Airfoil
An airfoil (American English) or aerofoil (British English) is a streamlined body that is capable of generating significantly more lift than drag.[1] Wings, sails and propeller blades are examples of airfoils. Foils of similar function designed with water as the working fluid are called hydrofoils.
When oriented at a suitable angle, a solid body moving through a
The lift on an airfoil is primarily the result of its
The air deflected by an airfoil causes it to generate a lower-pressure "shadow" above and behind itself. This pressure difference is accompanied by a velocity difference, via
Overview
The wings and stabilizers of
When the wind is obstructed by an object such as a flat plate, a building, or the deck of a bridge, the object will experience drag and also an aerodynamic force perpendicular to the wind. This does not mean the object qualifies as an airfoil. Airfoils are highly-efficient lifting shapes, able to generate more lift than similarly sized flat plates of the same area, and able to generate lift with significantly less drag. Airfoils are used in the design of aircraft, propellers, rotor blades, wind turbines and other applications of aeronautical engineering.
A lift and drag curve obtained in
Airfoil design is a major facet of
Movable high-lift devices,
A laminar flow wing has a maximum thickness in the middle camber line. Analyzing the Navier–Stokes equations in the linear regime shows that a negative pressure gradient along the flow has the same effect as reducing the speed. So with the maximum camber in the middle, maintaining a laminar flow over a larger percentage of the wing at a higher cruising speed is possible. However, some surface contamination will disrupt the laminar flow, making it turbulent. For example, with rain on the wing, the flow will be turbulent. Under certain conditions, insect debris on the wing will cause the loss of small regions of laminar flow as well.[7] Before NASA's research in the 1970s and 1980s the aircraft design community understood from application attempts in the WW II era that laminar flow wing designs were not practical using common manufacturing tolerances and surface imperfections. That belief changed after new manufacturing methods were developed with composite materials (e.g. laminar-flow airfoils developed by Professor Franz Wortmann for use with wings made of fibre-reinforced plastic). Machined metal methods were also introduced. NASA's research in the 1980s revealed the practicality and usefulness of laminar flow wing designs and opened the way for laminar-flow applications on modern practical aircraft surfaces, from subsonic general aviation aircraft to transonic large transport aircraft, to supersonic designs.[8]
Schemes have been devised to define airfoils – an example is the
Airfoil terminology
The various terms related to airfoils are defined below:[9]
- The suction surface (a.k.a. upper surface) is generally associated with higher velocity and lower static pressure.
- The pressure surface (a.k.a. lower surface) has a comparatively higher static pressure than the suction surface. The pressure gradient between these two surfaces contributes to the lift force generated for a given airfoil.
The geometry of the airfoil is described with a variety of terms :
- The leading edge is the point at the front of the airfoil that has maximum curvature (minimum radius).[10]
- The trailing edge is defined similarly as the point of maximum curvature at the rear of the airfoil.
- The chord lineis the straight line connecting leading and trailing edges. The chord length, or simply chord, , is the length of the chord line. That is the reference dimension of the airfoil section.
The shape of the airfoil is defined using the following geometrical parameters:
- The mean camber line or mean line is the locus of points midway between the upper and lower surfaces. Its shape depends on the thickness distribution along the chord;
- The thickness of an airfoil varies along the chord. It may be measured in either of two ways:
Some important parameters to describe an airfoil's shape are its camber and its thickness. For example, an airfoil of the NACA 4-digit series such as the NACA 2415 (to be read as 2 – 4 – 15) describes an airfoil with a camber of 0.02 chord located at 0.40 chord, with 0.15 chord of maximum thickness.
Finally, important concepts used to describe the airfoil's behaviour when moving through a fluid are:
- The aerodynamic center, which is the chord-wise location about which the pitching moment is independent of the lift coefficient and the angle of attack.
- The center of pressure, which is the chord-wise location about which the pitching moment is momentarily zero. On a cambered airfoil, the center of pressure is not a fixed location as it moves in response to changes in angle of attack and lift coefficient.
