Editing Lift (force) (section)

==Basic attributes of lift==

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

===Pressure differences===

[[Pressure]] is the [[Stress (mechanics)#Normal and shear stresses|normal force]] 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 pressure on the upper surface of the airfoil is lower than the average pressure on the underside.<ref>A uniform pressure surrounding a body does not create a net force. (See [[buoyancy]]). Therefore pressure differences are needed to exert a force on a body immersed in a fluid. For example, see: {{Citation|first=G.K.|last=Batchelor|author-link=George Batchelor|title=An Introduction to Fluid Dynamics|year=1967|publisher=Cambridge University Press|isbn=978-0-521-66396-0|pages=14–15}}</ref>

These pressure differences arise in conjunction with the curved airflow. When a fluid follows a curved path, there is a pressure [[gradient]] perpendicular to the flow direction with higher pressure on the outside of the curve and lower pressure on the inside.<ref>"''...if a streamline is curved, there must be a pressure gradient across the streamline...''" {{citation|journal=Physics Education|first=Holger|last=Babinsky|date=November 2003|title=How do wings work?|doi=10.1088/0031-9120/38/6/001|bibcode=2003PhyEd..38..497B|volume=38|issue=6|page=497|s2cid=1657792 }}</ref> This direct relationship between curved streamlines and pressure differences, sometimes called the [[Euler equations (fluid dynamics)#Streamline curvature theorem|streamline curvature theorem]], was derived from Newton's second law by [[Leonhard Euler]] in 1754:

:<math>\frac{\operatorname{d}p}{\operatorname{d}R}= \rho \frac{v^2}{R} </math>

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 differentials and that for straight flow (R → ∞), the pressure difference is zero.<ref>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." ''A comparison of explanations of the aerodynamic lifting force'' Klaus Weltner Am. J. Phys. Vol.55 No.January 1, 1987, p. 53 [http://aapt.scitation.org/doi/pdf/10.1119/1.14960] {{Webarchive|url=https://web.archive.org/web/20210428194849/https://aapt.scitation.org/doi/pdf/10.1119/1.14960|date=April 28, 2021}}</ref>

===Angle of attack===
{{main|Angle of attack}}
[[Image:Airfoil angle of attack.jpg|thumb|300px|Angle of attack of an airfoil]]
The [[angle of attack]] is the angle between the [[Chord (aeronautics)|chord line]] 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 symmetrical airfoil generates a lift force roughly proportional to the angle of attack.<ref>"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" ''Hyperphysics'' Georgia State University Dept. of Physics and Astronomy {{cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/angatt.html|title=Angle of Attack for Airfoil|access-date=26 July 2012|url-status=dead|archive-url=https://web.archive.org/web/20121014185450/http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/angatt.html|archive-date=October 14, 2012}}</ref><ref>"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 ''A comparison of explanations of the aerodynamic lifting force'' Am. J. Phys. 55(1), January 1987 p. 52</ref>

As the angle of attack increases, the lift reaches a maximum at some angle; increasing the angle of attack beyond this [[Angle of attack#Critical angle of attack|critical angle of attack]] 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 [[Stall (flight)|stalled]].<ref>"The decrease[d lift] of angles exceeding 25° is plausible. For large angles of attack we get turbulence and thus less deflection downward." Klaus Weltner ''A comparison of explanations of the aerodynamic lifting force'' ''Am. J. Phys.'' 55(1), January 1987 p. 52</ref>

===Airfoil shape===
[[Image:Airfoil camber.jpg|thumb|right|300px|An airfoil with camber compared to a symmetrical airfoil]]

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 [[Camber (aerodynamics)|camber]] (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.<ref>Clancy (1975), Section 5.2</ref><ref>Abbott, and von Doenhoff (1958), Section 4.2</ref>

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.<ref>"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 ''A comparison of explanations of the aerodynamic lifting force'' ''Am. J. Phys.'' 55(1), January 1987 p. 52</ref> When a cambered airfoil is upside down, the angle of attack can be adjusted so that the lift force is upward. This explains how a plane can fly upside down.<ref>"...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 ''Mechanics of Flight'' Physics Education July 1975 [http://iopscience.iop.org/0031-9120/10/5/009/pdf/0031-9120_10_5_009.pdf]</ref><ref>"It requires adjustment of the angle of attack, but as clearly demonstrated in almost every air show, it can be done." ''Hyperphysics'' GSU Dept. of Physics and Astronomy [http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html#c2] {{webarchive|url=https://web.archive.org/web/20120708102756/http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html|date=July 8, 2012}}</ref>

===Flow conditions===
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.

