it is not an example of the Coandă effect. Regardless of whether this broader definition of the "Coandă effect" is applicable, calling it the "Coandă effect" does not provide an explanation, it just gives the phenomenon a name.

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upper and lower surfaces. The flowing air reacts to the presence of the wing by reducing the pressure on the wing's upper surface and increasing the pressure on the lower surface. The pressure on the lower surface pushes up harder than the reduced pressure on the upper surface pushes down, and the net result is upward lift.

3177:"...do you remember hearing that troubling business about the particles moving over the curved top surface having to go faster than the particles that went underneath, because they have a longer path to travel but must still get there at the same time? This is simply not true. It does not happen." Charles N. Eastlake 1218: 732:. As the angle of attack is increased, a point is reached where the boundary layer can no longer remain attached to the upper surface. When the boundary layer separates, it leaves a region of recirculating flow above the upper surface, as illustrated in the flow-visualization photo at right. This is known as the 889:. When an airfoil produces lift, there is a diffuse region of low pressure above the airfoil, and usually a diffuse region of high pressure below, as illustrated by the isobars (curves of constant pressure) in the drawing. The pressure difference that acts on the surface is just part of this pressure field. 459:, producing a lift force requires maintaining pressure differences in both the vertical and horizontal directions. The Bernoulli-only explanations do not explain how the pressure differences in the vertical direction are sustained. That is, they leave out the flow-deflection part of the interaction. 1834:

The difference in the spanwise component of velocity above and below the wing (between being in the inboard direction above and in the outboard direction below) persists at the trailing edge and into the wake downstream. After the flow leaves the trailing edge, this difference in velocity takes place

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There is more downward turning of the flow than there would be in a two-dimensional flow with the same airfoil shape and sectional lift, and a higher sectional angle of attack is required to achieve the same lift compared to a two-dimensional flow. The wing is effectively flying in a downdraft of its

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are the NS equations without the viscosity, heat conduction, and turbulence effects. As with a RANS solution, an Euler solution consists of the velocity vector, pressure, density, and temperature defined at a dense grid of points surrounding the airfoil. While the Euler equations are simpler than the

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The amount of computation required is a minuscule fraction (billionths) of what would be required to resolve all of the turbulence motions in a raw NS calculation, and with large computers available it is now practical to carry out RANS calculations for complete airplanes in three dimensions. Because

944:

Sustaining the pressure difference that exerts the lift force on the airfoil surfaces requires sustaining a pattern of non-uniform pressure in a wide area around the airfoil. This requires maintaining pressure differences in both the vertical and horizontal directions, and thus requires both downward

849:

The net force exerted by the air occurs as a pressure difference over the airfoil's surfaces. Pressure in a fluid is always positive in an absolute sense, so that pressure must always be thought of as pushing, and never as pulling. The pressure thus pushes inward on the airfoil everywhere on both the

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per unit area exerted by the air on itself and on surfaces that it touches. The lift force is transmitted through the pressure, which acts perpendicular to the surface of the airfoil. Thus, the net force manifests itself as pressure differences. The direction of the net force implies that the average

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While it is true that the flow speeds up, a serious flaw in this explanation is that it does not correctly explain what causes the flow to speed up. The longer-path-length explanation is incorrect. No difference in path length is needed, and even when there is a difference, it is typically much too

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Dingle, Lloyd; Tooley, Michael H. (2005). Aircraft engineering principles. Boston: Elsevier Butterworth-Heinemann. p. 548. ISBN 0-7506-5015-X. The air travelling over the cambered top surface of the aerofoil shown in Figure 7.6, which is split as it passes around the aerofoil, will speed up, because

870:, which split into two – an upper and lower part – at the leading edge. A marked speed difference between the upper-and lower-surface streamlines is shown most clearly in the image animation, with the upper markers arriving at the trailing edge long before the lower ones. Colors of the dots indicate 672:

No matter how smooth the surface of an airfoil seems, any surface is rough on the scale of air molecules. Air molecules flying into the surface bounce off the rough surface in random directions relative to their original velocities. The result is that when the air is viewed as a continuous material,

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exerted by the airfoil on the fluid is manifested partly as momentum fluxes and partly as pressure differences at the outer boundary, in proportions that depend on the shape of the outer boundary, as shown in the diagram at right. For a flat horizontal rectangle that is much longer than it is tall,

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Because the velocity is deduced from the vorticity in such theories, some authors describe the situation to imply that the vorticity is the cause of the velocity perturbations, using terms such as "the velocity induced by the vortex", for example. But attributing mechanical cause-and-effect between

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The arrows ahead of the airfoil and behind also indicate that air passing through the low-pressure region above the airfoil is sped up as it enters, and slowed back down as it leaves. Air passing through the high-pressure region below the airfoil is slowed down as it enters and then sped back up as

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One serious flaw in the obstruction explanation is that it does not explain how streamtube pinching comes about, or why it is greater over the upper surface than the lower surface. For conventional wings that are flat on the bottom and curved on top this makes some intuitive sense, but it does not

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Like the equal transit time explanation, the "obstruction" or "streamtube pinching" explanation argues that the flow over the upper surface is faster than the flow over the lower surface, but gives a different reason for the difference in speed. It argues that the curved upper surface acts as more

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Another argument that is often made, as in several successive versions of the Knowledge article "Aerodynamic Lift," is that lift can always be explained either in terms of pressure or in terms of momentum and that the two explanations are somehow "equivalent." This "either/or" approach also misses

