Barrel Harmonics

R

Richardson

Inactive
I have the ability to do analysis at work(Finite Element Analysis - a computer simulation of mechanical systems). I was thinking of applying this to understanding barrel harmonics, so that I can effectively accurize my firearms. I have 2 questions. First, what frequency range should I be looking at? I figured I would use the equation: frequency=velocity/barrel_length to get in the ballpark. Second, what boundary conditions should I apply (i.e. should I "clamp" the barrell anywhere)? I look forward to your help. // Richardson
 
Hooweee! I gotta lotta rust to knock off to mess with this one! Anyhow, as I recall, the pressure wave propagation of the burning gunpowder is around 20,000 ft/sec--if that's germane. Actual velocity, of course, will be in the 3,000 ft/sec range.

I'd make the assumption that the barrel is clamped at the breech end. Dredging back in readings from years ago, the point of impact isn't dramatically different between hand-held and vise-clamped.

I believe it's factual that a minimal damping of a free-floated barrel gives the best accuracy from any given package. I'd recommend finding a very experienced bench-rest competitor for more ideas.

Dunno if this'll help,

Art
 
Richardson,

Art's right about the binding point. That's also the starting point of the accelerating mass.

The barrel volume is a resonant cavity. The volume of that cavity increases as the center of the projectile (ejectile) mass moves down the barrel. You begin to see the complexity. It is an infinite series of shock-impact nodes. We didn't have access to Finite Element Analysis tools for our project in '70-71.

The freqency is extremely broad band, as you can guess by the expanding resonant cavity dimensions and the model of a series of impact-shock nodes.

In an earlier life as an instrumentation techician for the US Gov't, I measured and recorded the behavior of internal ballistics energy on the outside of the barrel of the GAU-7 (caseless ammo, 25 mm gatling gun). It was abandoned due to the mechanical synchronization problem between feeder, loader and rotating chambers at high speeds. I believe the GAU-8 30 mm succeeded it and went on the A-10. The caseless ammo didn't like being skinned up during transport to the chamber. We started a fire once right in the middle of a 200 round burst.

The first thing we discovered was that we were unintentionally filtering the vibration frequencies with our instrumentation package. Remember the rule: you affect the behavior of a system by observing it? Well, we at least were affecting the data collected. Regroup. Reinstrument. Try again. Wow! Where did all that "stuff" come from?

The random vibrations damped out quickly, but the sine signals just went on and on ... 300 - 400 msec? 'Don't really remember. As the harmonics died out, the full barrel internal cavity's resonant frequency became most predominant. Each gun will be different. The broad banded vibration pulse packages would travel down the barrel chasing the moving mass (projectile) then run back up and and then down the barrel again until the energy was expended. I think the separation of pulses was due to the density of the barrel mass and the lateral dimensions of it, i.e., barrel thickness and center of the circumference mass center in the material cross-section. Also, the changing lateral dimensions as you move from breech to muzzle were a factor on the pulse train patterns, as I recall.

'Been a long time. All this was done on single shot barrels supplied for ammo testing. Yeah, the US Gov't was testing the guns, feeder/loaders AND the ammo at the same time. How smart is that?

Quite a show! I became quite impressed with the ability of barrel steel to temporarily lose it's mind, so to speak, then return to shape. The primary vibration (tail wagging) mode, as well as barrel mass (momentum), was a factor in the damping of the secondaries.

Knowing where to be in the primary vibration node at muzzle exit is the key to the B.O.S.S system of Browning.

Let me know how it goes. Try Varmint Al and click on the "Engineering" link on his site for some interesting reading. He may save you some time. He's a retired ME, I think, from Livermore Labs. Cool guy. I need to visit his site more often. Tell him I said, Hi!

[This message has been edited by sensop (edited March 30, 2000).]
 
Hey sensop,

Was that the Philco-Ford project? Wasn't this gun a possible replacement for the M61 to be put on the then-new F-15? Also, wasn't the caseless ammo less durable under the loving strokes of the average airman knocking the stuff about, due to the lack of a nice, strong brass case? Also, aren't the storage conditions of caseless a little more demanding than normal ammo? I seem to recall during the testing of the G-11 that they never really solved the "cook-off" problem, in spite of the sales literature. I guess that wouldn't be as much problem with a Gatling-type weapon, but still... How'd you put out that 200 round ammo fire anyhow? Barrel harmonics is a fascinating subject, but the math gets a little scary for me a bit too fast. I wonder what the barrel harmonics are of a barrel made of a thin steel sleeve wrapped by carbon fiber. I can't imagine they's be the same. Hmmm.
 
Gopher,

You're right. Philco-Ford was competing against GE. In the ammo dept it was Hercules against Brunswick (I think). GE and Philco, I believe were also competing feeders.

Each contractor supplied a gatling and a single shot breech loader (for ammo testing). GE's item had six barrels as I recall and Philco was five-barreled. I don't believe the GAU-7 was targeted for the F-15, but I could be wrong. I thought it was an A-10 project. The A-10 was a new project then too.

