I'm currently building a water rocket made out of carbon fiber pipes and fabric. Before that I built a simple water rocket made out of plastic bottles with my friend for a science competition. Now I want to take part in the science competition again but this time with my new water rocket. My friend did the height and velocity calculations for the last rocket while I was building the water rocket itself. Because of that I'm not really familiar with water rocket calculations. Of course I took a look at our old calculations but I discovered a terrible mistake. My friend just guessed the start velocity of the rocket because with the real values we'd have gotten results which would be far above the height we reached. That's also the reason why we splitted up and now I'm doing everything on my own. I looked all over the internet and in science book to find formulas with a close result to my actual height and velocity, sadly they were often too complicated and I just got into Highschool so I also didn't know if the formulas are right/verified. Can anyone recommend me formulas for the calculation of the height and velocity? I also did not find a formula for calculating the size(diameter) of my nozzle. Maybe one of you can also recommend me a formula for that. I'm really interest in rocket science and I'd love to learn more. The calculations can be complicated as long as they are close to the real height because I'm willing and ready to learn a lot about rocket science!

I'm sorry if there are some English mistakes. English is not my native language and with all these technical terms it's quite difficult for me.

I'm looking forward to your recommendations/replies!


You want to use the formulas found in these two documents:



They are ultimately the same, but presented in different ways. Basically you calculate the amount of water that will be pushed out of the nozzle due to the air pressure, calculate the acceleration that creates based on the dry mass and remaining water, and then integrate.

If you want to do it on a computer:


  • $\begingroup$ Thanks for your reply! I'll use them. I looked through them and found something which did confuse me a little bit. First of all I want to make an Excel sheet with these formulas but I don't really know how to integrate. Do you maybe know how to that in Excel? I also do have another question is the air resistance included? $\endgroup$
    – Jana
    Nov 12 '18 at 18:05
  • $\begingroup$ The first of the two documents deliberately ignores drag - and that can be notoriously difficult to model correctly - mount a fin off-center and your drag might go up 50%. The second document DOES include air resistance, which it simply says "is very low in this case". I'm not convinced that is true either. $\endgroup$ Nov 13 '18 at 16:46

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