Airfoil

Various components of the airfoil.

An airfoil (in American English, or aerofoil in British English) is the shape of a wing or blade (of a propeller, rotor or turbine) or sail as seen in cross-section.

An airfoil shaped body moved through a fluid produces a force perpendicular to the fluid called lift. Subsonic flight airfoils have a characteristic shape with a rounded leading edge, followed by a sharp trailing edge, often with asymmetric camber. Airfoils designed with water as the working fluid are also called hydrofoils.

Introduction

The historical evolution of airfoil sections, 1908 - 1944, NASA

Lift and Drag curves for a typical airfoil

A fixed-wing aircraft's wings, horizontal, and vertical stabilizers are built with airfoil-shaped cross sections, as are helicopter rotor blades. Airfoils are also found in propellers, fans, compressors and turbines. Sails are also airfoils, and the underwater surfaces of sailboats, such as the centerboard, and keel are similar in cross-section and operate on the same principles as airfoils. Swimming and flying creatures and even many plants and sessile organisms employ airfoils; common examples being bird wings, the bodies of fishes, and the shape of sand dollars. An airfoil shaped wing can create downforce on an automobile or other motor vehicle, improving traction.

1

http://en.wikipedia.org/wiki/Traction_(engineering)http://en.wikipedia.org/wiki/Automobilehttp://en.wikipedia.org/wiki/Downforcehttp://en.wikipedia.org/wiki/Sand_dollarhttp://en.wikipedia.org/wiki/Sand_dollarhttp://en.wikipedia.org/wiki/Sessilehttp://en.wikipedia.org/wiki/Keelhttp://en.wikipedia.org/wiki/Centerboardhttp://en.wikipedia.org/wiki/Sailhttp://en.wikipedia.org/wiki/Turbinehttp://en.wikipedia.org/wiki/Axial_compressorhttp://en.wikipedia.org/wiki/Fan_(implement)http://en.wikipedia.org/wiki/Propellerhttp://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Vertical_stabilizerhttp://en.wikipedia.org/wiki/Horizontal_stabilizerhttp://en.wikipedia.org/wiki/Winghttp://en.wikipedia.org/wiki/Fixed-wing_aircrafthttp://en.wikipedia.org/wiki/NASAhttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Camber_(aerodynamics)http://en.wikipedia.org/wiki/Subsonic_flighthttp://en.wikipedia.org/wiki/Lift_(force)http://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Sailhttp://en.wikipedia.org/wiki/Turbinehttp://en.wikipedia.org/wiki/Helicopter_rotorhttp://en.wikipedia.org/wiki/Propellerhttp://en.wikipedia.org/wiki/Winghttp://en.wikipedia.org/wiki/British_Englishhttp://en.wikipedia.org/wiki/American_Englishhttp://en.wikipedia.org/wiki/Image:Airfoil.svghttp://en.wikipedia.org/wiki/Image:Airfoil.svghttp://en.wikipedia.org/wiki/Image:Airfoil_Evolution.svghttp://en.wikipedia.org/wiki/Image:Airfoil_Evolution.svghttp://en.wikipedia.org/wiki/Image:Lift_drag_graph.JPGhttp://en.wikipedia.org/wiki/Image:Lift_drag_graph.JPG

Any object with an angle of attack in a moving fluid, such as a flat plate, a building, or the deck of a bridge, will generate an aerodynamic force perpendicular to the flow called lift. Airfoils are more efficient lifting shapes, generating lift with lower drag and maintaining lift at higher angles of attack. A lift and drag curve obtained in wind tunnel testing is shown on the right.

Airfoil design is a major facet of aerodynamics. Various airfoils serve different flight regimes. Asymmetric airfoils can generate lift at zero angle of attack, while a symmetric airfoil may better suit frequent inverted flight as in an aerobatic airplane. Supersonic airfoils are much more angular in shape and can have a very sharp leading edge. A supercritical airfoil, with its low camber, reduces transonic drag divergence. Movable high-lift devices, flaps and slats are fitted to airfoils on many aircraft.

Schemes have been devised to describe airfoils an example is the NACA system. Various ad-hoc naming systems are also used. An example of a general purpose airfoil that finds wide application, and predates the NACA system, is the Clark-Y. Today, airfoils are designed for specific functions using inverse design programs such as PROFIL and XFOIL. Modern aircraft wings may have different airfoil sections along the wing span, each one optimized for the conditions in each section of the wing.

An airfoil designed for winglets (PSU 90-125WL)

Airfoil terminology

The various terms related to airfoils are defined below:[1]

The mean camber line is a line drawn half way between the upper and lower surfaces. The chord line is a straight line connecting the leading and trailing edges of the airfoil,

at the ends of the mean camber line. The chord is the length of the chord line and is the characteristic dimension of the

airfoil section The maximum thickness and the location of maximum thickness are expressed as a

percentage of the chord

An airfoil section is nicely displayed at the tip of this Denney Kitfox aircraft (G-FOXC), built in 1991.

