# Drag coefficient

The drag coefficient (Cd, Cx or Cw, 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 Cd 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.
File:Cd flat plate.JPG
Flow around a plate, showing stagnation.

A Cd 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 Cd 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 Cd of a real square flat plate is often given as 1.17. Flow patterns and therefore Cd for some shapes can change with the Reynolds number and the roughness of the surfaces.

## Cd 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 generally slower traffic would save scarce petroleum. Improvements in automotive aerodynamics over the past several decades have rendered this observation inaccurate. Many modern vehicles can sustain economic fuel consumption at far greater speed than 55 miles per hour.

### CdA

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 CdA (or CxA), a multiplication of the Cd 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 CdA 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 CdA from the mass of the diver and equipment and terminal velocity. Skydiver CdA examples are in both  ft² and m² units.

File:Dragi.jpgFile:Dragm.jpg <P> To see more related information visit the Extreme High Altitude Conditions Calculator

Automobile examples of CdA ft² are shown below: [5]

### Drag in sports and racing cars

Reducing drag is also a factor in sports car design, where fuel efficiency is less of a factor, but where low drag helps a car achieve a high top speed. However, there are other important aspects of aerodynamics that affect cars designed for high speed, including racing cars. Notably, it is important to minimize lift, hence increasing downforce, to avoid the car ever becoming airborne. Also it is important to maximize aerodynamic stability: some racing cars have tested well at particular "attack angles", yet performed catastrophically, i.e. flipping over, when hitting a bump or experiencing turbulence from other vehicles (most notably the Mercedes-Benz CLR). For best cornering and racing performance, as required in Formula 1 cars, downforce and stability are crucial and these cars have very high Cd values.

### Typical values and examples

The typical modern automobile achieves a drag coefficient of between 0.30 and 0.35. SUVs, with their flatter shapes, typically achieve a Cd of 0.35–0.45. Notably, certain cars can achieve figures of 0.25-0.30, although sometimes designers deliberately increase drag in order to reduce lift.

Some examples of Cd:

• 0.137 - Ford Probe V prototype, 1985
• 0.12 - Reflex 1000, 1996 [7]
• 0.117 - Summers Brothers Goldenrod Bonneville race car, 1965 [8]

Figures given are generally for the basic model. Faster and more luxurious models often have higher drag, thanks to wider tires and extra spoilers.

## Cd in aircraft

Some examples of Cd [9]:

• 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

## Cd in other shapes

Some examples of Cd [10]

• 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 (Re = 106)
• 0.005 - turbulent flat plate (Re = 106)
• 1.0-1.3 - man (upright position)
• 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