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In addition to the vorticity in the trailing vortex wake there is vorticity in the wing's boundary layer, called 'bound vorticity', which connects the trailing sheets from the two sides of the wing into a vortex system in the general form of a horseshoe. The horseshoe form of the vortex system was

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The vertical pressure gradient at the wing tips causes air to flow sideways, out from under the wing then up and back over the upper surface. This reduces the pressure gradient at the wing tip, therefore also reducing lift. The lift tends to decrease in the spanwise direction from root to tip, and

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The Kutta–Joukowski model does not predict how much circulation or lift a two-dimensional airfoil produces. Calculating the lift per unit span using Kutta–Joukowski requires a known value for the circulation. In particular, if the Kutta condition is met, in which the rear stagnation point moves to

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Lift is proportional to the density of the air and approximately proportional to the square of the flow speed. Lift also depends on the size of the wing, being generally proportional to the wing's area projected in the lift direction. In calculations it is convenient to quantify lift in terms of a

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to adhere to a curved surface, not just the boundary layer accompanying a fluid jet. It is in this broader sense that the Coandă effect is used by some popular references to explain why airflow remains attached to the top side of an airfoil. This is a controversial use of the term "Coandă effect";

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As the airflow approaches the airfoil it is curving upward, but as it passes the airfoil it changes direction and follows a path that is curved downward. According to Newton's second law, this change in flow direction requires a downward force applied to the air by the airfoil. Then Newton's third

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One explanation of how a wing . . gives lift is that as a result of the shape of the airfoil, the air flows faster over the top than it does over the bottom because it has farther to travel. Of course, with our thin-airfoil sails, the distance along the top is the same as along the bottom so this

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Either Euler or potential-flow calculations predict the pressure distribution on the airfoil surfaces roughly correctly for angles of attack below stall, where they might miss the total lift by as much as 10–20%. At angles of attack above stall, inviscid calculations do not predict that stall has

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Thus changes in flow direction and speed are directly caused by the non-uniform pressure. But this cause-and-effect relationship is not just one-way; it works in both directions simultaneously. The air's motion is affected by the pressure differences, but the existence of the pressure differences

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Cambered airfoils generate lift at zero angle of attack. When the chord line is horizontal, the trailing edge has a downward direction and since the air follows the trailing edge it is deflected downward. When a cambered airfoil is upside down, the angle of attack can be adjusted so that the lift

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is exerted on the fluid by the airfoil. The outer boundary is usually either a large circle or a large rectangle. At this outer boundary distant from the airfoil, the velocity and pressure are well represented by the velocity and pressure associated with a uniform flow plus a vortex, and viscous

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of an airfoil and the oncoming airflow. A symmetrical airfoil generates zero lift at zero angle of attack. But as the angle of attack increases, the air is deflected through a larger angle and the vertical component of the airstream velocity increases, resulting in more lift. For small angles, a

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curvature top and bottom. Second, even if a humped-up (cambered) shape is used, the claim that the air must traverse the curved top surface in the same time as it does the flat bottom surface...is fictional. We can quote no physical law that tells us this. Third—and this is the most serious—the

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Control volumes of different shapes that have been used in analyzing the momentum balance in the 2D flow around a lifting airfoil. The airfoil is assumed to exert a downward force −L' per unit span on the air, and the proportions in which that force is manifested as momentum fluxes and pressure

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This is potential-flow theory with the further assumptions that the airfoil is very thin and the angle of attack is small. The linearized theory predicts the general character of the airfoil pressure distribution and how it is influenced by airfoil shape and angle of attack, but is not accurate

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The arrows ahead of the airfoil indicate that the flow ahead of the airfoil is deflected upward, and the arrows behind the airfoil indicate that the flow behind is deflected upward again, after being deflected downward over the airfoil. These deflections are also visible in the flow animation.

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In principle, the NS equations, combined with boundary conditions of no through-flow and no slip at the airfoil surface, could be used to predict lift in any situation in ordinary atmospheric flight with high accuracy. However, airflows in practical situations always involve turbulence in the

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The left side of this equation represents the pressure difference perpendicular to the fluid flow. On the right side of the equation, ρ is the density, v is the velocity, and R is the radius of curvature. This formula shows that higher velocities and tighter curvatures create larger pressure

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on it. It does not matter whether the object is moving through a stationary fluid (e.g. an aircraft flying through the air) or whether the object is stationary and the fluid is moving (e.g. a wing in a wind tunnel) or whether both are moving (e.g. a sailboat using the wind to move forward).

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theory, in which there is no boundary layer, the attached boundary layer reduces the lift by a modest amount and modifies the pressure distribution somewhat, which results in a viscosity-related pressure drag over and above the skin friction drag. The total of the skin friction drag and the

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A serious flaw common to all the Bernoulli-based explanations is that they imply that a speed difference can arise from causes other than a pressure difference, and that the speed difference then leads to a pressure difference, by Bernoulli's principle. This implied one-way causation is a

3650:"...the important thing about an aerofoil . . is not so much that its upper surface is humped and its lower surface is nearly flat, but simply that it moves through the air at an angle. This also avoids the otherwise difficult paradox that an aircraft can fly upside down!" N. H. Fletcher 462:

Although the two simple Bernoulli-based explanations above are incorrect, there is nothing incorrect about Bernoulli's principle or the fact that the air goes faster on the top of the wing, and Bernoulli's principle can be used correctly as part of a more complicated explanation of lift.

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The ability of a fluid flow to follow a curved path is not dependent on shear forces, viscosity of the fluid, or the presence of a boundary layer. Air flowing around an airfoil, adhering to both upper and lower surfaces, and generating lift, is accepted as a phenomenon in inviscid flow.

