## Drag Force in Physics

This article is about to dump a lot of information on you at once, so I'll try not to make it a drag.

In physics, **drag force** is the force that opposes the relative motion between an object and a fluid.

A **fluid** is anything that flows, such as a liquid or a gas. When the fluid is air, drag force is referred to as **air resistance.**

The object might move through the fluid, or the fluid might move around the object—either way, the **drag force acts in the opposite direction of the relative movement**. In this way, the drag force is similar to friction, but the motion is between a solid and a fluid instead of two solids. The image below shows a man running through air (a fluid). Since the man's motion is to the right, the drag force would act opposite to that motion, to the left, as shown by the arrows in the figure.

What if the man stands still and the air moves past him as wind, like in the image below? As you can see by the arrows in the figure, the drag force would act in the direction of the wind; this is because the relative motion between the man and the air is the same as in the image above, but instead of the man moving to the right, the air is just moving to the left.

What if the man was running in the direction of the wind? At this point, it depends on whether he runs faster or slower than the wind. It can help to think of the direction of drag as whichever direction you would feel pressure, or force, from the fluid. If he feels the breeze on his front, the drag force points towards his front; if he feels the breeze on his back, the drag force points towards his back.

If he runs at the same speed as the wind and thus feels no breeze, there would be no drag force since there would be no relative motion between him and the air around him. On the other hand, if he jumped off a balcony, he would feel wind upward so that the drag force would point up.

Drag force is an important consideration for engineering designs. Understanding drag and how to decrease it helps people design sturdier structures and bridges that hold up better to wind, more efficient cars and planes, and more efficient collection of wind energy and hydropower.

**Types of Drag Force**

There are different types of drag force, especially when considering the flight of airplanes:

- Parasitic Drag—Drag caused by the object's shape, material, and construction type.
- Form Drag—The drag due to the shape of the object moving through the fluid.
- Skin Friction Drag—The drag due to the roughness of the object's surface.
- Interference Drag—The drag resulting from two airflows of different speeds meeting and interfering.

- Induced Drag—The drag resulting from lift.
- Wave Drag—The drag due to shockwaves.

Phew, that was a lot of information to trudge through, if word density could be considered, this article would have a massive drag force.

## Examples of Drag Force

Here we go again—even more examples. It's like walking through honey.

Drag is present when there is relative motion between an object and a fluid. Some examples of drag force include the following:

- Any object falling through the air. For example, skydivers use principles of drag force to move and position themselves through the air, and when they open their parachutes, the greater drag force that's created helps slow them down to land.
- Drag force slows down cars, planes, and ships when they move. So engineers increase the aerodynamics of these vehicles to reduce drag and increase the vehicles' efficiency.
- Swimmers fight against drag force when they swim. Even shaving can reduce drag and increase swimmers' speeds.
- Flying squirrels use their wing-like skin to use drag force to control their flight and landings.
- If you were to stand on top of a quickly moving train, it wouldn't be as easy to stand or run as many movies make it seem because there would be a drag force pushing against you.
- Drag force causes kites to fly. You must run forward with the kite to get the drag force to push against it and lift it into the air.

## Drag Force Equation

The common equation or formula for drag force is shown below:

$$D=\frac{1}{2}\\C\rho Av^2\mathrm{.}$$

This equation is only accurate under certain conditions: the motion is fast enough that the fluid behind the object is turbulent, the fluid is not denser than air, and the object is not tiny. As with other forces, drag force is measured in \(\mathrm{newtons}\) \(\mathrm{N}\).

## Drag Force Formula

Above, you probably saw a bunch of variables that you have never seen before. To aid you in understanding what the drag force is, we'll go over each of these variables.

\(C\) is the **coefficient of drag**, which is a unitless number that has been determined experimentally. \(\rho\) represents the density of the fluid in \(\mathrm{kg/m^3}\); as the density increases, the drag force increases. In our opening example, water contributes to a higher drag force than air because it has a higher density.

\(A\) is the effective cross-sectional area of the object in \(\mathrm{m^2}\)—this is the area of the object that is perpendicular to the motion. So, for example, when sticking your hand outside a moving car's window, if you tilt your hand, so the side is facing the front of the car, you will feel less force than if you stick your hand out with the palm facing the front: this is because your hand has a smaller cross-section in the first orientation.

\(v\) is the relative velocity between the object and the fluid in \(\mathrm{m/s}\). If you put your hand in water and slam it down, you will feel more of a force fighting against you than if you slowly lower it. Drag force differs from friction because friction doesn't depend on the object's speed.

