Hacking The Benjamin Titan NP Break Barrel

[WhatUPSbox?]

Not sure who still visits this corner of the GTA universe, but here is a thought on testing.
Recently I got an accelerometer with a faster response/higher bandwidth. The thought was: Can one use a muzzle mounted accelerometer to measure/evaluate hold sensitivity?
The first picture shows the instrumentation block clamped near the muzzle of the Titan I used for the other testing. The accelerometer is on the circuit board on the side, with the sensitive axis vertical. On top of the block is a piezo microphone (in the cylindrical mount) that I use for a qualitative sanity check on the accel. The black sleeve on the right side of the instrument block holds the laser/detector pair that detects when the pellet leaves the muzzle. The other instrument is an accel in the barrel direction mounted as before in the surrogate scope on top of the tube (second picture). The laser, two accels, and the mic. use up the 4 channels of the DSO.
I set up two different support conditions on the benchtop (picture 2), bag supported and, on a roller and linear bearing. I also tried offhand and my (amateur) artillery hold (open palm support and medium press into shoulder). For the two benchtop supports, I pinched the trigger to minimize my contact with the rifle. the thought being that my two fingers can't compete with the recoil forces of the Titan.
The third image shows all the data on the scope screen. It shows the start of the cycle and when the pellet leaves the muzzle. The axial accel provides the basic shot cycle. The vertical accel and mic provide the response at the muzzle. Interesting that the Titan now appears to have a rough spot in the piston travel that also shows up on the muzzle response. The trace in the middle of the chart labeled vertical velocity is an integral of the vertical accel done by the DSO. The repeatability of that trace I think is part of hold sensitivity.
In the fourth image, traces from two different artillery hold shots. The difference between the two velocity traces at the instant the pellet leaves the muzzle would be part of the hold sensitivity error.
The fifth image shows these velocity traces for the different support conditions and the sixth zooms in on the instant when the pellet is leaving the muzzle. Any difference between a pair of equivalent traces would project to be an error on target. At least from this limited trial, the artillery hold was much more repeatable. The actual numerical value can be used for calculating a POI spread.
The results look promising enough to do some more testing. It would be interesting to be able to have a number for the recoil portion of hold sensitivity.

[mpbby]

Thank you for sharing. I suppose the muzzle path due recoils is not only vertical.  It would be interesting to complement your experiments with a laser device attached to the barrel and a slow motion camera filming the laser dot at the target.

That's my intuitive thinking to explain why a heavier pellet (slower..) has the POI changed to the side.

[WhatUPSbox?]

I only have one of the accels at this point so I chose the vertical because there the recoil forces are not on centerline. There will be lateral accelerations at the muzzle as well due to vibration modes in the barrel and other sources so adding a second sensor is a logical step.

High speed optical measurements are challenging. High speed video would probably want 10,00 frames/sec to capture the instant the pellet is leaving the muzzle. You could use low speed video or still camera and pulse the laser briefly as the pellet leaves the muzzle.

[mpbby]

I was thinking that, once the muzzle path is recorded, the point corresponding to the moment the pellet leaves the muzzle would be determined by calculation.

[mpbby]

Regarding the learning curve for springers, I think it would be valuable to know about some basics.

Once squeezed the trigger, and due recoils, the muzzle usually has a path, for instance, in this 'form' (known from the video).  Depending on the barrel length and the speed, a certain pellet would take a certain time to travel through the barrel.  At the exact moment it's leaving, it will be being leaded by the muzzle to a certain direction.

(on the other hand, I suspect that, depending on the holding, and the resting, the path's 'form' may have relevant changes)

[WhatUPSbox?]

In addition to the direction based on the tilt of the muzzle at pellet exit, the pellet also caries whatever sideways (vertical or lateral) velocity the muzzle has at the time the pellet exits. So if you are shooting at say 20m and the typical flight time is 0.1 sec, then, as an example, if the muzzle was moving at 5 cm/s up (or sideways) that would add 5mm of error on target in addition to any error due to pointing. That's what I'm trying to measure with this setup. To measure the pointing (tilt) I would need another accel near the rear of the rifle to calculate tilt. I have not seen any of the reasonable priced gyro modules (for RC drones, etc.) that output fast enough to measure the change in the pointing angle.