2487:"Lift is a force generated by turning a moving fluid... If the body is shaped, moved, or inclined in such a way as to produce a net deflection or turning of the flow, the local velocity is changed in magnitude, direction, or both. Changing the velocity creates a net force on the body." 430:

of an obstacle to the flow, forcing the streamlines to pinch closer together, making the streamtubes narrower. When streamtubes become narrower, conservation of mass requires that flow speed must increase. Reduced upper-surface pressure and upward lift follow from the higher speed by

2614:"...if the air is to produce an upward force on the wing, the wing must produce a downward force on the air. Because under these circumstances air cannot sustain a force, it is deflected, or accelerated, downward. Newton's second law gives us the means for quantifying the lift force: F 4179:"...whenever the velocity field is irrotational, it can be expressed as the gradient of a scalar function we call a velocity potential φ: V = ∇φ. The existence of a velocity potential can greatly simplify the analysis of inviscid flows by way of potential-flow theory..." Doug McLean 1893:

The flow around a lifting airfoil must satisfy Newton's second law regarding conservation of momentum, both locally at every point in the flow field, and in an integrated sense over any extended region of the flow. For an extended region, Newton's second law takes the form of the

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The lift generated by a conventional airfoil is dictated by both its design and the flight conditions, such as forward velocity, angle of attack and air density. Lift can be increased by artificially increasing the circulation, for example by boundary-layer blowing or the use of

3634:"With an angle of attack of 0°, we can explain why we already have a lifting force. The air stream behind the aerofoil follows the trailing edge. The trailing edge already has a downward direction, if the chord to the middle line of the profile is horizontal." Klaus Weltner 1757:

is formed and left behind, leading to the formation of circulation around the airfoil. Lift is then inferred from the Kutta-Joukowski theorem. This explanation is largely mathematical, and its general progression is based on logical inference, not physical cause-and-effect.

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is a streamlined shape that is capable of generating significantly more lift than drag. A flat plate can generate lift, but not as much as a streamlined airfoil, and with somewhat higher drag. Most simplified explanations follow one of two basic approaches, based either on

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Thus a distribution of the pressure is created which is given in Euler's equation. The physical reason is the aerofoil which forces the streamline to follow its curved surface. The low pressure at the upper side of the aerofoil is a consequence of the curved surface."

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relates the lift per unit width of span of a two-dimensional airfoil to this circulation component of the flow. It is a key element in an explanation of lift that follows the development of the flow around an airfoil as the airfoil starts its motion from rest and a

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law requires the air to exert an upward force on the airfoil; thus a reaction force, lift, is generated opposite to the directional change. In the case of an airplane wing, the wing exerts a downward force on the air and the air exerts an upward force on the wing.

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It is then assumed that these two elements must meet up at the trailing edge, and because the running distance over the top surface of the airfoil is longer than that over the bottom surface, the element over the top surface must move faster. This is simply not

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stress is negligible, so that the only force that must be integrated over the outer boundary is the pressure. The free-stream velocity is usually assumed to be horizontal, with lift vertically upward, so that the vertical momentum is the component of interest.

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and empirical information on how turbulence affects a boundary layer in a time-averaged average sense). A RANS solution consists of the time-averaged velocity vector, pressure, density, and temperature defined at a dense grid of points surrounding the airfoil.

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Illman, Paul (2000). The Pilot's Handbook of Aeronautical Knowledge. New York: McGraw-Hill. pp. 15–16. ISBN 0071345191. When air flows along the upper wing surface, it travels a greater distance in the same period of time as the airflow along the lower wing

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Burge, Cyril Gordon (1936). Encyclopædia of aviation. London: Pitman. p. 441. "… the fact that the air passing over the hump on the top of the wing has to speed up more than that flowing beneath the wing, in order to arrive at the trailing edge in the same

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own making, as if the freestream flow were tilted downward, with the result that the total aerodynamic force vector is tilted backward slightly compared to what it would be in two dimensions. The additional backward component of the force vector is called

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When the pressure distribution on the airfoil surface is known, determining the total lift requires adding up the contributions to the pressure force from local elements of the surface, each with its own local value of pressure. The total lift is thus the

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When an airfoil generates lift, several components of the overall velocity field contribute to a net circulation of air around it: the upward flow ahead of the airfoil, the accelerated flow above, the decelerated flow below, and the downward flow behind.

2677:" This happens to some extent on both the upper and lower surface of the airfoil, but it is much more pronounced on the forward portion of the upper surface, so the upper surface gets the credit for being the primary lift producer. " Charles N. Eastlake 845:

The airfoil shape and angle of attack work together so that the airfoil exerts a downward force on the air as it flows past. According to Newton's third law, the air must then exert an equal and opposite (upward) force on the airfoil, which is the lift.

1806:, two-dimensional theories may provide a poor model and three-dimensional flow effects can dominate. Even for wings of high aspect ratio, the three-dimensional effects associated with finite span can affect the whole span, not just close to the tips. 1508:

Mathematical theories of lift are based on continuum fluid mechanics, assuming that air flows as a continuous fluid. Lift is generated in accordance with the fundamental principles of physics, the most relevant being the following three principles:

1105: 393:

The "equal transit time" explanation starts by arguing that the flow over the upper surface is faster than the flow over the lower surface because the path length over the upper surface is longer and must be traversed in equal transit time.

