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.