Math in Parachuting and Skydiving

[amarie]

Hi, I've got a project for year 9 maths at my school where we got to choose our own topic and basically have to research most of the maths involved in it. I chose skydiving and parachuting. I'm getting a bit lost and having a little difficulty in finding useful information on the web, so I was wondering if anyone here could offer a little generic help. I don't have any particular question, I just kind of need a push in the right direction. Anything on terminal velocity, air resistance, factors put into consideration in the construction of parachutes would be fantastic. I think I'd also find any formulas/equations very useful. Thank you so much, I'll be eternally grateful to any assistance given.
Alyssa

 

[Mark]

skydiving and parachuting eh?
The main thing you will want to consider is terminal velocity.
Terminal velocity is the maximum speed one will reach while falling in free fall (falling where the force of gravity is equal to the force of air resistance), terminal velocity requires some physics, and I am not sure how fluent you are with this - if its grade 9 math, so i will make it simple.

First, draw a picture - i am too lazy to do so. You will see that there are two forces, air resistance and gravity - both pulling in opposite directions

The equation for gravity if Force = mass * gravity (F=mg)
The equation for air resistance is very complicated - mabye second year university level stuff.

But to sum it up, the formula for air resistance depends on your surface area - if you are falling in a ball you will fall fast, if you are falling flat out completely outstretched - your terminal velocity will be slower.

Paracheuting just creates more surface area (hence you can land without dying)
Skydiving creates less surface area (you are falling completely straight), thus your terminal velocitity will be higher.

In fact, people have actually sucessfully landed without out parachutes (From like 10 000feet up) simply by spreading themselves out, and other techniques (snow, etc.)

Yup, good luck.

 

[M98Ranger]

Hi Alyssa,

That sounds like an interesting project! Math plays a crucial role in skydiving and parachuting, and it's great that you have chosen to explore this topic for your project.

Let's start with terminal velocity. This is the maximum speed that an object can reach while falling through the air. It is determined by the balance between the force of gravity pulling the object down and the force of air resistance pushing against it. The formula for terminal velocity is v = √(2mg/pAC), where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, p is the density of air, A is the cross-sectional area of the object, and C is the drag coefficient. This formula can be derived using the principles of Newton's second law and the equations for air resistance.

Speaking of air resistance, this is another important factor to consider in parachuting and skydiving. Air resistance, also known as drag, is the force that opposes the motion of an object through the air. It is affected by factors such as the shape and size of the object, the density of the air, and the speed of the object. The formula for air resistance is F = 1/2pv²CA, where F is the force of air resistance, p is the density of air, v is the velocity of the object, C is the drag coefficient, and A is the cross-sectional area of the object. This formula can also be derived using the principles of fluid dynamics.

When it comes to the construction of parachutes, there are a few key factors to consider. These include the size and shape of the parachute, the materials used, and the weight of the object being dropped. The parachute needs to be designed in a way that will allow it to slow down the descent of the object, while also being strong enough to withstand the forces of air resistance. The design of the parachute also affects the drag coefficient, which we mentioned earlier in the formula for terminal velocity.

I hope this gives you a good starting point for your project. I would also recommend looking into the history of parachuting and how the technology and design of parachutes has evolved over time. This could also be a great opportunity to explore the concept of free-fall and how it relates to skydiving. Best of luck with your project!