Drag coefficient

In fluid dynamics, the drag coefficient (commonly denoted as:

c

d

{\displaystyle c_{\mathrm {d} }}

,

c

x

{\displaystyle c_{x}}

or

c

w

{\displaystyle c_{\rm {w}}}

) 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 in which 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.

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. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.

Definition

The drag coefficient

c

d

{\displaystyle c_{\mathrm {d} }}

is defined as

c

d

=

2

F

d

ρ

u

2

A

{\displaystyle c_{\mathrm {d} }={\dfrac {2F_{\mathrm {d} }}{\rho u^{2}A}}}

where:

F

d

{\displaystyle F_{\mathrm {d} }}

is the drag force, which is by definition the force component in the direction of the flow velocity;

ρ

{\displaystyle \rho }

is the mass density of the fluid;

u

{\displaystyle u}

is the flow speed of the object relative to the fluid;

A

{\displaystyle 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 vehicle's projected frontal area. This may not be the vehicle's cross-sectional area, depending on where the cross-section is measured. For example, for a sphere

A

=

π

r

2

{\displaystyle A=\pi r^{2}}

(note this is not the surface area =

4

π

r

2

{\displaystyle 4\pi r^{2}}

).