Barrel Length, the seldomly understood calculus

[Stubbers]

Muzzle energy / System energy = thermodynamic efficiency. I was the first over at the GTA to bring this to light, the idea was also rejected by Bob and the like...and later confirmed to be fact by a chap who is way smarter than I, named Domingo Tavella.

The reason Bob rejected the idea, is because he didn't believe my concept (confirmed by Domingo) that air has a finite, measurable amount of energy, depending on the state its compressed to. I owe Lane (from Lane Regulators) credit for opening my eyes to this concept (fpe per psi based on state of compression), and I ran with the concept from there to get where I am today.

-Matt

 

[Stubbers]

I don't mind going off-topic and derailing the original premise of the thread to cover some airgun basics(or advanced airgun mechanics)...

However, the point of this thread was to make it easily digestible for the average reader to understand why short barrels perform almost as well as long barrels, which has nothing to do with anything @Scotchmo has wrongfully stated, nor adiabatic expansion such as @Smitty911 pointed out, which is 100% correct.

-Matt

 

[Mr.H]

OK, I'd like to ask a question(s). First off, I'm not a math guy by any stretch of the imagination, yet I' am interested in this thread.

Can you explain in layman terms what happens to pellet velocity if you change the length of the barrel by 4" (13" to 17") without changing anything else? Pellet velocity increase or decrease, based on your data.

Gun in question: Taipan I Vet Compact .25 (330 CM), shooting JSB 25.39 @865 fps.

Thanks, and if anybody else wants to jump into this, please do.

 

[UDABEGGER]

At my age the one thing I do understand is the effects of passing gas . Can be dangerous . Why does this post remind me of a christmas goose ?

 

[PumaCarl]

This thread has been a great read! Please, everybody argue your points, respectfully of course, tenaciously if you must, and snarkically if you just want to interject. It is great to see actual discussions taking place somewhere. Somebody usually has to be wrong for somebody to be right. Don't worry about being wrong, worry about learning what's right.

 

[Stubbers]

OK, I'd like to ask a question(s). First off, I'm not a math guy by any stretch of the imagination, yet I' am interested in this thread.

Can you explain in layman terms what happens to pellet velocity if you change the length of the barrel by 4" (13" to 17") without changing anything else? Pellet velocity increase or decrease, based on your data.

Gun in question: Taipan I Vet Compact .25 (330 CM), shooting JSB 25.39 @865 fps.

Thanks, and if anybody else wants to jump into this, please do.

Loaded question and I can only really answer for plateau (peak fps for the gun), provided you add dwell to the longer barrel, you will see an increase in velocity unless your ports are so small the mass flow rate cannot feed enough additional air into the bore, which would be a 'choke' so to speak, and the additional barrel length will actually cost you a few fps, likewise the same would happen if you were tuned extremely efficiently in the current state and left it and only added more barrel, however the latter is unlikely being you're cranking out 865 fps with a 13" barrel.. Calculating based on state of tunes requires additional data, primarily your air usage per shot, then it becomes relatively easy.

Could you provide some more data on this particular gun.

1) Set point pressure (assuming regulated)
2) Plenum volume
3) Port diameter
4) Is 865 the plateau fps with 25.4 gr? Meaning adding more hammer strike does not result in more fps.

-Matt

 

[Mr.H]

Loaded question and I can only really answer for plateau (peak fps for the gun), provided you add dwell to the longer barrel, you will see an increase in velocity unless your ports are so small the mass flow rate cannot feed enough additional air into the bore, which would be a 'choke' so to speak, and the additional barrel length will actually cost you a few fps. Calculating based on state of tunes requires additional data, primarily your air usage per shot, then it becomes relatively easy.

Could you provide some more data on this particular gun.

1) Set point pressure (assuming regulated)
2) Plenum volume
3) Port diameter
4) Is 865 the plateau fps with 25.4 gr? Meaning adding more hammer strike does not result in more fps.

-Matt

The only number I can provide is the regulator is set at 150. I don’t know the size of the port or the Plenum volume, some other folks that own that rifle might have that information.

 

[Stubbers]

The only number I can provide is the regulator is set at 150. I don’t know the size of the port or the Plenum volume, some other folks that own that rifle might have that information.

Yea port diameter is very important as I said it is a variable that determines mass flow rate, plenum volume does as well as it determines average shot cycle pressure, and if the port were choking the system currently, opposed to your barrel length, then adding more barrel does nothing.

The below is NOT accurate because I do not have all the guns data necessary, its like trying to fly a kite without wind, but I'll drag my kite out anyhow just to give you a little idea.