325:

This explanation is correct but it is incomplete. It does not explain how the airfoil can impart downward turning to a much deeper swath of the flow than it actually touches. Furthermore, it does not mention that the lift force is exerted by

673:

it is seen to be unable to slide along the surface, and the air's velocity relative to the airfoil decreases to nearly zero at the surface (i.e., the air molecules "stick" to the surface instead of sliding along it), something known as the

570: 2605:, Pitman 1975, p. 76: "This lift force has its reaction in the downward momentum which is imparted to the air as it flows over the wing. Thus the lift of the wing is equal to the rate of transport of downward momentum of this air." 909:

The non-uniform pressure exerts forces on the air in the direction from higher pressure to lower pressure. The direction of the force is different at different locations around the airfoil, as indicated by the block arrows in the

344:

Some versions of the flow-deflection explanation of lift cite the Coandă effect as the reason the flow is able to follow the convex upper surface of the airfoil. The conventional definition in the aerodynamics field is that the

1978:

The results of all of the control-volume analyses described above are consistent with the Kutta–Joukowski theorem described above. Both the tall rectangle and circle control volumes have been used in derivations of the theorem.

1913:

The lifting flow around a 2D airfoil is usually analyzed in a control volume that completely surrounds the airfoil, so that the inner boundary of the control volume is the airfoil surface, where the downward force per unit span

3021:"Unfortunately, this explanation on three counts. First, an airfoil need not have more curvature on its top than on its bottom. Airplanes can and do fly with perfectly symmetrical airfoils; that is with airfoils that have the 1555:

To predict lift requires solving the equations for a particular airfoil shape and flow condition, which generally requires calculations that are so voluminous that they are practical only on a computer, through the methods of

696:

Under usual flight conditions, the boundary layer remains attached to both the upper and lower surfaces all the way to the trailing edge, and its effect on the rest of the flow is modest. Compared to the predictions of

494:

perpendicular to the flow direction with higher pressure on the outside of the curve and lower pressure on the inside. This direct relationship between curved streamlines and pressure differences, sometimes called the

3203:"The actual velocity over the top of an airfoil is much faster than that predicted by the "Longer Path" theory and particles moving over the top arrive at the trailing edge before particles moving under the airfoil." 2168:"There are many theories of how lift is generated. Unfortunately, many of the theories found in encyclopedias, on web sites, and even in some textbooks are incorrect, causing unnecessary confusion for students." NASA 1575:(NS) provide the potentially most accurate theory of lift, but in practice, capturing the effects of turbulence in the boundary layer on the airfoil surface requires sacrificing some accuracy, and requires use of the 5193:– A physicist and an aeronautical engineer explain flight in non-technical terms and specifically address the equal-transit-time myth. They attribute airfoil circulation to the Coanda effect, which is controversial. 1910:) of the momentum of fluid parcels passing through the interior of the control volume. For a steady flow, this can be expressed in the form of the net surface integral of the flux of momentum through the boundary. 1030: 813:

of the lift force – the resulting motion of the structure due to the lift fluctuations may be strongly enhanced. Such vibrations may pose problems and threaten collapse in tall man-made structures like industrial

786:

being shed in an alternating fashion from the cylinder's sides. The oscillatory nature of the flow produces a fluctuating lift force on the cylinder, even though the net (mean) force is negligible. The lift force

2434:"...the effect of the wing is to give the air stream a downward velocity component. The reaction force of the deflected air mass must then act on the wing to give it an equal and opposite upward component." In: 650:

The ambient flow conditions which affect lift include the fluid density, viscosity and speed of flow. Density is affected by temperature, and by the medium's acoustic velocity – i.e. by compressibility effects.

4062:"Analysis of fluid flow is typically presented to engineering students in terms of three fundamental principles: conservation of mass, conservation of momentum, and conservation of energy." Charles N. Eastlake 1851:

The wingtip flow leaving the wing creates a tip vortex. As the main vortex sheet passes downstream from the trailing edge, it rolls up at its outer edges, merging with the tip vortices. The combination of the

853:

The pressure difference which results in lift acts directly on the airfoil surfaces; however, understanding how the pressure difference is produced requires understanding what the flow does over a wider area.

216:" assumes that lift opposes weight, lift can be in any direction with respect to gravity, since it is defined with respect to the direction of flow rather than to the direction of gravity. When an aircraft is 1624:

turbulence models are not perfect, the accuracy of RANS calculations is imperfect, but it is adequate for practical aircraft design. Lift predicted by RANS is usually within a few percent of the actual lift.

2103:

of aerodynamic lift is (usually slightly) more or less than gravity depending on the thrust level and vertical alignment of the thrust line. A side thrust line results in some lift opposing side thrust as

5286:"Flight without Bernoulli" Chris Waltham Vol. 36, Nov. 1998 The Physics Teacher – using a physical model based on Newton's second law, the author presents a rigorous fluid dynamical treatment of flight. 5276:"Aerodynamics at the Particle Level", Charles A. Crummer (2005, revised 2012) – A treatment of aerodynamics emphasizing the particle nature of air, as opposed to the fluid approximation commonly used. 5235:– This is a text for a one-semester undergraduate course in mechanical or aeronautical engineering. Its sections on theory of flight are understandable with a passing knowledge of calculus and physics. 1704:" below), but a single potential function that is continuous throughout the domain around the airfoil cannot represent a flow with nonzero circulation. The solution to this problem is to introduce a 2999: 307:

When a wing generates lift, it deflects air downward, and to do this it must exert a downward force on the air. Newton's third law requires that the air must exert an equal upward force on the wing.

1110: 425:

Streamlines and streamtubes around an airfoil generating lift. The flow is two-dimensional and the airfoil has infinite span. Note the narrower streamtubes above and the wider streamtubes below.

