I used to know this stuff but seem to be having a major cranial burp here about expansion ratio. I know (think?) it is defined as the ratio of the volume of the bore over the volume of the cartridge case and basically describes the amount of room in which the powder gas has to expand, hence �expansion ratio�.

We speak of cartridges with a �high expansion ratio� or a �low ratio�. A �high expansion ratio� cartridge supposedly suffers less from an incremental decrease in barrel length than a low ratio cartridge, right? Now here is where the confusion sets in�

How can a cartridge have an expansion ratio? Isn�t this as much a funtion of barrel length as anything else? As barrel length decreases then since the vloume in the barrel is the numerator wouldn�t the ratio increase proportionately? To give an extreme example couldn�t a .45 ACP with a 6� barrel have the same expansion ratio as a 7mm Magnum with some barrel length X?

Ken Howell, if you are reading this � you just gave a very lucid and easy to follow explanation about the quickness of powders and the reasons behind same in the �Powders for shorter barrels� thread. I�d sure appreciate it if you�d have a go at this topic.

Expansion ratio is an expression of how fast the burn space behind the bullet expands as the bullet goes forward inside the barrel � how much, IOW, that space expands per inch, for example, of the bullet's forward travel.



A barrel ahead of a cylindrical case has a high expansion ratio � a smaller-diameter barrel ahead of a necked-down case has a lower expansion ratio, because the smaller-diameter bullet has to travel farther to expand the burn space behind it by as much as a case-body-diameter bullet expands it in a much shorter forward travel.



In two barrels of the same length, the bullet's trip to the muzzle can quickly double the burn space in a cylindrical case (in about the same distance in the rifling as the distance from the primer vent to the base of the seated bullet), but the burn space behind a bullet from an extremely necked-down case may not double before the bullet reaches the muzzle of a very short barrel.



Another way to look at it is how many times the bullet's travel to the muzzle expands the burn space behind it in a given length of barrel, for a given cartridge. A .22 Long Rifle has a much higher expansion ratio than a .220 Swift � because the bore volume of a rifle-length Long Rifle barrel is several times as much as the net volume of the case's powder cavity. The bullet from a .220 Swift would need an incredibly long barrel for its travel to expand the burn space an equal number of times the volume of the Swift cases's net powder cavity.

Yikes..I'm impressed but didn't under stand a word of it...


Dumb old Jayco.

Jayco



If you slow way down and read it two or three times it starts to make sense <img src="/ubbthreads/images/graemlins/grin.gif" alt="" />(not that I doubt that Ken knows what he's talking about but it is a challenge to input some of those thoughts. My goodness that guy can pack ideas into a small space and he wasn't even using big words!) But then again, this is one of those things which is almost easier to deal with in ones head if you have numbers to compare against each other- the 243 vs the 358; same case very different expansion ratios and then you can see how the numbers and "higher", "lower" terms fit.

Just for Jayco (coffee break for everyone else):

(a) Inside the loaded, unfired cartridge, there's a certain amount of space behind the bullet (between the primer vent and the base of the bullet)� nearly full or full of powder.

(b) When the powder burns, the bullet moves forward, pushed by the expansion of the powder gas.

(c) As the bullet moves forward, the space behind it (between the primer vent and the base of the bullet) increases with each inch or other increment of the bullet's travel.

(d) The space behind the bullet becomes larger than it was before all the fun started. It may or may not become twice as large as it was. If the case is close to the same diameter as the bore, the bullet doesn't have to go far to make the space behind it (between the primer vent and the base of the bullet) twice as large as it was in the unfired cartridge.

(e) A bullet from a cylindrical or nearly cylindrical case (e g .38-55, .444 Marlin, .45-70. .458 Winchester Magnum) doubles the space behind it in a relatively short run toward the muzzle.

(f) A bullet from a necked-down case � with the body of the case significantly larger in diameter than the diameter of the bore (e g .223, .25-06, 7mm Magnum, .300 Magnum) � must travel much farther down the smaller bore to increase the space behind it as much as the larger bullet (as in [e], above) increases it in a much shorter travel.

(g) The expansion ratio is the expression of relatively how much bullet travel it takes to increase the space behind the bullet from a caseful of space to a caseful plus more space.

Good point. The gas space behind the .358 bullet expands much more in each inch of travel than the gas space behind the .243 bullet.



Here are some other numbers for you to play with:



The net powder space behind a 75-grain A-Max in my .220 Howell at an OAL of 3.105 inches is 0.238 cubic inch. The volume of the bore is 0.039 cubic inch per inch of bore. An inch of bullet travel in the 0.224 barrel expands the net powder capacity of the case by about 16.8 percent.



The net powder space behind a 250-grain Nosler Partition in my friend Gary's .350 Howell at an OAL of 3.287 inches is 0.275 cubic inch. The volume of the bore is 0.0996 cubic inch per inch of bore. An inch of bullet travel in the 0.358 barrel expands the net powder capacity of the case by about 36.4 percent.



The difference in the expansion ratios of these two cartridges is great enough to make two different quicknesses of powders optimum for these two cartridges. The lower expansion ratio of the .220 Howell calls for a slower powder � IMR-7828 or Ramshot Magnum, for example. The higher expansion ratio of the .350 Howell calls for a quicker powder such as IMR-4895 or Ramshot Big Game.

