Cannon Length: Why does it matter?

[Flash Money Jr]

Aiight, so I pose this question: does the length of a cannon change the distance the projectile is able to go? Essentially, say we have a cannon eight feet long, and a cannon twelve feet long; the projectiles in both have the same mass and, thus, the same gravitational pull. Why, then, would one go further than the other? I can't be sure my results were entirely accurate, but I found that the projectile with the longer barrel went further than the one with the shorter barrel.

Now, though this was inspired by an assignment, it wasn't actually derived from it; more an idea that I need to figure out. I'm trying to relate the impulse/momentum change theory where Impulse=m*deltaV . Impulse=force*time. Now, here's my problem: if the mass is the same for each of the cannon balls, and the same air density resides in both barrels at the time of the blast- how does one differ from the other? Technically, the friction between the interior surface of the long cannon and the cannon balls should decrease the overall change in velocity which eventually translates into impulse and distance and all that jazz. Yet the projectile from that cannon still travels further. The only other reasoning I've developed is that the cannon with the longer barrel also has a greater period of time to accelerate. This is due to the longer period of time that the particles being pushed to accelerate the cannon ball are allowed to hit the cannon ball as it makes its way to the exit for a longer period of time. Thus, the cannon with the shorter barrel, in coherence with this theory, would travel a shorter distance because it's muzzle velocity was less than that of the other; the particles pushing it weren't confined for the same amount of time and dispersed earlier. Now, that would translate into this then: if Impulse equals force*time, and the force behind each of the cannon balls was the same, then the amount of time that the force was acting on it was changed by this 'continuous particle propulsion' idea. Am I totally off, or does the impulse/momentum change theorem apply in another way? Or is it a totally different theory in play? I hope my explanation was somewhat understandable.

 

[rcgldr]

A longer cannon is needed to effectively use all the pressure generated by the explosion of the charge. With a smaller charge, a shorter cannon will suffice. With a larger charge, a longer cannon is needed. The mass of the cannon, versus the mass of the projectile also helps affect the amount of recoil.

 

[Astronuc]

if the mass is the same for each of the cannon balls, and the same air density resides in both barrels at the time of the blast- how does one differ from the other?

Let the acceleration in the cannon bore be 'a', then equation of motion which relates kinetic energy to the work done by the gas pressure is :

v² = 2 a d,

where v is the velocity at exit (when the pressure drops and consequently the acceleration a stops) and 'd' is the distance over which the mass accelerates. So a longer cannon barrel enables higher muzzle velocity (at exit).

As Jeff Reid indicated, one could use more charge in the longer cannon. A greater barrel thickness is required for higher pressures due to greater charge.

 

[wysard]

Yep, that' physics for ya

Astronuc hit the nail on the head.

Just bear in mind that F=m*a

The longer barrel makes better use of the theoretical acceleration in the barrel. The downside is planning to ensure that the barrel length is not so long that friction of the projectile in the barrel does not retard velocity. That is why most projectiles leave the barrel with some percentage of unspent gas released to the environment.

At some point the small percentage of exit velocity gained by increasing barrel length are outweighed by the physical limitations of the barrel weighed against the other factors post ejection which affect flight performance such as rifeling.

 

[phlegmy]

i suppose if you make a barrel so long that the pressure behind the cannon ball reached atmospheric then any further length of barrel would cause a decrease in range as it could cause a vacuum pressure in the barrell. (as the momentum of the ball carries it forward simular to a plunger in a syringe)
many large barrels are compound to cope with high stress (one barrel shrunk onto another)(in some cases even 3) (i think you can see thins on the big guns on destroyer ships?)

 

[wysard]

Reaching for Zero

Phlemgy. In an ideal world, you could extend a barrel to the length where pressure reaches zero, but in practical applications it isn't done for a couple of reasons.

1) There is variation in powder load, and shot weight that make an ideal barrel impossible to define, so a best guess of the minimum is appropriate. IE: you would rather have all the projectiles go downrange with some known power applied and dump the excess than reach a situation where the pressure in the barrel drops below atmospheric and the projectile is seriously retarded in the barrel.

2) While pressure is pressure, the pressure in the barrel is caused not by heating the actual gas in the barrel, but conversion of powder from solid to extrememly hot gas which is behind the projectile trying to expand that actually forces the gas in the barrel out ahead of the projectile.

3) Given the hot ejetate is causing pressure is both the heat of gas, and also minute particles accelerating in all directions, although primarily in the direction of expansion recall that bits of super hot powder hit the inside of the barrel or the back of the breach which heats the barrel (duh, but direct heat transfer is the primary cause of barrel heating) Anyway, when the projectile leaves the barrel, it's still getting hammered from behind by that hot ejectate escaping. In other words the ejectate, while undergoing a very rapid drop in apparent pressure is still primarily traveling in the direction of the projectile after it leaves the barrel and still receives some small percentage of thrust from the unspent powder for a short distance even after it leaves the barrel. Another reason for number 1...lol

I am sure there are others, and I look forward to seeing them.