Hacking the CP-2

[George Schmermund]

Stan - I agree with you, this is a hobby. Let's move on.

[George Schmermund]

Here's a video of an impulse shock wave from an open ended shock tube. What I find interesting is that the tube is fired in a similar way that an airgun works. The pressure when fired is 750 psi. This is about the same pressure as the CO2 guns are working with. Note that there is an initial flat shock wave pulse that emerges from the muzzle. It's then followed by a series of diminishing vortex rings. There's more to be seen, but these are the early events that tell a lot about what happens between the breech and the Muzzle even when there's no pellet being fired. The main point being that the air sitting in the barrel doesn't whoosh or seep out of the muzzle when the valve discharge is initiated. The air at the muzzle end doesn't know it's being compressed right away. When it does come out it does it explosively as a series of shock waves.

These are the same events that were recorded with the microphone back when the muzzle measurements were made on the Vigilante with no pellet being shot. The mike was recording the initial pulse and the following vortex pressure pulses. If an axial slice was taken down through the shock tube pulse train in the video it would look similar to the o'scope display of the mike's pressure wave recording. These records can be seen in reply #138 in the Vigilante hacking thread. The use of different density gasses fired simultaneously w/o pellets in those experiments is a good demonstration of how these separate gas pressure plugs are formed and how they exit the barrel.

This information is probably an excellent way to evaluate the condition of the crown and how square it is to the end of the barrel. If your gun's muzzle treatment was as good as the shock tube's muzzle you should get the same images without a pellet being fired. We could then assume that any perturbation in the pulse train when shooting a pellet would be an anomaly introduce by the pellet itself. I've left plenty of room for second guessing here.

[dv8eod]

Something you might want to know. Shock tube or Nonel, as it is commonly referred to is HMX explosive powdered finer than flour. It is blown through a hollow tube so that a film is deposited on the inside, leaving it still hollow down the center. Each particle is its own little explosion in a 360 degree sphere, restrained on the side where it is touching the tube wall. The touching particles continue the propagation of the explosive wave. Any air contained in the tube is compressed and the heat generated is also applied to the propagation.
While not quite as fast as PETN, it does zip along at a pretty good clip. You can see the light generated through the tube and follow its progress to the shot. When it's removed from the firing device, you can hear a hissing sound as the pressure inside bleeds out. Really neat stuff.
I just wanted to contribute Something to the discussion instead of being just a lurker... 😀

[George Schmermund]

I've decided to backtrack to some of the work that was done on the vigilante's 10" barrel mods. This was prompted by some information that was presented in one of those scholarly University papers that I read sometime back concerning airgun internal ballistics. It's been festering in my mind for a while and resurfaced today after a few beers. I can't remember the names of the author(s) or other such details, but I was left with a lingering impression about the data presented. There was a comment made about the difficulty of modeling the air in the barrel in front of the pellet as the pellet moved toward the muzzle.

The paper concluded that it was reasonable to assume that the mass of air and it's inertia were not significant in terms of how it might effect the projectiles flight down the barrel. It was therefore ratified that the air would move as a continuous slug and be pushed forward by the pellet as a single column out through muzzle.

Rather than make any direct claims to the contrary I'll just show a couple of DSO screen shots from experiments that were done about a year ago. The first image shows the timing from hammer's impact on the valve stem to the pellet impacting the force transducer at the muzzle to be ~ 3.2 ms.

In the 2nd screen shot image the top trace shows the time between the barrel's compressed air's shock wave in front of the pellet and the impulse as the pellet leaves the muzzle to be ~ 230 µs. The amplitudes of both shock waves is almost the same. As I recall the The SPLs were in the 150 dB range. This double report of the shock waves shows them both at about equal in energy. My conclusion from experimental evidence is that more may be going on then is assumed by some investigators. Again, I'll leave this open for second guessing.

[George Schmermund]

I thought that it might be interesting to look at the difference between the resonance information that is provided from an impulse induced signal and that produced by a burst of energy from a sine wave set to the natural frequency of the horizontal mode of a barrel vibration.

The sine wave test starts as a tone burst with zero amplitude and rises to full amplitude within 1/2 cycle the moment the generator is triggered. It continues at full amplitude for the rest of the test. As can be seen the barrel requires ~ 100 ms to come up to full displacement. The pellet is long gone by this time.

The impulse test can be initiated by either the instrumented hammer or actually firing the gun and illustrates that the maximum displacement of the barrel is within the first ~ 4 or 5 ms after the impulse. The pellet can still be somewhere in the barrel within this time window.

