Editing Lift (force) (section)

==A more comprehensive physical explanation==

As described above under "[[#Simplified physical explanations of lift on an airfoil|Simplified physical explanations of lift on an airfoil]]", 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.<ref>McLean (2012), Section 7.3.3</ref>

===Lift at the airfoil surface===

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.<ref name="Langewiesche 1944"/>

The net force exerted by the air occurs as a pressure difference over the airfoil's surfaces.<ref name="Milne-Thomson 1966, Section 1.41">Milne-Thomson (1966), Section 1.41</ref> Pressure in a fluid is always positive in an absolute sense,<ref>Jeans (1967), Section 33.</ref> 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 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.<ref name="Milne-Thomson 1966, Section 1.41"/>

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.

===The wider flow around the airfoil===
[[File:Karman trefftz.gif|frame|right|Flow around an airfoil: the dots move with the flow. The black dots are on [[Streamlines, streaklines, and pathlines|time slices]], 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 [[Streamlines, streaklines, and pathlines|streamlines]].]]

An airfoil affects the speed and direction of the flow over a wide area, producing a pattern called a ''velocity field''. 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.<ref name="Clancy 1975, Section 4.5">Clancy (1975), Section 4.5</ref><ref>Milne-Thomson (1966.), Section 5.31</ref>

The pressure is also affected over a wide area, in a pattern of non-uniform pressure called a ''pressure field''. 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.<ref>McLean 2012, Section 7.3.3.7</ref>

===Mutual interaction of pressure differences and changes in flow velocity===
[[File:Pressures-around-aerofoil.svg|thumb|300px|Pressure field around an airfoil. The lines are [[isobar (meteorology)|isobars]] 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.]]
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 ''pressure field around an airfoil'' 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.

According to ''Newton's second law'', 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 "[[#Controversy regarding the Coandă effect|Controversy regarding the Coandă effect]]").

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.

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 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 ''Bernoulli's principle'', which states that in a steady flow without viscosity, lower pressure means higher speed, and higher pressure means lower speed.

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 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.<ref>McLean (2012), Section 3.5</ref> 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.<ref>McLean 2012, Section 7.3.3.9"</ref> This is why the air's mass is part of the calculation, and why lift depends on air density.

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 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.<ref>McLean 2012, Section 7.3.3.9</ref>

===How simpler explanations fall short===

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 [[#Simplified_physical_explanations_of_lift_on_an_airfoil|Simplified physical explanations of lift on an airfoil]] 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.<ref name="auto">{{cite book |last=McLean |first=Doug |date=2012 |title=Understanding Aerodynamics: Arguing from the Real Physics |chapter=7.3.3.12 |publisher=John Wiley & Sons |isbn=978-1119967514}} {{YouTube|id=QKCK4lJLQHU|title=Doug McLean, Common Misconceptions in Aerodynamics}}</ref>