Without some expensive video equipment, I think you could record a streak made by a laser dot (flashed) on a still image and measure its length. That could give you some idea of the muzzle sideways motion.

When the pellet leaves the muzzle is not that hard to measure. Trigger release is harder.

[WhatUPSbox?]

I suppose the muzzle path due recoils is not only vertical.

I took the accelerometer and moved it so that it measured the lateral direction (image 1). I then took 3 shots in the roller supported configuration. While it may not be realistic, it is relatively repeatable, and useful for checking things out. Unfortunately, at this time, I can't measure the vertical and the lateral with the same quality in one shot.
Image 2 shows a comparison of the muzzle motion (velocity) of the two sets of three shots.

Here is my speculation:
The vertical motion responds first to the piston being driven (first recoil) and then the piston being quickly stopped by the pressure spike (second recoil). The amplitudes are larger because the tube is offset from the center of gravity and from the support points. The motion in the lateral direction responds less to the first recoil and then more so to the sharper second recoil. Most of this motion is accounted for in the shooter's zeroing of the sights/scope using his/her preferred hold. The part that ends up in the error at the POI is the spread (at pellet exit) within each set of three shots in this case. Here the actual spread was similar for the two directions. If one does the calculation to get the muzzle position change, the results are similar, large difference in absolute value of the curves, but the spread is similar.

Taking a guess at why the the POI can move laterally for heavier pellets. When I did a double pellet shot earlier in this thread, the pellets spent an extra .001 sec in the barrel. So for that extreme weight change, the pellet exit point on the curve in image 2 would move to the right and the pellet lateral motion would have a new value, and a spread to go with it.

At this point this is speculation without enough testing to back it up, but that is how I interpret the trends.

[mpbby]

I am from another (distant) corner of the GTA universe. I would love to just point and shoot, with nothing in between in my mind. When I'm having a recurrent problem, the detective mode always needs a qualitative referential to start thinking about the suspects.

I understand your attention going to the quantitative. Thanks for your kindness by using "Brazilian" units..

Btw, I already had a misunderstanding when thinking only with the qualitative, until I found out the quantitative involved.  Top quality pellet, relevant vertical strings.., and always worried about a supposed need to improve the seals (minimise ES). Then, I found out the 'vertical stringing' tool in ChairGun.  It validated the rule of thumb .. while ES is up to 4% of the average fps, no worries (about vertical effects).  For my needs, I was free to think about another suspects.

Besides the pellet weight thing, I am currently considering the possibility that, as a component of POI changes (same pellet), some lack of repeatability when holding and/or resting may cause relevant changes in the muzzle path, and the specific tilt when the pellet is exiting.  To see some images would be fine.

But .. I am not a tech person. From my newbie times, I bought a Gamo laser device that I ended not using; it doesn't have a pulsing mode.  I only have a Sony 'handycam'. 

[WhatUPSbox?]

I think with the Handycam you can measure you more than the rifle, which is actually useful.

If your handycam shoots at 60 frames per second,  so about .017s per frame. The shot cycle for my Titan is about .014s so the rifle effects will look like a blur, probably split between two frames. On the other hand, everything you do prior to the pellet leaving the muzzle is slower so you may be able to get good information.

If you want to experiment, here is what I would try:
Set up a normal paper target to shoot at and sight your scope. Set up a second sheet of white paper off to the side where you can't see it in your scope (so it does not distract you). Somehow mount your Gamo or just a laser pointer so it hits the second sheet when your scope is on the bullseye. The mounting does not have to be very rigid since you will be measuring what happens before the recoil hits. Aim your handycam at the second sheet and measure the distance from the handycam to your muzzle. The speed of sound in air is about 343 m/s at 20C and 355 m/s at 40C so if you have the handycam 10m from the muzzle the time delay on the audio track is 10/343 = .029s or about two frames so you can get a better idea of when the pellet left the muzzle from the audio track. Looking at the video prior to that point will give you an idea of what your hold is doing up to the point when the recoil hits. You can compare that to how the pellets are hitting the bullseye. You probably want to use a multi-bull target (like benchrest) so you can keep track of each shot.