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of equal pressure along their length. The arrows show the pressure differential from high (red) to low (blue) and hence also the net force which causes the air to accelerate in that direction.

3026:

common textbook explanation, and the diagrams that accompany it, describe a force on the wing with no net disturbance to the airstream. This constitutes a violation of Newton's third law."

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of the velocity vector field is everywhere equal to zero. Irrotational flows have the convenient property that the velocity can be expressed as the gradient of a scalar function called a

398:

states that under certain conditions increased flow speed is associated with reduced pressure. It is concluded that the reduced pressure over the upper surface results in upward lift.

2546:"Birds and aircraft fly because they are constantly pushing air downwards: L = Δp/Δt where L= lift force, and Δp/Δt is the rate at which downward momentum is imparted to the airflow." 677:. Because the air at the surface has near-zero velocity but the air away from the surface is moving, there is a thin boundary layer in which air close to the surface is subjected to a 638:(curvature such that the upper surface is more convex than the lower surface, as illustrated at right). Increasing the camber generally increases the maximum lift at a given airspeed. 953:

Producing a lift force requires both downward turning of the flow and changes in flow speed consistent with Bernoulli's principle. Each of the simplified explanations given above in

863: 3119: 1696:

Applying potential-flow theory to a lifting flow requires special treatment and an additional assumption. The problem arises because lift on an airfoil in inviscid flow requires

322:

The downward turning of the flow is not produced solely by the lower surface of the airfoil, and the air flow above the airfoil accounts for much of the downward-turning action.

1871:

the vorticity and the velocity in this way is not consistent with the physics. The velocity perturbations in the flow around a wing are in fact produced by the pressure field.

914:

figure. Air above the airfoil is pushed toward the center of the low-pressure region, and air below the airfoil is pushed outward from the center of the high-pressure region.

1692:

Comparison of a non-lifting flow pattern around an airfoil; and a lifting flow pattern consistent with the Kutta condition in which the flow leaves the trailing edge smoothly

4068: 3400: 3350: 3188: 2688: 2359: 1213:{\displaystyle {\begin{aligned}D_{p}&=\oint p\mathbf {n} \cdot \mathbf {i} \;\mathrm {d} S,\\Y&=\oint p\mathbf {n} \cdot \mathbf {j} \;\mathrm {d} S.\end{aligned}}} 3345:"This answers the apparent mystery of how a symmetric airfoil can produce lift. ... This is also true of a flat plate at non-zero angle of attack." Charles N. Eastlake 2711: 5289: 2563: 1972: 1940: 247:

and propellers share the same physical principles and work in the same way, despite differences between air and water such as density, compressibility, and viscosity.

1685:

A solution of the potential equation directly determines only the velocity field. The pressure field is deduced from the velocity field through Bernoulli's equation.

933:

it leaves. Thus the non-uniform pressure is also the cause of the changes in flow speed visible in the flow animation. The changes in flow speed are consistent with

1490: 1411: 1299: 1269: 4219: 97:, in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, blimps, dirigibles, boats, and submarines. 5179:– Dr. Anderson is Curator of Aerodynamics at the Smithsonian Institution's National Air & Space Museum and Professor Emeritus at the University of Maryland. 2268:"An explanation frequently given is that the path along the upper side of the aerofoil is longer and the air thus has to be faster. This explanation is wrong." 1461: 1436: 1389: 509: 2219: 1241:

Lift depends on the size of the wing, being approximately proportional to the wing area. It is often convenient to quantify the lift of a given airfoil by its

3168:

A visualization of the typical retarded flow over the lower surface of the wing and the accelerated flow over the upper surface starts at 5:29 in the video.

1902:

can be any region of the flow chosen for analysis. The momentum theorem states that the integrated force exerted at the boundaries of the control volume (a

71:

force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of

957:

falls short by trying to explain lift in terms of only one or the other, thus explaining only part of the phenomenon and leaving other parts unexplained.

614:

causes the upper-surface flow to separate from the wing; there is less deflection downward so the airfoil generates less lift. The airfoil is said to be

1762:

the airfoil trailing edge and attaches there for the duration of flight, the lift can be calculated theoretically through the conformal mapping method.

5316: 101:, in which only the lower portion of the body is immersed in a liquid flow, is used by motorboats, surfboards, windsurfers, sailboats, and water-skis. 3252: 1611:

These are the NS equations with the turbulence motions averaged over time, and the effects of the turbulence on the time-averaged flow represented by

2069: 4939: 3600:"The decrease of angles exceeding 25° is plausible. For large angles of attack we get turbulence and thus less deflection downward." Klaus Weltner 5305: 2255: 1091:(which includes the pressure portion of the profile drag and, if the wing is three-dimensional, the induced drag). If we use the spanwise vector 496: 2662: 1666:

In potential-flow theory, the flow is assumed to be incompressible. Incompressible potential-flow theory has the advantage that the equation (

5408: 2406: 1576: 981: 634:

The maximum lift force that can be generated by an airfoil at a given airspeed depends on the shape of the airfoil, especially the amount of

5399: 3672: 2654:"...when one considers the downwash produced by a lifting airfoil, the upper surface contributes more flow turning than the lower surface." 4015: 3562: 2353:"Both approaches are equally valid and equally correct, a concept that is central to the conclusion of this article." Charles N. Eastlake 1798:

The flow around a three-dimensional wing involves significant additional issues, especially relating to the wing tips. For a wing of low

3123: 1644:

theory, which reduces the number of unknowns to be determined, and makes analytic solutions possible in some cases, as described below.