PUT THE FIRE OUT? ARE YOU CRAZY? We ran like fugitives! Pretty much ruined the firing bay it was in, but as I recall, the test item (gun) was unharmed. 'Don't remember which one it was (GE vs Philco).

Yes, handling and storage requirements were quite different, as in stringent. The rounds weren't permitted to touch each other in transit, for example. Special gloves, boots and aprons were required for handling. Static was a special concern.

Most of the wear and tear to the rounds came from the abuse of the firing environment. they were pretty much treated like brass rounds. Not enough thinking "out of the box" on that one. Of course, materials available today would make modification of that regimen easier: links, ammo storage compartment inflight, mechanical buffering between rotating chambers, barrels and feeder, etc.

As far as cook off goes ... I don't know about the G-11. What was it? The gatling problems are more severe than you may think. On the M-61, for example, the chambers are cleared after a burst by reversing the rotation of the gun far enough to back the rounds out that were left in barrel/chamber alignment. If left in, the chances of a cook-off are genuine. The F-15, to this day has a gun clearing solenoid that engages a reversing cycle for just that reason. Of course, the next burst entails a few milliseconds lag time while the rounds are pulled back into barrel alignment. The caseless rounds were sensitive to the latent heat cycle of the surrounding metal after a burst, but as I recall not much more than brass rounds. Remember what happens to your vehicle engine after you shut it off, though. It gets hotter before it cools off. These rounds were real static sensitive and once they got hot their static sensitivity went up even more. The worst damage done was the mechanical "slop" in the feeder/chamber/barrel interface I mentioned in the first post. The wear was progressive and aggravated by high rotation speeds. The propellant debris buildup was pretty dangerous.

All in all a fascinating project. I spent many hours scoring targets and measuring the length of bullet holes for tumbled rounds. Here is one for you: one of the rounds they used during GUN test objectives (as opposed to AMMO test objectives) at short range had an aluminum/teflon bullet. Never did figure out what the purpose of that was.

I do remember charting +5,000 fps within twenty feet of the muzzle with some special rounds, though! One day an AF Captain, a member of the test team, left the boresight tool in the Philco single shot and we sent it down range on the very next shot. Part of it anyway. The eyepiece is probably still embedded in the concrete ceiling of the firing bay. Killed the velocity screens too. I mean killed 'em dead! The debris field was awesome.

[This message has been edited by sensop (edited April 01, 2000).]
 
sensop,

LOL! I wouldn't have stuck around to spray a foam extinguisher on an ammo fire either! I see what you mean about the wear and tear on the ammo moving through the feed mechanism, considering it's moving so fast. So the feed mechanism on the M61 works in reverse just by running the motor backwards. Interesting. I guess the few msecs lag time is worth it not to have a cook-off in mid flight! It doesn't really sound practical to have to wear gloves, watch for static, etc. in a combat environment, when things get a little, er, hectic.

The G-11 was an H&K project in the early '80s to develop a rifle that fired caseless ammo. Others here are probably more knowledgeable about it than me. IIRC, it fired a 4.7mm caseless round in which the bullet was embedded in the propellant, and all that remained was a stub which was blown out the barrel by residual gas pressure. I think it was also a candidate for the Army's ACR tests in the '90s, but the cook-off problem was never really solved, so I hear. When the USSR went kablooie, there wasn't much interest in the project anymore.

That does sound like a fascinating project. I can't imagine what use a teflon/aluminum bullet would be, but I'm not in charge of all the whiz-kid neato stuff the AF does. 5000+fps does sound pretty impressive, though. I'll bet the bore obstruction did make a pretty impressive debris field. I guess when something like that happens, it's time to call it a day. Is that the same Brunswick that makes bowling accessories? Talk about diversifying! That reminds me of a story I heard about pool balls. The first ones were apparently made of compressed nitrocellulose, and when they took a particularly hard shot, the results were...interesting.
 
Did the G-11 have a magazine with the rounds stacked horizontally, with the bullet pointed upwards, then get tipped over for chambering? I remember an H&K that did that with caseless ammo.

The GAU-7A also embedded the projectile on a cylinder of preopellant. I think that's pretty standard for caseless ammo designs. The trick is how to get the bullet out of the propellant cylinder into the barrel ... ever thought about it?

Yes, same Brunswick.
 
Yep. G-11 fed the ammo horizontally along the top of the barrel. Gave the gun a boxy shape. Looks like a skinny suitcase.

I did think about it, but my meager brain was overheating. I thought that if the propellant was gone before the bullet entered the throat, nothing would support the bullet so it could rattle about the chamber, and gas would blow-by, etc. I guess you could modulate the burning rate of the propellant so it would keep the bullet supported until gas pressure built up enough to drive the bullet into the throat, but if the bullet's not in the rifling, then the gas takes the path of least resistance and goes right on past the bullet. Does the primer charge kick the bullet out of the propellant cylinder as the charge is igniting? Or, could there be some kinda really elongated forcing cone that allowed the bullet to slowly (in a relative sense) engage the rifling, but the massive gas leakage wouldn't do anything for accuracy or velocity, I s'pose. You got me.

[This message has been edited by Gopher a 45 (edited April 02, 2000).]
 
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