Lift coefficient

The lift coefficient ( or ) is a dimensionless coefficient that relates the lift generated by a lifting body, the dynamic pressure of the fluid flow around the body, and a reference area associated with the body. A lifting body is a foil or a complete foilbearing body such as a fixedwing aircraft.
Lift coefficient is also used to refer to the dynamic lift characteristics of a twodimensional foil section, whereby the reference area is taken as the foil chord.^{[1]}^{[2]}
Lift coefficient may be described as the ratio of lift pressure to dynamic pressure where lift pressure is the ratio of lift to reference area.
Lift coefficient may be used to relate the total lift generated by a foilequipped craft to the total area of the foil. In this application the lift coefficient is called the aircraft or planform lift coefficient
Watercraft and automobiles equipped with fixed foils can also be assigned a lift coefficient.
The lift coefficient is equal to:^{[2]}^{[3]}
where is the lift force,
 is fluid density,
 is true airspeed,(speed of the body relative to a static point on the earth's surface)
 is dynamic pressure, and
 is planform area.
The lift coefficient is a dimensionless number.
The aircraft lift coefficient can be approximated using the Liftingline theory^{[4]} or measured in a wind tunnel test of a complete aircraft configuration.
Contents
Section lift coefficient
Lift coefficient may also be used as a characteristic of a particular shape (or crosssection) of an airfoil. In this application it is called the section lift coefficient It is common to show, for a particular airfoil section, the relationship between section lift coefficient and angle of attack.^{[5]} It is also useful to show the relationship between section lift coefficient and drag coefficient.
The section lift coefficient is based on twodimensional flow  the concept of a wing with infinite span and nonvarying crosssection, the lift of which is bereft of any threedimensional effects. It is not relevant to define the section lift coefficient in terms of total lift and total area because they are infinitely large. Rather, the lift is defined per unit span of the wing In such a situation, the above formula becomes:
where is the chord length of the airfoil.
The section lift coefficient for a given angle of attack can be approximated using the thin airfoil theory,^{[6]} or determined from wind tunnel tests on a finitelength test piece, with endplates designed to ameliorate the threedimensional effects associated with the trailing vortex wake structure.
Note that the lift equation does not include terms for angle of attack — that is because the mathematical relationship between lift and angle of attack varies greatly between airfoils and is, therefore, not constant. (In contrast, there is a straightline relationship between lift and dynamic pressure; and between lift and area.) The relationship between the lift coefficient and angle of attack is complex and can only be determined by experimentation or complicated analysis. See the accompanying graph. The graph for section lift coefficient vs. angle of attack follows the same general shape for all airfoils, but the particular numbers will vary. The graph shows an almost linear increase in lift coefficient with increasing angle of attack, up to a maximum point, after which the lift coefficient reduces. The angle at which maximum lift coefficient occurs is the stall angle of the airfoil.
The lift coefficient is a dimensionless number.
Note that in the graph here, there is still a small but positive lift coefficient with angles of attack less than zero. This is true of any airfoil with camber (asymmetrical airfoils). On a cambered airfoil at zero angle of attack the pressures on the upper surface are lower than on the lower surface.
See also
 Fluid
 Density
 Foil (fluid mechanics)
 Drag coefficient
 Pitching moment
 Circulation control wing
 Zero lift axis
Notes
 ^ Clancy, L. J.: Aerodynamics. Sections 4.15 and 5.4
 ^ ^{a} ^{b} Abbott, Ira H., and Von Doenhoff, Albert E.: Theory of Wing Sections. Section 1.2
 ^ Clancy, L. J.: Aerodynamics. Section 4.15
 ^ Clancy, L. J.: Aerodynamics. Section 8.11
 ^ Abbott, Ira H., and Von Doenhoff, Albert E.: Theory of Wing Sections. Appendix IV
 ^ Clancy, L. J.: Aerodynamics. Section 8.2
References
 Clancy, L. J. (1975): Aerodynamics. Pitman Publishing Limited, London, ISBN 0 273 01120 0
 Abbott, Ira H., and Von Doenhoff, Albert E. (1959): Theory of Wing Sections. Dover Publications Inc., New York, Standard Book Number 486605868
Categories: Aerodynamics
 Wing design
 Dimensionless numbers
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