Barrel Length, the seldomly understood calculus

[thomasair]

Look...We could bicker about this all night but what's done is done. Dad, are you guys gonna invest or what?

 

[Stubbers]

Look...We could bicker about this all night but what's done is done. Dad, are you guys gonna invest or what?

We didn't start the fire, it was always burning since the world been turning. (time)

I wish calculating internal ballistics was as simple as barrel length (not to be confused with pellet travel distance which includes the dimension of time) x force = energy....would make all of our lives A LOT easier.

-Matt

 

[PumaCarl]

Matt, I do have to hand it to you for your consistent efforts to illustrate to everyone your thoughts on the science of airgun mechanics over the years. You have had some rather heated back and forths between Bob S., and Scott S., and others, but you always come back at it. Your Marauder build left me in the dust, there was no way I was going to do all that, but I am glad to know what's possible. Keep up the good fight. It is nice to read about the science of airgunning and not just about the latest and greatest new pieace of merch all the time. I often don't respond to posts, about things that I actually know well, because I just get tired of the repetitive nature of the same questions getting asked all the time, but you stay engaged fairly well. Kudos!

 

[cahil_2]

I feel like my head is going to explode. All I know is I can consistently hit a starling out to 50 yards.

 

[Stubbers]

Matt, I do have to hand it to you for your consistent efforts to illustrate to everyone your thoughts on the science of airgun mechanics over the years. You have had some rather heated back and forths between Bob S., and Scott S., and others, but you always come back at it. Your Marauder build left me in the dust, there was no way I was going to do all that, but I am glad to know what's possible. Keep up the good fight. It is nice to read about the science of airgunning and not just about the latest and greatest new pieace of merch all the time. I often don't respond to posts, about things that I actually know well, because I just get tired of the repetitive nature of the same questions getting asked all the time, but you stay engaged fairly well. Kudos!

Thanks man. People will often try to 'break' others logic/views by throwing curve balls (I'm highly targeted as I have targeted people such as Bob, Scott, Lloyd, and some people hold grudges/resentment).

To that, all logic can fault, hence why we use different formulas for Sub-sonic projectiles in flight vs Sonic ect, or even Ballistic Co-efficient based on the shape of a projectile. I wish physics was straightforward and streamlined in a fashion that doesn't require shifts in formulations to compensate for such variables...Another great example of 'logic models' would include ASME Div l pressure vessel safety factor of 3.5 (used for low pressure vessels) vs ASME Div ll SF of pressure vessels at 2.5 (commonly used for high pressure vessels 3000 psi+).

One great example of a time I was 'schooled', was when I claimed, given a fixed dwell, lighter pellets generally use more air than heavier pellets due to the time spent in the barrel, and decreased resistance of projectile mass...until you dry fire and experience sonic choking which chokes your ports and limits the 'mass flow rate' through said ports. Scott 'won' an argument with me there mentioning dry fires, which at first I disagreed. Albeit he didn't explain it as sonic choking. Once I learned and understood the effect and how it applied to that scenario I publicly apologized, relented, and stated he was right with the dry fire scenario due to the effects of sonic choking (although heavy enough ammo still uses less air than sonic choking, to the point if you filled your entire barrel with lead, you would use next to no air).... We all live and learn ya? I'm not always right, no one is from birth to death. I, much like you and all fellow readers, am only human. To err is human, to forgive is divine.

-Matt

 

[PumaCarl]

Thanks man. People will often try to 'break' others logic/views by throwing curve balls (I'm highly targeted as I have targeted people such as Bob, Scott, Lloyd, and some people hold grudges/resentment).

To that, all logic can fault, hence why we use different formulas for Sub-sonic projectiles in flight vs Sonic ect, or even Ballistic Co-efficient based on the shape of a projectile. I wish physics was straightforward and streamlined in a fashion that doesn't require shifts in formulations to compensate for such variables...Another great example of 'logic models' would include ASME Div l pressure vessel safety factor of 3.5 (used for low pressure vessels) vs ASME Div ll SF of pressure vessels at 2.5 (commonly used for high pressure vessels 3000 psi+).