Thin airfoil theory
Thin airfoil theory is a simple theory of airfoils that relates angle of attack to lift for incompressible, inviscid flows. It was devised by German mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others[14] in the 1920s. The theory idealizes the flow around an airfoil as two-dimensional flow around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite wingspan.
Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for the following important properties of airfoils in two-dimensional inviscid flow:[15][16]
- on a symmetric airfoil, the chordbehind the leading edge.
- on a cambered airfoil, the aerodynamic center lies exactly one quarter of the chord behind the leading edge, but the position of the center of pressure moves when the angle of attack changes.
- the slope of the lift coefficient versus angle of attack line is units per radian.
As a consequence of (3), the section lift coefficient of a symmetric airfoil of infinite wingspan is:
- where is the section lift coefficient,
- is the chordline.
(The above expression is also applicable to a cambered airfoil where is the angle of attack measured relative to the
Also as a consequence of (3), the section lift coefficient of a cambered airfoil of infinite wingspan is:
- where is the section lift coefficient when the angle of attack is zero.
Thin airfoil theory assumes the air is an
Derivation
In thin airfoil theory, the width of the (2D) airfoil is assumed negligible, and the airfoil itself replaced with a 1D blade along its camber line, oriented at the angle of attack α. Let the position along the blade be x, ranging from 0 at the wing's front to c at the trailing edge; the camber of the airfoil, dy⁄dx, is assumed sufficiently small that one need not distinguish between x and position relative to the fuselage.[22][23]
The flow across the airfoil generates a circulation around the blade, which can be modeled as a vortex sheet of position-varying strength γ(x). The Kutta condition implies that γ(c)=0, but the strength is singular at the bladefront, with γ(x)∝1⁄√x for x ≈ 0.[24] If the main flow V has density ρ, then the Kutta–Joukowski theorem gives that the total lift force F is proportional to[25][26]
From the Biot–Savart law, the vorticity γ(x) produces a flow field
An explicit solution can be obtained through first the change of variables
The lift coefficient satisfies
See also
- Circulation control wing
- Hydrofoil
- Kline–Fogleman airfoil
- Küssner effect
- Parafoil
- Wing configuration
References
Citations
- ^ Clancy 1975, §5.2.
- ^ Halliday & Resnick 1988, p. 378: "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."
- ^ Hall, Nancy R. "Lift from Flow Turning". NASA Glenn Research Center. Archived from the original on 5 July 2011. Retrieved 2011-06-29.
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.
- ^ “It has been known from the very beginning of flight that wings with a sharp trailing edge must be used in order to obtain a well-defined lift.” von Mises, Richard (1945), Theory of Flight, Section VIII.2, p.179, Dover Publications Inc. ISBN 0-486-60541-8
- ^ Weltner & Ingelman-Sundberg 1999.
- ^ Babinsky 2003, pp. 497–503: "If a streamline is curved, there must be a pressure gradient across the streamline."
- ^ Croom, C. C.; Holmes, B. J. (1985-04-01). Flight evaluation of an insect contamination protection system for laminar flow wings.
- ^ Holmes, B. J.; Obara, C. J.; Yip, L. P. (1984-06-01). "Natural laminar flow experiments on modern airplane surfaces". NASA Technical Reports.
- ^ Hurt, H. H. Jr. (January 1965) [1960]. Aerodynamics for Naval Aviators. U.S. Government Printing Office, Washington, D.C.: U.S. Navy, Aviation Training Division. pp. 21–22. NAVWEPS 00-80T-80.
- ^ Houghton et al. 2012, p. 18.
- ^ a b Houghton et al. 2012, p. 17.
- ^ Phillips 2004, p. 27.
- ^ Bertin & Cummings 2009, p. 199.
- ^ Abbott & Von Doenhoff 1959, §4.2.
- ^ Abbott & Von Doenhoff 1959, §4.3.
