I have a good question for the forums  what are the mathematics behind water rocketry?
Well, more specifically, how do I calculate the best water levels without having to guess and check with simulators?
It's just something I want to know more about. Also, since this is related to this topic, how do you calculate the force of drag without the drag coefficient? I need to know this so that I can build better, more aerodynamic rockets using simple materials.
Thanks!
Welcome to the Water Rocket Forum, sponsored by The Water Rocket Achievement World Record Association.
The largest, most sophisticated and ground breaking group supporting you, the serious water rocket flyer! Whether you are a beginner or an expert, the WRA2 has something for everyone.
A water rocket is a type of model rocket using water as its reaction mass. The pressure vessel (the engine of the rocket) is constructed from thin plastic or other non metallic materials (usually a used plastic soft drink bottle) weighing 1,500 grams or less. The water is forced out by compressed air. It is an example of Newton's third law of motion.
The largest, most sophisticated and ground breaking group supporting you, the serious water rocket flyer! Whether you are a beginner or an expert, the WRA2 has something for everyone.
A water rocket is a type of model rocket using water as its reaction mass. The pressure vessel (the engine of the rocket) is constructed from thin plastic or other non metallic materials (usually a used plastic soft drink bottle) weighing 1,500 grams or less. The water is forced out by compressed air. It is an example of Newton's third law of motion.
What is the Math behind bottle rocketry?

 WRA2 Member
 Posts: 15
 Joined: Sat Feb 27, 2016 8:31 pm
 anoymous
 Senior Member
 Posts: 128
 Joined: Thu Mar 19, 2015 2:52 pm
Re: What is the Math behind bottle rocketry?
Well, you can't calculate the drag force without the coefficient. But you could try to measure it indirect:
If you know the initial speed (after the thrust phase), and you know the height of apogee, you can calculate the deceleration of your rocket. When comparing this to g, I think you can calculate the drag (and maybe the drag coëfficient?
If you know the initial speed (after the thrust phase), and you know the height of apogee, you can calculate the deceleration of your rocket. When comparing this to g, I think you can calculate the drag (and maybe the drag coëfficient?
"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."
 Albert Einstein
Sorry for malconstructions in my sentences, I am Belgian. And I was never good at making easy sentences.
 Albert Einstein
Sorry for malconstructions in my sentences, I am Belgian. And I was never good at making easy sentences.

 WRA2 Member
 Posts: 15
 Joined: Sat Feb 27, 2016 8:31 pm
Re: What is the Math behind bottle rocketry?
So, I've come up with some more questions involving the Math behind bottle rocketry  How does one determine the Specific Impulse of a bottle rocket by using the volume of the pressure vessel, the pressure of the air inside the pressure chamber, and the volume water takes up?

 WRA2 Member
 Posts: 5
 Joined: Wed Mar 30, 2016 6:55 am
Re: What is the Math behind bottle rocketry?
Out of my own personal interest, I began looking into this.
Searching the web, brought up a few, quite insightful resources, mostly from educational institutions:
https://www.ohio.edu/mechanical/program ... ysis1.html which contains a link to an interesting .pdf file (nielson equations)
http://www.et.byu.edu/~wheeler/benchtop ... t_eqns.pdf
http://stemstates.org/assets/files/430_ ... %20430.pdf
and the most useful I found….
http://research.che.tamu.edu/groups/Sem ... CTIONS.doc page 21 onwards.
I plugged the equations into excel, iterating line by line over time, to come up with a mathematical simulator:
However, whilst the output looks good, I checked it against the Clifford Heath simulator, and the results were not the same….
Dave
Searching the web, brought up a few, quite insightful resources, mostly from educational institutions:
https://www.ohio.edu/mechanical/program ... ysis1.html which contains a link to an interesting .pdf file (nielson equations)
http://www.et.byu.edu/~wheeler/benchtop ... t_eqns.pdf
http://stemstates.org/assets/files/430_ ... %20430.pdf
and the most useful I found….
http://research.che.tamu.edu/groups/Sem ... CTIONS.doc page 21 onwards.
I plugged the equations into excel, iterating line by line over time, to come up with a mathematical simulator:
However, whilst the output looks good, I checked it against the Clifford Heath simulator, and the results were not the same….
Dave
 anachronist
 WRA2 Member
 Posts: 217
 Joined: Sun May 07, 2017 2:18 pm
Re: What is the Math behind bottle rocketry?
I just found this thread. Earlier this year I spent a few months developing my own simulator, which accounts for just about everything that can possibly be accounted for. I documented the calculations in 5 posts of my blog starting here: http://www.nablu.com/2017/07/thewaterrocket.html
To answer Astrofox's original question: For a given initial pressure (like 100 psi), there's an optimal combination of empty weight and total fill volume that achieves the maximum altitude, for a rocket with a given drag coefficient. Because all the mathematical relationships are nonlinear, the only realistic way to calculate this is by numerical analysis. So yes, you need a simulator.
Alex
To answer Astrofox's original question: For a given initial pressure (like 100 psi), there's an optimal combination of empty weight and total fill volume that achieves the maximum altitude, for a rocket with a given drag coefficient. Because all the mathematical relationships are nonlinear, the only realistic way to calculate this is by numerical analysis. So yes, you need a simulator.
Alex