Barrel Length, the seldomly understood calculus

Stubbers

Member
Mar 18, 2023
2,613
2,883
41
Colorado
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 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.)

1725037057474.png


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"

1725036622193.png


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.

1725037173532.png



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
 
Last edited:
… 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.



-Matt

That is not always true. It can be true but also for some other reasons you have yet to address.

For FPE, It’s not the time, per se, it’s the distance the projectile travels down the barrel under full pressure. Force x distance = energy. Pressure x volume = energy.

Some valve designs tend to dwell for a nearly fixed amount of time. There are instances where switching to a lighter projectile can result in more FPE. Where the heavier projectile moves only 30% of the way down the barrel in the .003 seconds of dwell, the lighter projectile might move 60% of the way down the barrel in the same .003 seconds. The lighter projectile travels over a larger barrel distance and volume. Subject to full pressure while the valve remains open. So higher FPE.
 
That is not always true. It can be true but also for some other reasons you have yet to address.

For FPE, It’s not the time, per se, it’s the distance the projectile travels down the barrel under full pressure. Force x distance = energy. Pressure x volume = energy.

Some valve designs tend to dwell for a nearly fixed amount of time. There are instances where switching to a lighter projectile can result in more FPE. Where the heavier projectile moves only 30% of the way down the barrel in the .003 seconds of dwell, the lighter projectile might move 60% of the way down the barrel in the same .003 seconds. The lighter projectile travels over a larger barrel distance and volume. Subject to full pressure while the valve remains open. So higher FPE.

Interesting, I'm unaware of instances where lighter projectiles produce higher fpe in nominal conditions, never experienced it personally, as I said the above applies for sub 30 gr projectiles. If you put a 1lb projectile in your bore, its quite obvious you won't increase FPE compared to 1/4 lb slug for most big bores...as I mentioned in another thread, any logic can be broken if you take it to an extreme, and for big bores 30g+ projectiles this is exactly what you're describing.

Also, its not as simple as force x distance = energy, and pressure x volume = energy.

Newtonian mechanics don't quite apply to internal ballistics for f=ma. You'd be better off with Lagrangian mechanics.

-Matt
 
Last edited:
Interesting, I'm unaware of instances where lighter projectiles produce higher fpe in nominal conditions, never experienced it personally, as I said the above applies for sub 30 gr projectiles. If you put a 1lb projectile in your bore, its quite obvious you won't increase FPE compared to 1/4 lb slug for big bores...as I mentioned in another thread, any logic can be broken if you take it to an extreme, and for big bores 30g+ projectiles this is exactly what you're describing.

Also, its not as simple as force x distance = energy, and pressure x volume = energy.

Newtonian mechanics don't quite apply to internal ballistics for f=ma. You'd be better off with Lagrangian mechanics.

-Matt

When dealing with a fixed dwell time, the same applies to light pellet guns as well as heavy slug guns. It just a matter of scale.

…force x distance = energy, and pressure x volume = energy….

That is the “system energy”. Merely to show that with a fixed dwell time, there is a higher system energy with the lighter projectile. I know there is more to it than that when getting to muzzle energy.
 
When dealing with a fixed dwell time, the same applies to light pellet guns as well as heavy slug guns. It just a matter of scale.



That is the “system energy”. Merely to show that with a fixed dwell time, there is a higher system energy with the lighter projectile. I know there is more to it than that when getting to muzzle energy.

You're imposing 'fixed dwell time' experience with your electronic airgun, where I never did. Of course fixed dwell times greatly effect this...you need more dwell on heavier projectiles because they're...moving...slower.

-Matt
 
  • Like
Reactions: Scotchmo
The primary limitations that will break this 'logic' are extremely heavy projectiles that overload the system with either mass (due to limitation on the mass of air your ports/system can eject, primarily being pressure and caliber specific when ported to full bore...) or friction, and extremely light projectiles that see diminishing returns as you approach the RMS (average velocity) of air molecules in the system.

It would be absurd to believe you could simply keep adding weight to projectiles and infinitely increase the energy output of a system / airgun...

Hence why above I said sub 30 gr just to eradicate this attempt at finding a flaw within such logic. I suppose I should have been more thorough...

-Matt
 
Last edited:
A logical model can handle the extremes.

A couple of other reasons why the lighter projectile will usually (but not always) yield a lower muzzle energy, even with a fixed dwell time:

Port size vs velocity:
Small ports become choked at a certain velocity. With a light projectile, we are operating close to, or exceeding that choke velocity. That restriction reduces the “system energy”, since the mass flow rate can be substantially less with a sonic port.

Air mass vs projectile mass:
The “system energy” must accelerate the air mass as well as the projectile mass. With a lighter projectile, a lower percentage of the available “system energy” ends up in the projectile. Ignoring other losses for this simplified equation,
KE(projectile) + KE(air) = system energy
 
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 :p

-Matt
 
Last edited:
  • Like
Reactions: beerthief
A logical model can handle the extremes.

