In fluid dynamics, the drag coefficient 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, where 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.
Definition The drag coefficient is defined as:
where: 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 speed of the object relative to the
fluid and 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 .
For airfoils, the reference area is the planform area. Since this tends to be a rather large
area compared to the projected frontal area, the resulting drag coefficients tend to be
low: much lower than for a car with the same drag and frontal area, and at the same 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. 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. Background
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 speed between the object and
the fluid. Cd is not a constant but varies as a function
of 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 or . is thus a function of . In compressible
flow, the speed of sound is relevant and is also a function of Mach number .
For a certain body shape, 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. So 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 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.
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. 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. 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
General In general, is not an absolute constant for
a given body shape. It varies with the speed of airflow. A smooth sphere, for example,
has a that varies from high values for laminar flow to 0.47 for turbulent flow.
Aircraft As noted above, aircraft use their wing area
as the reference area when computing , while automobiles 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 . Bluff and streamlined body flows
Concept Drag, in the context of fluid dynamics, refers
to forces that act on a solid object in the direction of the relative fluid flow velocity.
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 and pressure drag. The net drag force could be decomposed as follows:
where: 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 normal to the surface dA, forming a unit vector
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 bluff
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 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 bluff body.
A streamlined body looks like a fish or an airfoil with small angle of attack, whereas
a bluff 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 bluff
body. Cylinders and spheres are taken as bluff 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. This reduction is necessary in devices like cars, bicycle,
etc. to avoid vibration and noise production. Practical example
Aerodynamic design of cars has evolved from 1920s to the end of 20th century. This change
in design from a bluff body to a more streamlined body reduced the drag coefficient from about
0.95 to 0.30.
Time history of Aerodynamic drag of cars in comparison with change in geometry of streamlined
bodies. See also
Automotive aerodynamics Automobile drag coefficient
Ballistic coefficient Drag crisis
Zero-lift drag coefficient Notes
References Clancy, L. J.: 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.: Fluid-Dynamic Drag. Hoerner Fluid Dynamics, Brick Town, N. J., USA
Bluff Body: http:www.engineering.uiowa.edulecture.../Bluff%20Body2.pdf Drag of Blunt Bodies and Streamlined Bodies:
http:www.princeton.eduBicycle_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.