Thin Airfoil Theory

2

file:///E:\harm\missiles\MAHIII\Airfoil - Wikipedia, the free encyclopedia.htm#_note-0#_note-0http://en.wikipedia.org/wiki/Wingtip_devicehttp://en.wikipedia.org/wiki/Clark-Yhttp://en.wikipedia.org/wiki/NACA_airfoilhttp://en.wikipedia.org/wiki/Slatshttp://en.wikipedia.org/wiki/Flap_(aircraft)http://en.wikipedia.org/wiki/Transonichttp://en.wikipedia.org/wiki/Supercritical_airfoilhttp://en.wikipedia.org/wiki/Aerobatichttp://en.wikipedia.org/wiki/Aerodynamicshttp://en.wikipedia.org/wiki/Wind_tunnelhttp://en.wikipedia.org/wiki/Drag_(physics)http://en.wikipedia.org/wiki/Lift_(force)http://en.wikipedia.org/wiki/Angle_of_attackhttp://en.wikipedia.org/wiki/Image:PSU-90-125.PNGhttp://en.wikipedia.org/wiki/Image:PSU-90-125.PNGhttp://en.wikipedia.org/wiki/Image:Denney.kitfox.g-foxc.arp.jpghttp://en.wikipedia.org/wiki/Image:Denney.kitfox.g-foxc.arp.jpg

A simple mathematical theory of 2-D thin airfoils was devised by Ludwig Prandtl and others in the 1920s.

The airfoil, centre-line equation y(x), is considered to produce a distribution of vorticity (s) along the chord line s. By the Kutta condition, the vorticity is zero at the trailing edge. Since the airfoil is thin, x can be used instead of s, and all angles can be approximated as small.

From the Biot-Savart law, this vorticity produces a flow field w(s) where

Since there is no flow normal to the curved surface of the airfoil, w(x) balances that from the component of main flow V which locally normal to the plate - the main flow is locally inclined to the plate by an angle dy / dx. That is

This integral equation can by solved for (x), after replacing x by

x = c(1 cos()) / 2,

as a Fourier series in Ansin(n) with a modified lead term A0(1 + cos()) / sin()

That is

(These terms are known as the Glauert integral).

The coefficients are given by

and

By the Kutta-Joukowski theorem, the total lift force F is proportional to

and its moment M about the leading edge to

The calculated Lift coefficient depends only on the first two terms of the Fourier series, as

The moment M depends only on A0,A1andA2 , as

CM = 0.5(A0 + A1 A2 / 2)

3

http://en.wikipedia.org/wiki/Kutta-Joukowski_theoremhttp://en.wikipedia.org/wiki/Hermann_Glauerthttp://en.wikipedia.org/wiki/Biot-Savart_lawhttp://en.wikipedia.org/wiki/1920shttp://en.wikipedia.org/wiki/Ludwig_Prandtl

From this it follows that the center of lift is aft of the 'quarter-chord' point 0.25 c, by

x / c = 0.25((A1 A2) / CL)

The aerodynamic center is at the quarter-chord point. The AC is where the pitching moment M' does not vary with angle of attack ie

Angle of attack

In this diagram, the black lines represent the flow of the wind. The wing is shown end on. The angle is the angle of attack.

Angle of attack (AOA, , Greek letter alpha) is a term used in aerodynamics to describe the angle between the airfoil's chord line and the direction of airflow wind, effectively the direction in which the aircraft is currently moving. It can be described as the angle between where the wing is pointing and where it is going.

The amount of lift generated by a wing is directly related to the angle of attack, with greater angles generating more lift (and more drag). This remains true up to the stall point, where lift starts to decrease again because of flow separation.

Planes flying at high angles of attack can suddenly enter a stall if, for example, a strong wind gust changes the direction of the relative wind. Also, to maintain a given amount of lift, the angle of attack must be increased as speed through the air decreases. This is why stalling is an effect that occurs more frequently at low speeds.

Nonetheless, a wing (or any other airfoil) can stall at any speed. Planes that already have a high angle of attack, for example because they are pulling g or a heavy payload, will stall at speed well above the normal stall speed, since only a small increase in the angle of attack will take the wing above the critical angle.

The critical angle is typically around 15 for most airfoils. Using a variety of additional aerodynamic surfaces known as high-lift devices like leading edge extensions(leading edge wing root extensions), fighter aircraft have increased the potential flyable alpha from about 20 to over 45, and in some designs, 90 or more. That is, the plane remains flyable when the wing's chord is perpendicular to the direction of motion.

Some aircraft are equipped with a built-in flight computer that automatically prevents the plane from lifting its nose any further when the maximum angle of attack is reached, in spite of pilot input. This is called the angle of attack lim