Why heavier boolits are better: a thermodynamic view

[Xlucine]

Thinking about the effect of a heavier boolit on the combustion, it reminded me of what my thermo lecturer was talking about with the idealised otto cyle and diesel cycle - modelling the combustion as simple heat addition, a heavier boolit will get more PdV work.

 

So, the otto cycle is more efficient than a diesel cycle ceteris paribus - this is because the ignition of the fuel is so quick it's kinda like isochoric heat addition (i.e. constant volume), whereas diesels are limited by the time it takes to inject the fuel* so are better approximated by isobaric heat addition (constant pressure, so with volume increasing). Since some travel is taking place in the diesel cycle before all the heat is added, there's less area under the P-V diagram so less work is done.

 

*according to my lecturer, non-direct injection diesels are not halal

 

Something similar will happen with a heavier boolit - it will have moved less before all the propellant is combusted, so it's closer to the ideal of holding the bullet in place until all the propellant has combusted to maximise PdV work*. A light boolit, OTOH, will have moved down the tube more when the pressure in the chamber was low, so doesn't get as much work done on it. The rate of combustion is probably proportional to pressure and temp as well, giving an even more pronounced effect. All this is happening completely separate to the not-quasi-equilibrium thingy with the ratio of propellant gas speeds and boolit speed - that reduces efficiency towards the end of the barrel, whereas this reduces efficiency near the chamber where velocities are much lower

 

*maximum pressure limits are for wusses

[Collimatrix]

So crimping will increase efficiency.

[Xlucine]

In theory yes, although the effect is probably quite small - the forces to break that seal ought to be pretty minor in comparison. Might be interesting to see if someone could actually try it and see if there's an MV increase

[Donward]

The natives up in Alaska who buy 45-70 rifles for bear hunting assured me that caliber's efficiency thermodynamics was  their top choice for picking that cartridge...

[Sturgeon]

Crimping measurably increases efficiency, because it increases pressure. Because gun enthusiasts are typically backwards people, they consider this to be bad.

I agree with Xlucine's assessment that heavier bullets on top of the same propellant are more efficient - however once this is applied the advantages quickly shake out and you are compelled to bow before SCHV Zod.

[Donward]

It depends on what you're trying to do with the cartridge. There's a place for good old-fashioned slow-moving school bus bullets. Although with the advent of newer and better bullet technology, that niche is getting smaller and smaller.

[Sturgeon]

For hunting, heavier bullets (let's not confuse this with slow-moving, now) have an advantage in brush-busting and penetrative capabilities. In hunting, bows and atlatls are considered effective weapons.

[Donward]

Bows are also effective if you're a pair of fun-loving good, ol' boys driving a Dodge Charger or a tortured, world-weary Vietnam War vet fighting Commies in Afghanistan.

But yes, what makes something a good hunting round doesn't always make it a good military cartridge.

For the former, you're wanting something that kills the critter in one shot, cleanly so you don't have to track it down through the brush while not ruining too much meat.

Also deer rarely wear body armor.

[Collimatrix]

Could you get the same effect by moving to a faster-burning powder?

[Donward]

I'll leave that for the more knowledgable. All I know is that it's remarkable what they're doing with bullet and powder design.

[Xlucine]

Could you get the same effect by moving to a faster-burning powder?

 

Yep, since you'll end up with less time for the boolit to move before the powder is all burnt

[Collimatrix]

So this is another instance of the Carnot Equation.  Higher peak pressure means a higher difference between peak and exhaust temperatures, which means greater maximum possible efficiency.

[Xlucine]

Er, sorta. The carnot cycle assumes constant volume heat addition (so it'll underestimate the work done in a constant pressure system, since the pressure is held up for more of the shot travel), and the formula for maximum efficiency of an idealised diesel engine (or any heat engine with constant pressure heat addition) is not as neat as carnot

 

(walter should totally add this to his sig on the WoT forums)

 

Gamma is the ratio of specific heats, and alpha is the ratio of volumes before and after heat addition. The formula for PdV work for an actual gun is going to be a hell of a lot more complicated, because nothing is constant, but I can ignore messy situations like that till next year in my course.

[LostCosmonaut]

For reference, gamma in air is aboot 1.4. Helium is one of the highest at about 1.67. I think most exhaust gases for solid rockets are about 1.2-1.3ish, so I'd bet that gun gases are about the same.

 

Also, the most thermodynamically efficient AR-15;

 

[Toxn]

Speaking of which, wouldn't the best approach be to do the tank thing and use a large bore (15mm+) to fling sabots? I'd think that the option of being able to fit pretty much any boolit, moving at pretty much any velocity, down the same barrel would be pretty attractive. Not to mention the fact that you can now use stubby, straight-walled cases.

[Collimatrix]

Speaking of which, wouldn't the best approach be to do the tank thing and use a large bore (15mm+) to fling sabots? I'd think that the option of being able to fit pretty much any boolit, moving at pretty much any velocity, down the same barrel would be pretty attractive. Not to mention the fact that you can now use stubby, straight-walled cases.

 

 

That would give you the best swept volume, yes, and there would be less bore surface area for a given amount of swept volume, so your thermal leakage would probably be less severe as well.  However, there are several practical difficulties.

 

There's a relationship I don't entirely understand between the velocity, distance between the bullet's center of pressure and center of mass and rifling twist rate that needs to be within a certain range to achieve good accuracy.  If you start shooting sabots through existing barrels that were designed for a different load, it won't work that well.

 

Obviously, it works well enough in tanks so you'd think with some finagling you could scale it down and get it to work OK.  It could be that nobody has put the effort in yet.

 

The obscenely hard to find Collector's Grade book on the SPIW documents some of the problems with sabots and small arms.  They're probably soluble, but they're non-trivial.

[Toxn]

SPIW used existing small-bore barrels if I remember correctly.

Honestly, I think the main issues with a big-bore sabot slinger (beyond a conservative industry and bureaucratic inertia) are sabots as secondary projectiles and the small magazine sizes you'd end up with.

[Toxn]

I forgot the biggest issue with this idea: ammunition. Specifically, I suspect that it might be challenging to shit out a few billion saboted projectiles with the required tolerences for accurate shooting.

Then again, at 15mm we're well within the range of modern hmg/autocannon ammo where that is a solved problem.

[Xlucine]

If you just necked out current rounds then there shouldn't be any difference in magazine volume, since the case head would be the same

[Toxn]

But me want make boolit be big. 15-20mm case diameter or bust.

[LostCosmonaut]

Would larger rounds (15-20mm) be easier to manufacture with shitty machine tools?

 

Autocannons for the people!

[Toxn]

Neopup PAW-20 now the universal standard rifle for the Western hemisphere.

[Collimatrix]

Some day when I'm feeling lazy I should start a unified internal ballistics thread.

[Sturgeon]

BOW TO THE DEUS EX POWLIUS SCRIPTOR MACHINA

[Xlucine]

A mention of piezometric efficiency lead me to this site, which is worth reading. Read it