In fluid dynamics, the drag coefficient (commonly denoted as: , or ) 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.
This section needs additional citations for verification. (December 2018) (Learn how and when to remove this template message)
The drag coefficient is defined as
- is the drag force, which is by definition the force component in the direction of the flow velocity,
- is the mass density of the fluid,
- is the flow speed of the object relative to the fluid,
- 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 projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere (note this is not the surface area = ).
For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed.
Airships and some bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume (volume to the two-thirds power). Submerged streamlined bodies use the wetted surface area.
Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less.
where is the Reynold Number related to fluid path length L.
The drag equation
Cd is not a constant but varies as a function of flow speed, flow direction, object position, object size, fluid density and fluid viscosity. Speed, kinematic viscosity and a characteristic length scale of the object are incorporated into a dimensionless quantity called the Reynolds number . is thus a function of . In a compressible flow, the speed of sound is relevant, and is also a function of Mach number .
For certain body shapes, the drag coefficient only depends on the Reynolds number , Mach number and the direction of the flow. For low Mach number , the drag coefficient is independent of Mach number. Also, the variation with Reynolds number within a practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed, the incoming flow direction is also more-or-less the same. Therefore, the drag coefficient can often be treated as a constant.
For a streamlined body to achieve a low drag coefficient, the boundary layer around the body must remain attached to the surface of the body for as long as possible, causing the wake to be narrow. A high form drag results in a broad wake. The boundary layer will transition from laminar to turbulent if Reynolds number of the flow around the body is sufficiently great. Larger velocities, larger objects, and lower viscosities contribute to larger Reynolds numbers.
For other objects, such as small particles, one can no longer consider that the drag coefficient is constant, but certainly is a function of Reynolds number. At a low Reynolds number, the flow around the object does not transition to turbulent but remains laminar, even up to the point at which it separates from the surface of the object. At very low Reynolds numbers, without flow separation, the drag force is proportional to instead of ; for a sphere this is known as Stokes law. The Reynolds number will be low for small objects, low velocities, and high viscosity fluids.
A 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. Only considering the front side, the of a real flat plate would be less than 1; except that there will be suction on the back side: a negative pressure (relative to ambient). The overall of a real square flat plate perpendicular to the flow is often given as 1.17. Flow patterns and therefore for some shapes can change with the Reynolds number and the roughness of the surfaces.
Drag coefficient cd examples
In general, is not an absolute constant for a given body shape. It varies with the speed of airflow (or more generally with Reynolds number ). A smooth sphere, for example, has a that varies from high values for laminar flow to 0.47 for turbulent flow. Although the drag coefficient decreases with increasing , the drag force increases.
|0.001||Laminar flat plate parallel to the flow ()|
|0.005||Turbulent flat plate parallel to the flow ()|
|0.0512||Ecorunner V, 2015 |
|0.076||Milan SL (one of the fastest practical velomobiles) |
|0.1||Smooth sphere ()|
|0.47||Smooth sphere ()|
|0.81||Triangular trapeze (45°)|
|0.9-1.7||Trapeze with triangular basis (45°)|
|0.14||Fiat Turbina 1954|
|0.15||Schlörwagen 1939 |
|0.18||Mercedes-Benz T80 1939|
|0.186-0.189||Volkswagen XL1 2014|
|0.19||Alfa Romeo B.A.T. 7 1954|
|0.19||General Motors EV1 1996|
|0.212||Tatra 77A 1935|
|0.23||Tesla Model 3, Audi A4 B9 (2016)|
|0.23||Alfa Romeo Giulia Advanced Efficiency 2016|
|0.24||Tesla Model S|
|0.24||Hyundai Ioniq |
|0.24||Toyota Prius (4th Generation)|
|0.25||Toyota Prius (3rd Generation)|
|0.26||Nissan GT-R (2011-2014)|
|0.26||Toyota Prius (2nd Generation)|
|0.27||BMW E39 5 Series (1995-2003, Germany)|
|0.27||Mercedes-Benz CLS-Class Type C257|
|0.27||Nissan GT-R (2007-2010)|
|0.27||Chrysler 200 (2015-2017)|
|0.28||1959 Alfa Romeo Giulietta Sprint Speciale|
|0.28||1969 Dodge Charger Daytona and 1970 Plymouth Superbird|
|0.28||1986 Opel Omega saloon.|
|0.28||Mercedes-Benz CLA-Class Type C 117.|
|0.29||Mazda3 (2007) , Nissan 350Z (Track and Grand Touring models) |
|0.295||Bullet (not ogive, at subsonic velocity)|
|0.3||Saab 92 (1949), Audi 100 C3 (1982)|
|0.31||Maserati Ghibli (2013) , 0.29 after restyle|
|0.324||Ford Focus Mk2/2.5 (2004-2011, Europe)|
|0.33||BMW E30 3 Series (1984-1993, Germany)|
|0.35||Maserati Quattroporte V (M139, 2003–2012)|
|0.36||Citroen CX (1974-1991, France), Tesla Semi (2017, United States of America)|
|0.37||Ford Transit Custom Mk8 (2013, Turkey)|
|0.48||Rough sphere (),|
|0.58||Jeep Wrangler TJ (1997-2005)|
|0.75||A typical model rocket|
|1.0||Coffee filter, face-up[unreliable source?]|
|1.0||road bicycle plus cyclist, touring position|
|1.0–1.3||Wires and cables|
|1.0–1.3||Adult Human (upright position)|
|1.28||Flat plate perpendicular to flow (3D) |
|1.3–1.5||Empire State Building|
|1.4||Formula One car|
|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 , 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 .
