Aerofoil Lift: Bernoulli, Circulation and the Stall

Lift is a pressure difference, not a race to the trailing edge

An aerofoil generates lift because air moving over its curved upper surface accelerates and its pressure drops, while air along the flatter lower surface stays relatively slower and higher-pressure — the net upward push is the integral of that pressure difference over the whole surface. The popular 'equal transit time' explanation (that upper- and lower-surface air must arrive at the trailing edge simultaneously) is simply wrong; the real link between speed and pressure is Bernoulli's principle along a streamline, and the flow actually accelerates over the top by considerably more than equal-transit-time would predict.

p + ½ρv² + ρgh = const     along a streamline (Bernoulli, incompressible, inviscid)
                                 → where v is higher, p is lower

The more rigorous account uses circulation: viscosity at the sharp trailing edge forces the flow to leave smoothly rather than wrap around the edge (the Kutta condition), and satisfying that condition requires a net circulatory flow around the aerofoil — faster over the top, slower underneath. The Kutta–Joukowski theorem then gives lift per unit span directly from that circulation, L' = ρ·V∞·Γ, tying the intuitive pressure-difference picture and the rigorous vortex picture together.

Angle of attack and the lift curve

For small angles the lift coefficient rises almost perfectly linearly with angle of attack α:

C_L ≈ C_L0 + 2π·α          (thin aerofoil theory, α in radians, small-angle regime)
L = ½·ρ·V²·S·C_L            (lift force from the coefficient)

The 2π slope (about 0.11 per degree) is a strikingly clean result of thin-aerofoil theory and matches real aerofoils well up to roughly 10–15°. Camber — asymmetry between the upper and lower surface curvature — shifts the whole curve upward, giving lift even at zero angle of attack, which is why cambered aerofoils are used where you need lift at low speed (gliders, high-lift devices) while symmetric sections are preferred where you need zero lift at zero angle of attack (many aerobatic and tail surfaces). Thickness mainly affects the pressure distribution's severity and the stall behaviour rather than the linear-region slope.

Stall: when the boundary layer gives up

Lift does not increase forever with angle of attack. Past a critical angle — typically 12° to 20° depending on the section — the boundary layer on the upper surface can no longer follow the increasingly adverse pressure gradient near the trailing edge and separates: instead of smoothly reattaching, the flow peels away into a turbulent, recirculating wake. Lift collapses abruptly (C_L drops sharply) and drag rises sharply at the same moment, which is why a stalled wing is dangerous — the aircraft simultaneously loses the force holding it up and gains the force slowing it down.

Different sections stall differently. Thin, sharp-nosed aerofoils tend toward leading-edge stall — an abrupt, almost bubble-triggered separation right at the nose with little warning. Thicker, more rounded sections favour a gentler trailing-edge stall, where separation creeps forward gradually from the trailing edge as angle of attack increases, giving buffet and a soft, progressive loss of lift that pilots can feel and recover from — one reason general-aviation trainers deliberately use thicker, forgiving sections.

Reading the Cl/Cd polar

Plotting C_L against C_D (a drag polar) rather than against angle of attack reveals the aerodynamic trade-off directly. Total drag near the linear-lift region is dominated by parasite drag (skin friction plus form drag, roughly constant with α) and induced drag (the cost of generating lift itself, which for a finite wing grows as C_L²/(π·e·AR), where AR is aspect ratio and e is the span efficiency). The point of maximum L/D — the best glide ratio, and the angle a glider pilot or an efficient cruise flight targets — sits where a line from the origin is tangent to the drag polar; push past it toward stall and both C_L and, catastrophically, the ratio collapse together as separation dominates.

Frequently asked questions

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