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I started to think of a problem. I came up with a classic projectile problem: A cannon fires a projectile at some angle and impacts at some x-y coordinate, find the initial speed of the projectile, BORING!

Why not look at the more complete picture of cannon physics, specifically the propellant that accelerates the projectile.

I started by drawing a diagram of the barrel of the cannon, diameter/length. I know cannons have a charge (explosive) behind the projectile (chamber) which combusts to produce a high pressure gas in the chamber. The pressure exerts a force on the rear surface area of the projectile, which causes the projectile to acceleration until the rear of the projectile exits the end of the barrel.

Is this process adiabatic? Is it correct to say: the expansion of the gas happens so rapidly no energy can be transferred from the gas to the barrel or projectile as heat? However I know gun barrels get hot and so do the projectiles, thus Q does not equal zero? Can anyone steer me in the right direction here?

I then started to think about gas pressure. Pressure is related to temperature by the ideal gas law. However the ideal gas law operates under the assumption that the gas density is low enough to assume the gas particles don’t occupy a volume or interact with each other. I am fairly certain that this assumption cannot be made in this case due to the explosives being solid and thus dense before combustion occurs, so I conclude that the gas must be very dense after combustion. Writing this I’m now thinking my analysis to be inherently flawed.

Do I need to look at the energy of a shock wave? That is, the primary energy is transferred to the projectile through a shock wave? However the projectile has inertia which cannot by accelerated by a traveling wave?

If anyone knows what I’m talking about could you please help me understand (conceptually) the physics in a cannon? Even if the detail I’m eluding to can only be modeled by a computer simulation.