The limiting factor

[Stubbers]

We generally achieve, at best, about 2/3 of the most probable particle speed in a given gas at a given temp using off the shelf projectile mass.

For air at room temp, the most probable speed is around 1640 fps. 2/3 of that is 1100 fps.

At 900k or 1160F, the most probably speed is 700 m/s, or 2300 fps, which would give 1533 fps.

-Matt

 

[LayeredOgre]

We generally achieve, at best, about 2/3 of the most probable particle speed in a given gas at a given temp using off the shelf projectile mass.

For air at room temp, the most probable speed is around 1640 fps. 2/3 of that is 1100 fps.

At 900k or 1160F, the most probably speed is 700 m/s, or 2300 fps, which would give 1533 fps.

-Matt

Honestly surprised the energy conversion is that efficient. Apart from friction in the barrel obviously, is the bullet eventually “outrunning” the air? I’m guessing that’s something where tuning comes in but I’m probably missing something.

 

[Scotchmo]

We generally achieve, at best, about 2/3 of the most probable particle speed in a given gas at a given temp using off the shelf projectile mass.

For air at room temp, the most probable speed is around 1640 fps. 2/3 of that is 1100 fps.

At 900k or 1160F, the most probably speed is 700 m/s, or 2300 fps, which would give 1533 fps.

-Matt

A few years back, I derived a simple formula from Fanno flow relations to give the maximum possible air velocity in a barrel.

Vmax= SOS x sqrt((2/(k-1))+1)

That incorporates the maximum flow rate (Mach1) and maximum expansion rate. As soon as a resistance is introduced, it becomes less. So unless we had an infinitesimal projectile mass and/or an infinitely long barrel, it’s more of the limit that can’t be achieved with an airgun projectile.

For room temperature air at various pressures, this is the maximum velocity of air:

In tests, I get over 1250fps with 45gr pellets in my .308 slug gun. Over 1700fps with plastic pellets.

Neither is practical as they shed velocity at an extreme rate. Heavier and slower (subsonic) is better in an airgun.

 

[Stubbers]

Honestly surprised the energy conversion is that efficient. Apart from friction in the barrel obviously, is the bullet eventually “outrunning” the air? I’m guessing that’s something where tuning comes in but I’m probably missing something.

To obtain higher velocities, you use lower sectional density projectiles which do generally out pace the air, while heavier projectiles don't, but will absorb more ke which result in more muzzle energy at the cost of lower velocities.

If you use a light enough projectile, you can in theory come close to the RMS velocity of molecules at that particular set of conditions for any given gas.

-Matt

 

[Stubbers]

A few years back, I derived a simple formula from Fanno flow relations to give the maximum possible air velocity in a barrel.

Vmax= SOS x sqrt((2/(k-1))+1)

That incorporates the maximum flow rate (Mach1) and maximum expansion rate. As soon as a resistance is introduced, it becomes less. So unless we had an infinitesimal projectile mass and/or an infinitely long barrel, it’s more of the limit that can’t be achieved with an airgun projectile.

For room temperature air at various pressures, this is the maximum velocity of air:

View attachment 493921

In tests, I get over 1250fps with 45gr pellets in my .308 slug gun. Over 1700fps with plastic pellets.

Neither is practical as they shed velocity at an extreme rate. Heavier and slower (subsonic) is better in an airgun.

I kept things relatively practical for the above figures, I am well aware of hitting 2400~ fps with plastic pellets. Most of us aren't launching any off the shelf projectiles beyond 1100 fps for obvious ballistic reasons...

-Matt

 

[Stubbers]

1250 fps is inside the trans-sonic region of flight which would not be stable, hence I used 1100 fps as a cap or 'limiting factor' for air at room temperature, and showed the potential increase in velocity of a projectile with equal sectional density if you were to super heat the air to 440F at the same pressure.

-Matt

 

[Scotchmo]

To obtain higher velocities, you use lower sectional density projectiles which do generally out pace the air, while heavier projectiles don't, but will absorb more ke which result in more muzzle energy at the cost of lower velocities.

If you use a light enough projectile, you can in theory come close to the RMS velocity of molecules at that particular set of conditions for any given gas.

-Matt

RMS of 70 F air:

3000psi = 1900fps
4500psi = 2130fps

RMS might (note: I don’t really know) limit the expansion rate (the degree to which we “outpace” the air). Flow rate (pace of the air) allows the relative point from where expansion is occurring to be in motion down the barrel. So, in theory, even higher velocity.

It is possible, but not practical.

 

[Stubbers]

RMS of 70 F air:

3000psi = 1900fps
4500psi = 2130fps

RMS is going to limit the expansion rate (the degree to which we “outpace” the air). Flow rate (pace of the air) allows the relative point from where expansion is occurring to be in motion down the barrel. So, in theory, even higher velocity.

It is possible, but not practical.

I feel like we're having 2 different discussions, you're discussing theoreticals infinitesimal projectile mass and infinitely long barrel lengths/volumes which isn't possible to achieve, while I am trying to keep things practical within the scope of the thread 'limiting factors'.

