Lift coefficient

The lift coefficient (C_L, C_N or C_z) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area. A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. C_L is a function of the angle of the body to the flow, its Reynold number and its Mach number. The lift coefficient c_l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

The lift coefficient C_L is defined by

where ${\displaystyle L\,}$ is the lift force, ${\displaystyle S\,}$ is the relevant plan area and ${\displaystyle q\,}$ is the fluid dynamic pressure, in turn linked to the fluid density ${\displaystyle \rho \,}$, and to the flow speed ${\displaystyle u\,}$. The choice of the reference surface should be specified since it is arbitrary. For example, for an cylindric profiles (the 3D extrusion of and airfoil in the spanwise direction) it is always oriented in the spanwise direction, but while in aerodynamics and thin airfoil theory the second axis generating the surface is commonly the chordwise direction:

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