The point of this exercise is to show the difference between the gathering of reified data and that of potentially misleading data the is still in it's abstract form. this all relates to airgun barrel harmonics.

Virtually all vibration measurements used to be done using methods of continuous shaking of the test sample or structure at various frequencies and amplitudes until the natural frequencies of the DUT could be determined. This was expensive and time consuming in it's day. Transient events were very difficult to quantify back then.

Now most of the testing can be done easily and quickly using modal analysis and fast computers.

The photo shows the setup for doing the sine wave measurement. The barrel is being driven by the noncontact VRT in the B&K complex modulus apparatus. The barrel's vibration is being detected by an Endevco 2250 accelerometer in both tests. The DSO images should be self explanatory.


 

[WhatUPSbox?]

George, good info, as always. Have you tried running a sine sweep to also identify the other modes?
It will be interesting to see the response to a shot compared to the pellet exit time. It is not clear to me when that response is initiated. Velocity response may also be of interest (good excuse to try out the math functions on that shiny new DSO).
Also, at some point it may be worth running a broken wire across the muzzle to quantify to offset between muzzle exit and your impact response. At 400 fps even an inch of effective offset is a fraction of a ms and may be of interest for the muzzle accel responses.

Thanks for the updates

[George Schmermund]

Here's a DSO image of the entire shot cycle showing the pressure curve on channel 1, the vertical accelerometer (XCL) at the muzzle on channel 2, and the impact sensor on channel 3. The time scale is 1 ms/division and each horizontal dot is 200 µs.

The measurement was triggered by ch 1 and the pressure rose to a peak of ~ 500 psi in ~ 300 µs. The pellet exited at ~ 2.9 ms after the clock started as shown by ch 3. This is all consistent with previous tests. A point of interest is the little ramp at the base of the ch 3 signal as it starts it's vertical assent. This small signal may be the time it takes for the pellet to flatten against the force transducer. The transducer is ~ 1/8" in front of the muzzle.

All of this same information has been presented before. The point of this test is to demonstrate that the ch 2 trace shows that the barrel has gone through a full negative displacement and is on the other side of it's excursion back up about 3/4's of the way while the pellet is still in the barrel. The positive half of the displacement cycle looks different because it includes the combined positive interference of the horizontal movement of the barrel. If we were to do an FFT on the signal from just this one XCL the result would be the 2 discrete frequencies of the barrel's harmonic signature.

And I've still got 1 channel left!.... I guess I need a laser.

[WhatUPSbox?]

George, that is one beautiful chart. Kind of the Rosetta stone of the airgun cycle, everything in one place. Is the accel trace acceleration or has it been processed by your B&K box to be displacement? What is the sensitivity in g‘s/mv? Looks like at pellet exit the muzzle is near peak velocity.

Great job putting it all together. Channel 4 will be for the other accel?

[George Schmermund]

Stan - The XCL trace is from it's signal having been run through a Kistler 504E conditioning amplifier, then through a Kronhite 3500 band pass filter and then to the DSO. The data is for acceleration only. As far as I can tell the DSO's advanced math function will only take the integral once. This would only give velocity, so I'll stick with the B&K instruments for higher level operations. As you've pointed out it's easy to guess qualitatively what the velocity integral might be from the trace's information.

A more time consuming thing right now is to do the true calibration on the XCL and get real numbers for A,V,and D. The factory info says that A is 10 mV/g nominal, but considering the signal's path, I was only interest in getting each one of the transducers data displayed all in one place for these tests. Only the time and pressure information is accurate in the previously posted image.

All of the pressure measurements so far have a mild sort of roller coaster with bumps profile to them. It would be interesting to translate the ups and downs to the pellet's velocity at each point along the way and convert it into pellet drag information at any point as it moves down the barrel. The Endevco pressure transducer is exceptionally well suited to make these measurements. There's no shortage of things to experiment with as this project moves forward.

[WhatUPSbox?]

George, I've been looking at the eye-candy chart in your post 266. Such great information. I went back and looked at some of the harmonics data you provided in the past. Back in P166 you measured the modes of the 8" barrel at 104 and 164hz. In P165, I took a quick pass at a prediction using rough dimensions from my CP-1 and came up with a first mode around 230hz. I didn't quite resolve that in my head but set that aside. In P215, you took the barrel off to do some of the pressure rise tests. Now with the barrel reinstalled, you did a tap in P264 that if I read the settings right came in at around 200hz for the first mode. Finally, in the shot chart in P266, the muzzle response is a 1/2 wave in about 2ms or about 250hz. Looks like even though at the time you said the mount screws were snug, reinstalling the barrel may have set it more firmly and perhaps the pressure sensor tightens up the barrel mount to get closer to a true cantilever condition.