5437: 4100: 3382: 3332: 2783: 2588: 2391: 4856: 2881: 5336: 377:

There are two common versions of this explanation, one based on "equal transit time", and one based on "obstruction" of the airflow.

805:

For a flexible structure, this oscillatory lift force may induce vortex-induced vibrations. Under certain conditions – for instance

5357: 3269: 3206: 2489: 2170: 1592: 5348: 3300: 2366: 937:, which states that in a steady flow without viscosity, lower pressure means higher speed, and higher pressure means lower speed. 4075: 3357: 3185: 2685: 871: 867: 490:

These pressure differences arise in conjunction with the curved airflow. When a fluid follows a curved path, there is a pressure

3541: 2726:"There's always a tremendous amount of focus on the upper portion of the wing, but the lower surface also contributes to lift." 2202: 5478:

YouTube video presentation by Krzysztof Fidkowski, associate professor of Aerospace Engineering at the University of Michigan

5151: 4594: 4567: 3993: 3826: 3802: 3472: 3071: 2708: 1544:

Because an airfoil affects the flow in a wide area around it, the conservation laws of mechanics are embodied in the form of

766:

shape, or stalling airfoils – may also generate lift, in addition to a strong drag force. This lift may be steady, or it may

5287: 3433: 2859: 2556: 2519: 1721:

enough for design work. For a 2D airfoil, such calculations can be done in a fraction of a second in a spreadsheet on a PC.

1587:

These equations represent conservation of mass, Newton's second law (conservation of momentum), conservation of energy, the

693:. Over most of the surface of most airfoils, the boundary layer is naturally turbulent, which increases skin friction drag. 1564:) the forces due to pressure and shear determined by the CFD over every surface element of the airfoil as described under " 1301:

for a wing at a specified angle of attack is given, then the lift produced for specific flow conditions can be determined:

3036: 2286: 1655:, i.e. that small fluid parcels have no net rate of rotation. Mathematically, this is expressed by the statement that the 266:, but all leave significant parts of the phenomenon unexplained, while some also have elements that are simply incorrect. 5471: 5424: 2217: 774:. Interaction of the object's flexibility with the vortex shedding may enhance the effects of fluctuating lift and cause 4223: 3950: 3665:"It requires adjustment of the angle of attack, but as clearly demonstrated in almost every air show, it can be done." 3099: 2334: 1307: 610:

As the angle of attack increases, the lift reaches a maximum at some angle; increasing the angle of attack beyond this

5389: 5232: 5218: 5204: 5190: 5176: 4202: 17: 2226: 1991:

Illustration of the distribution of higher-than-ambient pressure on the ground under an airplane in subsonic flight

1633: 1599:

relating density, temperature, and pressure, and formulas for the viscosity and thermal conductivity of the fluid.

471:

Lift is a result of pressure differences and depends on angle of attack, airfoil shape, air density, and airspeed.

1794:

Cross-section of an airplane wing-body combination showing velocity vectors of the three-dimensional lifting flow

483: 3458:). Therefore pressure differences are needed to exert a force on a body immersed in a fluid. For example, see: 3155: 2981:

it must reach the trailing edge of the aerofoil at the same time as the air that flows underneath the section."

117:

that is perpendicular to the flow direction, and drag is the component that is parallel to the flow direction.

5365: 1545: 5313: 5302: 3078:

The first thing that is wrong is that the principle of equal transit times is not true for a wing with lift.

1786:

Cross-section of an airplane wing-body combination showing the isobars of the three-dimensional lifting flow

409:

than equal transit time predicts. The much higher flow speed over the upper surface can be clearly seen in

5496: 5070:

Wille, R.; Fernholz, H. (1965), "Report on the first European Mechanics Colloquium, on the Coanda effect",

3249: 2810:

Wille, R.; Fernholz, H. (1965), "Report on the first European Mechanics Colloquium, on the Coanda effect",

1697: 1557: 3655: 611: 5459: 2707:

David Guo, College of Engineering, Technology, and Aeronautics (CETA), Southern New Hampshire University

2065: 1749: 1572: 354: 135: 64: 1588: 1531: 3963: 1799: 1517: 288: 240:, or on the wing on a racing car. Lift may also be largely horizontal, for instance on a sailing ship. 197: 5377: 878:

An airfoil affects the speed and direction of the flow over a wide area, producing a pattern called a

1561: 779: 729: 3670: 1534:, including the assumption that the airfoil's surface is impermeable for the air flowing around, and 138:

of this force that is perpendicular to the oncoming flow direction. Lift is always accompanied by a

2659: 1513: 1223:

The validity of this integration generally requires the airfoil shape to be a closed curve that is

775: 753: 431: 395: 292: 212:, and even in the plant world by the seeds of certain trees. While the common meaning of the word " 5405: 2414: 487:

pressure on the upper surface of the airfoil is lower than the average pressure on the underside.

2618:= m∆v/∆t = ∆(mv)/∆t. The lift force is equal to the time rate of change of momentum of the air." 1675: 1552:

requirements which the flow has to satisfy at the airfoil surface and far away from the airfoil.

311:

An airfoil generates lift by exerting a downward force on the air as it flows past. According to

4009: 3566: 975:

of the pressure, in the direction perpendicular to the farfield flow, over the airfoil surface.

2218:

Arvel Gentry Proceedings of the Third AIAA Symposium on the Aero/Hydronautics of Sailing 1971.

