More Progress on Moment of Inertia

I epoxied the ring fins on Moment of Inertia.  For a motor retainer, I mounted the ring fins back off the end of the body tube far enough to have a fiberglass ring behind the motor.  The ring is attached to the ring fins with screws.  It’s probably easier to understand with a picture.

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I also got a Semroc elliptical balsa nose cone.

All that’s left is the recovery system.  I talked to a friend who is an electrical engineer and he said circuit boards should be good to a lot more than 100 Gs acceleration even with components like big capacitors soldered on.  Maybe there’s a particular component on that timer that limits the G rating.  I think I’m going to pick an off-the-shelf altimeter and hope for the best.

Dammit!

Further developments about the Moment of Inertia rocket:

There have been problems with ejection charges on Cesaroni Vmax motors not firing.  Apparently, the rapid change in chamber pressure at the end of the main burn snuffs them out.  NAR and TRA have enacted a safety restriction requiring electronic recovery deployment for rockets with Vmax motors.

No problem, I thought, I’ll just add an altimeter or timer to my design.  I was looking at the PerfectFlite miniTimer4 and I saw this:

  • acceleration limit: (best accuracy) 15G
  • acceleration limit: (accelerometer) 23G
  • acceleration limit: (timer function) 100G

Dammit!  Moment of Inertia is going to experience well over 100Gs.  Other boards I’ve looked at don’t list an acceleration limit, but I think I should be suspicious about any COTS electronics being reliable at those acceleration levels.

So what are my options?  I could make my own fully potted electronics and test them (somehow) at high G forces.  That seems like lots of work.  I could wait until Cesaroni fixes the ejection charge issue.  Cesaroni has a lot on their plate right now.  That fix might not be coming any time soon.

Dammit!

Cesaroni Vmax Motors are Probably Underexpanded

For the Moment of Inertia rocket I’m going to be using a Cesaroni Vmax motor.  In particular, the 29mm 3-grain H410.  410 Newtons is a lot for this size motor: 42 kgf, or 92 lbf.  It makes you wonder, how do they get that much thrust out of such a small motor?  It has to have either a high chamber pressure, a large throat, or both.

With a high chamber pressure you need a big expansion ratio to be properly expanded.  With lower chamber pressure and a large throat the expansion ratio would be lower, but multiplied by the large throat size the nozzle exit area still comes out large.  The thing is, the nozzle exit diameter is limited by the form factor of the rear closure, which I’m guessing was designed before they started making Vmax motors.

I’m betting that the nozzle design is size constrained such that Vmax motors are underexpanded.  To know for sure, I need to know the chamber pressure, throat area, and exit area.  I ordered one of the motors so I can measure the throat and exit areas.  For the chamber pressure I’m going to have to estimate.

I fiddled around in RPA until I got an engine model that matched pretty well the numbers I do know.  The thrust curve for the motor isn’t flat so the chamber pressure changes over the run, but I think using average thrust to get an average chamber pressure is a good strategy here.

Chamber pressure came out to 870 psia, and sure enough, the nozzle is properly expanded for one and a third atmospheres.

What can I do with this information?  Well, my plan is to make a graphite nozzle extension built into my motor retainer and get extra thrust.  This modification will make the motor be experimental so I’ll have to wait until I get level 2 certification to fly it.

The place where I launch is at 5000 ft elevation, about 0.83 atmospheres ambient pressure.  Proper expansion would be a nozzle area ratio of 8.8 instead of 6.25.  That would mean extending the exit diameter from 0.75″ to 0.89″.  It should get 1.6% more thrust, or 417 instead of 410 Newtons.

UPDATE:

I’ve been thinking about this a little more.  The amount of additional expansion in the nozzle extension is pretty small.  Basically, the existing nozzle expands from 59 atmospheres to 1.33, and the nozzle extension only goes from 1.33 to 0.83.  So the benefit of the nozzle extension is correspondingly small.  This raises a few questions.

How far off does my estimate of chamber pressure have to be to make the existing nozzle properly expanded in the first place?  In my RPA model I had to drop the chamber pressure to 650 psi to make it properly expanded for sea level.  I can’t see any way that the motor would make that much thrust at 650 psi.  I’ve measured the throat diameter at 0.3″ so the thrust coefficient would have to be 2, and the RPA model says it should only be 1.46.  I could be wrong about the chamber pressure and it’s not as underexpanded as I think, but I bet it’s not that low.

