Influid dynamics, thelift coefficient (C_L) is adimensionless quantity that relates thelift generated by alifting body to thefluid density around the body, thefluid velocity and an associated reference area. A lifting body is afoil or a complete foil-bearing body such as afixed-wing aircraft.C_L is a function of theangle of the body to the flow, itsReynolds number and itsMach number. The section lift coefficientc_l refers to the dynamic lift characteristics of atwo-dimensional foil section, with the reference area replaced by the foilchord.^[1][2]

The lift coefficientC_L is defined by^[2][3]

${\displaystyle C_{\mathrm{L}}\equiv \frac{L}{qS}=\frac{L}{\frac{1}{2}\rho u^{2}S}=\frac{2L}{\rho u^{2}S}}$ ,

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

${\displaystyle S_{aer}\equiv cs}$

resulting in a coefficient:

${\displaystyle C_{\mathrm{L},aer}\equiv \frac{L}{qcs},}$

While in marine dynamics and for thick airfoils, the second axis is sometimes taken in the thickness direction:

${\displaystyle S_{mar}=ts}$

resulting in a different coefficient:

${\displaystyle C_{\mathrm{L},mar}\equiv \frac{L}{qts}}$

The ratio between these two coefficients is the thickness ratio:

${\displaystyle C_{\mathrm{L},mar}\equiv \frac{c}{t}{C}_{\mathrm{L},aer}}$

The lift coefficient can be approximated using thelifting-line theory,^[4] numerically calculated or measured in awind tunnel test of a complete aircraft configuration.

Lift coefficient may also be used as a characteristic of a particular shape (or cross-section) of anairfoil. In this application it is called thesection lift coefficient${\displaystyle c_{\text{l}}}$. It is common to show, for a particular airfoil section, the relationship between section lift coefficient andangle of attack.^[5] It is also useful to show the relationship between section lift coefficient anddrag coefficient.

The section lift coefficient is based on two-dimensional flow over a wing of infinite span and non-varying cross-section so the lift is independent of spanwise effects and is defined in terms of${\displaystyle L^{\mathrm{\prime }}}$, the lift force per unit span of the wing. The definition becomes

${\displaystyle c_{\text{l}}=\frac{L^{\mathrm{\prime }}}{qc},}$

where${\displaystyle c}$ is the reference length that should always be specified: in aerodynamics and airfoil theory usually the airfoilchord is chosen, while in marine dynamics and for struts usually the thickness${\displaystyle t}$ is chosen. Note this is directly analogous to the drag coefficient since the chord can be interpreted as the "area per unit span".

For a given angle of attack,c_l can be calculated approximately using thethin airfoil theory,^[6] calculated numerically or determined from wind tunnel tests on a finite-length test piece, with end-plates designed to ameliorate the three-dimensional effects. Plots ofc_l versus angle of attack show the same general shape for allairfoils, but the particular numbers will vary. They show an almost linear increase in lift coefficient with increasingangle of attack with a gradient known as the lift slope. For a thin airfoil of any shape the lift slope is 2π per radian, or π²/90 ≃ 0.11 per degree. At higher angles a maximum point is reached, after which the lift coefficient reduces. The angle at which maximum lift coefficient occurs is thestall angle of the airfoil, which is approximately 10 to 15 degrees on a typical airfoil.

The stall angle for a given profile is also increasing with increasing values of the Reynolds number, at higher speeds indeed the flow tends to stay attached to the profile for longer delaying the stall condition.^[7][8] For this reason sometimeswind tunnel testing performed at lower Reynolds numbers than the simulated real life condition can sometimes give conservative feedback overestimating the profiles stall.

Symmetric airfoils necessarily have plots of c_l versus angle of attack symmetric about thec_l axis, but for any airfoil with positivecamber, i.e. asymmetrical, convex from above, there is still a small but positive lift coefficient with angles of attack less than zero. That is, the angle at whichc_l = 0 is negative. On such airfoils at zero angle of attack the pressures on the upper surface are lower than on the lower surface.

• Lift-to-drag ratio
• Drag coefficient
• Foil (fluid mechanics)
• Pitching moment
• Circulation control wing
• Zero lift axis

• L. J. Clancy (1975):Aerodynamics. Pitman Publishing Limited, London,ISBN 0-273-01120-0
• Abbott, Ira H., and Doenhoff, Albert E. von (1959):Theory of Wing Sections,Dover Publications New York, # 486-60586-8

• Aerodynamics
• Aircraft wing design
• Dimensionless numbers of fluid mechanics

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