Havoc821 wrote:
The case that I would be using would be 29mm x 12". I was trying to figure out what grain length, how many, core diamter, and nozzle diameter when I remember that Loki said to use for their casings. So i jumped over there and they have a 11.8" case with this information:
Motor diamter: 29mm
Case length: 11.8"
Case wall: 0.058"
Approx total impulse: 360
Liner length: 10"
Max propellant length: 9.75"
EX nozzle throat: 0.344"
Typical Bates Grain Geometry: Six 1-5/8" long grains, four with 3/8" cores and two with 7/16" cores
Jimmy kicks in:
I have a 3-grain Loki 29mm casing which I use for testing propellants. The graphite nozzle is 1.295 inches long, the head-end plug is 0.398 inch deep. Add to these the depth of the nozzle washer thickness, and the depth of the snap-ring cuts from either end of the case, and it all totals 2.047 inches. Subtract 2.047 inches from the 11.8 inch case length, and you have 9.753 inches of empty casing available for your propellant column.
The inside diameter of my 29mm casing is 1.007 inches. I will estimate that your case liner and grain inhibitor will take 0.1 inch on either side, so the diameter of the propellant grains is 0.8 inch.
So what's with all these numbers? Well, this is leading to the methods whereby one can figure out how to make a motor that will not blow up and maybe even work.
One must determine the maximum pressure that will be exerted upon the motor casing during the burn. The primary determinant of this pressure for any given propellant is the Kn ratio, which is the ratio of burning propellant surface to the area of the nozzle throat.
It is a fairly simple problem of solid geometry to figure out what the Kn ratio would be. It is made a bit more complex by the fact that the ratio changes as the burn progresses, and made much more complex when erosive burning occurs.
Running a sim with the case you described burning six 1.625 grains, 0.8 inch OD with 3/8 inch cores, one gets a maximum Kn ratio (near mid-burn) of 200. With KNO3/sucrose, this would generate a pressure of about 625 psi. With KN/Dextrose about 350 psi, and with KN/sorbitol about 375 psi.
(The pressure figures are from tables provided on Richard Nakka's website:
https://members.aol.com/kappadx/design1.html)
If using dextrose or sorbitol, you might consider a smaller nozzle throat, as propellant burns more efficiently at higher pressure, yielding higher ISP. With KN/dextrose, a 3/16 inch throat (.3125 inch) would generate a max pressure of about 600 psi.
A well-made and properly insulated aluminum casing should have no problem with 600psi. Even Sch40 PVC handles this pressure OK, with a fair safety margin. But changing the nozzle throat diameter will have a dramatic effect on Kn ratio, so it is important to run a sim or two on any prospective motor before even building it, much less testing it. (I have a little VB program for figuring Kn ratios, if you are interested - you still need to know the math, but once you know what it's doing, the program makes running simulations quick and easy.)
A problem with long, skinny cases is that the burning propellant gasses may reach supersonic speed within the casing. This creates shock waves that can rip propellant from the grain, leading to much faster burning, thus higher-than-anticipated pressures. (Remember those pretty mach diamonds on Matt's motor? You want them OUTSIDE the casing, not in it!)
The rationale for increasing the core diameter in the grains near the nozzle is that this allows the moving gas column to expand a bit so it doesn't hit Mach 1 prematurely. Ideally, the gas column should reach supersonic speed right at the nozzle throat.
I can't speak for dextrose or sorbitol as I have never used them to any extent. But if this motor were fired with recrystallized KN/sucrose, the propellant weight would be 107 grams, the burn time about 0.64 second, the average thrust about 42 lbf, and the total impulse about 120 Ns.
I suggest starting with a shorter casing, perhaps 3 or 4 grain, and not have to worry about erosive burning, at least until you have other matters worked-out.
Finally getting around to answering your question: Recrystallized propellant is made by dissolving KNO3 and sugar in boiling water with a texturizer (either Karo Syrup or a mixture of dextrose and fructose.) This solution is then poured into flat pans and baked in an oven until dried, scraped up, and kneaded into a pliable "dough."
Three advantages:
1. You don't have to stand over it and stir while cooking. I can sit a safe distance away until the magic moment arrives, turn off the oven, put on all my protective gear, and finish the processing well clear of potential ignition sources.
2. It does not require grinding of the ingredients beforehand - dissolving creates a very fine particle size, thank you! The moleular-fine particles provides for very smooth, efficient, and predictable burn.
3. And finally, it produces a "friendly" propellant that can be worked like modeling clay into any shape you might wish. Yes, you can hold a ball of propellant in your hand, and unless you do something truly idiotic you are not likely to be burned.
Some caveats:
1. It should not be done in the kitchen! Used ovens are often give-aways. Get one installed in your workshop, and cook a few pizzas in it so you know it works right. Invite me over!
2. There are some danger points in making this propellant - appropriate safety precautions are required at those points. I will not recite my safety instructions here, as they are many pages long, but they should be read and followed.
One more bit and I will quit for the night: You have found the fatal flaw. My stuff is KN/sucrose and thus not allowed at TRA EX launches.
Good news is that these techniques work OK with dextrose.
Medium-bad news is that my technique is unnecessary, as sorbitol and dextrose melt at a much lower temperature, rendering my beloved techniques unnecessary. Unless you hate grinding KNO3!
Postscript: I had vowed not to talk experimental on this forum, but don't seem to be able to help myself. I seek the guidance of the list moderators as to whether this level of detail is acceptable on this forum.
Jimmy Yawn
[email protected]
www.jamesyawn.com