Is it worth doing the nozzle extension?  Well, maybe, maybe not.  If you are looking from an objective performance standpoint it depends on how much you care about pushing for the last little bit.  You also have to balance the thrust increase against any mass increase to add the nozzle extension.  I’m planning on making the extension an integral part of the motor retaining ring that I need anyway so it shouldn’t add much weight, but it might add a little if it has to be bigger than it would otherwise need to be.  However, I’m really doing this because it’s something cool to do, and the nozzle extension is definitely a cool part of the project that I want to do.

How am I going to know if it’s working?  I would have to do static tests with and without the nozzle extension.  The difference is small enough that I’d have to test a number of motors to get a statistically significant result.  In certification test data that I’ve seen they generally test at least three and come up with a standard deviation around 1% or under.  I suppose if I come up with two groups at least one standard deviation apart I can conclude that it’s helping, but I’d probably need three standard deviations to be able to say how much it’s helping.  With each reload costing $20 it’s something that I might do some day, but It’s not on my to-do list.

I also realized that I don’t need to make the nozzle extension out of graphite.  The exhaust has cooled somewhat by the time it gets to the end of the nozzle, and the duration that it will be exposed to the hot exhaust is so short that I’m sure anodized aluminum will do fine.

Avionics Sled for Stretched Mustang

I got in touch with my friend who is working on his experimental hybrid engine.  He is getting close to being ready to use my stretched mustang to fly it so I’m switching my focus to that rocket for a while.

The propulsion section is done.  I just need to finish the recovery section.  This week I made a lot of progress on the avionics sled that slides into the recovery section.  It’s dual deployment, and for anyone not familiar with dual deployment the avionics sled is in the middle with one ejection charge on each end for drogue and main deployment.

The avionics sled has a Missile Works RRC3 altimeter that will do the deployments.  It’s a nice piece of equipment, but it was longer than the pre-drilled mounting holes on the off-the-shelf E-bay that I got.  I had to do some customization, but that was okay because I needed to do that anyway for the second thing I’m putting on the avionics sled.

That second thing is a GPS tracker.  The one I’m using is from a system meant to track hunting dogs.  I know they sell systems meant for rockets now, but this is some equipment I’ve had lying around for a while.  I’ll test it on low altitude flights where I won’t lose sight of the rocket before relying on it.  Even if it can’t track the flight it should re-acquire and report in after it has landed.  The primary purpose is not to lose the rocket.  The altimeter can give me the apogee altitude.  The unit on the right goes into the rocket, and on the left is the handheld used to track it.

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I’m not completely done with the sled.  Here is the layout with everything just taped in with masking tape.  I should be able to finish it soon.  Maybe I can fly it at Northern Colorado Rocketry Oktoberfest.

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Moment of Inertia

I’m starting on an extra little side project. I’m going to build a Mach-breaker rocket using the Cesaroni 29mm H410 Vmax motor. Here’s a picture of the basic layout.

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I imagine the fist question I’m going to get is, “Why did you choose tube fins? Tube fins are high drag. Don’t you need low drag for a Mach-breaker?”

Well…it depends.

The Vmax motor is a real beast. Approximately 100 lbs of thrust for four tenths of a second in a 29mm three grain reload. I ran a simulation. At Mach one, the rocket experiences 90 Newtons of drag. If drag were the only force on the rocket, it would be decelerating at 30 G’s. However, at that point in the simulation the motor is putting out 490 Newtons of thrust. The net result is that the rocket is accelerating at 135 G’s.

If I were to put in a heroic effort and reduce drag by 50%, the acceleration would increase to 150 G’s. I could get that same increase with only a 10% reduction in rocket mass. The moral is if you only care about max velocity and your drag is a small fraction of your thrust, then you get more bang for the buck minimizing mass than drag. The absolute magnitude of the drag doesn’t matter, only the ratio of drag to thrust.

So the real challenge with this rocket is structural. Withstand over a hundred G’s with minimum mass. Bundles of tubes have high strength-to-weight and stiffness-to-weight so tube fins are a good choice for minimizing mass.

The high drag of the tube fins also has a secondary advantage. I’m only going for maximum speed, not altitude, and I don’t want to lose this small rocket so I’d like to keep the apogee as low as possible. Once the motor burns out, the high drag of the tube fins helps accomplish that.

I’m going to call the rocket Moment of Inertia because all of the acceleration happens in a moment and is dominated by inertia. Drag and gravity have very little to say about it.

Rocket Weight

All of the major components are in for the first configuration of the 6″ rocket.  So I weighed them all together.  They came in at 40.8 lbs.  There’s little odds and ends that will still be needed so it will probably wind up closer to 45 lbs when it’s all ready.  And then the motor will be about 5 lbs.

That’s good because the Pro54 6GXL IMAX motor has an initial thrust of about 300 lbs so it will have a 6:1 liftoff T/W, which is good enough for a passively stable rocket.