Drag coefficient

From Wikipedia, the free encyclopedia

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 object much less.

$\mathbf{F}_d= {1 \over 2} \rho \mathbf{v}^2 C_d A$ explanation of terms on drag equation page.

Flow around a plate, showing stagnation.

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.

1 Cd in automobiles
2 Cd in aircraft
3 Cd in other shapes
4 See also
5 External links

[edit] 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 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.

[edit] 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).

[edit] More C_dA Examples

This value is extremely useful as the either the area or drag coefficent 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 weight and terminal velocity. Don't forget to add the weight of all the equipment! Skydiver C_dA examples are in both ft² and m² units.

Image:Wikisky.jpg

It should be possible to replace this fair use image with a freely licensed one. If you can, please do so as soon as is practical.

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

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

5.10 - 1999 Honda Insight
5.71 - 1990 Honda CR-X Si
5.76 - 1968 Toyota 2000GT
5.80 - 1986 Toyota MR2
5.81 - 1989 Mitsubishi Eclipse GSX
5.88 - 1990 Nissan 240SX
5.92 - 1994 Porsche 911 Speedster
5.95 - 1990 Mazda RX7
6.00 - 1970 Lamborghini Miura
6.13 - 1993 Acura NSX
6.17 - 1995 Lamborghini Diablo
6.27 - 1986 Porsche 911 Carrera
6.27 - 1992 Chevrolet Corvette
6.54 - 1991 Saturn Sports Coupe
6.40 - 1990 Lotus Esprit
6.57 - 1985 Chevrolet Corvette
6.77 - 1995 BMW M3
6.79 - 1993 Toyota Corolla DX
6.81 - 1991 Subaru Legacy
6.90 - 1993 Saturn Wagon
6.93 - 1982 Delorean DMC-12
6.96 - 1988 Porsche 944 S
6.96 - 1995 Chevy Lumina LS
7.02 - 1992 BMW 325I
7.04 - 1991 Honda Civic EX
7.10 - 1995 Saab 900
7.14 - 1995 Subaru Legacy L
7.34 - 2001 Honda Civic
7.39 - 1994 Honda Accord EX
7.48 - 1993 Camaro Z28
7.57 - 1992 Toyota Camry
7.69 - 1994 Chrysler LHS
7.72 - 1993 Subaru Impreza
8.70 - 1990 Volvo 740 Turbo
8.70 - 1992 Ford Crown Victoria
8.71 - 1991 Buick LeSabre Limited
9.54 - 1992 Chevy Caprice Wagon
10.7 - 1992 Chevy Blazer
11.7 - 1993 Jeep Grand Cherokee
16.8 - 2006 Hummer H3
17.4 - 1995 Land Rover Discovery
26.3 - 2003 Hummer H2

[edit] 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 C_d values.

[edit] 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 C_d:

0.7 to 1.1 - typical values for a Formula 1 car (downforce settings change for each circuit)
0.7 - Caterham Seven
at least 0.6 - a typical truck
0.57 - Hummer H2, 2003
0.51 - Citroën 2CV
over 0.5 - Dodge Viper
0.46 - Ford Mustang, 1979 (coupe)
0.44 - Ford Mustang, 1979 (fastback)
0.44 - Toyota Truck, 1990-1995

0.42 - Lamborghini Countach, 1974
0.42 - Triumph Spitfire Mk IV, 1971-1980
0.42 - Plymouth Duster, 1994

0.39 - Dodge Durango, 2004
0.39 - Triumph Spitfire, 1964-1970

0.38 - Volkswagen Beetle
0.38 - Mazda Miata, 1989

0.374 - Ford Capri Mk III, 1978-1986
0.372 - Ferrari F50, 1996
0.37 - Renault Twingo
0.36 - Eagle Talon, mid-1990s
0.36 - Citroën DS, 1955
0.36 - Ferrari Testarossa, 1986
0.36 - Opel GT, 1969
0.36 - Honda Civic, 2001
0.36 - Citroën CX, 1974 (the car was named after the term for drag coefficient)

0.355 - NSU Ro 80, 1967

0.34 - Ford Sierra, 1982
0.34 - Ferrari F40, 1987
0.34 - Chevrolet Caprice, 1994-1996
0.34 - Chevrolet Corvette Z06, 2006
0.338 - Chevrolet Camaro, 1995

0.33 - Dodge Charger, 2006
0.33 - Audi A3, 2006
0.33 - Subaru Impreza WRX STi, 2004
0.33 - Mazda RX-7 FC3C, 1987-91
0.33 - Citroën SM, 1970

0.32064 - Volkswagen GTI Mk V, 2006 (0.3216 with ground effects)
0.32 - Toyota Celica,1995-2005

0.31 - Citroën AX, 1986
0.31 - Citroën GS, 1970
0.31 - Eagle Vision
0.31 - Ford Falcon, 1995-1998
0.31 - Mazda RX-7 FC3S, 1986-91
0.31 - Renault 25, 1984
0.31 - Saab Sonett III, 1970
0.31 - Audi A4 B5, 1995-2000

0.30 - Audi 100, 1983
0.30 - BMW E90, 2006
0.30 - Porsche 996, 1997
0.30 - Saab 92, 1947

0.29 - Dodge Charger Daytona, 1969
0.29 - Honda CRX HF 1988
0.29 - Subaru XT, 1985
0.29 - BMW 8-Series, 1989
0.29 - Porsche Boxster, 2005
0.29 - Chevrolet Corvette, 2005
0.29 - Mazda RX-7 FC3S Aero Package, 1986-91
0.29 - Lexus LS 400, 1990
0.29 - Lancia Dedra, 1990-1998
0.29 - Honda Accord Hybrid, 2005
0.29 - Lotus Elite, 1958
0.29 - Mercedes-Benz W203 C-Class Coupe, 2001 - 2007

0.28 - Toyota Camry and sister model Lexus ES, 2005
0.28 - Porsche 997, 2004
0.28 - Renault 25 TS, 1984
0.28 - Saab 9-3, 2003

0.27 - Infiniti G35, 2002 (0.26 with "aero package")
0.27 - Mercedes-Benz W203 C-Class Sedan, 2001 - 2007
0.27 - Rumpler Tropfenwagen, 1921
0.27 - Toyota Camry Hybrid, 2007

0.26 - Alfa Romeo Disco Volante, 1952
0.26 - Hotchkiss Gregoire, 1951
0.26 - Lexus LS 430, 2001 (0.25 with air suspension)
0.26 - Mercedes-Benz W221 S-Class, 2006
0.26 - Toyota Prius, 2004
0.26 - Vauxhall Calibra, 1989

0.25 - Audi A2 1.2 TDI, 2001
0.25 - Dymaxion Car, 1933
0.25 - Honda Insight, 1999
0.25 - SmILE (an experimental car)

0.212 - Tatra T77 a, 1935

0.20 - Loremo Concept, 2006
0.20 - Opel Eco Speedster Concept, 2003

0.195 - General Motors EV1, 1996
0.19 - Alfa Romeo BAT Concept, 1953
0.19 - Dodge Intrepid ESX Concept , 1995
0.19 - Mercedes-Benz Bionic Concept, 2005 [6] (based on the boxfish)

0.16 - Daihatsu UFEIII Concept, 2005
0.16 - General Motors Precept Concept, 2000

0.14 - Fiat Turbina Concept, 1954

0.137 - Ford Probe V prototype, 1985
0.117 - Summers Brothers Goldenrod Bonneville race car, 1965

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

2.1 - a smooth brick	0.7 to 1.1 - typical values for a Formula 1 car	0.9 -a typical bicycle plus cyclist	0.7 - Caterham Seven
at least 0.6 - a typical truck	0.57 - Hummer H2, 2003	0.51 - Citroën 2CV	over 0.5 - Dodge Viper
0.42 - Lamborghini Countach, 1974	0.42 - Triumph Spitfire Mk IV, 1971-1980	0.38 - Volkswagen Beetle	0.38 - Mazda Miata, 1989
0.38 - Rolls-Royce Silver Seraph, 1998 [1]	0.374 - Ford Capri Mk III, 1978-1986	0.372 - Ferrari F50, 1996	0.36 - Citroën DS, 1955
0.36 - Ferrari Testarossa, 1986	0.36 - Honda Civic, 2001	0.36 - Citroën CX, 1974 (the car was named after the term for drag coefficient)	0.355 - NSU Ro 80, 1967
0.35, Audi TT, 1998 [2]	0.342 Pontiac Trans Am 1982 [3]	0.34 - Ford Sierra, 1982	0.34 - Ferrari F40, 1987
0.34 - Chevrolet Corvette Z06, 2006	0.338 - Chevrolet Camaro, 1995	0.33 - Citroën SM, 1970	0.31 - Citroën AX, 1986
0.31 - Citroën GS, 1970	0.31 - Renault 25, 1984	0.31 - Saab Sonett III, 1970	0.30 - Audi 100, 1983
0.30 - BMW E90, 2006	0.30 - Porsche 996, 1997	0.30 - Saab 92, 1947	0.29 - Honda CRX HF 1988
0.29 - Subaru XT, 1985	0.29 - Lancia Dedra, 1990-1998	0.29 - Lotus Elite, 1958	0.28 - Rumpler Tropfenwagen, 1921
0.28 - Toyota Camry and sister model Lexus ES, 2005	0.28 - Porsche 997, 2004	0.28 - Renault 25 TS, 1984	0.28 - Saab 9-3, 2003
0.28 - Audi A2, 1999 [4]. Note the Kammback shape.	0.27 - Infiniti G35, 2002 (0.26 with "aero package")	0.27 - Toyota Camry Hybrid, 2007	0.26 - Mercedes-Benz W221 S-Class, 2006
0.26 - Lexus LS 430, 2001 (0.25 with air suspension)	0.26 - Toyota Prius, 2004	0.26 - Vauxhall Calibra, 1989	0.25 - Audi A2 1.2 TDI, 2001
0.25 - Honda Insight, 1999	0.212 - Tatra T77 a, 1935