|cd||Drag Count||Aircraft type|
|0.021||210||F-4 Phantom II (subsonic)|
|0.044||440||F-4 Phantom II (supersonic)|
Blunt and streamlined body flows
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:
- is the pressure drag coefficient,
- is the friction drag coefficient,
- = Tangential direction to the surface with area dA,
- = Normal direction to the surface with area dA,
- is the shear Stress acting on the surface dA,
- is the pressure far away from the surface dA,
- is pressure at surface dA,
- 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 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.
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.
- Automotive aerodynamics
- Automobile drag coefficient
- Ballistic coefficient
- Drag crisis
- Zero-lift drag coefficient
- McCormick, Barnes W. (1979): Aerodynamics, Aeronautics, and Flight Mechanics. p. 24, John Wiley & Sons, Inc., New York, ISBN 0-471-03032-5
- Clancy, L. J.: Aerodynamics. Section 5.18
- Abbott, Ira H., and Von Doenhoff, Albert E.: Theory of Wing Sections. Sections 1.2 and 1.3
- "NASA's Modern Drag Equation". Wright.nasa.gov. 2010-03-25. Archived from the original on 2011-03-02. Retrieved 2010-12-07.
- Clancy, L. J.: Aerodynamics. Section 11.17
- See lift force and vortex induced vibration for a possible force components transverse to the flow direction.
- Note that for the Earth's atmosphere, the air density can be found using the barometric formula. Air is 1.293 kg/m3 at 0 °C and 1 atmosphere.
- Liversage, P., and Trancossi, M. (2018). Analysis of triangular sharkskin profiles according to second law, Modelling, Measurement and Control B. 87(3), 188-196. http://www.iieta.org/sites/default/files/Journals/MMC/MMC_B/87.03_11.pdf
- Clancy, L. J.: Aerodynamics. Sections 4.15 and 5.4
- Clancy, L. J.: Aerodynamics. Section 4.17
- Clift R., Grace J. R., Weber M. E.: Bubbles, drops, and particles. Academic Press NY (1978).
- Briens C. L.: Powder Technology. 67, 1991, 87-91.
- Haider A., Levenspiel O.: Powder Technology. 58, 1989, 63-70.
- eco runner team delft (Cd 0.0512 BEST) Create Car With Lowest Ever Drag Coefficient
- "Milan SL". Archived from the original on 2 April 2015. Retrieved 24 March 2015.
- Ludvigsen, Karl. "Turbine Speed with Style". Hemmings Daily. Retrieved 17 February 2009.
- "MB-Exotenforum". Archived from the original on 2014-02-01. Retrieved 2012-01-07.
- "1954 Alfa Romeo B.A.T. 7". conceptcarz.com. Retrieved 15 November 2019.
- MotorTrend: General Motors EV1 - Driving impression Archived 2012-11-03 at the Wayback Machine, June 1996
- Lambert, Fred. "Tesla Model 3 production specs revealed: up to 310 miles range, 140 mph top speed, and more". electrek. Archived from the original on 29 July 2017. Retrieved 28 July 2017.
- "A4 (B9) 2016: Limousine und Avant". pkw.de. Archived from the original on 29 March 2018. Retrieved 28 March 2018.
- "AWD Alfa Romeo Giulia Veloce gets 280-hp turbo 2.0-liter engine". motor1.com. Retrieved 15 November 2019.