As I said, achieving RMS of air is 'in theory possible' as a footnote, which I followed up with why its not practical ballistically more than anything.

-Matt

 

[Stubbers]

To retain ballistic integrity, you want to avoid the Trans-sonic region of flight, which depends on the projectiles critical mach number, but for general purposes it can be said that Mach 1 to Mach 1.2 or between 1125-1350 fps is a velocity in flight we don't want our projectiles to experience, anywhere between the muzzle and target, due to destabilization.

To obtain speeds above this region on air, due to the limiting natures discussed thus far, you'll have to sacrifice sectional density that becomes detrimental to the ballistic co-efficient profile (which is out performed ballistically and kinetically by projectiles with higher SD at lower velocities), or run barrel lengths that are, for the average user, incredibly cumbersome. Infinitely long barrels don't exist in nature, and for most, pushing barrel lengths beyond 24", and for others beyond 36" is really not practical. Could we theorize or discuss limits with 120" long barrels, sure, but imo that is just an unnecessary flex that doesn't apply to the reality of airguns we use today.


-Matt

 

[Stubbers]

For practical purposes, one limiting factor is the projectile to air mass ratio, which goes up with increased mass air flow rate. However for most pcp's that is around 1.5:1 or 1.6:1, while others could push upwards of 1:9:1 (full bore, incredibly high pressure, using helium, ect)

Mass air flow rate cannot be simplified, however for a system that can eject 100 grains of meaningful air before the projectile outpaces the air being ejected, you're looking at 160 grain projectile being rather optimal for that system. Pushing above and beyond that ratio will sacrifice muzzle velocity and in most cases will likely not produce more energy. Shooting below that ratio will sacrifice ballistic co-efficient and muzzle energy for more muzzle velocity.

It would take a huge leap forward in technology to push projectiles beyond the trans-sonic region during their entire flight on air while maintaining or exceeding the above optimal projectile to air ratio. The only way I see feasible, would be with super heated air.

-Matt

 

[Scotchmo]

I feel like we're having 2 different discussions, you're discussing theoreticals infinitesimal projectile mass and infinitely long barrel lengths/volumes which isn't possible to achieve, while I am trying to keep things practical within the scope of the thread 'limiting factors'.

As I said, achieving RMS of air is 'in theory possible' as a footnote, which I followed up with why its not practical ballistically more than anything.

-Matt

“The limiting factor” under discussion can be either theoretical or practical. It’s fun to discuss the theoretical limits. And it can be a reality check to keep our goals within practical limits. As far as my builds, I design according to what I consider to be the practical limits. The practical limit is different for different purposes. But the theoretical limit applies to all instances.

The jury is still out on going above 1100fps. Usually no good enough reason to do so in a practical airgun. There are some benefits to utilizing the Mach trimming affect in that speed range. But so far for me, better to go a little slower (<1080fps) and work on the mechanics/pneumatics to control the velocity spread. I’m kinda settling in on 1060fps for my ELR air rifles.

Barrels longer than 36” can be a “practical” solution for ELR with airguns. I think the new BIntac MCAR also has a barrel longer than that.

 

[Just Zack 2]

“The limiting factor” under discussion can be either theoretical or practical. It’s fun to discuss the theoretical limits. And it can be a reality check to keep our goals within practical limits. As far as my builds, I design according to what I consider to be the practical limits. The practical limit is different for different purposes. But the theoretical limit applies to all instances.

The jury is still out on going above 1100fps. Usually no good enough reason to do so in a practical airgun. There are some benefits to utilizing the Mach trimming affect in that speed range. But so far for me, better to go a little slower (<1080fps) and work on the mechanics/pneumatics to control the velocity spread. I’m kinda settling in on 1060fps for my ELR air rifles.

Barrels longer than 36” can be a “practical” solution for ELR with airguns. I think the new BIntac MCAR also has a barrel longer than that.

Maybe off topic to some degree, but I'd like to see more real world testing of airgun projectiles (slugs) at supersonic velocities. I understand the wind might be more problematic at 1100fps and higher, but there may be some benefit to flatter trajectory in some instances. The saying we've all heard of "it'll tumble" in reference to shooting barely supersonic... I don't fully buy into. Yes, some projectiles may tumble, some may group poorly and some can remain stable enough for decent results at range... As long as there's no wind. So far, I've only seen one video in which someone set out to purposely shoot supersonic, by U.A. I believe... Which was awesome. Seemed it was a "what if" turned into a "show me", then "we got to post this on YT".

Yes, there are more good reasons to stay subsonic than to go supersonic. I get it... But what if...

 

[Stubbers]

“The limiting factor” under discussion can be either theoretical or practical. It’s fun to discuss the theoretical limits. And it can be a reality check to keep our goals within practical limits. As far as my builds, I design according to what I consider to be the practical limits. The practical limit is different for different purposes. But the theoretical limit applies to all instances.

The jury is still out on going above 1100fps. Usually no good enough reason to do so in a practical airgun. There are some benefits to utilizing the Mach trimming affect in that speed range. But so far for me, better to go a little slower (<1080fps) and work on the mechanics/pneumatics to control the velocity spread. I’m kinda settling in on 1060fps for my ELR air rifles.