A couple of other reasons why the lighter projectile will usually (but not always) yield a lower muzzle energy, even with a fixed dwell time:

Port size vs velocity:
Small ports become choked at a certain velocity. With a light projectile, we are operating close to, or exceeding that choke velocity. That restriction reduces the “system energy”, since the mass flow rate can be substantially less with a sonic port.

Air mass vs projectile mass:
The “system energy” must accelerate the air mass as well as the projectile mass. With a lighter projectile, a lower percentage of the available “system energy” ends up in the projectile. Ignoring other losses for this simplified equation,
KE(projectile) + KE(air) = system energy

Incorrect, most logical model cannot handle extremes (Bobs Lofty goal formula and short (or long) barrels is a perfect example), hence why Newtonian mechanics cannot ever be applied to quantum mechanics or many others...Is Newtonian mechanics not a logical model? I explained in depth in the post above (and below) yours what can 'break' the logic...

-Matt
 
Also, to touch base on the sentiment @Scotchmo brought up with "Some valve designs tend to dwell for a nearly fixed amount of time.".


This is far from the truth, unless its a blow open valve such as the Cothran valve, which is just poor design...such valves are hardly tunable via hammer strike, and must be tuned via raising or lowering pressure, or by restricting the transfer path. Such is why Bob over at the GTA asked the community years ago for assistance on figuring out the 'Simplified Balance Valve', to which I obliged, which is essentially a corrected Cothran valve.

The limit on dwell for most valves is the hammer energy/momentum, and the limited travel distance of the poppet, to where you start hitting the back of the valve, if you increase both hammer energy and momentum along with poppet travel, you can keep increasing your valves dwell. Likewise, all well designed valves can be 'blipped' for minimal dwell, and in some designs can be held open for dwell so long you will empty your entire tank.

-Matt
 
Incorrect, most logical model cannot handle extremes (Bobs Lofty goal formula and short (or long) barrels is a perfect example), …

-Matt
Bob’s lofty goal formula is not a logical model in any sense. It’s mostly an efficiency or FPE goal.

…Also, to touch base on the sentiment @Scotchmo brought up with "Some valve designs tend to dwell for a nearly fixed amount of time.".

This is far from the truth, unless its a blow open valve such as the Cothran valve, which is just poor design…

The Cothran valve is a good example where lighter projectiles can be higher energy, but you won’t see it unless you have a long enough barrel. Cothran valves have been used on the guns that won the last three RMAC long range matches. So they have a specific purpose (high energy) for which they are well suited. So not a poor design in that light. My current build is a little more extreme so I’m using my own design of a “simplified balanced valve”. Though it has most of the same attributes as a Cothran valve, but with a higher mass flow rate potential.

We could spend a lot of time discussing when these different instances are likely to occur, but the bottom line to my original post in this thread: It’s not how much time the projectile spends under pressure, it’s the distance that the projectile travels down the barrel under pressure.
 
Bob’s lofty goal formula is not a logical model in any sense. It’s mostly an efficiency or FPE goal.



The Cothran valve is a good example where lighter projectiles can be higher energy, but you won’t see it unless you have a long enough barrel. Cothran valves have been used on the guns that won the last three RMAC long range matches. So they have a specific purpose (high energy) for which they are well suited. So not a poor design in that light. My current build is a little more extreme so I’m using my own design of a “simplified balanced valve”. Though it has most of the same attributes as a Cothran valve, but with a higher mass flow rate potential.

We could spend a lot of time discussing when these different instances are likely to occur, but the bottom line to my original post in this thread: It’s not how much time the projectile spends under pressure, it’s the distance that the projectile travels down the barrel under pressure.

Incorrect. I already debunked that to great length because the energy (or velocity) being transferred is non-linear and your sentiment would imply linearity. If the dimension of time doesn't matter to you, so be it...

I also debunked your theory on logical models don't break under extremes, but you dodge that as well from post #14. Touch base with that and we can continue the discussion, otherwise it's moot and we're just repeating ourselves.

-Matt
 
Last edited:
Or in other words, Bobs Lofty Goal formula would be 100% accurate for short barrels as it is long..if as @Scotchmo claims its simply distance x force = energy.

This is the entire premise of this post. Distance traveled requires time. If time didn't matter, and it was simply distance x force = energy, then a 19.5" barrel will over double the power output of a 8.2" barrel given you double the valve dwell (time) to which you expose the projectile to compressed air. If you remove time from all variables, you end up with 0 energy output. Pellet dwell (time again) is 100% tied into how much energy can be transferred, longer barrels allow more pellet dwell, however, the calculus is that its non-linear due to the limitations of the porting that feeds this system (mass flow rate), as well as the speed (and energy) of air molecules decaying as they bounce off the base of the projectile, transferring said speed and energy...
 
Last edited: