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The drag coefficient (C_d, C_x or C_w) is a dimensionless quantity which 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, where a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with with a particular surface area. ^[1] 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 induced drag.^[2][3] The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.^[4][5]

The dimensionless drag coefficient is a ratio between two numbers in the same units of area. The reference area chosen for comparison depends on what type of drag coefficient is being measured. For airfoils, the reference area is the square of the chord of the airfoil, which can be easily related to wing area. Since this tends to be a rather large area, the resulting drag coefficients tend to be low. For automobiles and many other objects, the reference area is the frontal area of the vehicle (i.e., the cross-sectional area when viewed from ahead); this area tends to be small, giving a higher drag coefficient than an airfoil with the same drag. Airships and bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume. 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 rough unstreamlined objects can be 1 or more, for streamlined objects much less.

    explanation of terms on drag equation page.

Flow around a plate, showing stagnation.

A is the reference area, usually projected frontal area. For example, for a sphere A = πr², (i.e., not the surface area.)

The drag equation is essentially a statement that the drag force on any object is proportional to the density of the fluid, and proportional to the square of the relative velocity between the object and the fluid. The drag coefficient of an object varies depending on its orientation to the vector representing the relative velocity between the object and the fluid.

C_d is not a constant but varies as a function of speed, object length, fluid density and fluid vicosity. These are generally combined to a dimensionless quantity called the Reynolds number or Re. C_d is thus a function of Re. Provided Re is the same and the flow is subsonic and steady, C_d is the same regardless of fluid or variation of other variables. Although Re and hence C_d can vary greatly, the variation within a practical range of interest is usually small, so that C_d is often treated as a constant. ^[6]

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 broad wake results in high form drag. The boundary layer will remain attached longer if it is turbulent than if it is laminar. The boundary layer will transition from laminar to turbulent providing the Reynolds number of the flow around the body is high enough. Larger velocities, larger objects, and lower viscosities contribute to larger Reynolds numbers.^[7]

At a low Reynolds number, the boundary layer 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. C_d is no longer constant but varies with velocity, and F_d is proportional to v instead of v². Reynolds number will be low for small objects, low velocities, and high viscosity fluids.^[8]

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.

[edit] 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.

[edit] C_d examples

As noted above, aircraft use wing area as the reference area when computing C_d, while automobiles (and many other objects) use frontal cross sectional area; thus, coefficients are not directly comparable between these classes of vehicles.

[edit] See also

• Automotive aerodynamics
• Automobile drag coefficient
• Zero-lift drag coefficient

[edit] References

• Clancy, L. J. (1975), Aerodynamics, Pitman Publishing Limited, London ISBN 0 273 01120 0
• Abbott, Ira H., and Von Doenhoff, Albert E., Theory of Wing Sections, Dover Publications Inc., New York, Standard Book Number 486-60586-8
• Hoerner, S. F. (1965), "Fluid-Dynamic Drag", Hoerner Fluid Dynamics, Brick Town, N. J. USA

[edit] Notes

[edit] External links

• A. Filippone's Advanced Topics in Aerodynamics: Drag
• Danish Wind Industry Association: Aerodynamics of Wind Turbines: Drag