Drag coefficient

The drag coefficient (C_d, C_x or C_w, depending on the country) is a dimensionless quantity that describes a characteristic amount of aerodynamic drag caused by fluid flow, used in the drag equation. Two objects of the same frontal area moving at the same speed through a fluid will experience a drag force proportional to their C_d numbers. Coefficients for rough unstreamlined objects can be 1 or more, for smooth objects much less.

\mathbf {F} _{d}={1 \over 2}\rho \mathbf {v} ^{2}C_{d}A

explanation of terms on drag equation page.

Usually $A$ is the projected frontal area. For example, for a sphere $A=\pi r^{2}$ .

The drag equation is essentially a statement that, under certain conditions, the drag force on any object is approximately proportional to the square of its velocity through the fluid. The required conditions are that the Reynolds number of the flow around the object must be high enough to create a turbulent wake (larger velocities, larger objects, and lower viscosities make for larger Reynolds numbers), and that the object does not approach the speed of sound in the fluid.

At low Reynolds number, that is for small object, low velocities or high viscosity fluids, the flow around the object is laminar, $C_{d}$ is no more constant but depend on velocity, and $F_{d}$ is proportional to $v$ , instead of $v^{2}$ .

A C_d equal to 1 would be obtained in a case where all of the fluid approaching the object is brought to rest, building up stagnation pressure over the whole front surface. The top figure shows a flat plate with the fluid coming from the right and stopping at the plate. The graph to the left of it shows equal pressure across the surface. In a real flat plate the fluid must turn around the sides, and full stagnation pressure is found only at the center, dropping off toward the edges as in the lower figure and graph. The C_d of a real flat plate would be less than 1, except that there will be a negative pressure (relative to ambient) on the back surface. The overall C_d of a real square flat plate is often given as 1.17. Flow patterns and therefore C_d for some shapes can change with the Reynolds number and the roughness of the surfaces.

C_d in automobiles

The drag coefficient is a common metric in automotive design, where designers strive to achieve a low coefficient. Minimizing drag is done to improve fuel efficiency at highway speeds, where aerodynamic effects represent a substantial fraction of the energy needed to keep the car moving. Indeed, aerodynamic drag increases with the square of speed. Aerodynamics are also of increasing concern to truck designers, where a lower drag coefficient translates directly into lower fuel costs.

About 60% of the power required to cruise at highway speeds is taken up overcoming air drag, and this increases very quickly at high speed. Therefore, a vehicle with substantially better aerodynamics will be much more fuel efficient. Additionally, because drag does increase with the square of speed, a somewhat lower speed can significantly improve fuel economy. This was the major reason for the United States adopting a nationwide 55 mile per hour speed limit during the early 1973 oil crisis as slower traffic would save scarce petroleum.

C_dA

While designers pay attention to the overall shape of the automobile, they also bear in mind that reducing the frontal area of the shape helps reduce the drag. The combination of drag coefficient and area is C_dA (or C_xA), a multiplication of the C_d value by the area.

In aerodynamics, the product of some reference area (such as cross-sectional area, total surface area, or similar) and the drag coefficient is called drag area. In 2003, Car and Driver adapted this metric and adopted it as a more intuitive way to compare the aerodynamic efficiency of various automobiles. Average full-size passenger cars have a drag area of roughly 8.5 ft² (.79 m²). Reported drag area ranges from the 1999 Honda Insight at 5.1 ft² (.47 m²) to the 2003 Hummer H2 at 26.3 ft² (2.44 m²).

More C_dA examples

This value is extremely useful as either the area or drag coefficient alone are not enough to be used in any equation. Sometimes it is not possible to get either value, but it might be possible to deduce it. For a skydiver example below, it is possible to deduce C_dA from the mass of the diver and equipment and terminal velocity. Skydiver C_dA examples are in both ft² and m² units.

C_dA (in m²) with Terminal Velocity & Mass (at 300m)
Terminal velocity	Mass 60kg	Mass 70kg	Mass 80kg	Mass 90kg	Mass 100kg
45 m/s	0.487	0.569	0.650	0.731	0.812
50 m/s	0.395	0.461	0.526	0.592	0.658
55 m/s	0.326	0.381	0.435	0.489	0.544
60 m/s	0.274	0.320	0.365	0.411	0.457
65 m/s	0.234	0.272	0.311	0.350	0.389
70 m/s	0.201	0.235	0.269	0.302	0.336
75 m/s	0.175	0.205	0.234	0.263	0.292

To see more related information visit the Extreme High Altitude Conditions Calculator

C_d in aircraft

Some examples of C_d in aircraft are presented below.[1]

C_d	Aircraft model
0.027	Cessna 172/182
0.027	Cessna 310
0.022	Learjet 24
0.048	F-104 Starfighter
0.021	F-4 Phantom II (subsonic)
0.044	F-4 Phantom II (supersonic)
0.031	Boeing 747
0.095	X-15

C_d in other shapes

Finally, here is a table of the C_d value of other miscellaneous shapes.[2]

C_d	Item
2.1	a smooth brick
0.9	a typical bicycle plus cyclist
0.4	rough sphere (Re = 10⁶)
0.1	smooth sphere (Re = 10⁶)
0.001	laminar flat plate parallel to the flow (Re = 10⁶)
0.005	turbulent flat plate parallel to the flow (Re = 10⁶)
0.295	bullet
1.0-1.3	man (upright position)
1.28	flat plate perpendicular to flow
1.0-1.1	skier
1.0-1.3	wires and cables
1.3-1.5	Empire State Building
1.8-2.0	Eiffel Tower

External links

Cd in automobiles

CdA

More CdA examples

Cd in aircraft

Cd in other shapes

See also