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Water rocket academic paper

Posted: Thu Sep 28, 2017 12:07 pm
by Pere Ubu
I really had no idea the whole thing was that complicated! ;)

A more thorough analysis of water rockets: Moist adiabats, transient flows, and inertial forces in a soda bottle

Although water rockets are widely used to illustrate first year physics principles, accurate measurements show that they outperform the usual textbook analysis at the beginning of the thrust phase. This paper gives a more thorough analysis of this problem. It is shown that the air expansion in the rocket is accompanied by water vapor condensation, which provides an extra thrust; the downward acceleration of water within the rocket also contributes to the thrust, an effect that is negligible in other types of rockets; the apparent gravity resulting from the acceleration of the rocket contributes as much to water ejection as does the pressure difference between the inside and outside of the rocket; and the water flow is transient, which precludes the use of Bernoulli’s equation. Although none of these effects is negligible, they mostly cancel each other, and the overall accuracy of the analysis is only marginally improved. There remains a difference between theory and experiment with water rockets.


Re: Water rocket academic paper

Posted: Thu Sep 28, 2017 2:46 pm
by anachronist
It's more complicated than that abstract makes it out to be. I put all the equations on my blog in a series of 5 posts here:

That abstract is interesting. My own simulator accounts for all these things and more, although I disagree that you cannot use the Bernoulli equation for calculation of mass flow rate. You can, but you must modify the gravitational term to account for the rocket's nonlinear acceleration.

One significant omission I see from most attempts to model a water rocket, is failing to take into account atmospheric conditions (pressure, temperature, and relative humidity). I find that this makes a significant difference in final predicted altitude (hot humid day versus cold dry day). I still have to update the spreadsheet available on my blog to account for that.

Do you have a link, or DOI, or journal reference I can look at?

Re: Water rocket academic paper

Posted: Thu Sep 28, 2017 10:08 pm
by Pere Ubu
There's a PDF downloadable here:

The original appears to have been the American Journal of Physics, Volume 78, Issue 3, pp. 236-243

Re: Water rocket academic paper

Posted: Thu Sep 28, 2017 11:53 pm
by anachronist
Thanks. I obtained the fulltext paper. It thoroughly accounts for nearly everything although it has one or two glaring omissions.

The usage of Euler's equation rather than Bernoulli's equation for modeling thrust from water is interesting, but they're wrong in their assessment of the Bernoulli equation under-estimating the outlet velocity; it works fine if you iterate it numerically rather than assume a steady state. I'm happy to see that they accounted for the fact that the compressed air inside the rocket is humid instead of dry, and they did it the same way I did, by adjusting 'gamma' (which they call 'beta') to a value around 1.35 or less. They mention the density of air only once in the context of drag, but don't seem to recognize that the effects of ambient temperature, pressure, and humidity have a significant effect on air density, and consequently drag, which affects the final altitude.

The paper concludes that an actual water rocket outperforms the prediction, and I can see why right away: They neglect to account for the thrust from the air pressure remaining in the bottle after all the water is gone. This final burst of air can add 30% to the velocity of the rocket. That makes a huge difference.