===Air speed and density===
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 [[lift coefficient]] based on these factors.

===Boundary layer and profile drag===
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, 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 [[no-slip condition]].<ref>White (1991), Section 1-4</ref> 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 [[shear force|shearing]] motion.<ref>White (1991), Section 1-2</ref><ref name="Anderson 1991, Chapter 17">Anderson (1991), Chapter 17</ref> The air's [[viscosity]] resists the shearing, giving rise to a [[shear stress]] at the airfoil's surface called [[skin friction drag]]. Over most of the surface of most airfoils, the boundary layer is naturally turbulent, which increases skin friction drag.<ref name="Anderson 1991, Chapter 17"/><ref name="Doenhoff 1958">Abbott and von Doenhoff (1958), Chapter 5</ref>

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 [[inviscid flow]] 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 viscosity-related pressure drag is usually called the [[profile drag]].<ref name="Doenhoff 1958"/><ref>Schlichting (1979), Chapter XXIV</ref>

===Stalling===
{{Main|Stall (fluid dynamics)}}

[[File:1915ca abger fluegel (cropped and mirrored).jpg|thumb|300px|Airflow separating from a wing at a high angle of attack]]

An airfoil's maximum lift at a given airspeed is limited by [[Boundary layer separation|boundary-layer separation]]. 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 ''stall'', or ''stalling''. 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.<ref>Abbott and Doenhoff (1958), Chapter 8</ref>

===Bluff bodies===
{{Further|Vortex shedding|Vortex-induced vibration}}
The flow around [[bluff body|bluff bodies]] – i.e. without a [[:wikt:streamline|streamlined]] shape, or stalling airfoils – may also generate lift, in addition to a strong drag force. This lift may be steady, or it may [[oscillation|oscillate]] due to [[vortex shedding]]. Interaction of the object's flexibility with the vortex shedding may enhance the effects of fluctuating lift and cause [[vortex-induced vibration]]s.<ref name=Williamson>{{citation|journal=Annual Review of Fluid Mechanics|volume=36|pages=413–455|year=2004|doi=10.1146/annurev.fluid.36.050802.122128|title=Vortex-induced vibrations|first1=C. H. K.|last1=Williamson|first2=R.|last2=Govardhan|bibcode=2004AnRFM..36..413W|s2cid=58937745}}</ref> For instance, the flow around a circular cylinder generates a [[Kármán vortex street]]: [[vortex|vortices]] 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 [[frequency]] is characterised by the [[dimensionless]] [[Strouhal number]], which depends on the [[Reynolds number]] of the flow.<ref>{{citation|title=Hydrodynamics around cylindrical structures|first1=B. Mutlu|last1=Sumer|first2=Jørgen|last2=Fredsøe|edition=revised|publisher=World Scientific|year=2006|isbn=978-981-270-039-1|pages=6–13, 42–45 & 50–52}}</ref><ref>{{citation|title=Flow around circular cylinders|first=M.M.|last=Zdravkovich|publisher=Oxford University Press|year=2003|isbn=978-0-19-856561-1|volume=2|pages=850–855}}</ref>

For a flexible structure, this oscillatory lift force may induce vortex-induced vibrations. Under certain conditions – for instance [[resonance]] or strong spanwise [[correlation]] 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 [[chimney]]s.<ref name=Williamson/>

In the [[Magnus effect]], 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.<ref>Clancy, L. J., ''Aerodynamics'', Sections 4.5, 4.6</ref>