Adjustable Barrel Tensioner - Harmonics Study

[ericw]

I've been watching this thread with interest in what really is going on during the shot cycle to cause the POI shifts.  Is it really the muzzle effectively pointing in a different direction as the wave propagates down the barrel or some other effect?  The propagation speed of the impulse down the barrel and reflection of the wave back from the muzzle will change with tension in the barrel so the fundamental frequency will go up.  Other effects like mass loading on the muzzle will also effect the experiment.  One thing that I didn't think of is that the shock wave actually changes the bore diameter as it goes down the barrel.  I found this study (http://www.the-long-family.com/shock%20wave%20theory%20summary%20explanation.pdf)  that was done by a fellow electrical engineer and explores all of this in powder burners to some depth with some surprising results (to me at least).  I would be interested to hear how this relates to your results, Bob and if it brings more understanding to why the tensioning works.   It seems that simply changing the vibration frequency of the barrel would not accomplish much w.r.t. reducing the amplitude of the wave at the end of the barrel.  There are so many factors involved but this study filled in a few of the blanks for me

[rsterne]

QVTom, how is the ferrule attached to the barrel, silver solder?.... not that I have the ability to machine anything that nice anyway.... *eyeroll*

I'll have some whine with those cheese-balls, please.... Sometimes you just gotta do what you can....

Bob

[rsterne]

Eric, the magnitude of the pressure pulse / shockwave is much greater with a PB, but on the other hand, we tend to play with skinnier barrels.... I will read that study to ponder what might apply to us, thanks for the link.... There is a barrel harmonics calculator online, and one of the inputs is the chamber pressure, and we play in hundreds of psi, not thousands.... so the initial disturbance is an order of magnitude less for airguns....

Part of the success of tensioning the barrel is that the effective OD is increased by the shroud, which basically stiffens the barrel.... Since the resonant frequency increases with stiffness, the result is the same, IMO, regardless of the mechanism to get there....While a complete understanding of the Physics involved would be nice, just the practical result is at least as important....

I have used untensioned shrouds, supported by an O-ringed barrel band, in the past, and they CAN help the accuracy, by supporting the muzzle.... Often they are improved by an intermediate support of the barrel inside the shroud, just as a barrel is sometimes aided by a barrel band at the right location.... Tensioning the barrel inside the shroud seems to stabilize the assembly even more.... but a lot more work is going to be required to really prove anything.... QVTom has already proven that the system can work with a rigid shroud, rigidly mounted barrel, and a lot of tension (~800 lbs.).... 

Bob

[QVTom]

QVTom, how is the ferrule attached to the barrel, silver solder?.... not that I have the ability to machine anything that nice anyway.... *eyeroll*

I'll have some whine with those cheese-balls, please.... Sometimes you just gotta do what you can....

Bob

Yes silver bearing solder.  The soldering is a lot of work so next time around I will tread and install with permanent loctite.

[rsterne]

Eric, I found one thing that is hugely different on an airgun RE the article in that link before I got very far into it.... Using the speed of sound in steel given (0.227" per microsecond), and 24" barrel, we get ~211 microseconds for one round trip of the shockwave.... The typical time a pellet spends in the barrel is about 2.8 milliseconds (2,800 microseconds) at 950 fps MV, allowing time for about ~13 round trips during the time the pellet travels up the bore, compared to "4-5 trips" for a typical PB according to that article....

In addition, the stress applied to the barrel is proportional to the pressure, and we are dealing with, as I said earlier, pressures about 1/20th that of a PB.... Therefore, we have 1/20th of the disturbance, varying over a timeframe 3 times as fast, relative to the pellet leaving the muzzle.... I had a quick look at the graphs explaining the timing, and the magnitude of the event is obviously related to the chamber pressure, as is the change in muzzle diameter.... At our pressures, instead of a total bore diameter change of ~ 0.00025", we would be dealing with ~ 0.00001"....  Imagine if you will, graph #4 with the peaks 1/20th of the magnitude.... and then graph # 5 adjusted for that and the much slower relative bullet exit timing....  At that point (rightly or wrongly) I decided that while the model and method may be valid, it is not likely a major concern for us....

Bob

[CarsonRatSniper]

The way we're doing the Millennium top ends is to try and make the entire assembly as rigid as possible...the barrels are threaded into the breech for approx 1.5" then the last 2" or so is turned down to .500" with .0005" clearance inside the breech. The barrel step down at the breech shoulder sets against the breech giving .010" clearance from the magazine port.
The breech shoulder is .750" OD x .400" long...to stiffen the junction of the breech and barrel we are using a 1" wide barrel band that locks this joint together and also acts as the forward breech securement, eliminating the tiny 4-48 breech screw (our mag ball detent is located there anyway).

I am designing the 1.25" OD CF shroud to thread onto the muzzle threads and the o ring floated rear tube cap over the barrel will tension against the breech band.
Both caps will be permanently attached to the CF tube.
The muzzle will be an insert with an air stripper built in that threads onto the muzzle and will have aluminum cups that slide into the sleeve, followed by the muzzle cap.

I'm not sure *how much* tension will be applied - we may make holes for a spanner wrench to really tighten into tension...

I won't know how well it works for a couple of weeks when I can test a completed rifle but I will post my findings.

Thanks for this thread Bob...it shows an improvement in using a tensioned barrel for sure.

Mike

[Tomg]

Carson.........PIC's!

[ericw]

Eric, I found one thing that is hugely different on an airgun RE the article in that link before I got very far into it.... Using the speed of sound in steel given (0.227" per microsecond), and 24" barrel, we get ~211 microseconds for one round trip of the shockwave.... The typical time a pellet spends in the barrel is about 2.8 milliseconds (2,800 microseconds) at 950 fps MV, allowing time for about ~13 round trips during the time the pellet travels up the bore, compared to "4-5 trips" for a typical PB according to that article....

In addition, the stress applied to the barrel is proportional to the pressure, and we are dealing with, as I said earlier, pressures about 1/20th that of a PB.... Therefore, we have 1/20th of the disturbance, varying over a timeframe 3 times as fast, relative to the pellet leaving the muzzle.... I had a quick look at the graphs explaining the timing, and the magnitude of the event is obviously related to the chamber pressure, as is the change in muzzle diameter.... At our pressures, instead of a total bore diameter change of ~ 0.00025", we would be dealing with ~ 0.00001"....  Imagine if you will, graph #4 with the peaks 1/20th of the magnitude.... and then graph # 5 adjusted for that and the much slower relative bullet exit timing....  At that point (rightly or wrongly) I decided that while the model and method may be valid, it is not likely a major concern for us....

Bob

Bob your numbers all make sense but the point that the impulse timing and pressure effects are minimal compared to a PB  for airguns raises the question  ...Then why does adding tension which should only serve to raise the velocity of the impulse down the barrel (slightly)  v~ sqrt (T/M)  have any appreciable effect in airguns?    It sounded like the pressure wave down the barrel was what the tensioning was supposed to fix, right?    I would suspect that without adding some kind of lossy mechanism (ala dashpot in mechanical models), all that is being done is  changing timing so the pellet doesn't reach the end of the barrel at the wrong time when an impulse hits the same place.   If adding tension will do that I would maintain that it would only work for one particular gun setup (pellet, barrel length, pressure).  Otherwise, it seems there is something else going on.  It seems that adding some material around the barrel that will dampen the wave impulse would give the best result over all.   Other things that come to mind are adding vibrational "nodes" to the barrel by hanging weights  or by placing barrel supports to the shroud or stock at critical points.  This again doesnt dump the vibration energy ... it just moves the standing wave pattern around so the end of the barrel doesnt move as much for that particular setup.   
My linear system analysis training is rusty so maybe I'm missing something here.  Thanks for all your experimental work.  Obviously there is something very cool going on there.

Eric

[CarsonRatSniper]

I will take more pics as we progress the week of Feb 8.







These are all the pics I have so far but you can see what's going on.
It will be much clearer when we have the barrels CF sleeved to .750" OD.

The barrel TP ports are married to each breech to avoid clocking issues - the barrels will be tightened down then spot marked for the TP location.
We *could* vice tighten the barrels to the breech AND tension the 1.25" CF shroud in the fashion I mentioned but it will requite a vice to remove the barrel for caliber/barrel changes.
They will be screwed in tightly but will not require any special tools to unscrew from the breech.
There will still be a grub screw in the top of the breech to ensure it cannot loosen at all.

Mike

[moorepower]

Hi Bob,

I have found that removing even a small amount of material (threading) from the OD of most barrels will open up the ID.  Don't know if that is an issue with your barrel or not.......just mentioning it, as the muzzle can be a bad place to loosen things up. 

Mike

Except a Hammer forged barrel, which will constrict the bore when removing material of off of the O.D.