13" barrel (assuming plateau) (illustration/demonstration only, not actual representation)

17" barrel

One may ask why 2078 psi and not 2170 at the pellet base? That is because of the transfer port 'wasted volume' where high pressure mixes with low pressure, and you experience pressure loss. However, it is likely even less than that because I truly simplify the heck out of my graph, its very unlikely you even see 2078 psi at the pellet base. So while the numbers on pressure themselves are NOT 100% representation, the gradient occurring is.

-Matt

 

[Stubbers]

Another way to view the air parcel being ejected in the bore is like a compressed spring.

Once decompressed, its the front most coil (and for air or compressed gas, the fastest of molecules in the parcel which as they decay are replaced by the next fastest molecule, until outpaced by projectile to where no more transfer occurs) transferring the springs combined coils energy to the pellet, the energy within the coil in compressed state is finite and during the decompression stage, you cannot add coils mid way which dump more energy (akin to additional super speedy molecules) into the spring than it can handle, it has its rating, and depending on its compressed state the energy is measurable. Likewise the super speedy air molecules velocity is decayed by the projectile its forcing down the bore, until the projectile outpaces the remaining molecules, you can't keep adding coils into a spring to increase its rating, one must redesign the spring od and wire diameter for that...(design limits of mass flow rate per every caliber airgun)

The springs highest force is where its most compressed (beginning of your barrel /beginning of springs decompression stroke), and the more it decompresses, the less energy it has to expend (end of longer barrels)...

Turtle vs the hare. The rabbit will out gas itself, and the turtle will win the race, in nominal settings. You cut a barrel so short, the hare while losing to the turtle, will still have a ton of gas left in his tank to keep going (effective distance/volume), akin to a GK1's muzzle report when cranked out ...you lengthen a barrel too far, it will choke the mass flow rate of the port/caliber and the hare will fall flat somewhere along the bore/race. A long enough barrel will psst out near atmospheric pressure in huge volume...


-Matt

 

[Stubbers]

Adding 'adiabatic expansion' to the pressure gradient...of the above graphs. Illustration purposes only, not actual. What changes primarily is peak pressure, and the required barrel volume/distance needed to make sense of the energy output. Quite likely a better representation of whats going on internally.

13" barrel Vet 25 cal 25.4 gr

17" barrel

Again the estimate in increase of energy is 100% BALLPARK without knowing all the guns data, primarily as port diameter, plenum volume and state of tune.

The top graph formula from post #48 was originally written when I believed Bob, that adiabatic expansion was not occurring, and that the common barrel volume being used was not more than 50%, where as with adiabatic expansion, it grows well over 50%...which makes a lot of more sense if you ask me.

-Matt

 

[Scotchmo]

...Riddle me this, what is my guns plateau with the following data? Since you have your own spreadsheet. Show a snap shot of the answer. Provide BOTH system energy AND muzzle energy, since you think I am conflating, which I am not, I calculate both and neither use your formula (barrel length x force = energy)

25 cal
19.5" barrel
.225" porting
2040 psi regulated set point
53 cc plenum
20.06 gr projectile
5280 ft elevation
70f ambient temp

-Matt

Note: I just realized that I entered 2050psi rather than the 2040psi that you specified. It does not make a huge difference.

I guessed at any other info that I needed beyond what you gave me. I closed the valve when the pellet_mass/air_mass ratio hit 1.6, as that seems to be what you like to use, and that is a pretty good value to use in any design. Realize that my spreadsheet was done years ago, and I know more now then I did at that time. It still serves it's purpose for what-if comparisons. Even if it does not give an exact prediction, it provides a wealth of info for my airgun designs. And designing and building my airguns takes priority over re-working the spreadsheet model these days. This model uses numerical integration. I used both rectangular and trapezoidal rules in different columns, so there are rounding errors. Enough with the excuses. Here are the screenshots from the three sheets of interest in my multi-level spreadsheet:

Input screen:

I think column V is the "system energy", though that is not something I really even look at these days. Results screen:

Distilled data = Barrel length vs Velocity, including FPE:

 

[Stubbers]

You think column V is system energy? I mean...ok?

Close on muzzle energy, but no cigar....really close.

And system energy? If 111.6 joules = 82.3 fpe.

With 51.8 fpe muzzle energy over 82.3 fpe, your spreadsheet is stating I am 63% efficient with extracting energy thermally...with 20.06 gr in 25 cal? Wow, not even remotely possible.

Here is actual, tested...and confirmed via chornograph.

https://www.researchgate.net/publication/326191398_Internal_Ballistics_of_PCP_Airguns

According to this, airguns are generally at best 25-30% efficient, and that is at best with heavier ammo...and tuned a bit from plateau. Under nominal conditions...

