# Terminal Velocity

#### Bydreamtravel

Aug 22, 2022

Table of Contents

## The Science Behind Parachutes

How do parachutes work? Reasonable question if you’re about to make a skydive (or even if you’re just interested in learning the mechanics behind skydiving)! After all, if you’re going to launch yourself out of an airplane and put your trust in a big ball of fabric, it helps to know the science behind parachutes.

You’ll be relieved to know they are much more than a haphazard hodgepodge of material and stitches, there’s a fine-tuned design behind it all. How does a parachute work? The simple answer is with the magic of air resistance and human ingenuity.

Here’s a quick science refresher to get us started on our journey to discover how parachutes work.

The strength of gravity pulls us all to Earth uniformly: whether a stone or a feather, no matter the object, it will have an acceleration of 9.8 m/s ² downward to Earth. In a vacuum with no air, you’d see a feather and a stone hitting the ground at the same time. So, how exactly is it that in the real world the stone reaches the ground first? Well, this is where air resistance makes its appearance. The feather hits the ground after the stone not because it’s lighter, but because the feather catches more air as it falls; the drag of its surface area slows it down.

## Air Resistance

In part, the science behind parachutes is that they make clever use of air resistance. You see, though it’s invisible, air is composed of gas molecules and as you move around, they’re pushed aside. The larger space you occupy and the larger surface area you have, a greater amount of air resistance results.

To take advantage of this fact, parachutes are often made from a lightweight nylon that has been specially treated to be less porous (that is, it doesn’t let as much air through). This allows your open parachute to create more air resistance and to drift toward the ground slowly and safely.

## Terminal Velocity

Terminal velocity is a point at which there can be no further acceleration. This constant speed is reached when the force of gravity is countered and balanced by the resistance of the medium an object is falling through (like air).

How does this apply? Your parachute allows you to descend more slowly because it lowers terminal velocity by increasing your air resistance. Most parachutes are designed to create a large amount of drag and allow you to land at a safe, low speed.

## Parachutes Today

Photos by Animare

Parachutes today are designed for a myriad of functions. Military operations utilize a parachute that is dome-shaped, providing only basic steering and are used by the military for the insertion of paratroopers and gear. On the other hand, civilian jumpers most commonly use a rectangular Ram-air parachute, one constructed with a series of tubular cells that inflate as air is forced into each chamber. The result is a semi-rigid, curved airfoil wing that delivers higher performance and increased maneuverability.

## Parachute Deployment Systems

All recreational skydivers’ jump equipment contains a dual-parachute system: a main parachute and a reserve parachute (the back-up). These two parachutes are packed within a single backpack-looking apparatus we call the container.

The main parachute is deployed by a miniature chute, known as the pilot chute. At the appropriate altitude, a jumper will extract the pilot chute from the elastic pouch, where it is securely stored, sewn on the bottom of the container. The pilot chute inflates and creates enough force to extract the main parachute from the container. The main parachute is designed to fill with air and inflate in a slow, efficient manner. The reason for the delayed opening is to avoid too much opening shock on the body. Think coming to a slow, steady stop at a red light versus slamming on the breaks.

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Now that you’ve got the physics down low to the science behind parachutes, why not let us show you firsthand? Schedule your skydive with Skydive Paraclete XP today.

## Terminal Velocity

The force of gravity acts between all masses. It is an attractive force – you are pulled towards all other masses. The force of gravity is proportional to the product of the masses it acts between. therefore the only mass you notice being attracted to is the Earth!

On Earth each kilogram of mass is pulled with a force of 10N (the weight of that mass) along a line drawn towards the centre of the Earth.

A skydiver has this force exerted on him/her even though there is no direct contact between the skydiver and the Earth. This type of force, when two objects exert forces on one another even though they are not touching, is known as a noncontact force.

According to Newton’s second law, the acceleration of an object as produced by a force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object; or

Fnet = ma

The weight of an object is a product of its mass and acceleration due to gravity or

w = mg

The acceleration due to gravity (g) near the Earth’s surface is a 9.81 m/s 2 (at GCSE rounded to 10 m/s 2 ) . So, the weight of an object depends on how much mass an object has.

### The upward force acing on a skydiver – the Air Resistance – FAR

Air resistance is due to an object colliding with molecules of air.

A falling skydiver collides with air molecules during the downward fall. These air molecules create a force pushing upward which is opposite to the skydiver’s direction of travel – this is called ‘drag‘.

The amount of air resistance or drag encountered by the skydiver depends on three factors:

1: The speed of the skydiver.

The faster he goes the more air particles he collides with per second therefore the bigger the air resistance will be. If he is not moving the air resistance will be zero.

2: The area of intercept of the skydiver.

The area of intercept of the skydiver is the cross section of him (at right angles to his direction of travel). The larger this is the more air particles he will bump into per second and the higher the air resistance will be. If he is very streamlined the area of intercept will be small and there will be less air resistance than if he was bulky with lots of areas that could trap pockets of air as he fell.

A skydiver who has his arms and legs spread out (usually referred to as the arch position) will meet with more air resistance than one who falls straight down down. The skydiver can therefore control air resistance to a certain degree by repositioning him/herself.

Opening a parachute dramatically increases this area of intercept. Opening the parachute can make the skydiver decelerate rapidly by making the force of air resistance bigger than the force of weight.

3. The air density

The greater the density of the air (it is less dense at higher altitudes – the air is said to be ‘thinner’) the more air particles the skydiver will bump into each second making the air resistance greater.

### Terminal Velocity

The resultant force of gravity minus air resistance acting on the skydiver as he fall makes him accelerate according to the equation F = ma.

So,

FW – FAR = ma

As long as Fw is greater than the FAR the skydiver will accelerate – get faster.

If Fw is smaller than FAR s/he will decelerate – undergo negative acceleration – get slower.

 When s/he steps out of the plane his/her vertical velocity component is 0 m/s so air resistance is zero. That means only the force of gravity acting on his mass – his weight – is acting. That means his vertical velocity rapidly increases.
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 As the speed of the skydiver increases every second as he or she plummets towards the ground there is an increase in air resistance (as this gets bigger as his/her speed increases). This results in a smaller net force acting on the skydiver. S/he is still getting faster, but not at the same rate as s/he did initially. Look at the graph representing how the vertical velocity changes duing the fall. You can see that the gradient decreases as the speed increases.

Eventually the gradient of the graph is zero.

That happens when Fw = FAR

No net force means no acceleration and that means the velocity will remain constant. It is the final velocity – terminal velocity.

### How a Parachute Works

When the parachute is opened the force of air resistance becomes much, much greater than the force of gravity.

The net force on the descending skydiver now has an acceleration that points upward – negative acceleration or deceleration.

This causes a rapid decrease in the skydiver’s velocity.

Look at the graph representing how the vertical velocity changes duing the fall. You can see that the gradient becomes strongly negative when the parachute is opened.

As the speed of descent decreases, the amount of air resistance also falls, until once again a terminal velocity is reached because Fw = FAR. This second terminal velocity is now slow enough to allow the skydiver can land safely on terra firma without his legs snapping in two – assuming s/he lands correctly.

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## Parachutes, Gravity and Air Resistance

As you’ve most likely taught your students, gravity is the force that exists between any two objects that have mass. Weight is a measure of the force of gravity pulling on an object. So, does that mean heavier objects will fall faster?

In about 1590, as the story goes, Galileo Galilei went to the top of the Leaning Tower of Pisa and simultaneously dropped many pairs of items, such as cannon balls, musket balls, gold, silver and wood. Each time, one object was heavier than the other, yet they otherwise had the same shape and size. They both hit the ground at the same time! Up until then, people figured that heavier objects fell faster than light objects. But Galileo determined that gravity accelerates all objects at the same rate, regardless of their mass or composition.

Challenge kids to prove this! First use a ping pong ball and golf ball to let them see Galileo’s discovery about gravity.

Use two pieces of paper for the next activity. One should be heavier, such as cardboard. Now ask them what would happen if they scrunch up just the lighter weight piece of paper and drop both at the same time from the same height. Will the heavier piece land first, or the lighter piece? After the ball demonstration, hopefully they get the answer right. Drop – lighter piece will land first.

What happened? Resistance and friction are what cause changes in acceleration. Air resistance (also called drag) slowed down the heavier piece. Drag opposes the direction that the object is moving and slows it down.

Now unfold the lighter piece and drop both at the same time from a high spot, such as a desk or ladder. They should land at about the same time.

So, regardless of weight, the more resistance/friction an object has, the slower the fall.

Finally, drop a rock and a feather that are about the same size. The heavier rock will land first. But it’s not because it weighs more, as you’ve already proven. There is more friction between the feather and the air around it. If there were no air, the two objects would hit the ground at the same time.

To slow down a fall of an object, you will want to create more drag. That’s the goal of a parachute. Feathers make better parachutes than rocks.

An early concept of a parachute was found in an anonymous manuscript from the 1470s, long before Galileo was dropping stuff off the Tower of Pisa. It wasn’t the best design – the parachute is too small to offer enough resistance – but the design introduced a new concept to artist-engineers of the times. A few years later, Leonardo da Vinci sketched a similar design with better proportions of the canopy to the jumper. Most give Leonardo credit for the concept of falling safely using a “maximum drag decelerator” aka parachute.

The concept wasn’t new, however. The use of air resistance to slow down a fall can be dated back to 90 B.C. According to Chinese historian Si Ma Chian, a legend described an emperor using two bamboo hats to jump off a roof and land safely on the ground. Chinese acrobats also used parachutes of some kind to perform falling stunts. There are other stories based on legends about parachutes that date long before Leonardo da Vinci’s design.

By the way, don’t try these stunts at home, we don’t know how successful they really were.

Parachute designs continued to evolve and be tested. In 1785 Jean Pierre Blanchard made the first emergency use of a parachute after the hot air balloon he was in exploded. He also designed a foldable silk parachute. Before that, parachutes were built with a rigid frame. About a hundred years later, parachutes came with a harness and folded into a knapsack-like container.

Parachutes are used to deploy troops and support into war zones, deliver supplies and cargo, save lives, decelerate aircraft, and more recently, for the sport of skydiving. The simple concept has evolved into a masterful invention that can be steered and manipulated almost like an airplane, just by using lift, drag, and gravity.

Challenge: Build a Better Parachute

Here are instructions for a toy parachute. Your classroom can divide into groups or teams and try altering the materials and design, always using identical objects as the jumper:

1. Cut a circle out of a paper bag, plastic bag, piece of tissue, cotton cloth, silk, etc. Let them decide the size (bigger will be better)

2. Punch holes around the edge of the circle, at least four. Tissue will need some reinforcement first, a piece of tape will work.

3. Tie string to each hole. The pieces should be the same length.

4. Tie the strings together under the parachute and secure the jumper.

The variables are numerous in this – for one thing, the height from which the parachute is dropped: it will pick up speed before air resistance slows it down so the higher the better. Does the parachute want to rock back and forth? Maybe it needs a hole in the middle to allow air to flow through the middle. See if one of your students figures that out. Did the larger parachutes work better? Did material make any difference? Did number of strings have an impact on performance?

Hopefully this experiment and the others help your students understand and even better, get excited about gravity and air resistance!

Robin Koontz is an award-winning freelance author/illustrator/designer of a wide variety of nonfiction and fiction books, educational blogs, and magazine articles for children and young adults. Raised in Maryland and Alabama, Robin now lives with her husband in the Coast Range of western Oregon where she especially enjoys observing the wildlife on her property. You can learn more on her blog, robinkoontz.wordpress.com.

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Source https://skydiveparacletexp.com/2019/07/18/science-behind-parachutes/

Source https://www.cyberphysics.co.uk/topics/forces/terminal_velocity.htm

Source https://kidsdiscover.com/teacherresources/parachutes-gravity-air-resistance/