Drag coefficient

In general, ${\displaystyle c_{d}}$ is not an absolute constant for a given body shape. It varies with the speed of airflow (or more generally with Reynolds number ${\displaystyle Re}$). A smooth sphere, for example, has a ${\displaystyle c_{d}}$ that varies from high values for laminar flow to 0.47 for turbulent flow. Although the drag coefficient decreases with increasing ${\displaystyle Re}$, the drag force increases.

cd	Item[17]
0.001	Laminar flat plate parallel to the flow (${\displaystyle Re<10^{6}}$)
0.005	Turbulent flat plate parallel to the flow (${\displaystyle Re>10^{6}}$)
0.1	Smooth sphere (${\displaystyle Re=10^{6}}$)
0.47	Smooth sphere (${\displaystyle Re=10^{5}}$)
0.81	Triangular trapeze (45°)
0.9-1.7	Trapeze with triangular basis (45°)
0.295	Bullet (not ogive, at subsonic velocity)
0.48	Rough sphere (${\displaystyle Re=10^{6}}$)
1.0–1.1	Skier
1.0–1.3	Wires and cables
1.0–1.3	Adult human (upright position)
1.1-1.3	Ski jumper[18]
1.28	Flat plate perpendicular to flow (3D)[19]
1.3–1.5	Empire State Building
1.8–2.0	Eiffel Tower
1.98–2.05	Long flat plate perpendicular to flow (2D)

As noted above, aircraft use their wing area as the reference area when computing ${\displaystyle c_{\mathrm {d} }}$, while automobiles (and many other objects) use frontal cross-sectional area; thus, coefficients are not directly comparable between these classes of vehicles. In the aerospace industry, the drag coefficient is sometimes expressed in drag counts where 1 drag count = 0.0001 of a ${\displaystyle C_{d}}$.[20]

Drag, in the context of fluid dynamics, refers to forces that act on a solid object in the direction of the relative flow velocity (note that the diagram below shows the drag in the opposite direction to the flow). The aerodynamic forces on a body come primarily from differences in pressure and viscous shearing stresses. Thereby, the drag force on a body could be divided into two components, namely frictional drag (viscous drag) and pressure drag (form drag). The net drag force could be decomposed as follows:

Flow across an airfoil showing the relative impact of drag force to the direction of motion of fluid over the body. This drag force gets divided into frictional drag and pressure drag. The same airfoil is considered as a streamlined body if friction drag (viscous drag) dominates pressure drag and is considered a blunt body when pressure drag (form drag) dominates friction drag.

${\displaystyle {\begin{aligned}c_{\mathrm {d} }&={\dfrac {2F_{\mathrm {d} }}{\rho v^{2}A}}\\&=c_{\mathrm {p} }+c_{\mathrm {f} }\\&=\underbrace {{\dfrac {1}{\rho v^{2}A}}\displaystyle \int \limits _{S}\mathrm {d} A(p-p_{o})\left({\hat {\mathbf {n} }}\cdot {\hat {\mathbf {i} }}\right)} _{c_{\mathrm {p} }}+\underbrace {{\dfrac {1}{\rho v^{2}A}}\displaystyle \int \limits _{S}\mathrm {d} A\left({\hat {\mathbf {t} }}\cdot {\hat {\mathbf {i} }}\right)T_{w}} _{c_{\mathrm {f} }}\end{aligned}}}$

where:

${\displaystyle c_{\mathrm {p} }}$ is the pressure drag coefficient,

${\displaystyle c_{\mathrm {f} }}$ is the friction drag coefficient,

${\displaystyle {\hat {\mathbf {t} }}}$ = Tangential direction to the surface with area dA,

${\displaystyle {\hat {\mathbf {n} }}}$ = Normal direction to the surface with area dA,

${\displaystyle T_{\mathrm {w} }}$ is the shear Stress acting on the surface dA,

${\displaystyle p_{\mathrm {o} }}$ is the pressure far away from the surface dA,

${\displaystyle p}$ is pressure at surface dA,

${\displaystyle {\hat {\mathbf {i} }}}$ is the unit vector in direction of free stream flow

Therefore, when the drag is dominated by a frictional component, the body is called a streamlined body; whereas in the case of dominant pressure drag, the body is called a blunt or bluff body. Thus, the shape of the body and the angle of attack determine the type of drag. For example, an airfoil is considered as a body with a small angle of attack by the fluid flowing across it. This means that it has attached boundary layers, which produce much less pressure drag.

Trade-off relationship between zero-lift drag and lift induced drag

The wake produced is very small and drag is dominated by the friction component. Therefore, such a body (here an airfoil) is described as streamlined, whereas for bodies with fluid flow at high angles of attack, boundary layer separation takes place. This mainly occurs due to adverse pressure gradients at the top and rear parts of an airfoil.

Due to this, wake formation takes place, which consequently leads to eddy formation and pressure loss due to pressure drag. In such situations, the airfoil is stalled and has higher pressure drag than friction drag. In this case, the body is described as a blunt body.

A streamlined body looks like a fish (Tuna), Oropesa, etc. or an airfoil with small angle of attack, whereas a blunt body looks like a brick, a cylinder or an airfoil with high angle of attack. For a given frontal area and velocity, a streamlined body will have lower resistance than a blunt body. Cylinders and spheres are taken as blunt bodies because the drag is dominated by the pressure component in the wake region at high Reynolds number.

To reduce this drag, either the flow separation could be reduced or the surface area in contact with the fluid could be reduced (to reduce friction drag). This reduction is necessary in devices like cars, bicycle, etc. to avoid vibration and noise production.

The aerodynamic design of cars has evolved from the 1920s to the end of the 20th century. This change in design from a blunt body to a more streamlined body reduced the drag coefficient from about 0.95 to 0.30.

Time history of aerodynamic drag of cars in comparison with change in geometry of streamlined bodies (blunt to streamline).