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Drag coefficient

In fluid dynamics, the drag coefficient (commonly denoted as: ''cd'', ''cx'' or ''cw'') is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.〔McCormick, Barnes W. (1979): ''Aerodynamics, Aeronautics, and Flight Mechanics''. p. 24, John Wiley & Sons, Inc., New York, ISBN 0-471-03032-5〕
The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag.〔Clancy, L. J.: ''Aerodynamics''. Section 5.18〕〔Abbott, Ira H., and Von Doenhoff, Albert E.: ''Theory of Wing Sections''. Sections 1.2 and 1.3〕 The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.〔Clancy, L. J.: ''Aerodynamics''. Section 11.17〕
==Definition==
The drag coefficient $c_\mathrm d\,$ is defined as:
:$c_\mathrm d = \dfrac\,$
where:
:$F_\mathrm d\,$ is the drag force, which is by definition the force component in the direction of the flow velocity,〔See lift force and vortex induced vibration for a possible force components transverse to the flow direction.〕
:$\rho\,$ is the mass density of the fluid,〔Note that for the Earth's atmosphere, the air density can be found using the barometric formula. Air is 1.293 kg/m3 at 0 °C and 1 atmosphere.〕
:$u\,$ is the flow speed of the object relative to the fluid,
:$A\,$ is the reference area.
The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross sectional area of the vehicle, depending on where the cross section is taken. For example, for a sphere $A = \pi r^2\,$ (note this is not the surface area = $\!\ 4 \pi r^2$).
For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low: much lower than for a car with the same drag and frontal area, and at the same speed.
Airships and some bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume (volume to the two-thirds power). Submerged streamlined bodies use the wetted surface area.
Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less.

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