In firearms there is also loss of energy transfer simply because the bullet approaches the sonic velocity in the gases and because it has to compress the gas in the barrel ahead of it. There was an interesting episode of the Mythbusters in which they attempted to use a very long barrel on a compressed air gun to get higher velocity. They quickly exceeded the length of diminishing returns. Instead they found that evacuating the barrel was very effective in getting high velocity. But it is still limited to a little over sonic velocity. Brent On 11/5/2018 6:10 AM, Henry Baker wrote:
Interesting comparison of a rifle barrel to a piston engine from Wikipedia. Piston engines are more efficient with higher compression ratios (= higher pressures + temperatures), but also require *slower* burning -- e.g., higher *octane* rating of the fuel. Too-high burning rate ("detonation") increases peak pressures and loads while lowering energy transfer due to an impedance mismatch.
https://en.wikipedia.org/wiki/Internal_ballistics#Bore_diameter_and_energy_t...
'A firearm, in many ways, is like a piston engine on the power stroke. There is a certain amount of high-pressure gas available, and energy is extracted from it by making the gas move a piston in this case, the projectile is the piston. The swept volume of the piston determines how much energy can be extracted from the given gas. The more volume that is swept by the piston, the lower is the exhaust pressure (in this case, the muzzle pressure). Any remaining pressure at the muzzle or at the end of the engine's power stroke represents lost energy.
'To extract the maximum amount of energy, then, the swept volume is maximized. This can be done in one of two ways increasing the length of the barrel or increasing the diameter of the projectile.'
--- Also, it appears that bullets spin at close to their structural limits -- e.g., a bullet designed to spin at 150,000 RPM may disintegrate at 300,000 RPM, so too much rifling "twist" may be counterproductive.
At 02:13 PM 11/4/2018, Brent Meeker wrote:
The constraint is that the translational and rotational energy should have certain values at the muzzle.
For the problem to be interesting there must not only be a "cost" associated with giving these motions to the bullet but that cost must vary in some way depending on how the energy is induced.
Rifling of fixed pitch means that the translational and rotational speed are proportional as the bullet is accelerated.
The energy for both of course comes from the combustion gases of the cartridge.
I can't think of any energy efficiency reason for other than constant pitch rifling.
Anyway, energy efficiency is way down the priority list in designing a gun (notice the big flash that follows the bullet out).
Brent
On 11/3/2018 4:53 PM, Henry Baker wrote:
I was watching an old WWII movie, which showed the rifled insides of a cannon barrel.
A similar view (of a smaller gun) is found at the beginning of one (or more!) of the James Bond movies.
This rifling all seems to be of a *fixed* pitch -- i.e., a helix of constant twist angle.
But if you think about it, a bullet starts at velocity zero and angular momentum zero, so *ideally*, this rifling should start out relatively shallow, with slightly more twist angle as the bullet travels further down the barrel.
On the other hand, the bullet is also travelling *faster* at the end of the barrel, than at the breech of the barrel, so the twist could actually be less at the end, since it may already have achieved the correct angular momentum.
So what's the ideal rifling -- by "ideal" here I will choose that rifling that maximizes the energy transferred to the bullet, while still achieving a given angular momentum ? We have to transfer a certain amount of energy from linear motion to rotating motion, and I presume that there is a certain cost associated with this transfer.
Obviously, the ratio of the moment of inertia to the mass of the bullet should enter into the calculation at some point. In order to maximize the power transfer, there needs to be a kind of *impedance match* of the bullet to the rifling pitch.
https://en.wikipedia.org/wiki/Rifling
"In some cases, rifling will have twist rates that increase down the length of the barrel, called a *gain twist* or *progressive twist*".
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