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 motion 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

Introduction

Aerofoil terminology

Thin Airfoil Theory

Reference (thin airfoil/aerofoil theory)

See also

External links

References

Introduction

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.
While 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, able generate more lift (up to a point), and to generate lift with less drag.
A lift and drag curve obtained in wind tunnel testing is shown on the right. The curve represents an airfoil with a positive camber so lift is produced at zero angle of attack. With increased angle of attack, lift increases in a roughly linear relation. At about eighteen degrees this airfoil stalls and lift falls off quickly beyond that. Drag is least at a slight negative angle for this particular airfoil, and increases rapidly with higher angles.
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.

Aerofoil 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

Thin Airfoil Theory

A simple mathematical theory of 2-D thin airfoils was devised by Ludwig Prandtl and others in the 1920s.
The airfoil is modeled as a thin lifting mean-line (camber line). The mean-line, y(x), is considered to produce a distribution of vorticity $gamma\; (s)$ along the line, s. By the Kutta condition, the vorticity is zero at the trailing edge. Since the airfoil is thin, x (chord position) 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

where x is the location at which induced velocity is produced, x' is the location of the vortex element producing the velocity and c is the chord length of the aerofoil.
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 is locally normal to the plate - the main flow is locally inclined to the plate by an angle . That is

This integral equation can by solved for $gamma(x)$, after replacing x by
$x\; =\; c(1\; -\; cos\; (\; heta\; ))/2$ ,
as a Fourier series in $A\_n\; sin(n\; heta)$ with a modified lead term $A\_0\; (1+cos\; (\; heta))\; /sin(\; heta)$
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
$$
ho V int_{0}^{c} gamma (x). dx
and its moment M about the leading edge to
$$
ho V int_{0}^{c} x.gamma (x) . dx
The calculated Lift coefficient depends only on the first two terms of the Fourier series, as
$C\_L\; =\; 2\; pi\; (A\_0\; +\; A\_1/2)$
The moment M about the leading edge depends only on $A\_0,\; A\_1\; and\; A\_2$
, as
$C\_M\; =\; -\; 0.5\; pi\; (A\_0+A\_1-A\_2/2)$
The moment about the 1/4 chord point will thus be,
$C\_M(1/4c)\; =\; -\; pi\; /4\; (A\_1\; -\; A\_2)$.
From this it follows that the center of lift is aft of the 'quarter-chord' point 0.25 c, by
$Delta\; x\; /c\; =\; pi\; /4\; ((A\_1-A\_2)/C\_L)$
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

Reference (thin airfoil/aerofoil theory)

The following is typical of many references on this subject
[1]
[2]

See also

★ Lift (force)

★ Angle of attack

★ Coefficient of lift

★ Stall (flight)

★ Supercritical airfoil

★ Foil (fluid mechanics)

★ NACA airfoil

★ Parafoil

External links

★ UIUC Airfoil Coordinates Database

★ The Joukowski Airfoil

References

1. Aerodynamics for Naval Aviators, , H. H., Jr., Hurt, U.S. Navy, Aviation Training Division, 1965, NAVWEPS 00-80T-80