Drag Coefficient – Explanation, Applications and Calculation

What is the Coefficient of Drag?

Car.
Image Source: Reddit.

Drag is a very important phenomenon in physics and engineering. In the design of lots of kinds of engineering systems such as automobiles and aircraft, drag and drag coefficient studies are very important. Here, you can find detailed information about drag and terminology about drag coefficient. Also, you can find this information;

  • What is the drag coefficient?
  • Application areas of it.
  • How to calculate the drag coefficient?
  • Additional terminology about drag in fluid mechanics.
  • FAQs about the drag in aerodynamical applications.

What is the Coefficient of Drag?

If there is a solid body in a fluid stream, there will be a force acting on the flow direction of that body. This is the drag force. Drag force is a very important physical phenomenon that engineers consider. But before understanding what is drag coefficient, we need to understand some terminology about external fluid flow.

In general, solving external fluid flow problems are very hard to solve analytically. In general, engineers are using experimental data and equations to see the results of external flows. And also, there are lots of applications of external flows in engineering.

Also, there are lots of computational solution methods to solve external fluid flow problems. Engineers are using CAE tools for it. But in general, they rely on the experimental data that they carry out in laboratories. If they have consistent results in FEA or CFD analyses and the experimental analyses, they will obtain the prototype.

Free-Stream Velocity

Before seeing the drag coefficient and drag force effects of fluid streams, we need to know what is free-stream velocity. Free-stream velocity is the total flowing velocity of the fluid without an object in it. Because, if we immerse a body, the regime of the flow will change.

So, this change in the flow is important for us. Because of it, we call free-stream velocity approach velocity or upstream velocity. In the design phase, we assume that free-stream velocity is a steady flow.

If we immerse a body inside a free stream, we will feel the effects of that body. The velocity of the fluid will increase from zero because of the no-slip condition at the surface of the body, to free-stream velocity. After a distance from the surface, we will not feel the surface effects.

Drag Force

Drag force.
General forces on a drag(Image Source: Wikimedia).

So, this free-stream fluid flow will apply a force to these bodies. This force is the drag force. There are two reasons for drag forces on bodies. These two reasons are;

  • Drag force is caused by the pressure of the fluid at the front side of the body.
  • Drag force is caused by the tangential wall shear force because of the no-slip condition.

Total drag force is the addition of these two elements.

Wall shear force has also a normal direction of force to the free-stream velocity. This force is called lift force which is very important in aerospace.

Pressure drag is proportional to the total area of the body that is against the free-stream velocity. So in general, they want to decrease this area to decrease the pressure drag in aerodynamics applications. We generally measure the pressure drag with the pressure difference between the front side and the back side of the bodies.

Effect of Surface Roughness on Friction Drag

Surface roughness of the body that undergoes wall friction stress has a very important effect on bodies. For laminar flows, there is no effect of the surface roughnessç But for turbulent flows, the total area increases with the increasing surface roughness. So, it is very important to consider surface roughness value.

Two Theoretical Cases to Understand These Effects

Firstly, if we immerse a flat plate horizontally inside a free-stream fluid flow, the only cause of the drag is wall shear stress. Because there is no pressure effect on the front side of the plate. Because the thickness of the plate is negligible.

Also, if we place this plate vertically against free-stream fluid flow, you will see that the only cause of the drag force is the pressure. Because there is no surface for the no-slip condition. And there will be a great pressure effect on the surface.

How to Calculate the Coefficient of Drag?

We can calculate the drag coefficient with this formula below;

drag coefficient formula

As you see here, the calculation is very basic. In here;

  • Fd is the drag force that has the unit of N or lbf in English units.
  • p is the density of the free-stream fluid. The unit of density is kg/m2 or lb/ft2.
  • V is the velocity of the upstream velocity. The unit is m/s or ft/s.
  • A is the area of the frontal section of the body. We can calculate by reflecting the total frontal area in the direction upstream. The unit is m2 or ft2.

The drag coefficient is a unitless value.

So if we take a look at this formula, we can say these deductions. With the increasing drag coefficient, the drag force increases.

Also with the increasing density of the fluid, the drag force increases. Because the density of the fluid has a direct effect on the pressure drag force.

And also with the increasing free-stream velocity, the drag force increases. This is because, with the increasing velocity, the total wall shear friction increases. Also the total pressure at the front of the body increases.

So, with the increasing area, the total drag force increases. Because with the increasing area, the total drag pressure increases.

Effect of Reynolds Number on Drag Coefficient

Reynolds number is a very important parameter to show the turbulence situation of a fluid flow. So, the Reynolds number near the surface of the bodies in aerospace applications is very important. Because, with the decreasing Reynolds number, the drag force due to the pressure decreases.

So, if the Reynolds number is low enough, the only drag force effect is the skin friction effect. Because of this effect of the Reynolds number, engineers prefer the laminar flows for aerodynamical applications. Also, the designed aerodynamic body would not affect this laminar flow.

Flow Separation and Wake Region

flow separation and wake region on airfoil.
Flow separation and wake region(Image Source: ScienceBuzz).

These two terms are very important in fluid flow analyses. If we immerse a body, there will be a no-slip condition on the surface. After a point, fluid separated from the surface. We call this phenomenon flow separation.

Also and in the flow separation region, there is an unsteady flow condition where the pressure is low and lots of eddies and turbulences occur. After a distance, these two flow separation regions from the upper and bottom side of the body unites. And then, the flow becomes an ordinary free stream where the existence of the body is not felt.

We call this total unsteady region is wake region. In aerodynamic applications, it is very important to lower the wake region. Because low pressure in the wake region causes higher pressure drags.

