Drag coefficient

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Hoerner fluid dynamic drag coefficients

Cd flat plate

Drag coefficient on a sphere vs. Reynolds number - main trends

Drag curves for aircraft in flight

Drag coefficient (Cd or C_d) 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 field of fluid dynamics and is an indicator of how smoothly or aerodynamically a body moves through a fluid medium. The drag coefficient is a crucial factor in the design and performance of a wide range of products, including automobiles, aircraft, and buildings, as well as in the study of natural phenomena.

Definition

The drag coefficient is defined as:

C_d = 2F_d / (ρv²A)

where:

• F_d is the drag force, which is by definition the force component in the direction of the flow velocity,
• ρ is the density of the fluid,
• v is the speed of the object relative to the fluid, and
• A is the reference area.

The reference area depends on what kind of object is being measured. For example, for an object with a complex shape, the reference area is typically the projected frontal area of the object. In contrast, for a wing, the reference area is the planform area.

Factors Affecting Drag Coefficient

Several factors can affect the drag coefficient of an object, including its shape, the roughness of its surface, and the Reynolds number, which is a dimensionless quantity that describes the flow condition of the fluid. The Reynolds number itself is influenced by the speed of the object, the viscosity of the fluid, and the characteristic length (or size) of the object.

Shape

The shape of an object is the most significant factor in determining its drag coefficient. Streamlined shapes are designed to minimize the drag coefficient, allowing the object to move through the fluid more efficiently.

Surface Roughness

Surface roughness can increase the drag coefficient because it increases the turbulence in the boundary layer around the object. A smoother surface typically results in a lower drag coefficient.

Reynolds Number

The drag coefficient can vary with the Reynolds number, especially for objects in the laminar flow regime. As the Reynolds number increases, indicating either a higher velocity, a larger size, or a lower viscosity, the flow can transition from laminar to turbulent, significantly affecting the drag coefficient.

Applications

The concept of the drag coefficient is applied in various fields to design objects that have optimal aerodynamic properties. In the automotive industry, reducing the drag coefficient of a vehicle can lead to improved fuel efficiency and higher speeds. In aerospace engineering, a lower drag coefficient can enhance the performance of aircraft and spacecraft. In sports, equipment and apparel are designed with low drag coefficients to improve performance and reduce fatigue.

Measurement

The drag coefficient of an object can be measured in a wind tunnel, where the conditions (air speed, density, and viscosity) can be controlled. Alternatively, computational fluid dynamics (CFD) simulations can be used to estimate the drag coefficient based on numerical solutions to the equations of fluid motion.

See Also

• Aerodynamics
• Bernoulli's principle
• Fluid dynamics
• Lift coefficient
• Reynolds number