Let's talk about that expanding sphere of gas.

I understand that the propellant creates a sphere of expanding gas inside the chamber, and the bullet moves and creates a vector of least resistance. Fine.

The bullet moves out the barrel, and as soon as it leaves the bore, it stops accelerating. Also fine.

Therefore, the longer the bullet remains in the barrel, the longer it accelerates, and that's why rifle create higher muzzle velocities than handguns. Third fine.

That tells me that the sphere of expanding gas has a minimum radius that is greater than the length of the barrel.

So here's the question: (obviously, depending on the brand and type of the propellant) how big can that radius be?

Rifle powders need a sphere with a diameter of at least forty inches, but how big would it get? How big could it get?

If you had a theoretical rifle barrel that was eight feet long, could you create a sphere of expanding gas that is really sixteen feet across and still expanding?

Now it seems to me that there's some hanky-panky going on with the numbers in that radius-- the gas can only expand in one direction, so you don't need to fill the whole sphere. You just need to fill the barrel. So it's not a straight up calculation for "this powder will generate a sphere this size for this many grains".

I suppose another way to ask this question is what is the longest barrel you've ever fired? (Yes, I actually mean you, personally, not some anecdote you got from a guy at the range who was talking about his girl friend's ex-cellmate's best friend and her custom AR with the eighty-two inch barrel. You, personally, with your own two hands, putting at least one round in the berm.)

I'm stumbling around, trying to ask the extremely intelligent (I promise) question that's been keeping me awake, but I don't have the math training to even know the vocabulary to ask the question correctly. So if you catch a glimpse of my question as it wanders aimlessly through my post, hidden and invisible as it is, try to explain either the answer or the vocabulary so I can ask it without sounding like a rambling idiot.

Or, you know, don't. Either way, we're running out of stuffing. And I love stuffing. As far as I'm concerned, the turkey is there to go with the stuffing.

Carry on.

This looks like a fun read

/https://apps.dtic.mil/sti/pdfs/ADA590866.pdf

Leave it to the Army for a pdf page to be intentionally left blank.

For me, the physics of ballistics is one of the more appealing parts of shooting. Kinesthetics aside.

A gun barrel - rifle, handgun, shotgun, doesn't matter - is not spherical, it's cylindrical. So there's a fundamental difference between a cartridge and a grenade. Gas expansion from an unconfined explosion increases as a cube of radius - 4/3 pi r^3 - but if we assume an inelastic chamber and barrel, expansion increases linearly in one direction. The equation here is pi r^2 h, but r is not the same between the two equations! In the first, it is distance from the center of the explosion, equivalent to h in the second equation. For a gun barrel, r is 1/2 the bore diameter, and should be constant outside of a blunderbuss.

Point of this being, the pressure in a gun barrel decreases linearly, not as a cube. It is opposed not just by atmospheric pressure, but also by the compression of air in the barrel. From a theoretical perspective, there will be positive force imparted on the bullet by propellant until the opposing pressure is equal or greater. Air compression shouldn't play a major role for subsonic projectiles in short barrels, like .45 ACP in a 1911, but may be more important for high-velocity smallbore rifles. We also need to account for friction along the barrel - the latter is a function of surface area and coefficient of friction, which depends on lubrication.

I prefer a more empirical approach. Are you familiar with BBTI? They did a lot of experimental work looking at the role of barrel length in controlling bullet velocity across a range of cartridges, running the gauntlet from .22 to .223, using sawed-off barrels in a T/C Encore. They're friends of the LGC.
http://www.ballisticsbytheinch.com/

One of the things from their data is the recognition that pistol cartridges tend to have very flat velocity / barrel length curves - it doesn't matter a whole lot for 9mm Luger or .45 ACP. On the other hand, magnums and .22 LR show much more dramatic sensitivity to short barrel lengths. The bullet energy graphs for each cartridge are informative here. However, it is useful to remember a few caveats. They also tested real life firearms spanning a range of barrel lengths for each cartridge, and you'll see some variability outside of barrel length. To pick an outrageous example, .22 Magnum out of a Rossi Circuit Judge - despite the increased barrel length, it scores like a handgun. One part cylinder gap, one part poor fit at the forcing cone. One thing I take from a close look at their real-gun data is that gas escape from the cylinder gap is an important limitation to driving force in revolvers, and increasingly limits the increase in velocity for higher-pressure magnum rounds in longer barrels. Magnums do really well in leverguns, but a long-barreled revolver will shoot more like a snubby than a carbine. By contrast, snubbies overperform BBTI barrel-length data because the chamber length should be added to the barrel if you want to compare them to a bottom-feeder. For the longest barrels, they often find velocity leveling off or dropping - friction within the barrel balances out the pressure driving the bullet, so there is an optimum barrel length for any given cartridge.

Velocity is only one part of the equation - mass and caliber are also important, depending on what your objectives are.

Kinesthetics aside.

Do you mean how recoil affects the shooter? Sometimes I think my .223 just makes noise and shakes a bit, but my .300 Win. (barley 7lb. w/scope), is kin to Mike Tyson.

My appreciation of rifle ballistics is mostly academic.

My academic appreciation of handgun ballistics is greatly enhanced by the way a grip transfers momentum to my hands.

When I first started reloading, the worst thing that could have happened, happened.

I followed all the directions in the ABC's of Reloading, very carefully, half afraid I was going to burn our house down, and went to the range.

Careful, aimed shots, all in the black. I looked at the target, and nodded to myself. I had this reloading stuff wired. It's not as difficult as everyone makes out.

Then I noticed a flyer.

One shot, way out in right field, at about two o'clock and a foot and a half from the bull. (I exaggerate. Slightly.)

So...

These all hit the black. What's wrong with this one?

And I've been chasing that flyer, trying to get ALL of the holes in the black, for twenty years.

Ylatkit wrote: Mon Nov 28, 2022 6:47 pm When I first started reloading, the worst thing that could have happened, happened.

I followed all the directions in the ABC's of Reloading, very carefully, half afraid I was going to burn our house down, and went to the range.

Careful, aimed shots, all in the black. I looked at the target, and nodded to myself. I had this reloading stuff wired. It's not as difficult as everyone makes out.

Then I noticed a flyer.

One shot, way out in right field, at about two o'clock and a foot and a half from the bull. (I exaggerate. Slightly.)

So...

These all hit the black. What's wrong with this one?

And I've been chasing that flyer, trying to get ALL of the holes in the black, for twenty years.

I’m just happy when the bullet leaves the barrel.

Worst accuracy I ever had was with handloads assembled with bullets cast using these (this?) handle(s), The moulds were the same, the alloy the same, the casting furnace, lube, sizing die, guns, idiot behind the whole operation. All the same, save these handles. Flyer is a good term for what the heck just happened? Like finding the number of licks it takes to get to the center of a Tootsie Roll Pop, the World may never know.