Air Resistance in Fall Protection

Fall protection and physics are very closely linked with one another because they are both related to the laws of motion. Fall protection is mostly concerned with the process of preventing and arresting falls, whereas physics is a science that explores matter, energy, and their interactions. However, many of the concepts used in the study of physics can be applied to the engineering and design of fall protection systems and devices. 

When a person is skydiving, they are mostly being subjected to the forces of gravity and air resistance as they are traveling. Because a person is at such a high altitude when they are making their descent, there is enough time and space for that person to reach terminal velocity. This concept made our safety professionals curious about the circumstances that would allow a person to achieve terminal velocity during a fall in the workplace.

In its simplest form, terminal velocity is defined as the condition of the force of the air pressure on a moving object or body becoming equal to the weight of the object or body that is moving. 

Keeping that definition in mind, the question of the week is:
How far will a person need to fall in order to reach terminal velocity?

For the purposes of the scenario we are proposing in this blog, we are making a few assumptions. The first thing we are assuming in our scenario is that the terminal velocity for an average weight and sized person will be 120 mph. The second thing that we are assuming is that air resistance will not develop a significant force until 120 mph.

Our engineering manager has simplified this scenario to one relatively accurate equation to demonstrate the incredible distance a person would need to fall in order for air resistance to stop acceleration and achieve terminal velocity.

In our equation, these letters below will represent the following things:

A=Acceleration due to gravity

FV= Final velocity after falling distance “X”

X = Overall distance the worker has fallen

The equation we are going to use is:

FV^2/2A = X

This equation could also be explained as:

The overall distance the worker has fallen is equal to the final velocity squared and then divided by the acceleration of gravity multiplied by 2.

Due to the gravitational forces of the earth, objects fall at a speed of 32.2 feet per second squared (“A” in this equation).

And if we are assuming that the final velocity (FV) of our falling worker is 120 mph, we need to convert the miles per hour unit to feet per second. So, 120 mph is equal to 176 feet per second.

And when we convert the final velocity to the feet per second unit, we are able to multiply the denominator in our equation without needing to convert additional units.

So, written in numbers, this equation looks like this:

(176 ft/second) = 481 ft.
32.2 (2)

By using this equation, we determined that a person of average weight and size would need to fall from a height of 481 feet (or roughly a 50 story building) in order to reach terminal velocity while falling. Since most workplace falls occur between 4 and 30 feet, the average person will never reach terminal velocity while falling.

Terminal velocity is not a phrase that people want to hear when they think about fall protection. And, because fall arrest products are designed to limit the overall distance that a person travels after an unintended loss of balance, there is no chance that a person would ever reach terminal velocity while attached to a properly installed and functioning fall arrest device.

Until the next time, stay safe up there! 

Do you want to know more about the physics of fall protection? Let us know your questions in the comments section below!