- ^ Clancy 1975, §8.1 to §8.8.
- ^ Scott 2003: "The equation can only be used for aircraft with medium to large aspect ratio wings and only up to the stall angle, which is usually between 10° and 15° for typical aircraft configurations."
- ^ Morris 2009.
- ^ Morris & Rusak 2013, pp. 439–472.
- ^ Traub 2016, p. 9.
- S2CID 121962230.
- ^ Auld & Srinivas 1995: "A simple solution for general two-dimensional aerofoil sections can be obtained by neglecting thickness effects and using a mean-line only section model.... This also means small changes in position are equivalent so that ds ≈ dx."
- ^ Batchelor 1967, p. 467.
- ^ a b Batchelor 1967, p. 467-9.
- ^ a b c Auld & Srinivas 1995.
- ^ Acheson, D. J. (1990). Elementary Fluid Dynamics. Oxford Applied Mathematics and Computing Science. Oxford: Clarendon Press (published 2009). pp. 140–141, 143–145.
- ^ Batchelor 1967, p. 467-468.
- ^ Batchelor 1967, p. 469-470.
- ^ Batchelor 1967, p. 470.
General Sources
- ISBN 978-0-486-60586-9.
- Auld, Douglass; Srinivas (1995). "2-D Thin Aerofoil Theory". Aerodynamics for Students. University of Sydney.
- Babinsky, Holger (November 2003). "How do wings work?" (PDF). Physics Education. 38 (6): 497–503. S2CID 1657792.
- Batchelor, George. K (1967). An Introduction to Fluid Dynamics. Cambridge UP. pp. 467–471.
- Bertin, John J.; Cummings, Russel M. (2009). Aerodynamics for Engineers (5th ed.). Pearson Prentice Hall. ISBN 978-0-13-227268-1.
- Clancy, L.J. (1975). Aerodynamics. London: Pitman. ISBN 0-273-01120-0.
- Halliday, David; Resnick, Robert (1988). Fundamentals of Physics (3rd ed.). John Wiley & Sons.
- Houghton, E. L.; Carpenter, P. W.; Collicott, Steven H.; Valentine, Daniel (2012). Aerodynamics for Engineering Students (6th ed.). Elsevier. ISBN 978-0-08-096633-5.
- Morris, Wallace J. II (2009). A universal prediction of stall onset for airfoils at a wide range of Reynolds number flows (PhD). Harvard University. Bibcode:2009PhDT.......146M.
- Morris, Wallace J.; Rusak, Zvi (October 2013). "Stall onset on aerofoils at low to moderately high Reynolds number flows". Journal of Fluid Mechanics. 733: 439–472. S2CID 122817884.
- Phillips, Warren F. (2004). Mechanics of Flight. John Wiley & Sons. ISBN 978-0-471-33458-3.
- Scott, Jeff (10 August 2003). "Question #136: Lift Coefficient & Thin Airfoil Theory". Ask a Rocket Scientist: Aerodynamics. Aerospaceweb.org.
- Traub, Lance W. (24 March 2016). "Semi-Empirical Prediction of Airfoil Hysteresis". Aerospace. 3 (2): 9. .
- Weltner, Klaus; Ingelman-Sundberg, Martin (1999). "Physics of flight - revisited". Archived from the original on 29 September 2011. Retrieved 25 April 2021.
Further reading
- Anderson, John, D (2007). Fundamentals of Aerodynamics. McGraw-Hill.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - Ali Kamranpay, Alireza Mehrabadi. Numerical Analysis of NACA Airfoil 0012 at Different Attack Angles and Obtaining its Aerodynamic Coefficients. Journal of Mechatronics and Automation. 2019; 6(3): 8–16p.
- Bearman, Matt (2019). "Going with the Flow? Britain's Contribution to Laminar-Flow Research, 1930–1947". The Aviation Historian (29): 74–87. ISSN 2051-1930.