2023: 1537: 715: 885:

The pressure is also affected over a wide area, in a pattern of non-uniform pressure called a

720: 5491: 1667: 635: 312: 220:

in straight and level flight, most of the lift opposes gravity. However, when an aircraft is

75:, but it is defined to act perpendicular to the flow and therefore can act in any direction. 31: 5434: 2789: 452: 372: 5248: 5127: 5115: 5079: 5042: 5014: 4977: 4897: 4862: 4738: 4666: 4630: 3772: 3760: 3501: 2887: 2819: 2749: 2629: 2043: 1889:

differences at the outer boundary are indicated for each different shape of control volume.

1678:

of other known solutions. The incompressible-potential-flow equation can also be solved by

1616: 1468: 1396: 1277: 1247: 902: 438:, claiming the upper surface of the wing acts like a venturi nozzle to constrict the flow. 5333: 2709:

https://www.jove.com/v/10453/airfoil-behavior-pressure-distribution-over-a-clark-y-14-wing

1774:

the entire airfoil is circular and spins about a spanwise axis to create the circulation.

892: 565:{\displaystyle {\frac {\operatorname {d} p}{\operatorname {d} R}}=\rho {\frac {v^{2}}{R}}} 353:

to stay attached to an adjacent surface that curves away from the flow, and the resultant

67:

of this force that is perpendicular to the oncoming flow direction. It contrasts with the

8: 3273: 3210: 2493: 2197:

Quibbles, Misunderstandings, and Egregious Mistakes – Survey of High-School Physics Texts

2174: 2038: 1949: 1917: 1907: 1864: 1612: 603: 315:, the air must exert an equal and opposite (upward) force on the airfoil, which is lift. 221: 150: 5252: 5119: 5083: 5046: 5018: 4989: 4981: 4901: 4742: 4670: 4634: 3764: 3505: 3488:...if a streamline is curved, there must be a pressure gradient across the streamline... 2823: 2753: 2633: 607:

symmetrical airfoil generates a lift force roughly proportional to the angle of attack.

5345: 5277: 5131: 5095: 4754: 4682: 4646: 3776: 3517: 3307: 2835: 2765: 2033: 1656: 1560:(CFD). Determining the net aerodynamic force from a CFD solution requires "adding up" ( 1549: 1446: 1421: 1374: 690: 262:

that captures all of the essential aspects is necessarily complex. There are also many

225: 243:

The lift discussed in this article is mainly in relation to airfoils, although marine

5228: 5214: 5200: 5186: 5172: 5147: 5099: 5033:

Weltner, K. (1987), "A comparison of explanations of the aerodynamic lifting force",

4933: 4758: 4678: 4650: 4642: 4590: 4563: 4198: 4094: 3989: 3946: 3822: 3798: 3513: 3468: 3376: 3326: 3095: 3067: 2839: 2769: 2761: 2582: 2385: 2330: 2249: 2200: 1820: 1679: 1596: 1042:

is the projected (planform) area of the airfoil, measured normal to the mean airflow;

674: 170: 114: 79: 5135: 4143:

Spalart, Philippe R. (2000) Amsterdam, the Netherlands. Elsevier Science Publishers.

3780: 3539: 2028: 445: 434:, just as in the equal transit time explanation. Sometimes an analogy is made to a 380: 5256: 5123: 5087: 5050: 5022: 4985: 4905: 4746: 4729:

Eastlake, C. N. (2002), "An Aerodynamicist's View of Lift, Bernoulli, and Newton",

4686: 4674: 4638: 4190: 3768: 3521: 3509: 3460: 2827: 2757: 2637: 2008: 1903: 1853: 1236: 1224: 661: 576:

differentials and that for straight flow (R → ∞), the pressure difference is zero.

166: 142:

force, which is the component of the surface force parallel to the flow direction.

4776:

Paleoaerodynamic Explorations Part I: Evolution of Biological and Technical Flight

339: 229: 5475: 5463: 5441: 5428: 5412: 5393: 5381: 5369: 5352: 5340: 5320: 5293: 5270: 5213:, McCormick, Barnes W., (1979), Chapter 3, John Wiley & Sons, Inc., New York 3676: 3545: 3429: 3256: 3192: 2853: 2715: 2692: 2666: 2206: 2013: 1995:

An airfoil produces a pressure field in the surrounding air, as explained under "

1987: 1754: 1709: 1497: 799: 795: 771: 749: 599: 585: 421: 251: 217: 763: 384:

An illustration of the incorrect equal transit-time explanation of airfoil lift.

232:

in a turn the lift is tilted with respect to the vertical. Lift may also act as

5501: 5446:(referred by "One Minute Physics How Does a Wing actually work?" YouTube video) 3154:. National Committee for Fluid Mechanics Films/Educational Development Center. 3040: 2290: 2018: 1982: 1899: 1771: 1641: 615: 500: 361: 139: 98: 83: 68: 5468: 5421: 5334:

Discussion of the apparent "conflict" between the various explanations of lift

5239:

Craig, Paul P. (1957). "Observation of Perfect Potential Flow in Superfluid".

