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A loss of the approximately attached-flow relation between angle of attack and lift coefficient, associated with substantial flow separation. A stalled airfoil can still produce lift; its behavior must be measured or modeled beyond thin airfoil theory.

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. ^[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 $L^{\prime }$. A wing of span $b$ has a spanwise distribution $L^{\prime }(z)$ and total lift $L={\int }_{-b/2}^{b/2}{L}^{\prime }(z)dz$. 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 $L^{\prime }$ by $b$. The wing aspect ratio $b^2/S$ measures its span relative to its reference area and helps characterize these three-dimensional effects. ^[ref]

For a thin section with small camber slopes and small angle of attack, thin airfoil theory predictswhere 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 $L^{\prime }=-{\rho }_{\infty }{U}_{\infty }\Gamma$ 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 ${\alpha }_{L=0}$. ^{[ref] [ref]}

A symmetric airfoil has ${\alpha }_{L=0}=0$ in this model: at $\alpha =4{}^{\circ }=\pi /45$ the predicted lift coefficient is $c_l\simeq 0.439$, and reversing $\alpha$ reverses lift. A stipulated cambered section with ${\alpha }_{L=0}=-2{}^{\circ }$ instead predicts $c_l\simeq 0.219$ 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. ^[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. ^[ref]

The signed angle between a lifting surface's chord and its incoming relative flow. Positive incidence in the planar convention used in airfoil raises the leading edge relative to the trailing edge in a horizontal left-to-right flow. It is distinct from orientation relative to the ground; an induced velocity can change the local effective incidence.

The signed lift divided by dynamic pressure times a stated reference area. For a two-dimensional airfoil, use $c_l=L^{\prime }/(q_{\infty }c)$ instead. Reference area and experimental flow conditions are part of the definition of a reported coefficient; see lift for a worked scale and a pressure/balance experiment.

Lift is the component of the fluid force perpendicular to the far-field flow relative to the body. It need not point vertically: a tilted flow changes the lift direction, and a banked wing can produce a sideways component. In a planar problem choose a unit vector ${\mathbf{e}}_D$ along the incoming relative velocity ${\mathbf{U}}_{\infty }$ and a perpendicular unit vector ${\mathbf{e}}_L$ pointing towards the chosen positive-lift side. ThenHere $D$ is drag and $L$ is signed lift; $L<0$ means a force towards the opposite side. In three dimensions the plane perpendicular to ${\mathbf{U}}_{\infty }$ also admits a separate side-force direction, so a lift axis must be specified. Lift is also distinct from buoyancy, which can exist without a relative flow. ^[ref]

The force comes from adding local surface tractions, rather than assigning a single pressure to each side. Let $\Sigma$ be the wetted body surface and $\mathbf{n}$ its unit normal vector pointing out of the body into the fluid. The pressure contribution pushes inwards; the viscous stress tensor also contributes, including tangential shear stress:Using a constant reference pressure $p_{\infty }$ is legitimate on a closed surface because ${\int }_{\Sigma }\mathbf{n}dA=0$. This surface integral makes the direction explicit: a surface-normal force is generally neither pure lift nor pure drag. Pressure and skin shear stress both enter the resultant, although the pressure term usually dominates lift on an airfoil. ^[ref]

The lift coefficient isolates a useful scale. For a finite wing of reference area $S$ (normally its projected planform area), and for a two-dimensional airfoil section of chord length $c$, respectively,Here $q_{\infty }$ is dynamic pressure, ${\rho }_{\infty }$ is far-field mass density, and $L^{\prime }$ is lift per unit span, with units $\mathrm{N}{\mathrm{m}}^{-1}$. The signs of $C_L$ and $c_l$ follow the chosen lift axis. For stipulated values ${\rho }_{\infty }=1.20\mathrm{kg}{\mathrm{m}}^{-3}$, $U_{\infty }=20\mathrm{m}{\mathrm{s}}^{-1}$, $S=0.50{\mathrm{m}}^2$ and $C_L=0.60$, $q_{\infty }=240\mathrm{Pa}$ and $L=72\mathrm{N}$. Doubling $U_{\infty }$ gives four times the lift only if $C_L$ stays fixed: changes in Reynolds number, Mach number, surface condition or angle of attack can change it. ^[ref]

A motivating experiment is to compare two independently observed quantities: the lift registered by a force balance, and the lift inferred from surface pressures. A low-speed wind tunnel holds the model fixed while air passes it at adjustable speed; a calibrated balance measures forces, while small flush holes on both surfaces connect by tubing to differential-pressure sensors referenced to $p_{\infty }$. Iowa State's GA(W)-1 teaching model has $43$ taps around a $101\mathrm{mm}$ chord; its instructions give their coordinates and close the contour by repeating the first tap. A classroom comparison can combine this pressure-panel method with a balance on the same model; this is an experiment design, not a claim that those instructions report a combined measurement. ^{[ref] [ref]}

Before turning on the wind, apply known positive and negative loads to the balance through its resolving centre; use $mg$ for the known load from a mass. Record all balance channels during loading and unloading, including response to drag and torque loads, to detect cross coupling, hysteresis and zero drift. Record a wind-off tare at each model orientation so its weight does not become an aerodynamic lift reading. Map tunnel flow direction and uniformity, rather than using the fan setting as a speed measurement. Covert's MIT guide describes these calibration, tare and flow-survey requirements. ^[ref]

For each pressure channel, apply zero and several known pressure differences spanning the expected range; determine the voltage-to-pressure relation and recheck it after a run. Inspect tubing for leaks and blocked taps, and wait for readings to settle before averaging: tubing can delay a pressure signal. This calibration principle is used in NASA's electronically scanned pressure systems, where several applied calibration pressures determine each sensor's response and repeated calibration tracks drift. A simple pressure standard can instead use a liquid-column height difference and the hydrostatic pressure law. ^[ref]

Measure far-field static and total pressure outside the model's fluid wake; in low-speed incompressible flow their difference gives $q_{\infty }$ by the Bernoulli equation, so $U_{\infty }=\sqrt{2q_{\infty }/{\rho }_{\infty }}$. Record temperature and ambient pressure to determine mass density using the ideal gas law. At fixed $q_{\infty }$, step the angle of attack, repeat selected settings, and sweep back down to check reproducibility. Record balance lift, each tap's mean pressure, and fluctuation sizes. NASA describes pressure probes connected to differential transducers and emphasizes recording their reference pressure. ^[ref]

Convert each tap to a pressure coefficient $C_{p,i}=(p_i-p_{\infty })/q_{\infty }$. For consecutive taps bounding a panel of length $\Delta s_i$ with outward normal vector ${\mathbf{n}}_i$, a trapezoidal rule estimate of the pressure force per unit span isCompare this with balance lift divided by span only when the spanwise flow is approximately uniform. Agreement tests the pressure-resultant picture; disagreement calls for checking unresolved leading-edge pressure variations, skin shear stress, support loads and three-dimensional end effects before rejecting it. A force balance senses the total load, while taps alone reconstruct the pressure part. Tunnel walls and model blockage alter the effective flow and require corrections; end plates or a model extending between walls approximate two-dimensional flow but do not guarantee it. Record the Reynolds number and Mach number with the result, and do not interpret tunnel lift coefficients as universal wing data. ^{[ref] [ref]}

A small-disturbance, two-dimensional potential flow model for a thin airfoil, using surface tangency and smooth flow departure at its trailing edge to determine circulation. Its lift coefficient slope is $2\pi$ per radian, with camber shifting the zero-lift angle of attack. See airfoil for assumptions, examples and the aerodynamic stall limit.