What is a Drag Coefficient?


What is a Drag Coefficient?

Drag Coefficients (Cd) are used to quantify the resistance of an object as it moves through a fluid. They are a dimensionless quantity and allow aerodynamicists to account for the influence of shape, inclination and flow conditions when calculating aerodynamic drag.

Essentially, the more streamlined an object is, the lower its drag coefficient. Whereas, blunt and bulky objects will have a high drag coefficient.

To visualise this, think of a tear drop shaped object. As air flows around it, it remains attached and therefore, the object will have a low Cd value of around 0.05. On the other hand, a flat plate that is perpendicular to the airflow, will create a large wake of turbulent air behind it. This will cause it to have a high Cd value of approximately 1.1.

Scale of drag coefficient values
Scale of drag coefficient values

An example in the automotive world is the streamlined Tesla Model 3 which has a Cd of 0.23. Whereas the more bulky Tesla Cybertruck has a Cd of 0.48 (from initial AirShaper simulations).

How are drag coefficients calculated?

Drag coefficients can also be used to calculate the hydrodynamic (water) or aerodynamic (air) force on an object. This is given by the drag equation below:

Drag force equation
Drag force equation

Where: Fd = drag force (N) ρ = density (kg/m³) u = velocity (m/s²) Cd = drag coefficient A = frontal area (m²)

If you know the drag force on an object at a certain speed, such as after a wind tunnel test, you can rearrange the aerodynamic drag equation above to calculate the drag coefficient. Once you have established the drag coefficient for a specific geometry, you can use the above equation again to recalculate the drag force for different sizes and velocities. This can be particularly useful when sizing engines or battery capacities, for example.

However, it’s important to remember that drag coefficient varies with Reynolds number. The Reynolds number is another dimensionless quantity. It is the ratio between the inertial forces and the viscous forces of a fluid. It essentially describes how the behaviour of air changes with temperature, pressure, velocity and the type of fluid.

For example, the Reynolds number changes as you move along a racecar. Therefore, the Reynolds number in a radiator duct will be different to the Reynolds number at the rear of the car. So bear this in mind when using the equation above and extrapolating for large speeds, sizes or densities.

Graph showing how the drag of a sphere changes with Reynolds number
Graph showing how the drag of a sphere changes with Reynolds number

How are drag coefficients used?

Drag coefficients allow aerodynamicists to analyse the aerodynamic efficiency of an object, regardless of its size or velocity. This means that you can compare the aerodynamics of a cyclist with a building. Although they are extremely different, they both have a normalised drag coefficient.

Drag coefficients are also an essential consideration throughout the design process. When determining which design has the highest performance, you can rank them in order of drag coefficient. You can also take inspiration from other aerodynamic shapes with low drag coefficients – no matter what industry they come from. Mercedes once designed a road car that was inspired by the hydrodynamics of a fish!

So, whether you are developing a drone that needs to fly as far as possible on a single charge, or helping a cyclist achieve a higher top speed - your aim will be to reduce the drag coefficient.

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