5091: 4194: 3957: 2831: 1729: 5485: 5309: 5266: 5260: 4956: 1863:

Given the distribution of bound vorticity and the vorticity in the wake, the

1830:

Euler computation of a tip vortex rolling up from the trailed vorticity sheet

1439: 1082: 1067: 822: 792: 698: 209: 126: 44: 897: 360:

More broadly, some consider the effect to include the tendency of any fluid

303: 213: 5451:

From Summit to Seafloor – Lifted Weight as a Function of Altitude and Depth

1652: 954: 866:

Flow around an airfoil: the dots move with the flow. The black dots are on

834: 703: 686: 451:

misconception. The real relationship between pressure and flow speed is a

435: 263: 178: 5269:

conditions, resulting in the vanishing of lift in inviscid flow since the

1884: 1688: 590: 5386: 4920:, vol. 21, International Journal of Heat and Fluid Flow, p. 252 3751:

Williamson, C. H. K.; Govardhan, R. (2004), "Vortex-induced vibrations",

1493: 1414: 810: 767: 678: 373:

Explanations based on an increase in flow speed and Bernoulli's principle

350: 298: 269: 201: 154: 90: 5106:

Williamson, C. H. K.; Govardhan, R (2004), "Vortex-induced vibrations",

3797:(revised ed.), World Scientific, pp. 6–13, 42–45 & 50–52, 3454:

A uniform pressure surrounding a body does not create a net force. (See

3250:

https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/venturi-theory/

1843: 1790: 1741:

The circulation can be understood as the total amount of "spinning" (or

274: 109: 5375:

A treatment of why and how wings generate lift that focuses on pressure

5199:, Clancy, L. J. (1975), Section 4.8, Pitman Publishing Limited, London 1803: 1767: 1705: 1671: 1637:

NS equations, they do not lend themselves to exact analytic solutions.

1055: 1025:{\displaystyle L=\oint p\mathbf {n} \cdot \mathbf {k} \;\mathrm {d} S,} 893:

Mutual interaction of pressure differences and changes in flow velocity

759: 254:

phenomenon that can be understood on essentially two levels: There are

244: 237: 162: 4909: 4750: 2641: 1271:, which defines its overall lift in terms of a unit area of the wing. 5281: 5026: 1879: 1742: 1660: 1579:(RANS). Simpler but less accurate theories have also been developed. 806: 788: 682: 330:, and does not explain how those pressure differences are sustained. 233: 193: 158: 39: 5054: 3298:

Section 4.3 American Institute of Aeronautics and Astronautics 2001

3149: 2620:

Smith, Norman F. (1972). "Bernoulli and Newton in Fluid Mechanics".

1826: 4217:

Elements of Potential Flow California State University Los Angeles

3861: 3859: 3455: 1860:

recognized by the British aeronautical pioneer Lanchester in 1907.

1606: 1525: 972: 491: 479: 182: 94: 5363:

Explanation of Lift with animation of fluid flow around an airfoil

5362: 89:

Dynamic lift is distinguished from other kinds of lift in fluids.

862: 815: 626: 446:

Issues common to both versions of the Bernoulli-based explanation

283: 72: 4888:

Smith, N. F. (1972), "Bernoulli and Newton in Fluid Mechanics",

4471:

Lissaman (1996), "Lift in thin slices: the two dimensional case"

3856: 2660:

https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/foilw2/

1701: 778:. For instance, the flow around a circular cylinder generates a 642:

force is upward. This explains how a plane can fly upside down.

388: 1782: 1627: 783: 189: 5456: 5301:

Norman F. Smith School Science and Mathematics vol 73 Part I:

2705:

Airfoil Behavior: Pressure Distribution over a Clark Y-14 Wing

2141:

Aerodynamic Lift, Part 2: A comprehensive Physical Explanation

1856:

and the vortex sheets feeding them is called the vortex wake.

1724: 1648:

happened, and as a result they grossly overestimate the lift.

456: 259: 4185:"Continuum Fluid Mechanics and the Navier–Stokes Equations". 3636:

A comparison of explanations of the aerodynamic lifting force

3602:

A comparison of explanations of the aerodynamic lifting force

3589:

A comparison of explanations of the aerodynamic lifting force

3536:

A comparison of explanations of the aerodynamic lifting force

2270:

A comparison of explanations of the aerodynamic lifting force

1521: 122: 56: 52: 5227:, Richard S. Shevell, Prentice-Hall International Editions, 4614:

Vectors, Tensors, and the basic Equations of Fluid Mechanics

3704: 3702: 3538:

Klaus Weltner Am. J. Phys. Vol.55 No.January 1, 1987, p. 53

1983:

Lift reacted by overpressure on the ground under an airplane

1835:

across a relatively thin shear layer called a vortex sheet.

922: 828: 728:

An airfoil's maximum lift at a given airspeed is limited by

5374: 4968:

Van Dyke, M. (1969), "Higher-Order Boundary-Layer Theory",

4924: 3882: 3880: 2444: 1663:. A flow represented in this way is called potential flow. 185: 174: 146: 4881:

The Dynamics and Thermodynamics of Compressible Fluid Flow

4830:

Understanding Aerodynamics – Arguing from the Real Physics

4560:

Computational Fluid Dynamics, The Basics With Applications

3821:, vol. 2, Oxford University Press, pp. 850–855, 2492:. NASA Glenn Research Center. May 27, 2000. Archived from 1615:(an additional set of equations based on a combination of 1540:, which says that energy is neither created nor destroyed. 333: 4927:

Hydrodynamics around cylindrical structures (revised ed.)

4495: 4493: 4491: 4181:

Understanding Aerodynamics: Arguing from the Real Physics

3943:

Understanding Aerodynamics: Arguing from the Real Physics

3699: 2327:

Understanding Aerodynamics: Arguing from the Real Physics

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forces, which are small compared to the pressure forces.

205: 3877: 3560:

Georgia State University Dept. of Physics and Astronomy

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Babinsky, Holger (November 2003), "How do wings work?",

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is the lift coefficient at the desired angle of attack,

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Airflow separating from a wing at a high angle of attack

630:

An airfoil with camber compared to a symmetrical airfoil

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If the surrounding fluid is air, the force is called an

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