Glossary term
Lift Coefficient
A dimensionless coefficient relating aerodynamic lift force to dynamic pressure and reference area.
Definition
quantityLift coefficient is a dimensionless measure of lift force normalized by dynamic pressure and reference area.
The coefficient allows lift performance to be compared across different speeds, sizes, and fluid densities. It is usually written CL = L / (0.5 rho V^2 S), where L is lift, rho is fluid density, V is freestream speed, and S is reference area. Lift coefficient depends on airfoil shape, angle of attack, Reynolds number, Mach number, surface roughness, flap setting, three-dimensional wing effects, and flow separation.
Lift coefficient normalizes lift force so aerodynamic performance can be compared across scale and speed:
where L is lift force, \rho is fluid density, V is freestream speed, and S is reference area. For an aircraft wing, S is usually planform wing area. For other bodies, the chosen reference area must be stated because it affects the numerical value.
Dependence on operating condition
Lift coefficient is not a fixed property of a wing. It varies with angle of attack, airfoil geometry, Reynolds number, Mach number, surface roughness, flap or slat deployment, sweep, aspect ratio, ground effect, icing, and flow separation. At moderate angles of attack, lift coefficient often increases approximately linearly with angle of attack. Near stall, flow separates and C_L reaches a maximum before decreasing.
Three-dimensional wings differ from two-dimensional airfoil sections because finite span creates tip vortices and downwash. The same section can therefore have different effective lift behaviour in a real wing than in a two-dimensional airfoil test.
Engineering use
Lift coefficient is used in aircraft sizing, takeoff and landing analysis, stall margin, wind-tunnel testing, CFD validation, rotor blades, hydrofoils, wind turbines, and vehicle aerodynamics. The lift equation can be rearranged to estimate required speed, wing area, or lift margin for a given weight.
High maximum lift coefficient reduces takeoff and landing speed, but it may require complex high-lift devices, stronger structure, more weight, more drag, or tighter control of stall behaviour. For high-speed aircraft, compressibility and shock effects can change lift curve slope and stall characteristics.
Common mistakes
A common mistake is comparing lift coefficients without checking reference area, Reynolds number, Mach number, and configuration. Another is assuming published airfoil data applies directly to a finite wing with fuselage, nacelles, control surfaces, roughness, and manufacturing tolerances. Good aerodynamic documentation states reference area, coordinate convention, sign convention, angle-of-attack definition, test or simulation condition, and uncertainty.