Home Forums Hunting & Shooting Ask The Gunwriters Expansion Ratio for Dummies

Ken great to see you back, keep up the "good works".

my head hurts...

Ken's not "back" (more's the pity).

This excellent thread is six years old until the last few posts - perhaps that's how long it took friend clarkma to craft that visual aid. It would have taken me longer.

But not in a gun.

At the point of peak pressure in a modern rifle, the gases are so compressed the volume of molecules and their atoms take up a significant amount of space. This is sometimes referred to as the "covolume" of the gases. Computing volume to pressure ratios using the ideal gas equation gives an error on the order of 100% at peak pressure.

I've never seen "expansion ratio" defined as Ken has here. Ken's comments regarding how the expansion per inch of bullet travel determines powder quickness are spot on, but I've always seen ER defined as expanded volume divided by compressed.

When a gas expands against a piston or bullet, it does work. The compressed gases have a certain energy potential in them, limited by the energy released by the burning propellant. The ER largely determines what percentage of the chemical energy is converted to kinetic energy in the bullet. Powley's computer puts this concept to good use.

The ER is a crude reading of the expansive work potential in the rifle. It's complicated by the fact that as the bullet just starts to move, the chamber is largely full of a nearly incompressible solid: the propellant.

In engineering terms, you may be right. But in gun-speak, Ken defined Expansion Ratio the way it's used here.

In firearms, the expansion ratio is the bore volume plus case volume compared to the case volume alone. It attempts to quantify the "before firing" volume to the volume at the point in time when the bullet base is at the muzzle. The case volume is expressed as "1" and the ratio is X/1 -- the "X" being case plus bore volume.

That's what I meant by "expanded over compressed." Expanded is with the bullet just exiting the barrel, and compressed is at the start of bullet motion. Yes, ER is also properly applied with the bullet at any position.

As I noted, the ER so defined is a misnomer. It doesn't account for the volume of the powder grains. Worse, the charge is burning over many inches of bore, further reducing the accuracy of the term. However, as Powley showed, it works well enough for rifle length barrel.



Ken was relating ER at position to required powder quickness. How ER varies with bullet travel expresses how fast pressure is relieved by a given bullet motion, or conversely, how fast gases must be generated to keep up with the bullet. There's a simpler way to look at the problem, though.

Quickness is largely determined by three quantities: 1) the sectional density of the bullet; 2) a related concept, the ratio of the case capacity to the bore area (which is along Ken's line of thought); and 3) the working pressure. Bullet construction also has an effect, along with several other factors, but the principle three are used in the Powley computer (where working pressure is held fixed).

Computing case capacity relative to bore gives one directly the concept Ken was aiming for.

I think you will find that the example I gave fits the ideal gas laws better than most, as the primer is half the energy, and the number of expansion multiples is very high.

My father came up with a system for balancing a barrel when the gas law does not match the equation for elevating a barrel. It also nulls the turrets tendency to swing down hill, and he used it on the M55, M110, and M107.
http://www.freepatentsonline.com/2857815.pdf

agreed

At high pressures:

P(V-Cb)=CRT
C = Wt of Propellant (lb)
b = covolume = 26.3in3/lb

Interior Ballistics E.D. Lowry

One might apply Lowry's number, to a common cartridge, the .30-06.

The net case capacity is about 62 gn. Assuming the peak pressure occurs at about 2" of bullet travel, we have about 99 gn (water) of space behind the bullet, or about .40 cu in. The charge is about 54 gn, so with the covolume term given, we have about .20 cu in. This, then, reduces the volume term from .40 to .20, and a halving of the volume causes a doubling of the pressure.

The covolume is a rough approximation. More detailed calculations are done in internal ballistics simulations.

1st edit: I goofed. Only about half the charge will be burned at peak pressure, so the covolume will be about .10 cu in. The unburned charge will displace about 30 gn or .12 cu in of the .40 cu in behind the bullet. The covolume effect is .28 cu in less .10, about a 1/3 drop so the pressure is raised a bit over 3/2 at this point.

2nd edit: I goofed again. I used bulk density instead of material density. The unburned charge is about .07 cu in, so the covolume effect at peak pressure is only about 43%.

Fun with numbers...

This thread is a gem. Thanks to all contributers and the Clarkma for digging it up.

Sorry to re-dredge this, but I'm having trouble finding something that 2525 posted -somewhere- before.

Would you please remind me of the approximate burn rate of smokeless powder in inches/sec? And if it varies in single- versus double-based? I can't recall what thread that was in.