Airfoil (source code)
= Airfoil
{wiki}
= Aerofoil
{synonym}
An <airfoil> (British spelling: <aerofoil>) is the cross-sectional profile of a lifting surface, such as a wing or blade. Its chord is the straight segment from leading edge to trailing edge, with length $c$; its mean camber line runs midway between its upper and lower surfaces, and its thickness measures their separation. Camber is the departure of that mean line from the chord. The <angle of attack> describes the profile's orientation relative to the incoming flow. These independent choices let a designer alter the distribution of <pressure>, <lift> and <drag>, rather than simply enlarging the surface. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/wing-geometry/[NASA Glenn, Wing Geometry, Airfoil Geometry subsection]{ref}
The distinction between an <airfoil> and a finite wing matters. A two-dimensional section model assumes no variation along span and predicts <lift> per unit span $L'$. A wing of span $b$ has a spanwise distribution $L'(z)$ and total <lift> $L=\int_{-b/2}^{b/2}L'(z)\,dz$. Its tip flow and trailing <vortices> generate a downward induced <velocity>, called downwash, which changes the local flow seen by the sections. Thus one cannot generally multiply the isolated two-dimensional $L'$ by $b$. The wing aspect ratio $b^2/S$ measures its span relative to its reference area and helps characterize these three-dimensional effects. https://pressbooks.lib.vt.edu/aerodynamics/chapter/chapter-3-additional-aerodynamic-tools/[James F. Marchman III, Aerodynamics and Aircraft Performance, chapter 3.4: finite wings]{ref}
For a thin section with small camber slopes and small <angle of attack>, <thin airfoil theory> predicts
$$
c_l\simeq2\pi(\alpha-\alpha_{L=0}),\qquad
\frac{dc_l}{d\alpha}\simeq2\pi,
$$
where both <angles> are in <radians> and $\alpha_{L=0}$ is the zero-lift <angle of attack>. The model assumes two-dimensional, <steady flow>, <incompressible flow>, <inviscid flow>, an attached outer flow, and smooth departure at a sharp trailing edge (the Kutta condition). This last condition selects the <circulation> used by the <Kutta–Joukowski theorem>; with counterclockwise <circulation> $\Gamma$ positive and $\mathbf U_\infty=U_\infty\mathbf e_x$, that theorem gives $L'=-\rho_\infty U_\infty\Gamma$ for positive lift towards $+\mathbf e_y$. The beauty is that a detailed <velocity field> collapses to a simple force law, while the geometry enters through $\alpha_{L=0}$. https://ocw.mit.edu/courses/16-01-unified-engineering-i-ii-iii-iv-fall-2005-spring-2006/d721171c42af48a056aaccec784a6d10_f03_0304.pdf[MIT Unified Engineering, F3 lecture notes, pp. 2–4: camber and lift slope]{ref} https://ocw.mit.edu/courses/16-01-unified-engineering-i-ii-iii-iv-fall-2005-spring-2006/cc3f20c40c9451bde6a595fdd96a7e9e_f02_mud_0304.pdf[MIT Unified Engineering, F2 questions 7 and 9: symmetric sections and Kutta condition]{ref}
A symmetric <airfoil> has $\alpha_{L=0}=0$ in this model: at $\alpha=4\,{}^\circ=\pi/45$ the predicted <lift coefficient> is $c_l\simeq0.439$, and reversing $\alpha$ reverses <lift>. A stipulated cambered section with $\alpha_{L=0}=-2\,{}^\circ$ instead predicts $c_l\simeq0.219$ at zero <angle of attack>. These are ideal calculations, not measurements or guarantees for a particular profile. Air parcels on the upper and lower surfaces have no obligation to arrive together at the trailing edge; the <pressure> and <velocity field> must satisfy the flow problem. A symmetric lifting section already makes an unequal-path-length explanation inadequate. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/bernoulli-and-newton/[NASA Glenn, Bernoulli and Newton: the equal-transit explanation is incorrect]{ref}
Real <airfoils> have a viscous <boundary layer>, even when <inviscid flow> approximates the outer motion. At sufficiently demanding incidence, <flow separation> can become extensive and the <lift coefficient> departs from its approximately linear law, reaches a maximum and may fall: this is <aerodynamic stall>. <Lift> does not generally vanish at <aerodynamic stall>. The onset depends on profile, <Reynolds number>, surface condition and motion history; $2\pi(\alpha-\alpha_{L=0})$ predicts neither a universal stall angle nor post-stall behavior. The pressure/balance experiment in <lift> makes this limit observable by measuring changes in the surface <pressure> distribution alongside the total <force>. https://pressbooks.lib.vt.edu/aerodynamics/chapter/chapter-3-additional-aerodynamic-tools/[James F. Marchman, chapter 3.3: separation invalidates thin-airfoil assumptions]{ref}
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