Ballistics, trajectory and jerk.

[Chaffers]

Could the rate of change of accelaration (or jerk in m/s3) affect the trajectory of a projectile? If so could it be to a noticeable extent?

Given two systems where projectiles are fired by different propellants, say gasses with different rates of expansion. One reaches its maximum velocity at the end of the barrel whereas the other reaches its maximum velocity half way, or less for higher jerk, along the barrel.

Would the rate of change of acceleration of the two projectiles have any effect on their overall trajectories even though both would have the same muzzle energy, as in attain the same velocity as they exit the end of the barrel?

 

[WhyIsItSo]

Could the rate of change of accelaration (or jerk in m/s3) affect the trajectory of a projectile? If so could it be to a noticeable extent?

Given two systems where projectiles are fired by different propellants, say gasses with different rates of expansion. One reaches its maximum velocity at the end of the barrel whereas the other reaches its maximum velocity half way, or less for higher jerk, along the barrel.

Would the rate of change of acceleration of the two projectiles have any effect on their overall trajectories even though both would have the same muzzle energy, as in attain the same velocity as they exit the end of the barrel?

Your third paragraph sets a condition by which I would answer "no, their trajectories are the same". I believe it is irrelevant "how" the projectiles attain a given velocity, so since you specify they have the same velocity (and I assume you mean same vector too), then there is no difference.

The apparent assumption you make in the third paragraph is not necessarily supported by the conditions you describe in your preceding text. If we are discussing a rifle, for example, then there is rifling (the spiral grooves that impart spin on the bullet) inside the barrel. If the propellant has accelerated the bullet to the maximum it is capable of halfway up the barrel, then the bullet is going to lose inertia through friction with the barrel during the second half of this journey. For this bullet to have the same velocity exiting the barrel as one accelerating the full length of the barrel, it would have to achieve a higher velocity at the halfway point to have the same velocity as the other bullet when it exits the barrel.

Let propellant "A" represent one which accelerates the bullet the full length of the barrel, and propellant "B" be the one which accelerates for only half this trip. For both rifles to expel a bullet at the same velocity, "B" would have to produce a more violent expansion than "A" (to achieve a higher halfway velocity), but be a smaller quantity so that it expends its energy while the bullet is only halfway down the barrel.

Does that make sense?

 

[Chaffers]

Yes it makes sense...

Maybe muzzle energy was the wrong term to use as clearly propellant A has a greater energy component. The rate of change of momentum with time would be far greater for bullet A compared to B.

My thinking was that propellant A, being of higher quantity but a lower rate of expansion would give rise to a jerk which may well still be positive (as in the acceleration of the bullet is still increasing, even though at a lower rate compared with the bullets position nearer the firing chamber) as the bullet exits the barrel...

Given that snapshot in time where both bullets are about to exit the barrel propellant B's bullet would clearly be decelerating, even before air resistance took effect.

What of propellant A though which still appears to have a positive rate of change of acceleration?

I doubt the effect would last long, if indeed it has any effect, but is it possible that propellant A's bullet continues to accelerate past the end of the barrel despite not having a force directly acting upon it?

 

[rcgldr]

but is it possible that propellant A's bullet continues to accelerate past the end of the barrel despite not having a force directly acting upon it?

No, it needs a force to accelerate. The expansion of gases would apply some force to the bullet for a short distance past the end of the barrel, but there is also the air that has been compressed in the barrel just in front of the bullet that is adding to the deceleration force. I don't know how close to the end of the barrel the point of net decleration on the bullet occurs. Anyway, the difference in trajectory would be due to the diffference in net forces on the bullets in the two cases.