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joe chip
02-15-2009, 11:07 PM
What decides the distance a shell or bullet can travel before its energy is expended? If it were possible for a breach to contain sufficient energy to expel such a projectile (without destruction) with the explosive power of an atomic bomb what maximum span could it attain? Is it related to the weight of displaced air?

puppygod
02-16-2009, 03:56 AM
If it has enough energy to break away from gravity well, then the upper limit is infinity...

In more practical terms, most important factors are drag coefficient and, of course, gravity.

Gravity is for practical purposes constant, and drag coefficient... well, that gets really more and more complicated the more you look at it, so just say it's about shape. If you wan't to know more, check under "fluid dynamics", but as I said - it gets more and more complicated from that point.

smiling bandit
02-16-2009, 10:18 AM
Sending him off to study fluid dynamics is a bit cruel... and like shooting a gnat with a bazooka. It's a lot more than he requires.

Artillery shells - all motion - is determined by energy transfer.

When you fire a shell, the potential energy from the chemical explosives is transferred to the shell. It's also transferred to the gun. It's shared equally. However, the gun is being braced by the entire planet earth (or at least the local bedrock). It ain't moving much. The shell, on the other hand, moves a lot.

It's simple action and reaction.

What ultimately determines how far it goes is simple the combination of gravity and friction. The air slows down the shell; it transfers energy to the air in order to push along. Gravity also tends to pull the shell back to earth, where it encounters even more friction by slamming into the ground. If there were no air or earth, your shell can indeed go on forever. So your intuition is correct - it is related to the air there, and denser air has more drag (that's the friction again) than less dense air.

Squink
02-16-2009, 10:50 AM
If it were possible for a breach to contain sufficient energy to expel such a projectile (without destruction) with the explosive power of an atomic bomb...Atomic cannon:
Operation Upshot-Knothole test Grable (http://en.wikipedia.org/wiki/Operation_Upshot-Knothole)

Dog80
02-16-2009, 10:55 AM
Atomic cannon:
Operation Upshot-Knothole test Grable (http://en.wikipedia.org/wiki/Operation_Upshot-Knothole)

Not exactly what the OP had in mind. The projectiles have a small atomic bomb as a warhead but are otherwise propelled by conventional explosives.

smithsb
02-16-2009, 01:08 PM
IANA projectile ballistics scientist but do work with munitions. Gravity is pretty much a constant. Aerodynamic drag is lessened the higher the projectile is launched into the air. Similar to a airplane, getting the projectile to altitude quickly increases range. Both standard long range and rocket assisted projectiles (RAP rounds) are fired at angles above 45 deg. (upper 50s) to get to the thinner air quicker. Ranges for current 155mm projectiles go out to 55km or so. Adding a guidance and control system with some glide capability moves you out a bit further.

Not sure what you mean by displacement of air; standard aerodynamic drag?

Your theoretical atomic bomb propellant charge would send projectiles into orbit and beyond since the man below believed orbit could be achieved with conventional propelling charges.

Look up is Gerald Bull. He was a Canadian scientist specializing in ultra-long range artillery. He was working on using artillery to launch satellites in to earth orbit (HARP project). The funding for this was cut off and he went to work for various governments / security agencies ending up Saddam Hussein developing a "super gun" for extreme ranges. He was assassinated by ??? See the book "Bull's Eye: The Assassination and Life of Supergun Inventor Gerald Bull",

Remains of a supergun installation were found in Iraq. Saddam was planning on artillery bombardment (possibly bio/chem) of Israel. The Germans in WWII had a similar design (very long buried tube with multiple propellant chamber arrayed along the length of the tube to accelerate the projectile without over pressurizing the cannon walls).

Stealth Potato
02-16-2009, 07:24 PM
When you fire a shell, the potential energy from the chemical explosives is transferred to the shell. It's also transferred to the gun. It's shared equally.

Just a nitpick: the energy released by the chemical propellant is not shared equally between the gun and projectile; it is the momentum of the gun-bullet system (well, strictly gun-bullet-ejected gasses system) that is conserved, and that's probably what you're thinking of.

For example, suppose I fire a 158-grain JSP .357 magnum bullet (which has a mass of about 10 grams) from a Colt Python revolver (which we'll say has a mass of about 1100 grams). A typical muzzle velocity for that cartridge is around 380 meters per second, so the bullet itself carries upon leaving the barrel an energy of approximately

(1/2) * (10 grams) * (380 meters / second)^2 ~= 720 joules.

Let's ignore the fact that there would usually be a person as part of the system; suppose the revolver is fixed to a free-swinging pendulum, the exact opposite of a ballistic pendulum, as it were. Total momentum will be conserved, so (if we ignore the mass of the ejected gas and smokeless powder particles) we can compute the corresponding velocity of the gun itself thusly:

Bullet momentum = Revolver momentum in opposite direction
(380 meters / second) * (10 grams) = (x meters / second) * (1100 grams)
x ~= 3.5 meters / second

That gives the gun total kinetic energy of

(1100 grams) * (3.5 meters / second)^2 ~= 13.5 joules

In this situation, the bullet and the gun have momentum of equal magnitude, but the bullet winds up with nearly all of the energy.

Elendil's Heir
02-16-2009, 07:45 PM
Jules Verne gave the matter some thought: http://en.wikipedia.org/wiki/From_the_Earth_to_the_Moon

Xema
02-16-2009, 09:27 PM
If it were possible for a breach to contain sufficient energy to expel such a projectile (without destruction) with the explosive power of an atomic bomb what maximum span could it attain?
My back-of-the envelope calculations suggest that the energy of a typical nuclear bomb could propel a 500-kg projectile in excess of 1000 km/sec. This is around 100 times escape velocity, and about 0.3% of the speed of light.

There would of course be huge problems with frictional heating in the barrel, and with the projectile burning in the atmosphere.

Santo Rugger
02-16-2009, 11:22 PM
My back-of-the envelope calculations suggest that the energy of a typical nuclear bomb could propel a 500-kg projectile in excess of 1000 km/sec. This is around 100 times escape velocity, and about 0.3% of the speed of light.

There would of course be huge problems with frictional heating in the barrel, and with the projectile burning in the atmosphere.Barrel? What barrel?