Practical Applications of Drag Coefficient

The drag coefficient is a very important topic in engineering. In the design of different engineering systems, we use drag coefficient. In most aerodynamical applications, we want low drag coefficients and low drag forces. Check the general examples below.

Aerospace

Shape of an airfoil.
Airfoil section(Image Source: Researchgate.com).

In aerospace applications, the drag coefficient is very important. Because to obtain efficient aerial vehicles, they need to make the drag coefficient as low as possible.

They are doing this by designing special airfoils. These are the general cut sections of the wings of the planes. Airfoils have very specific shapes. This specific shape provides the minimum drag forces and maximum lift. Lift force from wall shear stress is very important for flying airplanes. Because it lifts the vehicle.

This lift force is provided with the contour that provides the maximum normal lift force and minimum pressure drag. After a fluid velocity, wings can produce the total lift force to take off the aerial vehicle. Also, normal lift force takes place at the inclined surface to flow velocity.

Also, these airfoils are specially designed to minimize the pressure drag force. As we stated above, pressure drag occurs because of the pressure difference between the front side of the bodies and the wake region. The wake region is minimum for airfoil designs. And pressures are lowest as possible because the area is very low.

So, the biggest drag force effect is the friction drag on airfoil shapes.

Helicopters

Also, the same working principle of airfoils is valid for helicopters. If we take a look at the cross-section of the helicopter propeller, the design is an airfoil. Engineers design these wings to obtain minimum drag coefficients. Also, they try to obtain the maximum lift force with the wall friction.

If the helicopter propeller rotates a specific high RPMs, the force to lift the helicopter is obtained. Also, altitude can be adjusted with the speed of rotation.

Also, there is tail propeller of helicopters is very important. Because of the rotation of the main propeller, there will be a rotation moment that rotates the whole helicopter body in the inverse direction. To prevent it, they use a tail propeller to orientate the body.

Automotive

In automotive, aerodynamics is very important for efficiency. Also for ergonomics and driving comfort, it is very important to design good aerodynamic designs. But here, the approach is slightly different from aerospace.

In today’s technology, aerodynamics are very important in automotive design. Engineers are trying to obtain the minimum drag coefficients and maximum downforces for better driver comfort. Think that, the lift force is applied reverse in automotive.

The external bodies of automobiles are made to minimize the pressure drags, drag coefficients, and wage regions. Also for spoilers of high-speed vehicles, they are designed to produce more downforce.

If you take a look at the shape of the spoilers of sports cars, you will see that the shape of it is an inverted airfoil. If you invert the airfoil, you will produce down forces instead of lift forces. This downforce provides extra drive comfort and safety.

Marine Applications

In marine applications, aerodynamics is very important. If you take a look at the surfaces of ships that contacts water, there is an aerodynamic design.

The density of water is higher than the air. So, the drag coefficients must be minimum for the efficiency of ships and marine vehicles.

These contacting sections are designed to obtain minimum pressure drags and drag coefficients and minimum skin friction drags. And also, engineers design this section of marine vehicles to obtain a minimum wake region.

Turbine Blades

We use the turbine systems mainly for energy production facilities or in jet engines. In turbine systems, there is always a fluid flow over the blades. Because of this fluid flow, the turbine rotates. Engineers design these blades in a special way to obtain the most efficient system.

If you take a look at the cross-section shapes of turbine blades, the cross-section is like an airfoil. To rotate the turbine blades, we utilize the lift force generated by an airfoil section. Also, the pressure difference between the fluid entrance and the fluid outlet must be minimized to prevent inefficiencies.

So, we can see airfoil applications in turbine systems also.

Conclusion

The drag coefficient is a very important aspect of engineering. There are various kinds of applications of coefficient of drag. This phenomenon depends on different things such as total surface area and the density o the flow.

Moreover, engineers are designing systems that have minimum drag coefficient. In the design of airplanes, it is intended to have minimum values. This is also valid for marine and automotive applications.

Finally, this is the general information about the drag force. Do not forget to leave your comments and questions below about the coefficient of drag.

Your precious feedbacks are very important to us.

FAQs About Coefficient of Drag

What is the drag coefficient?

It is the coefficient that shows the amount of drag force between a body and a fluid flow. Different parameters affect the drag coefficient between fluid and bodies. For different types of interfaces, this coefficient differs.

Which car has the lowest drag coefficient?

Of the cars, the Mercedes A-Class Sedan type offers the lowest drag coefficient. So with these features, it is the most efficient car in terms of aerodynamics.

Is the higher or lower drag coefficient better?

It depends on the applications. But in general aerodynamical applications, lower drag coefficients are desired.

Does drag coefficient change with velocity?

Yes. The velocity of fluid or the velocity of the body is a very important parameter of drag force. If you take a look at the formula above, you will see that with the increasing velocities, the total drag increases.

Does drag coefficient change with size?

Yes, it changes with size. Moreover, this size is the total area in that fluid flow exerts pressure. Because, with the increasing area, the total force increases.

What determines the drag coefficient? 

There are different kinds of parameters that affect drag. The velocity of the fluid or body, the total area of the body, and the density of the fluid are among the general parameters.

Does drag coefficient change with altitude?

Yes, it changes with the altitude. With the increasing altitude, the density of the atmosphere decreases. Because of this decrement, drag decreases. Planes generally fly over an altitude for the optimum drag and lift forces.

How drag coefficient is calculated?

There is a formula to calculate it which includes the parameters of, velocity, density, and area. You can find the formula in this article above.

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