One great example of a time I was 'schooled', was when I claimed, given a fixed dwell, lighter pellets generally use more air than heavier pellets due to the time spent in the barrel, and decreased resistance of projectile mass...until you dry fire and experience sonic choking which chokes your ports and limits the 'mass flow rate' through said ports. Scott 'won' an argument with me there mentioning dry fires, which at first I disagreed. Albeit he didn't explain it as sonic choking. Once I learned and understood the effect and how it applied to that scenario I publicly apologized, relented, and stated he was right with the dry fire scenario due to the effects of sonic choking (although heavy enough ammo still uses less air than sonic choking, to the point if you filled your entire barrel with lead, you would use next to no air).... We all live and learn ya? I'm not always right, no one is from birth to death. I, much like you and all fellow readers, am only human. To err is human, to forgive is divine.

-Matt

I have been reading, pretty much all the forums, since they all, the internet, started. I forget a lot, but I do remember a few things. I know that all the ballisticians go nuts whenever someone says something incorrectly, but I do like reading all of it. The flare ups often bring a lot of points to light that often wouldn't be talked about, so they're great too. And yes, I do remember you getting it wrong and owning it, which is why I always read what you have to say. Getting back up and shaking hands is the way things use to be done, and it worked better than shadowing banning or blocking ever will.

 

[Stubbers]

I have been reading, pretty much all the forums, since they all, the internet, started. I forget a lot, but I do remember a few things. I know that all the ballisticians go nuts whenever someone says something incorrectly, but I do like reading all of it. The flare ups often bring a lot of points to light that often wouldn't be talked about, so they're great too. And yes, I do remember you getting it wrong and owning it, which is why I always read what you have to say. Getting back up and shaking hands is the way things use to be done, and it worked better than shadowing banning or blocking ever will.

I appreciate your words very much Carl. Honestly, thanks man.

I wholeheartedly agree about having flare ups and two (or more) adults at the end of the day should be able to shake hands even if they choose to agree to disagree on a matter. If only I could share the PM's between Bob and I after I revealed my identity (was hidden prior) after assisting him (and the community, aka SS valve) with the simplified balanced valve at the GTA. It was a shock to experience. He couldn't forgive me for past hiccups, and be grateful for my willingness to still help him to say the least. Essentially he denied my contribution and stated very clearly they would have figured it out on their own without me anyway...lol. So yea I kind of doubled down on him after that and find it hard to 'let up' in debunking some of his theories, including the Lofty Goal formula which...I corrected to be far more precise with port sizes, pellet weight and a few other variables, and include barrel lengths opposed to assuming 50% barrel volume being effective. I shared some of this info with him as well, which of course he would never give me credit for nor even use moving forward, heh. I will always be proud of my contributions there, and will take them to my grave.

Ya can't re-write history (unless its his stories), especially history that has already been written.

-Matt

 

[stovepipe]

Look...We could bicker about this all night but what's done is done. Dad, are you guys gonna invest or what?

This seems like a very unprofessional comment to me.

stovepipe

 

[thomasair]

This seems like a very unprofessional comment to me.

stovepipe

It's a nonsensical reference to to the movie Stepbrothers. If you can't appreciate that, that's ok.

 

[Mr.H]

I feel like my head is going to explode. All I know is I can consistently hit a starling out to 50 yards.

Ditto. And with a 13" barrel.

 

[Stubbers]

Also note, Don Cothran valves are blow open valves with fixed dwells determined by its internals. If you are not exceeding 1.5-1.6:1 pellet:air mass ratio, it is very likely you will experience reduced energy with heavier ammo because you're not able to obtain enough dwell without modifying the internals (which cannot easily be done in the field..), on top of additional projectile break away force that is common in heavier slugs, as well as projectile to bore friction. It is rather a simple concept to understand.

So this anecdotal outlier condition that allows lighter projectiles to exceed heavier projectiles in energy production is most likely either the Cothran valve's design limitation, exceeding the thermodynamic limits of the system (1.5-1.7:1 ratio, which changes with mass flow rate) or otherwise explained by friction...and another side note, @Scotchmo's current .308 build is using the simplified balanced valve and not a Don Cothran valve, which was conveniently left out of the discussion. You can't just slap a Don Cothran valve in any airgun with any barrel length and caliber, with any projectile weight on stock internals and expect it to reach plateau.

-Matt

 

[UDABEGGER]

Forgive my Ignorance Please ! but this all sounds highly Invenereal and totally Circumcisional to an old shooter Again sorry .

 

[L.Leon]

I am not going to claim to have full understanding of the calculus behind how projectile velocity determines effective barrel length, but this thread will briefly go over what I have learned, and how pellet weight/velocity alone greatly impacts the 'effective barrel length' in a pcp (and most airguns).