Barrels longer than 36” can be a “practical” solution for ELR with airguns. I think the new BIntac MCAR also has a barrel longer than that.

I think it just muddy's the water when you include theoretical circumstances that aren't applicable or ones that don't see the forest for the trees so to speak.

You must consider the practical limits of mass flow rate, effective barrel volume and ballistics as a whole to understand limiting factors of airguns, ya?

Plus, infinitely long barrels or infinitesimal projectiles aren't even theoretical imo, they're just not even possible.

For the most part, I am trying to limit my discussion on limiting factors with what is readily available, off the shelf, from projectile mass to barrel length.

Sure, it can be fun to stretch our imagination, but realistically it's not applied physics which would help us understand what is needed to make tangible advancements with airguns allowing them to push velocities similarly to firearms.

-Matt

 

[Stubbers]

Maybe off topic to some degree, but I'd like to see more real world testing of airgun projectiles (slugs) at supersonic velocities. I understand the wind might be more problematic at 1100fps and higher, but there may be some benefit to flatter trajectory in some instances. The saying we've all heard of "it'll tumble" in reference to shooting barely supersonic... I don't fully buy into. Yes, some projectiles may tumble, some may group poorly and some can remain stable enough for decent results at range... As long as there's no wind. So far, I've only seen one video in which someone set out to purposely shoot supersonic, by U.A. I believe... Which was awesome. Seemed it was a "what if" turned into a "show me", then "we got to post this on YT".

Yes, there are more good reasons to stay subsonic than to go supersonic. I get it... But what if...

This is a valid thought, I am not a ballistician by any means, but I do understand that the shape of projectiles greatly effects their critical mach number, to which they are unstable within a certain velocity region. Diabolo pellets for example destabilize at much lower velocities than most common slug shapes. Could perhaps a specific shape push that region upwards to where 1100-1200 fps flight is stable, perhaps. Not a question I can answer for now at least, but certainly one to be pondered.

-Matt

 

[beerthief]

Very loaded question, depends on sectional density of your projectile. However, for practical purposes...

300k / room temp (80f) nets 1000-1100 fps at most in most calibers for most readily available off the shelf projectiles
500k would net closer to 1300-1400 fps

-Matt

so ....... if i have a solar cell to charge a capacitor connected to a heating transfer port , i can boost my wimpy 1000 FPS rifle into a super charged 1400 FPS gun ? of course this would be banned in California because a heating element that close to ones eye would cause fried eye syndrome.

Just some humor injected into your AM

 

[Stubbers]

so ....... if i have a solar cell to charge a capacitor connected to a heating transfer port , i can boost my wimpy 1000 FPS rifle into a super charged 1400 FPS gun ? of course this would be banned in California because a heating element that close to ones eye would cause fried eye syndrome.

Just some humor injected into your AM

Haha, so long as you don't melt the lead you're shooting, your poppet, o-rings, or any other plastic parts within the gun.

Which brings to thought the fallacy that a few airgun manufacturers claim "all metal no plastic"......hmmmphf! Lol, yep looking at you JTS.

-Matt

 

[3Crows]

Newton's Second Law:

F = M X A

And it all seems like a lot of effort to duplicate this:



There is always an answer, we just might not like it.

 

[Stubbers]

Touching base on the limit of effective barrel length, which has a limiting factor due to the limits of mass air flow.

The only way to exceed a certain barrel length while still transferring energy from air to projectile with a given gas at a given pressure per a given port diameter, would be multi point/port injection. A singular port is what severely limits barrel length, however timing the ejections of air from a secondary or multiple ports somewhere further down the barrel would be...very tricky given you'd be attempting to do such within a very small window of time, roughly, sub 1ms, ideally measured in micro seconds.

From that, you could extend your barrel length, until your projectile velocity peaks at what air could ever provide, regardless of SD, propelling a projectile faster than what a single port could due to the limits of mass flow rates through a single port and the subsequent decay of fuel so to speak.

Chew on that!

-Matt

 

[Sawney Bean]

so ....... if i have a solar cell to charge a capacitor connected to a heating transfer port , i can boost my wimpy 1000 FPS rifle into a super charged 1400 FPS gun ? of course this would be banned in California because a heating element that close to ones eye would cause fried eye syndrome.

Just some humor injected into your AM

This actually sounds somewhat feasible, only instead of heating the transfer port, why not heat the reservoir or the plenum?

The speed of sound goes up about 1 fps per degree Fahrenheit, so it probably wouldn't be worth it.

 

[Stubbers]

This actually sounds somewhat feasible, only instead of heating the transfer port, why not heat the reservoir or the plenum?

The speed of sound goes up about 1 fps per degree Fahrenheit, so it probably wouldn't be worth it.

+300 Fahrenheit later you get a potential 300 fps boost!

Issue is your pressure would increase, so you would have to backwards calculate to have a starting pressure that would yield the ideal shot pressure once heated up 300F higher...

Then, you have to worry about o-rings, poppets, and what not melting.

-Matt