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Would someone please explain the physics behind the theory that an air gap creates a “pipe bomb” To my knowledge pipe bombs are usually stuffed full (no aireap) and in the bp rifle the potassium nitrate is producing all the oxygen the sulphur and charcoal need to burn. So pleas explain how a little extra air causes such a violent rise in pressure so as to damage a barrel. As far as I’m concerned the bore obstruction theory is pure BS unless there is another projectile loaded behind it. No anecdotes here please, just pure physics.
A pressure rise does happen with an air gap. I mentioned the reason in my other post, but I'll try to do it more clearly.
The reason is inertia of the stationary bore obstruction, the kinetic energy of a powder column rapidly moving up the bore, and possibly a bit of potential energy of the yet unburned powder.
First a disclaimer. I'm not a structural engineer and it's been over 20 years since I had physics at school, but let's do few "back of an envelope" kind of calculations I marked the tedious bit as quote so you can skip it easily for your convenience.
Few assumptions, 70 gr of powder, 50 cal lead ball. 1471 fps normal muzzle velocity(851ft/lbs muzzle energy) . Ball located 3 inches before muzzle.
We assume the kinetic energy that usually is contained in the projectile is now contained in a powder column rapidly moving up the bore to meet a stationary projectile. Let's calculate the speed of powder column before it hits.
70 grains of powder is 0.00454kg in SI units. Sorry I learned physics in SI units. 851ft/lbs is 1153 Joules.
Let's assume that when it slams into that ball it will transfer 80% of its energy to the projectile. The other 20% will get lost as heat, residual pressure discharge etc.
So the ball will end up with a muzzle energy of 922.4J and velocity of 400m/s (50 cal ball, 178 grains or 0.0115kg mass). The ball has to accelerate to that speed in 3 in or 0.076m so if it starts at 0 speed ends at 400m/s after 0.076m it's average speed is half the maximum therefore 200m/s. We need this to calculate time for the ball to exit the muzzle from the moment of impact, it is t=S/V so 0.00038s. For the ball to reach that speed in that time it has to experience acceleration of a=v/t = 1052631 m/s2. From this we can calculate the force acting on the ball a=f/m or f=am 12105N.
Now the final part, to experience this force a 50 cal projectile with a cross section area of 0.000126m.sq. has to have pressure acting on it to be P=F/area P~96Mpa or almost 14000 psi.
So our no doubt flawed back of the envelope calculation results is 14k psi near the muzzle at point of impact where barrels are usually weaker. Mind that we also assumed constant acceleration at impact over whole 3 inch. Almost certainly it is not constant but significantly higher at start and lower towards the end so I wouldn't be surprised if the real pressure was at least few times what was calculated (50~60k psi) . Normal pressure at the breech for this load given in Lyman's black powder handbook it 5400psi. So we're talking 10 times normal pressure. Definitely et least bulge-worthy.
Also I as well as others have experienced bulges by short starting.
Good steel will just deform. Bad steel with flaws (for example original wrought iron) might crack.
My questioning is not that it couldn't happen, but that a good Italian barrel shouldn't experience such a huge failure with bp pressures. However, crappy products slip through best quality check systems from time to time, corrosion happens etc so anything can happen. All I'm saying is that the extent of that damage is a freak accident rather than norm.
Op, I'm sorry if you felt my questioning was accusatory in tone. That wasn't my intention.
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