Originally posted by n3tjm
Um, Black Powder is a Monopropellant. That means it contains its own oxidizer. In Black Powder's Case, it is Potassium Nitrate. I am not sure what the issue with the aurora project was...
I don't think monopropellant applies. I think that's when a single chemical compound is used and interacts with a catalyst that causes a breakdown reaction from that single chemical to exhuast products. Like 2 H2O2 --> 2 H2O + O2. BP still has an oxidizer and two fuel components even though it's mixed to homogeneity.
Here's the text from their paper on testing BP for Aurora.
I decided plain text was fine because of the three referenced graphs on the paper, there is graph #1, two graph #2, and no graph #3. Graph #2 is attached.
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When Aurora was envisioned, Dad, Pat and I knew we would need to come up with some alternative to black powder deployment. The record for large high altitude rockets is not good. Ballistic recovery seems to be a common occurrence. Given the skill of the rocketeers involved, something other than carelessness is at work. That gremlin is air density. In the standard atmosphere model, at 30,000 ft the air is 27.6% of the density at sea level. Not only is there just 28% of oxygen available, but more insidious still, there is only 28% of air mass for the expanding black powder gases to expand against. Exploding black powder does NOT create enough gas to fill the empty spaces of a larger rocket all on its own. Pressurized liquid CO2 can provide the needed gas, and it can be packed in a nice small package.
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Soon after we began spinning our brains on the problem, we came upon the CD3 system developed by Tom Rouse. This was the perfect type of system to do the job. However, the CO2 cylinders that were compatible with his method were way too small for Aurora (Tom has since added bigger CO2 cylinders.) Being an avid paintball player, I knew of just the thing; Paintball CO2 canisters. After a little hunting Dad found pre-filled 4oz one-time-use CO2 paintball cylinders at Wal-Mart. After machining our own copies of Tom Rouses CD3 that would fit the bigger threads we had the perfect system. Now it was time for testing, testing, and more testing. Ill spare you the blow-by-blow account of our experiment and skip right to the findings. This is what you need to make your own rocket work anyway, eh?
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CO2 works slightly different from black powder. There is one more variable at work and that variable is time. You can ignore this factor and everything may work out great. Or it may not. To understand, lets start by looking at how black powder does its job.
Imagine a sealed rocket using black powder. Graph 1 shows the internal/external pressure difference vs. time. Because black powder acts so quickly, its as if the internal pressure just instantly jumps from zero to Pmax (The graph trails off after Pmax because of the vent hole.) As long as the pressure required to remove the nosecone (Pnose) is less than Pmax, everything is hunky-dory. Pmax is NOT effected by the size of the vent hole (unless its way way big) However, Pmax is not the same at every ejection altitude (see Graph 2.) It may not take much altitude to reduce your Pmax below Pnose. You can increase the size of your charges but how are you going to get to 30,000 ft to test whether you have enough?_ Even then, as Pat has told us, the BP won't burn completely after certain volume levels. Now lets take a look at a CO2 system.
Using the same sealed rocket, Graph 3 shows the internal/external pressure difference vs. time for a typical CO2 system. Our pressure still changes from zero to Pmax at the ejection event but now it takes a measurable time for this to occur. The delay comes as the liquid CO2 evaporates into gas and vents out of the cylinder. The typical vent time for Auroras 4oz cylinders is .1 to .5 seconds. The crucial fact for high altitude rockets here is that Pmax is NOT dependent on altitude (it actually does vary slightly but it is a negligible amount.) Because your vent hole will be trying to reduce Pmax during the vent time, you must get the balance right so that Pmax is greater than Pnose. Fortunately, you dont need to work out any complicated equations to get your CO2 system to work. All you need do is test your flight configuration. With CO2, IF THE NOSE WILL COME OFF IN A GROUND TEST, IT WILL COME OFF IN THE AIR. In practice, the main problem is that your nose will come off TOO easily before internal pressure has built up. You will likely want to restrain your nose in some way. This will allow the pressure to build enough so that the nose pops off with force. (It does so within .25 seconds)
If you ground test your CO2 ejection you will not need to work any equations. However, in the process of tweaking your rocket deployment system you may find some of the following equations and relations helpful.
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First remember the general relation F=PA (force = pressure * area)
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You may also want to note that
h=V0t ½gt2
Where h= height nose cone will be ejected above the rocket.
V0 = velocity nosecone leaves the body tube.
t= time nosecone takes to accelerate off the coupler shoulder.
g = acceleration of gravity (9.8m/s2)
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This last relation is not very useful because V0 and t are not known. However if you throw in the ballistic relations V=at and x=1/2at2 you can come up with something much more useful
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h = 2s gsm/PAn
Where h= height nose cone will be ejected above the rocket.
s = length of coupler shoulder
g = acceleration of gravity (9.8m/s2)
m = mass of nosecone
P = internal pressure differential
An = Cross sectional area of nosecone base
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This last equation is exactly what we used with Aurora. We started with the assumption that we would need the nosecone to pop off at least 5 feet. Using this last equation we then found the required internal pressure. From F=PA we could then say exactly how much force we needed to restrain the nosecone with.
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One last word about these equations; Use only metric values (any guesses what the English unit of mass is? One clue. Its not pounds) and convert everything to consistent units. I recommend meters, seconds, kilograms, and their derived units like m/s and newtons (kgm/s2)
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So there you have it. The maximum ejection pressure from black powder varies with altitude but provides a nice instant shock load that is very forgiving of variations in your restraining nose force. CO2 maximum ejection pressure does NOT vary with altitude but has a measurable venting time that causes a concern not found with BP. However, CO2 has some nice benefits like non-corroding waste gasses and reproducible flight conditions at sea level. If it will work on the ground using CO2, it will work in the air.