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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
drag equation.
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 viscosity 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 objects, low velocities or high viscosity fluids, the flow around the object is
laminar flow, C_d is no longer constant but depends on velocity, and F_d is proportional to v instead of v^2.
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
aerodynamics 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 National Maximum Speed Law during the early 1973 oil crisis as slower traffic would save scarce petroleum.
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.
{| class="wikitable"|+CdA (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
Cd in aircraft
Some examples of
Cd in aircraft are presented below.{| class="wikitable"! Cd !! 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|}
Cd in other shapes
Finally, here is a table of the
Cd value of other miscellaneous shapes.{| class=sortable! Cd !! Item|-| 2.1 || a smooth brick|-| 0.9 || a typical
bicycle plus cyclist] = 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|}
See also
External links
- A. Filippone's Advanced Topics in Aerodynamics: Drag
- Danish Wind Industry Association: Aerodynamics of Wind Turbines: Drag
- Improving Aerodynamics to Boost Fuel Economy
- Tel Aviv University reduces drag on trucks by 10%
- Simple roll-down test for measuring Cd and Crr for cars and bikes
- Variation of drag coefficient with Reynolds number
- Drag of Blunt Bodies and Streamlined Bodies
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 drag equation.
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
viscosity 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 objects, low velocities or high viscosity fluids, the flow around the object is
laminar flow, C_d is no longer constant but depends on velocity, and F_d is proportional to v instead of v^2.
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 aerodynamics 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
National Maximum Speed Law during the early
1973 oil crisis as slower traffic would save scarce
petroleum.
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.
{| class="wikitable"|+CdA (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
Cd in aircraft
Some examples of
Cd in aircraft are presented below.{| class="wikitable"! Cd !! 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|}
Cd in other shapes
Finally, here is a table of the
Cd value of other miscellaneous shapes.{| class=sortable! Cd !! Item|-| 2.1 || a smooth brick|-| 0.9 || a typical bicycle plus cyclist] = 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|}
See also
External links
- A. Filippone's Advanced Topics in Aerodynamics: Drag
- Danish Wind Industry Association: Aerodynamics of Wind Turbines: Drag
- Improving Aerodynamics to Boost Fuel Economy
- Tel Aviv University reduces drag on trucks by 10%
- Simple roll-down test for measuring Cd and Crr for cars and bikes
- Variation of drag coefficient with Reynolds number
- Drag of Blunt Bodies and Streamlined Bodies
Drag coefficient - 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 ...
Automobile drag coefficients - Wikipedia, the free encyclopedia
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The Drag Coefficient
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Coefficient Drag Partners
Coefficient Drag. All Rights Reserved.
Design Tips – drag coefficient :: School of Engineering Sciences
Greenpower Electric Car Racing design website: drag coefficient. This is run by the School of Engineering Sciences at the University of Southampton.
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Aerodynamics in Car Design
Home. Aerodynamics in Car Design . Coe fficien t of Drag : Introduction . Drag comparisons between cars are normally made on a drag coefficient basis since CD is non-dimensional, i ...
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