Airfoil

From Wikipedia, the free encyclopedia

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.

Contents 1 Introduction 2 Airfoil terminology 3 Thin Airfoil Theory 4 Reference (thin airfoil/aerofoil theory) 5 See also 6 External links 7 References

[edit] Introduction

A fixed-wing aircraft's wing horizontal and vertical stabilizer are built with airfoil shaped cross sections. 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.

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 (force). Some objects, asymmetric airfoils that are curved on the top and flat on the bottom, however, can generate lift at zero angle of attack. Airfoils are efficient shapes, generating high lift with low 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. A supercritical airfoil, with its low camber, reduces transonic drag divergence, 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. Moveable 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 purposely designed for specific functions using computational fluid dynamics. Modern aircraft wings may have different airfoil sections along the wing span, each one optimized for the aerodynamic conditions in each section of the wing.

[edit] 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

[edit] Thin Airfoil Theory

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

The airfoil, centre-line equation y(x), is considered to produce a distribution of vorticity γ(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 α − dy / dx. That is

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

x = c(1 − cos(θ)) / 2,

as a Fourier series in A_nsin(nθ) with a modified lead term A₀(1 + cos(θ)) / sin(θ)

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

C_M = − 0.5π(A₀ + A₁ − A₂ / 2)

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

Δx / c = 0.25π((A₁ − A₂) / C_L)

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

[edit] Reference (thin airfoil/aerofoil theory)

The following is typical of many references on this subject

[1]

[edit] See also

• Lift (force)
• Angle of attack
• Coefficient of lift
• Stall (flight)
• Supercritical airfoil
• Foil (fluid mechanics)
• NACA airfoil
• Parafoil

[edit] External links

• UIUC Airfoil Coordinates Database

[edit] References

1. ^ Hurt, H. H., Jr. [1960] (January 1965). 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.