What I was thinking, and I'm at least as much of a layman on this, is that some rounds' shape could be more susceptible to tumble, or something. I wasn't thinking of it in principle as the discussion has bent towards, but in terms of the difference between NS37 and MK108. Maybe the 108 had a combo of projectile shape and too little barrel to result in more dispersion. Or maybe HTC based the difference in dispersion on historical data..
I think your last statement is probably correct. There's data to support modeling a "generic" dispersion for a given gun.
It's not a "too little barrel" issue. It really doesn't take much barrel to stabilize a round. As an example, I have a flintlock dueling pistol with a rifled 10" barrel that shoots three shots into a 1" group at 50 yards. That's about the max I've tried, due to the sights, but knowing what I do about stability there's no reason to suspect the projectile would lose stability beyond that range.
Tumble---
When it comes to stability, the actual RPM (and its resulting gyroscopic forces) of the rotating projectile is the critical factor (and it's controlled by velocity and rifling). Let's assume a round is fired at 100yds, out of a barrel that is rifled to cause the projectile to rotate once every 18". No matter what the velocity of the projectile is, the projectile will rotate twice every three feet traveled, so will rotate 200 times in its 300ft flight. Now, let's assume one shot is fired at 1000fps, while another shot is fired at 500fps. In both cases the bullet will spin 200 times before it hits the target, but... the RPM of the faster-flying bullet is twice that of the slower bullet. It hits the target quicker, so squeezes those 200 revolutions into a smaller time-period.
When it comes to shape... You're right, some shapes are more prone to tumbling, which is why the RPM is adjusted through velocity and rifling. The most stable shape for a projectile is a ball. It can be stabilized at slow velocity and with a slow rate of twist. As an example, my .54 muzzle-loader only uses a 1-70" rate of twist (the ball rotates once in 70" of travel), and doesn't require a high velocity to stabilize the ball. However, a ball is a terrible shape to resist drag and maintain velocity because it presents to much frontal (and rear) area to the slipstream, making it a very high-drag shape.
To decrease drag, bullets are elongated to present less frontal area with a similar (or even greater) mass. The problem with that is that as a projectile gets longer in relation to its diameter it gets less stable (more likely to tumble). This longer bullet will require a higher RPM to stabilize. That can be done by either increasing the rate of rifling twist in the barrel, or by increasing the velocity (more powder, or a
different powder, or both) or by increasing both.
To make it more complicated, the overall diameter of the projectile dictates the required RPM as well (i.e a .32 round ball needs to spin faster than a .54 round ball to remain stable. Same shape, but a different RPM requirement). A smaller diameter projectile needs a faster rate-of twist.
Compare those numbers to modern center-fire barrels which generally have rifling between 1-10" and 1-14", and often a much higher velocity as well (resulting in a much higher RPM.
What this eventually leads to is a "best" round for a given barrel. A round that delivers the proper velocity to result in the proper RPM for
that bullet, out of
that barrel.
Vibration-
This can actually lead to a lot of "dispersion", even without any "outside" influence from the engine, etc. When a gun is fired, it creates vibration in the barrel. This vibration will alter depending on the bullet weight and powder charge, among other things. This vibration leads to the muzzle vibrating. Imagine the muzzle vibrating left/right or up/down, or a combination of both. The timing of when the projectile leaves the muzzle is at play here. If the rounds leave while the muzzle is in vibratory transit from left to right, you'll get more dispersion. If the timing is "perfect" and the round leaves when the muzzle momentarily pauses at the right or left before reversing direction, you'll get less dispersion. It sounds crazy, but explains why one brand of factory-spec ammo will fire large, ineffective groups out of a barrel, while a different brand will fire much tighter groups. The "sound" is different, resulting in a differetn vibration, and a different time-of-exit for the projectile. Even changing the projectile within the same brand matters (or can).
And in the end, it means that once a "best" round is found, other rounds fired out of the same barrel aren't as good. This is one reason why tracer rounds may not fly like non-tracer rounds, etc... It also means that less-stringent tolerances results in greater dispersion (or can). Maybe two rounds have precisely the same amount of powder, and precisely-matched bullets. What if the
composition of the powder isn't identical? Or what if one bullet has an off-center air bubble within it? What if two barrels are made by two different manufacturer's (or by the same one) and aren't
exactly identical? Do they fire the same bullet to the same place? Not usually...
Range-
The RPM of the projectile doesn't slow at anywhere near the rate that the overall velocity of the round slows. That means that the projectile doesn't lose stability as quickly as it loses effectiveness. When it loses 1/2 of its forward speed, it has not lost 1/2 of its stability.
All those things, and more, contribute to dispersal. Most are "nit-picky" for airplane guns, so probably weren't really worried about (and probably still aren't) which just leads to more dispersal in the end...
