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Lately I've been exploring the idea of cold gas thrusters, or in this case cold gas rocket engines, to be used in model rockets.

I've read that nitrogen gas can get 73 seconds and helium can get 2.5 times nitrogen, which would be 182.5 seconds. That would be pretty darn good as far as model rockets go. (However, those were for vacuum performances and idk what they might be at sea level.)

I've been using equation 1.22 and finally got it making sense after some difficulty with R (the ideal gas constant).

There's something else I want to know, but haven't found. How noisy would a helium rocket engine be? I'm thinking for an engine on the order of 10 to 50 N. I'm really hoping it would be less noise than a solid rocket motor of equivalent thrust, since it would have no combustion.

Tank weight is probably going to be the biggest drawback. I've handled those large cylinders of helium at party stores, and they are heavy. However, let's just consider the state of the art: a very small spherical tank of highly compressed helium. I don't know how to calculate tank weight based on max pressure and volume, but I'm hoping it won't be too heavy.

I know nitrogen is cheaper, but honestly, we fill up party balloons with helium all the time so how much more expensive could it be? I'm guessing the "fuel" costs would be not much different from a solid rocket. Besides, I prefer to take the ideal case first, and then see how close we can get. (Helium is more ideal because of its lower molecular mass compared to N2.) I was even considering preheating the helium to like 2000 K or something in the tank, to get better thrust, but one thing at a time.

EDIT: Okay, in bullet points, here are the equations I'm looking for:

  • an equation to tell me how noisy a cold gas engine would be for a given thrust (at sea level).

  • an equation to tell me how heavy a spherical gas tank would be, given internal pressure of helium (500 atmospheres).

  • an equation to tell me how thrust would vary with time.

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  • $\begingroup$ Each of those bullet points is a question in its own right. Though you ask for the purpose of the same model rocket, each one is a separate matter that applies to different rocket systems and different areas of physics. $\endgroup$
    – kim holder
    Apr 29, 2016 at 1:23
  • $\begingroup$ @kimholder I'm happy to open 3 separate questions for them if need be, but I think this question about overall viability of a cold gas engine for model rocketry is a good question. Cold gas engines are pretty simple things so you have to wonder why not in model rocketry? I'm guessing there's a performance limit somewhere. $\endgroup$
    – DrZ214
    Apr 29, 2016 at 11:34
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    $\begingroup$ Plans for a cold gas thruster rocket: instructables.com/id/2-Liter-Rocket $\endgroup$
    – Jacob Krall
    May 28, 2016 at 14:54
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    $\begingroup$ The dry mass fraction is just as important as Isp. Pressure vessels are heavy and don't hold much gas. You could use very small cold gas systems on a small rocket for attitude control, but cold gas would certainly not be competitive for primary propulsion, if you could get it off the ground at all. $\endgroup$
    – Mark Adler
    Jul 15, 2016 at 19:46
  • $\begingroup$ They certainly are practical, as Estes sold commercial Freon-powered model rockets back before Freon was banned. Maybe there was a phase change involved there, though. $\endgroup$
    – antlersoft
    Mar 6, 2018 at 18:17

3 Answers 3

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I think you're doing something wrong in the calculation; with those figures I get Ve = 1694.6 m/s, or 172.7 seconds.

I used this python code:

import math

k = 1.66
M = 4.0
Tc = 300.0
Pe = 1.0
Pc = 500.0 

R = 8314.4621

T1 = 2.0*k/(k-1.0)
T2 = (R*Tc)/M
x = (k-1.0)/k
T3 = 1.0-math.pow((Pe/Pc),x)

Ve = math.sqrt( T1*T2*T3 )

print "Ve %.1f m/s or %.1f s"%(Ve,Ve/9.81)
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    $\begingroup$ Thank you. It was my R. I was using 8.314 instead of 8,314. (Do you know why, though? 8.314 is in J/(K mol) which seems to be the pure SI base units.) I will edit the OP now. If you can provide anything about cold gas engine viability at sea level, please let me know. $\endgroup$
    – DrZ214
    Apr 29, 2016 at 0:07
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    $\begingroup$ I think it's because the mole is tied to grams (CGS metric units) while the Newton is tied to kilograms (MKS)? Can't help you on the rest of the questions, though. I'd change my answer to a comment but the Python is conceivably useful to someone someday... $\endgroup$
    – Russell Borogove
    Apr 29, 2016 at 0:12
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In the early 1970s Estes sold model rocket kits which used pressurized gas instead of traditional solid propellant model rocket engines.

enter image description here

They were too expensive for me; I stuck with the standard models. So I am not sure what gas they used, but I have read it was some kind of Freon.

enter image description here

Pictures from here

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  • $\begingroup$ +1 for vintage images $\endgroup$
    – uhoh
    Mar 11, 2019 at 11:10
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I tried this wall thickness calculator. For a 500 bar pressure vessel with an internal radius of 2" and perfect joints it gives a wall thickness of 4".
The next step would be to calculate thrust and duration from that volume, then a thrust/weight ratio. My prediction is that you won't get a T/W of over 1.

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