“Ejection Pressure Measurements”: A response

Oh, I do love Interlibrary Loan. I wanted to look at “Ejection Pressure Measurements” by Janice and Harold Larson from the Jan/Feb 2007 Sport Rocketry, but no one in our local club seemed to have it and Worldcat showed no libraries holding Sport Rocketry closer than the Library of Congress, 289 miles away. So last night I put in a request for a copy. 24 hours later a scan, in PDF form, was in my email inbox.

It’s not perfect; I think they didn’t scan the whole article, and it’s in black and white (the graphs use color), and a few things got lost in the binding. Never mind, I can get most of what I want from what they sent.

So here’s my evaluation.

What the article, or at least the portion I have, is about is ejection pressure measurements in a Quest Courier egglofter using a variety of Estes black powder motors. They set up a test stand, put pressure sensors at the fore and aft ends of the Courier’s 239 cc of pressurized volume, loaded up the egg capsule with 60 g of modeling clay (“for obvious reasons”), and ignited motors in the motor mount. They sampled the pressure sensors every 0.15 ms for 25 ms after the ejection charge went off.

First, the business of the ejection charge sizes is a mess. I was wrong; the authors didn’t quote Ed Brown. Rather, they cited a posting to the NARTARC Yahoo! group which cannot be read by non group members; an editorial note then says it’s a post by “doctor_dynasoar” who quotes Ed Brown. So, to recap, that’s the editors elucidating a reference by the Larsons to a post by “doctor_dynasoar” quoting Ed Brown. No surprise, then, that something apparently got garbled in translation. What they say, and what the Larsons use, is that  (this is me paraphrasing the editors elucidat… oh, never mind) 13, 18, and 24 mm Estes black powder motors have 0.4, 0.6, and 1.0 (respectively) grains of ejection charge.

But in this YORF thread Terry Dean says Brown says (here we go again) he was misquoted and it’s 0.4, 0.6, and 1.0 grams, not grains. (A factor of about 15 larger.) And here it’s claimed (with no source cited) that D motors have 0.85 grams charge.

Okay so far? But then the Larsons took the 0.6 grain number seriously and plugged it into an ejection charge calculator along with 239 cm^3 for the volume, and found that it said it’d produce about 5 PSI gauge pressure. Then they took measurements with a B motor, and typically got about 5 PSI! So it really is grains, not grams, right?

Well, no, I don’t think so. The Larsons took that as confirmation; I don’t. If you look at their plots, in every case what you see is an increase in pressure (roughly linearly in time, over about 10 ms for B motors) up to some maximum, followed by a sharp dropoff (over about 1 ms) to zero pressure. That’s the nose cone popping off and relieving the pressure. You don’t ever see the pressure plateauing before ejection. So is the 5 PSI because that’s how much pressure the charge can produce? Or because that’s as far as it builds before the nose cone pops off? It looks like the latter to me.

If it really were the maximum pressure produced by the charge, you’d expect it to be about twice as large for the 24 mm motors. Instead, it’s hard to tell with the variation they see from motor to motor, but to me the 24 mm motors look as if they produce about the same peak pressures as the 18 mm motors. As if the nose cone were acting as a crude 5 PSI relief valve.

But wait, there’s more. The Larsons made ejection canisters out of miniature Christmas tree lights and put 1.6 grains (not grams) black powder in them, and tested those. They expected about 12 PSI pressure; they got about 5 PSI. “This indicates that our canisters are not particularly efficient combustors of BP”, they write, but more likely, again, the peak pressure is being determined by the nose cone release and not the charge size.

If they’d done measurements in a sealed pressure vessel, rather than a rocket with an ejectable nose cone, I think they’d have seen something very different.

Not everything is 5 PSI; some tests saw less, some saw much more. One A motor went to 16 PSI, about three times their expected maximum. The Larsons don’t venture an explanation, but if 0.6 grains is supposed to produce only 5 PSI then 16 PSI seemingly could be produced only if the motor had three times as much charge as it was supposed to. That doesn’t seem likely to me. I think it’s more reasonable to conclude there’s more than three times 0.6 grains in all the motors.

So I disagree with the Larsons’ interpretation of their data, and I believe the corrected values of the ejection charges — grams rather than grains — are closer to being correct. But this means the calculated (maximum) ejection pressure, at least in the conditions the Larsons measured, is irrelevant! What matters instead is the pressure as a function of time. And that seems complicated. It’s not obvious that 24 mm charges build pressure any faster than 18 mm ones, or that the 1.6 grain charges are any slower. What does look to be the case, and it’s hard to be sure due to all the fluctuations, is that higher pressures build faster than small pressures; the nose cone releases earlier when the pressure is higher.

What’s going on there? Why did they get 10 to 20 PSI in a few of their tests? One thought I had was that perhaps the nose cone was tighter in those tests than in others — due to soot buildup, maybe, or some such cause. But it’s popping off sooner in those tests, which doesn’t seem to make sense. It seems more consistent with the nose cone behaving reproducibly and something else causing the pressure to build faster, with the nose cone getting pushed out sooner but not so much sooner that the pressure doesn’t go to high values.

Could it be venting through the motor nozzle? If venting significantly decreases the rate of pressure increase, then perhaps sometimes something partially clogs the nozzle when the ejection charge goes off, and the pressure then builds faster. Might make sense?

Anyway, this just adds to the complication of figuring out shock cords. I’ve been assuming the pressure builds to its maximum on a short time scale compared to the nose cone ejection time, and that’s just wrong; it looks like it’s the other way around, in fact. That explains why the separation velocities I’ve been calculating have seemed much too high. But a better model will take some thinking. It’d be nice to have similar data for rockets of different length and diameter, and with lighter (non “egg” bearing) nose cones. I’m not going to do that experiment anytime soon, though, so feel free to run with it if you want.

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