I think the easiest way to get the displacement may be to store the trace data points and do the integration outside. I think this is just a test run for the longer barrel configuration. The muzzle velocity will be interesting to see if it reaches on the order of 1"/sec. For a 20 yd shot at 400 ft/sec, that would be about .15" error, it would be interesting to see how that compares to the velocity deviations people worry about. Any muzzle tilt error would combine with that.

For the accel calibration, does the little shaker you showed in an earlier post get you there? For the harmonics studies getting within 10% on amplitude is probably good enough.

Thanks for providing all this data to chew on

[George Schmermund]

Stan - The discrepancies in the resonant frequencies may well be caused by the varying stiffness of the breech and barrel mounting. Even if the barrel is really secured tightly into the breech block there can be variations in their compliance due to the way the breech/barrel combo is attached to the main tube. The screw beneath the pellet tray is really minuscule considering the job it's assigned to.

The bolt that holds down the breech block in the rear runs through the piston cover. This long bolt was much more substantial in it's original implementation, but I've modified it to allow a shorter bolt to work in it's stead. The new short bolt allows the clamping of the piston cover to pull the breech tightly against the main tube, but only uses the top half of the piston cover, which is plastic. This arrangement was done in order to allow another bolt to pass through the center of the piston cover for the possibility of setting the hammer spring tension. Thus, the breech block to main tube clamping force achievable is considerably lower than the force that can be developed if the longer bolt went through both sides of the main tube. See post #69 and #88. Also, some of the testing was done with and with out the pellet tray, which may change the breech block compliance at that point.

These are some possible conditions that may have effected the resonances values, but now need to be tested as new variables. Thanks for paying more attention than I do to these things. I'm still in my shotgun approach to doing all of this. Don't forget the beer factor.

As far as the using the time line as a source of frequency information it's important to remember that the first 1/2 cycle (and subsequent wave train) info contains a compound waveform of the real breech/barrel movement and gets more complicated as time goes on because there is no simultaneous phase, amplitude, and frequency separation. This is demonstrated very well in the Lissajous patterns.

The B&K mini shaker is the best method I have for doing the XCL calibration.

[WhatUPSbox?]

George, I don't think the modifications you made to the rear cap significantly affect the first mode of the barrel. At the loads we are dealing with, as long as you have enough preload to compress the breech to tube interface, avoiding a point load, the stiffness of the bolt and to a great extent the plastic cap do not drive the stiffness of that joint. If you could get enough torque on it you could use a nylon bolt. The same is true for the small bolt up front, as long as there is enough preload, its small size does not drive it. I don't think the pellet tray is in the load path at all. If I understand what you did with the pressure sensor mount, I think what you did was augment the two small set screws that are radially compressing two o-rings with a large thread compressing an o-ring face seal against the barrel so you changed the preload and the geometry to something stiffer....Of course, this evaluation is only valid until the next test.

I understand the complex waveform concern, I was just noting (celebrating) the general agreement with your latest tap test (and of course, my analysis). One thing I've been wondering about is whether the force that initiates the natural frequency response is repeatable enough to always initiate the barrel motion in the same general direction. In that case, much of the error might be removed in zeroing the sights. I think as you add the other direction accel and run a several cases, that will become apparent.

I love that little B&K shaker. What is the bandwidth?

I've been thinking about how to characterize the transient response of a pressure sensor. I have a low cost, 1000psi unit coming across the pacific. Not much in the way of specs other than that it uses a ceramic sensor. It is water compatible so maybe a hydraulic shock configuration of some sort....another thought exercise. 

[George Schmermund]

It was a good exercise to redo the barrel resonances. The vertical frequency was a reassuring 104 HZ and the horizontal 164 Hz. The screws were then loosened and the new H was 90 Hz and the V was 136 Hz. That's 12.2% and 13.5 % lower respectively. The Q dropped quite a bit too, as would be expected. The pellet tray, in or out, made no difference as Stan had predicted.