- Sherman, Don (2014). "Drag Queens" (PDF). Car and Driver. Archived (PDF) from the original on 4 September 2014. Retrieved 30 May 2014.
- "Manufacturer's specifications". Hyundai USA. Retrieved 5 October 2019.
- Seabaugh, Christian. "2016 Toyota Prius First Drive Review". MotorTrend. Archived from the original on 19 November 2015. Retrieved 18 November 2015.
- "Motor Trend 2004 Car of the Year Winner: Toyota Prius". MotorTrend. Retrieved 12 August 2019.
- "The BMW 5 Series History. The 4th Generation (E39)". YouTube. Retrieved 12 May 2018.
- "2019 CLS 450 Luxury Coupe | Mercedes-Benz".
- "1959-'66 Alfa Romeo Sprint Speciale". hemmings.com. Retrieved 15 November 2019.
- "Opel Omega A" (in German). Archived from the original on 2007-10-13.
- "Mercedes-Benz CLA-Class Type C 117". Archived from the original on 2018-04-29.
- "2007 Mazda 3 - Features & Specs". Edmund's. Archived from the original on 13 August 2014. Retrieved 13 August 2014.
- "350Z Aerodynamics". howstuffworks. 2007-11-24. Retrieved 2019-03-07.
- "2014 Maserati Ghibli Sedan - Features & Specs". Edmund's. Archived from the original on 8 December 2015. Retrieved 2 December 2015.
- "Technique of the VW Beetle". Maggiolinoweb.it. Archived from the original on 2010-01-11. Retrieved 2009-10-24.
- "The Mayfield Homepage - Coefficient of Drag for Selected Vehicles". Mayfco.com. Archived from the original on 2009-09-18. Retrieved 2009-10-24.
- "Vehicle Coefficient of Drag List". Archived from the original on 25 April 2010. Retrieved 13 August 2014.
- "Terminal Velocity". Goddard Space Center. Archived from the original on 2012-03-06. Retrieved 2012-02-16.
- "TerminalVelocity". www.exo.net. Archived from the original on 7 December 2016. Retrieved 29 April 2018.
- Wilson, David Gordon (2004): Bicycling Science, 3rd ed.. p. 197, Massachusetts Institute of Technology, Cambridge, ISBN 0-262-23237-5
- "Drag Coefficient". Engineeringtoolbox.com. Archived from the original on 2010-12-04. Retrieved 2010-12-07.
- Hernandez-Gomez, J J; Marquina, V; Gomez, R W (25 July 2013). "On the performance of Usain Bolt in the 100 m sprint". Eur. J. Phys. 34 (5): 1227–1233. arXiv:1305.3947. Bibcode:2013EJPh...34.1227H. doi:10.1088/0143-0807/34/5/1227. Archived from the original on 27 April 2016. Retrieved 23 April 2016.
- "Shape Effects on Drag". NASA. Archived from the original on 2013-02-16. Retrieved 2013-03-11.
- Basha, W. A. and Ghaly, W. S., "Drag Prediction in Transitional Flow over Airfoils," Journal of Aircraft, Vol. 44, 2007, p. 824–32.
- "Ask Us - Drag Coefficient & Lifting Line Theory". Aerospaceweb.org. 2004-07-11. Retrieved 2010-12-07.
- "Boeing 787 Dreamliner : Analysis". Lissys.demon.co.uk. 2006-06-21. Archived from the original on 2010-08-13. Retrieved 2010-12-07.
- "Airbus A380" (PDF). 2005-05-02. Archived (PDF) from the original on 2015-09-23. Retrieved 2014-10-06.
- L. J. Clancy (1975): Aerodynamics. Pitman Publishing Limited, London, ISBN 0-273-01120-0
- Abbott, Ira H., and Von Doenhoff, Albert E. (1959): Theory of Wing Sections. Dover Publications Inc., New York, Standard Book Number 486-60586-8
- Hoerner, Dr. Sighard F., Fluid-Dynamic Drag, Hoerner Fluid Dynamics, Bricktown New Jersey, 1965.
- Bluff Body: http://user.engineering.uiowa.edu/~me_160/lecture_notes/Bluff%20Body2.pdf
- Drag of Blunt Bodies and Streamlined Bodies: http://www.princeton.edu/~asmits/Bicycle_web/blunt.html
- Hucho, W.H., Janssen, L.J., Emmelmann, H.J. 6(1975): The optimization of body details-A method for reducing the aerodynamics drag. SAE 760185.