Generally speaking, a well tuned airgun rifle's valve will close by the time the pellet reaches between 30-50% of the barrel length, however this applies to rifles with the common 18-24" barrel, and just happens to coincide with physics. Some may notice, a heavier pellet will produce more FPE than a lighter one. The physics here is easy to explain, as the heavier pellet moves slower, it spends more time in the barrel (pellet dwell), which allows the mass of air ejected to transfer more energy to the projectile, and likewise, if you go really light, you'll notice a huge decrease in energy, because the pellet is traveling down the bore so fast, the 'effective barrel length' is reduced, however marginal it may be, it is physics and a race of air molecule velocity versus your pellet velocity.

"Bobs lofty goal" formula from the GTA does not take this effective length into account whatsoever, hence why short barrels crush his lofty goal, because it assumes 50% barrel use, where short barrels will exceed this.

Do note, it takes a huge shift in projectile weight to drastically shift the effective barrel length, and the science behind the mass of air working on the mass of lead within the barrel is not simple. Once projectile velocity decreases below 950 fps the effect becomes more and more noticeable

The GK1 really brought to light to many, myself included, just how impactful this is, hence why a 8-9" barrel can really pack a punch, the first 9" of any airgun is commonly their peak 'effective' range for the common sub 30gr pellet, but for big bores and the like, getting up heavier and heavier in ammo (100gr+), they really begin to take advantage of much longer barrels, producing gobs of power and pushing the effective barrel distance towards much further than 9-10", meaning many heavy ammo shooters greatly benefit from 30"+ barrels (provided they desire a fairly non-violent shot cycle airguns are known for while producing gobs of power).

Below is an example of the pressure and fps/energy gradient of a very standard airgun. 22 cal, 19.5" barrel, 25 cc plenum volume, 2000 psi set point, .187" ported, shooting 18.1 gr. (also to be noted, the effective barrel length used @ 19.5"/495mm opposed to 20" @ 500mm is because we're measuring the pellets traversal distance, which is from where it sits in front of the transfer port to muzzle.)

View attachment 492362

The valves closure distance here is at 9.3" or 47.5%~ of the barrel length, why 47.5% and not 45% or 50%, well, because I said so! LOL (for demonstration and based on my tests of 19.5" barrels with nominal pellet weights)

But what happens when we compare this to a GK1 that has all identical features (and a theoretical regulated 25 cc plenum), where we only reduce its barrel length to 8.2"

View attachment 492355

Say whaaaaaat? The difference in power between the two power plants here is minimal, and its simply the calculus of air molecules chasing the pellet down the bore, where the gk1 is able to use upwards of 90-100% of its barrel length effectively, the 20" barrel uses 45%-50% to transfer energy, where the remainder is primarily reducing pressure for muzzle noise/flip. The above graphs are not 100% actual representations, rather theoretical, for demonstration only.

So what about really long barrels and heavy ammo? Well, I am not claiming to have it all figured out, and the mad men that do have it all figured out, well feel free to chime in! The below is a 36" barrel that would in theory use 35% of its barrel length, however, I have done zero tests to even begin to grasp very long barrel lengths, as I am simply fudging numbers based on theoretical peak projectile velocity and estimated pellet dwell extrapolated from that, so take the actual figures below with a grain of salt, where the above figures are fairly reasonable.

View attachment 492365


In any case, with all pcps, the moment the valve shuts, the bore experiences a sharp drop in pressure, and the gradient of this pressure is one reason that makes our pcps so delightful to shoot, from minimal muzzle noise, to minimal muzzle flip. I hope this helps paint a picture how projectile velocity greatly effects the 'effective barrel length' in pcps, where the majority of energy transfer occurs sharply in the first 10", and as the projectile outpaces air, energy transfer greatly stagnates.

This concludes my Ted Talk for the day.


-Matt

This explains why my short barrel Atomic and Pathfinder XR have been murderous on pests. Thanks for bringing “science” to my “juju”… Nicely explains to this hack why my short barrel PCPs perform so well.

 

[Stubbers]

I have a confession, I like to beat dead horses.. I must put the final nail in the coffin with the over simplified formula "barrel length * force (pressure) = energy".

If the above were true, changing gas from compressed dry air to helium would not result in an increase in velocity / energy...

This is why its better to state f=ma (force = mass*acceleration), although this is another gross oversimplification that is not 100% valid with internal ballistics. Force being energy obtained, mass being your projectile, accelerant is your gas/compressed air.

As the molecular mass of the gas becomes lighter, such as helium, the molecules acting within the same pressure are moving faster. So 2,000 psi compressed helium will produce more energy than 2,000 psi compressed dry air due to the molecules being more energized with helium, (more energy per psi) which perfectly ties into mass flow rate formulas. The pressure remains unchanged, yet the effects acting upon the projectile down the bore are.


-Matt

 

[Scotchmo]

I

I have a confession, I like to beat dead horses.. I must put the final nail in the coffin with the over simplified formula "barrel length * force (pressure) = energy".

If the above were true, changing gas from compressed dry air to helium would not result in an increase in velocity / energy...

This is why its better to state f=ma (force = mass*acceleration), although this is another gross oversimplification that is not 100% valid with internal ballistics. Force being energy obtained, mass being your projectile, accelerant is your gas/compressed air.

As the molecular mass of the gas becomes lighter, such as helium, the molecules acting within the same pressure are moving faster. So 2,000 psi compressed helium will produce more energy than 2,000 psi compressed dry air due to the molecules being more energized with helium, (more energy per psi) which perfectly ties into mass flow rate formulas. The pressure remains unchanged, yet the effects acting upon the projectile down the bore are.


-Matt

You’re still conflating that simplified formula for energy with muzzle energy. See “system energy” in my posts #7 and #10.

 

[Smitty911]

Ahhhh, Point of order...... I didn't see this little issue addressed: As the air drops in pressure it is also cooling down therefore exerting less pressure.

I'm going to go shot now, or at least later this week.

Good read though.

Smitty

 

[Scotchmo]

Ahhhh, Point of order...... I didn't see this little issue addressed: As the air drops in pressure it is also cooling down therefore exerting less pressure.

I'm going to go shot now, or at least later this week.

Good read though.

Smitty

I use adiabatic expansion in my internal ballistics spreadsheet model. So the temperature drop (and subsequent reduced pressure) is accounted for. I would guess that Stubbers does the same.

 

[beerthief]

The critical pellet to air ratio is not static, but in most airguns, commonly it is about 1.5:1 to 1.6:1 (meaning once the pellet mass becomes greater than 1.5x/1.6x of your air parcels mass, energy stagnates)

For example, in a .22 caliber ported 90% at 2040 psi, you may eject 16 gr of air to propel a 25.4 gr to the guns plateau (926 fps @ 48.4 fpe) in energy output in many cases. Adding more pellet weight only stagnates the energy, thus lower velocity (813 fps) and identical power (48.4 fpe) when shooting a 33 gr from that system. This is just an example, not stating it applies to all .22 calibers...

Or another .22 cal slug gun with a 24" barrel, .19" ports, 100 cc plenum and 3500 psi shooting 54 grain at 920 fps for 101.5 fpe, increasing this theoretical guns projectile mass to 72 grain results in 797 fps and 101.5 fpe (provided all frictional forces are equal).


Why 1.5:1? Idk, ask thermodynamics! I'm still learning

-Matt

I am enjoying this read and really it does help answer some questions i had a long time ago , but the truth is this showed me i was in fact using the wrong wording .

 

[Stubbers]

I

You’re still conflating that simplified formula for energy with muzzle energy. See “system energy” in my posts #7 and #10.

Uhh, no, I am not. You're still unable to just accept you're wrong, your formula doesn't apply in any way shape or form. You're still dodging post #14...

Barrel Length, the seldomly understood calculus

I am not going to claim to have full understanding of the calculus behind how projectile velocity determines effective barrel length, but this thread will briefly go over what I have learned, and how pellet weight and most importantly pellet velocity alone greatly impacts the 'effective barrel...

www.airgunnation.com

You tried to omit time as a dimension that matters, while contradicting yourself using the term distance which requires the dimension of time...Care to elaborate?


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

 

[Stubbers]

Ahhhh, Point of order...... I didn't see this little issue addressed: As the air drops in pressure it is also cooling down therefore exerting less pressure.

I'm going to go shot now, or at least later this week.

Good read though.

Smitty

Not relevant to the main thread premise (barrel length) as the effect is linear across the length of your bore, but I certainly am open to discuss it...as I was one of (if not the) first in the tuning community at the GTA to claim airguns experienced adiabatic expansion, to which many over there disagreed, Bob claimed its a mix of both adiabatic and isothermal (only way he could get Lloyds spreadsheet to align with his real world findings)...anyhow, that is an entirely different discussion.

-Matt