[rsterne]

Eric, I think the primary thing that is happening is getting rid of the fundamental frequency (the muzzle waving from side to side like clamping a ruler to the table and bending it and letting go) because the shroud, which is twice as large as the barrel stiffens the assembly by like a factor of eight (think of what happens if you double the thickness of the ruler).... Then in addition to that, the first and all other harmonics increase in frequency and reduce in amplitude as well, just like tightening a guitar string.... At least that is my understanding of what is going on.... Any effect that the tensioning has on fore-and-aft pulses, while theoretically helpful, is IMO insignificant....

Bob

[Kailua]

If a dial indicator was placed at the muzzle end.  Would the dial movement show the harmonic movement?

[nervoustrigger]

The issue with using a contact method is measuring without influencing the outcome.  Maybe with an interferometer.

Bob's shop is decently equipped but I don't think he's been holding out on us

[ericw]

Bob, That may be what is happening but at the same time, depending on the spectrum content of the exciting source (shot impulse), the actual amplitude of a tensioned string or barrel may actually go up.  You can sort of see that when listening to how your guitar sounds when you strike the string with a pick versus a soft thumb. Think of it as a filter on the input excitation source ... higher tension filters out the lower frequency content.  So, it really depends on what that pulse spectrum looks like.  If it were a true impulse, the power would be equally spread across all frequencies and that would make it an equal amplitude response for the higher or lower tension cases.  If we knew what the excitation pulse looked like we could tune things to have a minimum response with some assurance.  I guess without pushing the experiment too far we can make some assumptions based on results.   
Reading your post on the "hooked barrel" being moved by the pellet may be the most credible explanation for what is going on.   Good info.
Eric

[Tomg]

After reading the "hooked barrel/shot wants to straighten it" theorem, it certainly explains the effect you documented, and also the effect of tensioning the barrel combating it. Which brings back the practice of indexing a barrel to where any POI change is in the vertical plane.
Some really good information by all participants, thank you all for the free flow of info!!!

[nervoustrigger]

I'm still having a hard time wrapping my mind around the pellet inducing the sideways excitation forces.

What magnitude forces are at play?  Presumably the barrel (an/or the bore) isn't shaped like a banana.  I'm assuming more like 0.030" arc swept gently over the length of a 20" barrel.  A pellet striking a blade of grass would have its trajectory changed more than that, right? 

I would have thought the impulse of the blast of high pressure air would impart more energy into the rifle by several orders of magnitude, setting up vibrations in the barrel and causing it to buzz like a guitar string.

[Tomg]

It doesnt take much to produce a slight horizontal shift in the flight path.

I think this is how it works: If the barrel is bent, even slightly, the harmonic wave propagation will be most notable in the perpendicular plane to the bend.
But smarter heads than mine might explain this better.

[rsterne]

A dial indicator would need some kind of telltales to give a minimum/maximum reading.... however, I can tell you that for the group to move side to side 0.26" at 20 ft., the end of the 2 ft. barrel has to be moving 0.026".... That isn't necessarily on one shot, that is the maximum difference between the right deflection of the group center at 638 fps to the left deflection of the group center at 871 fps.... The barrel may in fact be swinging further than that on any given shot (or less).... Using any measuring device that touched the barrel would likely affect the result, as mentioned....

I think what may be getting lost here is that we don't really care WHAT is causing the vibration (although that is interesting by itself).... We are more interested in the dance the barrel does once disturbed, and how we can minimize that.... Thicker barrels, or shorter barrels, both are stiffer, bend less, and at a higher frequency.... This tensioning, using a shroud with twice the diameter, makes the barrel act like it is thicker, bending less, and at a higher frequency.... but without the weight penalty.... If weight is an advantage, as in a bench-rest gun, then forget all this nonsense, and use a barrel that is 7/8" OD instead of 7/16".... It will weigh over 4 times as much, but be even stiffer (and more accurate) than the tensioned one....

Bob

[nervoustrigger]

It doesnt take much to produce a slight horizontal shift in the flight path.

Well, that is precisely what I was saying.  If it doesn't take much force to deflect a pellet's path a few 10 thousandths of an inch, the other way of saying it is that the pellet does not exert much lateral force on the barrel as its course is altered.  Thus not inducing much in the way of vibration.

[rsterne]

You could get a feel for the force applied to the barrel using Newton.... for every action there is an equal and opposite reaction.... If the barrel is bent 0.10" it has to change the path of the pellet by that much, compared to the direction it started out in at the breech.... If the flight down the barrel takes 3 mSec, you can calculate the lateral acceleration on the pellet, in the direction of the bend, and hence the force.... The barrel will see that same force away from the bend.... Using the mass of the barrel, you can calculate how much the barrel will "recoil" away from the bend....

and NO, I'm not going to do the math, 'cause I'm not that interested, suffice it to say that it happens....

Bob