-Matt

 

[Scotchmo]

You think column V is system energy? I mean...ok?

Close on muzzle energy, but no cigar....really close.

And system energy? If 110 joules = 81 fpe.

With 51.8 fpe muzzle energy over 81.1 fpe, your spreadsheet is stating I am 63.8% efficient with extracting energy thermally...with 20.06 gr? Wow, not even remotely possible.

Here is actual, tested...and confirmed via chornograph.

View attachment 492731
View attachment 492732

https://www.researchgate.net/publication/326191398_Internal_Ballistics_of_PCP_Airguns

According to this, airguns are generally at best 25-30% efficient, and that is at best with heavier ammo...and tuned a bit from plateau. Under nominal conditions...

View attachment 492736

-Matt

I looked closer at the formulas in those columns, and its probably column AA, not column V. Since its been years, I don't even remember why I put in some of those columns.

The predicted velocity of 1077fps is not far off from the from your tested velocity of 1068fps. Easily within a typical velocity spread. Wow! Close enough for my purposes.

 

[Stubbers]

I looked closer at the formulas in those columns, and its probably column AA, not column V. Since its been years, I don't even remember why I put in some of those columns.

The predicted velocity of 1078fps is not far off from the from your tested velocity of 1068fps. Wow! Close enough for my purposes.

Kudos, yes, I applaud your 1078 fps findings. I use entirely different methods to calculate muzzle energy, and am generally sub 1% accurate, and in my case, sub .01%, as I calculate 1068, and obtain, 1068.

Column AA makes much more sense...and I won't argue its validity, however based on my findings its a hair off as well.

Thanks for sharing.

-Matt

 

[Stubbers]

Ehh, I thought the 300 was FPE, not Joules...

300 J = 221 FPE

51.8 FPE / 221 FPE = 23%.

Not sure what Column AB (total efficiency) is doing, but not adding up. Neither 23% or 36% efficiency with such a light pellet at plateau makes sense, especially when you consider nominal conditions use around 30% less air alone.

-Matt

 

[Stubbers]

Also note the 1.6:1 pellet to air ratio is for plateau where exceeding this ratio does not increase energy, being such a light pellet, the pellet/air ratio is far, far less...more like .9:1 or 1:1, meaning the system should eject around 20 gr of air to plateau the 20gr pellet, however, increasing pellet weight doesn't allow the system to eject more air, it only changes the ratio, hence going to 34 gr gives us a 1.6:1 ratio...for 20 gr air to 34 gr pellet. Adding more weight beyond 34 gr on my gun, produces no additional energy. 34 gr would produce 62.9 fpe or 913 fps roughly, and efficiency climbs from .85 to 1.05 fpe/ci.

Meaning my systems peak air output within the allotted time available to transfer the energy to the projectile, is 20gr. If I increase my port from .225" to .25" (full bore), that jumps from 20 grain to roughly 22.6 grain of air being ejected. Hope this makes sense?

If I were to decrease my port size to .15", the system can only eject closer to 18 gr of air before 'Elvis leaves the building'.

Tis' one of the reasons I challenged ya with a really light projectile for this test. You did great on muzzle energy, curious what happens if you change the pellet to air ratio to .9:1 or 1:1 for the 20.06 gr. Maybe your system energy (Column AA) would make more sense.

-Matt

 

[Scotchmo]

Kudos, yes, I applaud your 1078 fps findings. I use entirely different methods to calculate muzzle energy, and am generally sub 1% accurate, and in my case, sub .01%, as I calculate 1068, and obtain, 1068.

Column AA makes much more sense...and I won't argue its validity, however based on my findings its a hair off as well.

Thanks for sharing.

-Matt

Getting exact predictions is commendable. You have a good spreadsheet model. My chronograph can't even read that accurately/consistently. I changed the plenum pressure in the spreadsheet input from 2050 to 2040psi and the new prediction is 1075fps. I know what I need to do to make my spreadsheet better, but I just do not have the wherewithal to do it. At this point in time, I call it good enough.

 

[Stubbers]

Do note, the below data is accurate, both calculated and tested for plateau. The nominal tune is from tested data. As stated, when you tune nominally, you use around 30% less air, shown below with volumetric efficiency

Plateau tune - - - - - - vs - - - - - - Nominal tune

And thermal efficiency, which is in line with the above article. As you increase energy output with larger calibers that number does go down hair by hair..but more important is the system as a whole (port dia, barrel length, ect)

-Matt

 

[Stubbers]

My chronograph manufacturer states:

"guarantee an accuracy of +/- 0.25%"

-Matt

 

[Scotchmo]

Now then…about barrel length for an airgun: