Pressure going to zero (and by extension force, acceleration) means the SLOPE of velocity goes to zero. Velocity would flatten.Oh, and if the acceleration were constant, you will find the pressure-time curve would have to look like this:
Actually, it does not require calculus, even if you want numbers (quantitative information), if you have a plot of the pressure time curve.
You break the P-T curve down into small time intervals, say 0.01 msec, so for each point on the P-T curve you can calculate:
Average Pressure (from time tx to time tx+1) x area (constant) = Average Force (over time interval tx+1)
(Force - friction*) x mass (constant) = acceleration (over time interval tx+1)
And with acceleration and given a small time interval you can calculate delta V and thus delta S over the time interval, and the sum of all the delta V = total velocity and delta S = total travel
The acceleration is the slope of the velocity curve, the closer the line is to vertical, the higher the acceleration. (Qualitatively, it is shaped like the pressure curve)
View attachment 1087111
______________
* found by simply pushing a bullet down the barrel, you can measure the engraving force too, so the friction is a function of travel S.
Yes, I do.As you probably realize, that is the numerical method approximation of integral calculus.
You can integrate with distance on the X axis to get work, or you can integrate with time on the X axis to get kinetic energy. If you know bullet mass, you can work out MV either way.
Re-read my comment. Nowhere did I say that acceleration was linear, only that it continues. I agree that powder type, as well as bullet weight, affect the rate of acceleration, but as long as there is gas pressure behind the bullet in the barrel, it will continue to accelerate until it leaves the muzzle.
Generally speaking, you are correct, but the 80% is a bit high for rifles. The first 2 inches of a 16 inch barrel accounts for just under 50% of the velocity.The statement you originally commented on was "You'll find that acceleration is almost all accomplished in the first couple inches," to which you said "The "almost" doesn't quite qualify your statement. If that were true, barrel length would make no difference to muzzle velocity, and as we all know, longer barrel = greater MV (to a practical maximum) for a given cartridge."
My response was that the "almost all" was a valid qualification, because most of the cartridge's ultimate muzzle velocity is obtained within the first couple of inches of barrel travel, with the remainder of the travel down the bullet adding much less to the muzzle velocity.
Depending on bullet, powder, and barrel length, the first couple of inches of barrel travel can provide upwards of 80% of the bullet's ultimate muzzle velocity, whereas the final 14 inches of a 16 inch barrel provides an additional 20%.
To me, 80% qualifies as "almost all."
Umm, isn’t ms time?
My apologies, Archie. It was not my intent to insult you.Tell you what: If you don't like this, make up your own plan. Just ignore me.
Thank you very much for the very thorough research and the inclusion of the various graphs. I concede that 2" = 80% is inaccurate, but in fairness it wasn't meant to be an exact metric.Generally speaking, you are correct, but the 80% is a bit high for rifles. The first 2 inches of a 16 inch barrel accounts for just under 50% of the velocity.
View attachment 1087170
I would say that it is typical that the first 20% of travel accounts for just under 50% of the velocity, approximately.
View attachment 1087171
Even for pistol cartridges in pistol length barrels your 80% is a a little high, 5/8 being a good approximation
View attachment 1087172
I remember reading somewhere years ago that barrel life is measured in minutes, with 10 minutes being about the max./QUOTE]
I think the barrel life would be measured in seconds. .00123 dwell time per round x 10,000 .30-06 rounds would be about 12 seconds
One variable you've all missed is pressure curve from the burning powder. If it peaks and falls before the bullet leaves the barrel, then velocity will start to fall. For any calculations to be valid, that peak must occur just as the bullet is at the muzzle.
The velocity will not fall, the rate at which it increases (acceleration) with decrease, but the velocity will always increase provided the force from the gas pressure behind the bullet is more than the friction.One variable you've all missed is pressure curve from the burning powder. If it peaks and falls before the bullet leaves the barrel, then velocity will start to fall. For any calculations to be valid, that peak must occur just as the bullet is at the muzzle.
Shoot indoors?All this wonderful minds and calculations , and yet we still miss the target, due to the one variable we have no control...wind.
Still enough time to buck and throw the shot off.