Parachutes can be simple toys, lifesaving emergency equipment, used to deliver materials to remote locations and help return astronauts from space to earth. They are a fascinating and fun area to learn about and to experiment with.

Parachutes come in all different shapes and sizes and are made from a range of materials. The most common type of parachute that is often sold as a toy is a flat circle parachute. The flat circle parachute is as simple as it sounds, a circle of material is cut out and cords are attached around the edge that are then tied together and attached to the “payload”. Payload is a term for something which is carried by a vehicle but isn’t itself part of the vehicle, whatever the payload is, it adds weight to the system.

A parachute works, in simple terms, by creating drag which is a force that resists the direction of travel. As the parachute inflates (unfolds into its position for descent) it fills with air, drag is created and the payload descent rate slows. You might have seen that sometimes parachutes have holes in them that have been added on purpose. It seems odd at first to add a hole to a parachute but there are some very valid reasons for doing so. Adding a hole in a flat sheet parachute will usually reduce the drag force so if you fly the same parachute first without a hole, then with a hole with the same weight payload the holed version will descend quicker. This is useful for example in model rockets where if there is a slight crosswind a slower descending rocket will get blown further away and you’ll have a longer walk to find it!

Sometimes holes in parachutes are referred to as “spill holes” and this hints at another reason to add holes. If you have a full circle flat sheet parachute and watch it descend, particularly one made from plastic that doesn’t allow any air to seep through the material, you will see that it tends to rock from side to side and swing the payload around. This is because the filled parachute (often called a “canopy” when it is fully inflated in flight) has no way of letting the air inside it out, the air then tends to overflow and “spill” out of one side of the canopy and this causes it to swing one way, then air spills out of the opposite side and the swinging continues. As an experiment, make a flat sheet parachute and see if you can see this effect, then cut a hole that’s around 1/5 of the diameter of the full parachute and see if it makes a difference. This can be really useful if you want to have a smooth descent for your payload.

To make a simple parachute suitable for a small toy we can use some tape, a thin plastic bag, some string and some paper hole reinforcer stickers. You can experiment with shapes and designs as much as you like and let your imagination run wild. For a first attempt though it might be good to make a simple parachute design. Find a larger plastic bag made out of thinner plastic material. A good source of material is often plastic bags designed to line household bins.

Cut the bag to make it into a big flat sheet and then draw a circle onto the bag. It can help to tape the plastic material in the corners to stop it moving around and you can use a pin with a piece of string attached to guide a pen in a circle if you can’t find a circular object big enough for your parachute. Next we need to cut some string to make our “shroud” lines. Again try some experiments when you build parachutes but a good starting point is to have each line a similar length as the diameter of your parachute circle.

Measure your string against the diameter of the parachute canopy and cut 6 lengths adding a small amount to tie the shroud line to the parachute. You can just tape your lines to the parachute canopy edge but for a stronger connection you can use paper hole reinforcer stickers to create a reinforced hole in your sheet you can tie the shroud lines too.

Attach the parachute to a small toy, find a high spot (but make sure it’s a safe place) check your landing zone is clear and launch your payload and parachute. You should see that the parachute takes a little time to inflate and then the payload slows down a little to descend.

Getting into the maths behind parachutes can be fun and help us to design parachutes that can hopefully give us more accurate control of how fast a payload descends. Parachute maths can get incredibly complex so we have simplified the maths and made some presumptions to make it a little easier.

A lot of the time we will want to have a payload that we know the mass of and we have a parachute and we want to work out how fast the payload will descend. So for example we might have a payload that weighs 5 kilograms and we might have a parachute that has a radius of 2m.

We can use an equation to work out the terminal velocity, or put simply how fast the payload will be travelling as it hits the ground. Below is the formula, it looks complex, but don’t worry we will break it down into small parts and look at each part in turn to make it simple to use.

So the left hand side of this equation has “V” V is the velocity we want to calculate and will be given in meters per second. Moving across to the right we can see the whole of the right hand side is inside a square root, so when we calculate the formula inside the square root we will have to perform a square root as the last thing we do to get V. The rest of the formula is a fraction with the top line reading 2 multiplied by “m” multiplied by “g”. Here “m” is the mass of the payload in kg, so in our example it is 5kg. The next item “g” represents gravity which is given as 9.81m/s2 (on earth!). So we can simply calculate the top line of our fraction.

**2*5*9.81 = 98.1**

The lower line of our fraction reads “P” which stands for “Pho” which is a greek letter often used to represent pressure. In our equation we are using P to represent air pressure at sea level. This is a simplification for a few reasons. One is that air pressure decreases with altitude so a parachute falling from 1km up will be subject to less air pressure than when it is closer to the ground. Other factors such as the air temperature can effect air pressure so we are going to use a common approximate value for air pressure at sea level which is 1.22. Cd is the next term and this is a “drag coefficient”, in simple terms different parachute designs produce different amounts of drag for a given area, drag coefficients are calculated for designs of parachutes either by real world drop testing and measurement or by wind tunnel type testing. If you are making a well researched design of parachute you may be able to find accurate drag coefficient values for it, for our simple canopy we think a value of 0.9 is reasonably accurate. The final part of the fraction is “A” which stands for the area of the parachute which will be given in meters squared. We need to do a quick little other piece of maths to calculate the area from our radius using the equation;

Where r is the radius in meters. So for our example r = 2 therefore r2 =4 and therefore pi multiplied by 4 gives us an area of 12.566370614 m2.

So we now need to use a calculator to work out 1.22*0.9*12.566370614 which returns 13.7979072.

So now our Velocity equation looks like this.

Next let’s calculate the fraction;

And finally using a calculator let’s work out the square root of 7.109773865 to give

**V = 2.666415921**

Finally let’s round that answer to a couple of decimal places to give our final velocity as 2.67m/s.

If you are able, it’s not too hard to rearrange the above equation to be useful in other ways when designing parachute systems. It’s common for example to have a payload you know the mass off and a desired velocity you want your payload to land at but you don’t know what size parachute you need. Rearranging the equation to solve for A is therefore really useful.

#### Sidebar, types of parachute

### Learn More

#### Make your own parachute

https://www.scienceworld.ca/resource/make-your-own-parachute/

#### Stem activities – parachutes

https://www.sciencebuddies.org/stem-activities/parachutes

#### Different parachute types

https://awe365.com/a-summary-of-different-parachute-types/

#### Parachute design

https://www.msichicago.org/science-at-home/hands-on-science/parachute-design/

#### Parachutes

https://en.wikipedia.org/wiki/Parachute

#### Five parachute facts

https://skydivecalifornia.com/blog/5-parachute-facts-types-parachutes/

#### How parachutes work

https://wisconsinskydivingcenter.com/blog/how-parachutes-work/

#### How parachutes work

https://www.explainthatstuff.com/how-parachutes-work.html

#### Playtime with Parachutes: How they work

https://www.youtube.com/watch?v=Ab_g5sLoXoY

#### Materials used to make parachutes

https://www.azom.com/article.aspx?ArticleID=10429

#### How to make a parachute at home

https://www.youtube.com/watch?v=uA_qzmaDF_8

#### The First Parachutist

https://www.history.com/this-day-in-history/the-first-parachutist