[mpbby]

When I say ‘repeatability’ of holding and resting, I was not referring to any motion from the shooter.. It was only about the position of the hand under the rifle, relaxed palm or some grip, materials where resting the hand, position of the elbows, pressure on the shoulder, ..

Your wider perspective is more realistic and thank you for the guidelines.  Nevertheless, I don’t believe I would be able to have useful results to correlate the sound and the poor image within the very short timeline.  So, I will remain curious about actually seeing the muzzle path, mainly after the second recoil.

Well, just figuring about the path reinforces to me two wise advices .. tame it = ‘artillery hold’, or similar. Let it be repeatable = ‘follow-trough’.

[WhatUPSbox?]

I did a little more testing. This time I used, what I would call a casual artillery hold, off-hand sitting in a chair with the pellet box inches away. Since I'm starting the accelerometer clock at the point when the piston is released and tracking it for about 15 millisec, I think the typical slow pointing drift should not muddy the results too much. Since I only have one of the high bandwidth accelerometers, the vertical and the horizontal results are from separate shots (yeah, I probably should spend the $50 for another one). I made 3 shots with vertical data and 3 shots with horizontal data. I also included the two offhand vertical results from the pervious testing.

The first chart shows an overview of the muzzle vertical and horizontal velocity traces based on a simple integration of the accelerometer data. The integration is started with zero at -14 millisec (piston release). Each shot follows a similar trend, even though some of my pulling the trigger may still be included, the forces are probably small compared to the shot cycle.

The second chart just zooms in on the time between peak recoil (or surge) and pellet exit. Looking at the average vertical, for a 200m/s muzzle velocity, this corresponds to about 2.8 MOA with a spread of 2. For the horizontal it is about 1 MOA with a spread of 1.

The third chart does a second integration to get the muzzle vertical displacement. If the motion was a result of the rifle pivoting (as a rigid body) at my shoulder the average would be about 2.5 MOA and the spread larger at about 2.8 MOA. These MOA numbers would be larger if they were due to barrel flex (harmonics?) and smaller if they are just due to the riffle rising without tilt (yes, a second sensor would help here as well). These would be potentially additive to the vertical velocity generated MOA errors.

Is it real? Is it useful? (note: an adult beverage or two may help with this section)
Real? I admit, to make the data more robust, I need to proof and scrub the data processing in the spreadsheet for any errors.
Is it useful? It could be. I think you can use such results to evaluate tuning improvements, including potentially barrel harmonics tuning. It may also help finetune the hold technique. It may also help in picking the number of shots to use for zeroing a scope. You can also put printouts up on the wall of the man-cave to impress any visitors.     

 

[WhatUPSbox?]

Went back to thinking about the pellet motion in the shot cycle. I tried a couple of way of holding the probe wire inside the barrel. First was on the tip of a bamboo shaft (spear?). This worked OK but there is a chance that the shot cycle recoil/surge moves the probe tip and affects the measured launch time. I considered the coiled wire probe George used last year but I wasn't sure it would not jam even using wadcutters. I settled on a felt-like plug (image 1). This is similar to cleaning pellet plugs (which I didn't have on hand) but is cut square so there is some room for air to get by. Unfortunately I cut it from the pads you put under furniture feet and it is synthetic so I now have some plastic to clean out of the barrel. I think it worked well to capture the initial motion but I'll need something else to capture the motion later in the cycle as the gas motion builds up in front of the pellet.

The second image shows the results for the first inch or so of motion. It shows the shot cycle (Hobby wadcutter 11.9 gr) as captured by an axial accelerometer. The inset graph shows the position from multiple shots as a function of time. It also shows the volume behind the pellet (based on a .217 barrel diameter, but not including the skirt volume). As a comparison, my estimate for the transfer port volume is 154 mm^3. 

[WhatUPSbox?]

I took some more data to track the pellet motion during the surge spike which I'm treating as equivalent to the pressure spike in the compression chamber. I switched to a wooden holder for the probe wire (image 1). This is a tighter fit and has a narrower cross section so it is not moved by the air moving in front of the pellet at the higher velocities.
The position is mapped on the surge acceleration trace (image 2) and shows that the pellet is a little over 8 inches down the barrel when the surge is ending. The Titan has a 18.5 inch (470 mm) barrel.
The third image shows the same data plotted against time from the surge peak, I added a trendline and a simple estimate of the velocity from the slope of the trendline.

[Mole2017]

Stan, I'm trying to figure out how you are using the wire. Is this inserted down the barrel or just at the muzzle? (It does go in the barrel, correct?)

[WhatUPSbox?]

I thread the loose end in through the breech until the wood block hits the leade with the wire tip facing the transfer port. I then use a skewer to push the block/wire to the desired depth for that shot. For the very shallow ones, I check it with a depth gage but for the rest, a marking on the skewer is good enough. The wire is long enough to go out the muzzle and reach a connector on the barrel. The pellet closes the circuit on contact. The pellet, wood, and the wire go flying into a length of PVC pipe partly filled with plastic bags.

[George Schmermund]

I've been reading an excellent book that was published by Bruel & Kjaer back in 1980. It's titled Mechanical Vibration and Shock Measurements. This is the second edition and has many revisions not included in the first edition. Since my purpose for hacking the Titan was mainly to measure and evaluate what happens during the shot cycle I've found this tome to be rewarding, to say the least.

I decided after the last set of measurements (back when) that there was not going to be an easy path toward getting the second large impulse in the cycle under control. In the overall scheme of thing it seems that the gun has no big problems surviving the impulses. It's the scope that takes the real beating.

The Titan project was left there and I got distracted with several other experiments in different areas in the mean time. My mind did wander back occasionally to an assortment of unusual damping arrangements that might be investigated using mechanical impedance measurements. This book may instigate some experiments in that arena. It shouldn't be too difficult to put together an impedance head transducer to help design a new type of scope mount.

The photos show a copy of a page in this book that got me interested in making a few bench measurements. I set up some instruments that would allow me to use the DSO to simultaneously capture a single cycle (one period) of a 1 kHz sine wave along with its 2 integrals  -  velocity and displacement. I was pleased to see the DSO's resemblance to Fig E. 4. The 3 channel overlay gives some idea of the amplitude and phase relationship of the signals.

[WhatUPSbox?]

Did you mean this pamphlet? https://www.bksv.com/media/doc/bn1330.pdf (large pdf)

I'm impressed with your DSO's math function. I don't think I can do a double integral in mine, other than by post processing the waveform file.

[George Schmermund]

Yes, that's the publication. I bought it in book form from a bookstore online. It was about $8. Saved a lot of time, paper, and toner.

The measurement setup Includes several pieces of instrumentation. The DSO is only doing one of the integrations. The other one is done by a B&K charge amplifier which can do either or both integrals plus low and/or high pass filtering. The DSO's digital filters are used as bandpass limiters.

Mixing and matching between the 2 different instrument's integrators is interesting and instructive. They both do equally well at this task.

[George Schmermund]

Stan - One of the toys you might consider saving up for is a Bruel & kjaer 2635 Charge Amplifier. It would open up a whole new world of accelerometer measurement capabilities for you. They're real sleepers on eBay. I've acquired several of these amps over time and not had to pay more than $100 each for any of them. They're current catalog items from B&K and list for $7500 apiece. Go figure!?

[WhatUPSbox?]

That's a good thought. I probably should think about having an industrial based comparison for some of my instrumentation. I've hesitated both because of the cost that comes with that eco system and because a good part of my interest in this testing was to see how far one can utilize the chip based sensors. One area where it is difficult to duplicate the industrial instrumentation is in fast response pressure measurements like you did with the Titan.