## Tuesday, January 20, 2015

### Rocket calculations, critical orifice, ideal design

EPA method 5 section 16.2.3.3 describes theoretical max for air to flow through an orifice at a given pressure difference and temperature at the inlet.

fps corrected to STANDARD conditions = 17.6*(in Hg)/SQRT(Rankins)
Mass/second of exit fluid is proportional to this, times area of orifice.
Ambient is about 30 in Hg, Rankin = 460+F
Orifices (holes) have a theoretical correction factor of C=0.61, a typical value of 0.7 due to none-sharp edges, and short tubes have 0.8.
For a 1/16" nozzle and 10 atm (what 6 layers of 0.016 mm aluminum foil should handle, 20 atm being max) and ambient temperate, this gives 3000 ml/sec.   At 1800 F candle temperature, the fps is half as much, 1500 ml/sec.  The 1000x volume expansion of gun powder is 250 volume expansion and 4x this due to heat.  So air volume not allowed to expand increases by 4*T, or from 530 R to 2000 R (1500 F). Aluminum melts at 1200 F, so allowing powder to expand x2 should prevent it from melting. Cooler air also increases FPS, or aka mass escape.  So it appears 1.5 ml = 1.5 g bulk gun powder (22.5 grains) could exhaust in 1 second.  A nozzle cools the exhaust, reducing the volume, but not the mass.  The cooling receives a push from the reduction in energy, possibly not changing the orifice correction factor.

Design ideal

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March 2 2017 post to someone's video where they got 40 feet with matchstick rocket.
I got 130 feet with this design using a very small amount of gun powder from the blank of a nail-driver (equal in power to 3 matchstick heads but it might burn quicker) and a little longer rocket. I have a trick for raising the pressure inside the chamber. At the base you let there be only 2 layers of aluminum foil which is about what you're doing with that taper. You use a wood skewer and drill the smallest hole you can with a drill bit. Then you stick in a finishing nail through the two layers, into the hole. Using tensile strength of aluminum you can calculate the layers needed to get the max pressure in the chamber and you calculate the max pressure your chamber can allow also with it's tensile strength. Theoretically based on this and density of aluminum and if there were no air resistance, you could get up to 2000 feet. But what I found out is that aluminum weakens with heat and bursts so I doubt over 200 feet is possible without a major redesign. I tried a little to fix this by using a mechanical pencil's steel eraser cover as the "ignition chamber" but gave up after a few tries. A steel design theoretically could reach 40,000 feet distance, minus air resistance. It would have to be incredibly small to use only 1 matchstick making air resistant a big factor (500 feet probably the limit). If you use 10 match sticks, it's as much explosive powder as a small bullet and a similar distance can be reached. This is not really a rocket design because there is no nozzle exhaust pressure after lift off. This is a more efficient use of the fuel than a rocket can achieve, as long as air resistance is a bigger factor than the gain in efficiency. This is like putting gun powder in a gun barrel, then sticking it onto a shaft and making the gun barrel as light as possible. So the shaft is like a bullet that's held in place and the gun is allowed to recoil. I actually tried making it a two-stage pressure build-up using a long tail on the end of the aluminum with slack in it and another nail. So it does not break from the 1st nail until pressure is high and assuming the powder has not finished burning, it lets it expand to where it is almost off the stick, then 2nd nail makes it pause until more pressure builds up. But I'm not sure that can help.