The mystery of the tapped resonance in the #264 being ~ 200 Hz was solved by taking a larger number of wave peaks from the DSO image and averaging them. I came up with 160 Hz. That's close enough for me. If I had done this first it would have been comforting to know that the measurements were good to start with, but I wouldn't have thought to do the loose screw tests. All's well that ends well.

As far as the XCL info on ch 2 in #266, I wouldn't read too much into it other than curiosity at this point. A lot more testing will have to be done with calibrated XCL's down the road. Here's a link to some info on the B&K 8210 mini shaker.

https://www.bksv.com/-/media/literature/Product-Data/bp0232.ashx

[George Schmermund]

Awhile back I did a 4 shot average using CPHP pellets and recorded the pressure curve. The averaging smoothed out the trace, but still left the curve with some up and downs on the descending slope. What's interesting to me is that if those ups and downs weren't averaged out along with the noise, then they must be real and part of the pellet's flight down the barrel.

The pressure peak is 500 psi (5 divisions) and the full scale resolution of the screen is 256 steps in the full 8 divisions ( the image is cropped). The number of steps used to draw this curve is therefore only 5/8's of full resolution. These pressure changes would probably be variations in the barrel's diameter or roughness causing drag. The curves might be a good way to evaluate bore and rifling treatments such as moly coating, lapping, and chokes. Higher resolution data collection should show a much better picture of what's going on.


   

[George Schmermund]

After giving some thought to the pressure curve vs time experiment it came to me that there was an HP 7090A Measurement Plotting System up in the attic that hasn't been used for a long time. It was one of those instruments that became a hybrid between an digital plotter and a three channel data acquisitions system. It was born in the era of early PC's and laboratory measurements. One of it's virtues that I want to explore is the ability to do 12 bit data capture into a buffer and then plot the buffer out as a hardcopy. Sounds crude, I know, but it may be able to do an accurate plot of the actual pellet transit down the barrel with a resolution of over 4,000 vertical points instead of the 256 points of an 8 bit scope.

The data collection bandwidth is limited to about 3 KHz, so the rise time on the pressure will have to be slowed down. This can be done by reducing the throughput of the transfer port. The transit time on the pellet going down the barrel should be increased accordingly. The roller coaster shape of the pellet's barrel transit should look the same as the faster rise time data, just stretched out to allow the slower ADC to capture everything. This is another Saturday night beer infused thought experiment, but I'll try to reify it tomorrow.

[George Schmermund]

The HP 7090A system was put to the task today, but was found wanting. It was inspirational, though, because of the lack of noise on the curve. The short coming was the low 3.3 kHz bandwidth limitation of its ADC. I've been looking at some of the cheap Dataq instruments and may reinvest in a newer one of them for a followup of these time/pressure curves. I'm pretty sure that the release time can be detected with a faster and higher resolution ADC without the need for a probe down the barrel.

[George Schmermund]

The ability to see what the external hammer action was doing on the Vigilante hack was easy with an XCL attached directly to it. The CP2 in another matter because the hammer is buried inside the main tube. It wasn't hard to do the CP2 shim switch arrangement by milling a slot for hammer/valve access, but it still didn't give all of the sequence information nor do it reliably.

I'm going to try and install an XCL into the hammer and bring the leads out through another milled slot in the tube. this should give a blow by blow time sequence that will define the valve action with good timing information. 

[WhatUPSbox?]

George, with all that is going on with gas flow, I‘m not sure it will be easy to attribute pressure fluctuations to pellet motion. One possible check might be to compare the curves of a new pellet vs. one that has been pre-sized by pushing it down a barrel. The two should have enough starting force difference to see with the 8 bit system.

[WhatUPSbox?]

I love those small accels. I was wondering if you could take one of your piezo disks and put it on the face of the hammer, covered with a steel disk. It may give a sharper valve closed indicator than the accel

[George Schmermund]

Stan - The mini 2250A XCL's are indeed nice little instruments. You got me thinking about what I'd be in for if I wanted to replace or add to any of the ones I've been using. I called Endevco to see what they cost. It turns out that they're over $1500 each! There's a 2% break for 11 of them. I think I'll start taking much better care of the ones I have.

On that note, your idea to use the < 1 cent piezo discs on the hammer is compelling. Originally the disc was going to be on the face of the valve as posted previously, but I chickened out because of the possibility of ceramic chips from the PZT crystal getting into the valve stem seal. With your suggestion of sandwiching the disc between the hammer face and a steel striker disc sounds much safer. Some sort of adhesive can bind everything together and hopefully contain the dust.