### Stokes's Law

Have you enjoyed the terrible puns so far? I don't mean to stoak the fire burning in your heart even more from all these dad jokes, but I just have to.

When the conditions don't meet the requirements listed above, we can use **Stokes's Law** to find the friction force:

$$F_s = 6\pi \eta r v$$

where \(\eta \) is the viscosity of the fluid in SI units of Pascal-seconds \(\mathrm{Pa\,s}\), which is the same as kilograms per meter-second \(\mathrm{kg/m\,s}\), \(r\) is the radius of the object in meters, and \(v\) is the velocity in meters per second \(\mathrm{m/s}\). In this case, the drag force is proportional to the velocity rather than the velocity squared. With this equation, the drag force may be referred to as a **viscous drag force**, where the drag force is dependent on the fluid's viscosity.

### Drag Force in Free-Fall—Terminal Velocity

If you drop a bouncy ball off the empire state building, initially the force acting against the ball is negligible since the velocity starts at zero. Instead, the main force acting on it is the force of gravity, which pulls it down and causes it to accelerate. As the velocity increases, the drag force acting against the ball's fall will increase. This opposite force causes the ball's acceleration to slow until, eventually, the drag force equals the force of gravity and the ball no longer accelerates. At this point, the ball will reach a constant speed at its **terminal velocity**.

## Example Problem Using Drag Force

Now, it's time for an example.

A box falls through the air at a speed of \(12\,\mathrm{m/s}\). Its dimensions are \(0.5\,\mathrm{m} \cdot 0.5\,\mathrm{m} \cdot 2\,\mathrm{m}\), oriented vertically as shown in the image below. The density of air is \(1.225\,\mathrm{kg/m^3}\), and the drag coefficient for the box is \(2.1\). What is the drag force?

Most of the variables are fairly self-explanatory, and we can plug them straight into our drag force equation. The trickiest one to know what numbers to use is the area. We need the effective cross-sectional area, which is the area of the box that is facing the motion—in this case, we can think of it as the area facing the wind as it falls. This area is \(0.5\,\mathrm{m} \cdot 0.5\,\mathrm{m}\), or \(0.25\,\mathrm{m^2}\). Now we can write our equation

$$D=\frac{1}{2}\\ C\rho A v^2\mathrm{,}$$

and plug everything in

$$D=\frac{1}{2}\\(2.1)(1.225\,\mathrm{kg/m^3})(0.25\,\mathrm{m^2})(12\,\mathrm{m/s^2})^2\mathrm{,}$$

which gives us the answer

$$D=46.3\,\mathrm{N.}$$

If we double-check the units in our equation, we can see that they all cancel out to give us \(\mathrm{kg\,m/s^2}\), which is the same as \(\mathrm{newtons}\).

Hopefully, finishing this article wasn't too much of a drag—more like walking through a luscious breeze rather than cold honey. If your answer was the honey, don't panic, you're almost done: here are the most important points you need to remember.

## Drag Force - Key takeaways

- The drag force is the force that opposes the relative motion between an object and a fluid.
- The direction of the drag force is always opposite to the relative motion.
- Common types of drag force include parasitic drag, form drag, skin friction drag, interference drag, induced drag, and wave drag.
- For most simple scenarios (if the velocity is high, the viscosity of the fluid is low, and the object isn't tiny), the equation for drag force is \(D=\frac{1}{2}\\C\rho Av^2\).
- We can use Stokes's Law to find the drag force when a situation doesn't meet the requirements necessary to use the drag force.

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##### Frequently Asked Questions about Drag Force

What is drag force?

Drag force is the force that opposes the relative motion between an object and a fluid.

How to calculate drag force?

For most simple scenarios, drag force can be found by multiplying one half, the coefficient of drag, the density of the fluid the object moves through, the cross-sectional area of the object, and the object's velocity together.

What are the types of drag force?

The types of drag force include parasitic drag, form drag, skin friction drag, interference drag, induced drag, and wave drag. These types of drag are applicable to flying an airplane.

What is the importance of drag force?

Drag force is an important consideration in engineering design. It impacts the performance of products such as cars, planes, ships, structures, wind turbines, and water turbines.

What is viscous drag force?

Viscous drag force occurs when the fluid is too viscous for the normal drag force equation to apply. In this case, the viscosity of the liquid is an important factor in determining the drag force.

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