# I Calculations on a fireworks rocket?

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1. Dec 8, 2018

### Patrick5234

So I'll soon be writing an assigntment on the physics and chemistry behind firework rockets and thats why i'm here! I've already prepared for the chemistry part but when it comes to the physics part then im a bit lost. Bare in mind that i'm supposed to learn something new (myself) and explain that in my assignment, that being said i haven't learned what im about to write about. I thought about aerodynamics on the rocket and i can figure that out on my own but then i thought about the rocket itself and its travel.

I thought about calculating the rocket trajectory with fuel and so on. A fireworks rocket of course doesn't go into orbit as it explodes in the end. I've already learned the physics behind projectile motion but it isn't quite the same. As an actual rocket has a motor.

My question is, where do i find stuff like this? I've searched around a little bit but i'm a bit confused. Where can i find the formulas for stuff like this?

2. Dec 8, 2018

### Drakkith

Staff Emeritus
The most important thing with rockets is their propulsion method. It's what makes them rockets and not something else after all. The basic idea is that a rocket uses a rocket engine to 'throw' mass out the back, which by Newton's laws generates a reaction force that throws the rocket forwards. There's a lot of math involved here, so I'd choose one specific thing and focus on that.
Here are a few links for you:

https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
https://en.wikipedia.org/wiki/Delta-v
https://en.wikipedia.org/wiki/Rocket_engine

The Tsiolkovsky rocket equation (commonly just called "The Rocket Equation") is one of the most basic equations for rockets. It gives you the total amount of delta-v as a function of starting mass, ending mass, and isp. Delta-v stands for 'change in velocity', and gives you the total change in velocity that a rocket potentially has (because rockets often operate in space, where they are constantly in motion even without thrusting, we can't specify a maximum distance for them like we can with cars or planes.).For a simple rocket you can basically choose how much delta-v you want, choose your fuel type, and then use the rocket equation to figure out how much fuel you'll need versus your dry mass. That's a very, very rough overview of the process of course. The actual design process involves a lot of iterations, modeling, and even trial and error.

If you're interested, you can find an enormous number of books on rockets on Amazon or other similar websites.

3. Dec 10, 2018

### Patrick5234

Thanks for replying :), would it be enough to cover Tsiolkovsky rocket equation though? I feel like im missing something with the actual fireworks part. Yeah a rocket is a rocket and the principle is the same wether its outer space or in the bounds of earths atmosphere. Covering the equation is of course a really good idea but what about stuff like the launch of the rocket under gravitys force?

4. Dec 10, 2018

### CWatters

Classic exam questions invitee you to apply conservation of momentum to the parts of an exploding shell.

5. Dec 10, 2018

### Patrick5234

Ah yes, ill note that down. Thanks :)

6. Dec 10, 2018

### DrStupid

That's quite easy. You just need to transform the trajectory from an inertial system into a free falling system, simply by adding g·t²/2.

Including aerodynamics is much more complicate. You will need to solve the equation of motion that results from thrust, gravity and drag.

7. Dec 10, 2018

### Patrick5234

I already thought about talking about aerodynamics but only about the coneshape on the rocket (the point). Including stuff like differential equations was a part of the plan when i get around to starting the project.