Boy, can he!



Jim, great question.



Ken, thanks for the "a through f" explanation- I'm glad I didn't go for coffee <img src="/ubbthreads/images/graemlins/wink.gif" alt="" /> . I'm with Jayco here.



So then, the expansion ratio is one of the parameters used in selecting the powder with the proper burn rate, along with relative bullet weight. Yes?



Thanks for "dumbing it down" for us partly lits here (It helps me!).



-Dan

Yes.

The expansion ratio is a factor in the relative difficulty of shoving the bullet forward � or, IOW, how (relatively) tightly or loosely it resists the expansion of the powder gas. The tighter that containment is, the faster the powder burns. A too-quick powder raises the pressure too fast � a too-slow powder doesn't burn fast enough to develop the desired pressure.

An extremely too-slow powder � a caseful of 50BMG in a 9mm Luger, say � may not even ignite as the primer pressure blows it out the muzzle.

An extremely too-fast powder � a caseful of Bullseye in a .340 Weatherby, for example � builds a straight, vertical pressure "curve" that doesn't reach its potential peak before the breech becomes a rapidly expanding cloud of itty-bitty pieces of jagged, high-velocity fragments.

Neither is good, but at least a faint floop! is harmless.

Burning rate, BTW, is the technical term for how fast two opposite surfaces of a kernel of a designated powder burn toward each other under a designated pressure, in units of distance per unit of time (microns per nanosecond, say). The technical term for what handloaders mean by "burning rate" is quickness. The two concepts are related but neither synonymous nor identical.

Two chemically identical powders with different kernel dimensions would have the same burning rate but different quicknesses.

Two chemically different powders may have two very different burning rates but roughly identical quicknesses because of their different shapes and dimensions (sticks and spheres, for example).

Never thought of the importance of surface area:volume ration in regards to gun powder. But, your explanation shows why. Thanks.

Dr. Howell,

Thanks. This is great information for people like me, who wondered how everything tied together (in interior ballistics). Is this "stuff" in your book?

-Dan

Interesting that you bring this up just now. Not long ago, a friend here got downright bellicose in his resistance to the concept that the smaller kernels have a larger surface-to-volume ratio � therefore ignite and burn faster � than the larger kernels.

He could see that a pile of excelsior would ignite and burn faster than the log that it was shredded from, but his thinking bogged-down trying to grasp the numbers that my explanation applied to the comparison of the surface-to-volume ratios of (a) a four-inch cube and (b) that cube sliced into one-inch cubes.

I still don't grasp why it's so hard for some folks to see.

The ratio of the four-inch cube is 4 x 4 x 6 inches (96 square inches) to 4 x 4 x 4 inches (64 cubic inches), or 1.5 to 1 (96/64). The ratio of each one-inch cube is 1 x 1 x 6 inches (6 square inches) to 1 x 1 x 1 inch (1 cubic inch), or 6 to 1 (6/1). My friend's brain froze on the fact that the surface-to-volume ratio of a one-foot cube would be 6 square feet to 1 cubic foot � but expressed in square inches per cubic inch would be 12 x 12 x 6 inches (864 square inches) to 12 x 12 x 12 inches (1,728 cubic inches), or 0.5 to 1 (854/1,728).

"I don't see why the numbers change," he kept saying.

"Because the ratio relates squares to cubes," I kept trying to explain.

If this is as confusing to my Campfire buddies as it is to my Stevensville friend, holler, and I'll try to make it clearer. As I told him when he said that he didn't want to continue arguing about it, my sole intent and purpose is not to win an argument but to make the concept clear and understandable to anyone who wants to understand it.

Yeah, it was a 'lightbuld' type thing for me. My use/familiarity of SA:V is from the biological field, so it wasn't immediately apparent, but makes mucho sense now.

I too first learned of the relevance of the surface-to-volume ratio as a biology student (my first degree is a BS in wildlife-management). For decades now, I've been unable to either remember or find the name "______'s Law" that enunciates that relevance. Several folks whom I know remember having "learned" it but can't remember the name of it or where to find it.

It will be in Inside the Rifle and possibly in Loading and Testing Custom Cartridges.

This is one of the chief reasons that the book (Inside ...) is taking so long to finish � stuff keeps coming-up, that should be included, that I realize that we've overlooked.

It occurred to me recently that I should shoot crisp, sharp ultra-close-up photos of all of the more than a hundred component powders that are available to American handloaders. Such a series of photos, shot with a macro lens or through a microscope, would help to make a number of interior-ballistics matters and concepts clearer and easier to see.

But rest easy � especially you extremely patient fellows who've ordered copies of the book and haven't (not one!) pestered me about how tardy its completion continues to be � I'm not going to delay completion further just to include such a series of photographs.

Ken
I believe you are thinking of Bergmann's Law? More northern populations of a given species will be larger-bodied for heat efficiency advantages... due of course to the surface area to volume ratio.
art

Sitka-

Is that the name of the law that applies to raptors where each crrespndingly larger species is 1/3 larger than the next smallest?

pointer
I remember three laws related to that sort of thing;
Allen's Rule- Animals in warmer climates have longer extremities than those of the same species in cold climates.

Bergmann's Rule- Animals in cold climates are larger than those of the same species in warm climates.

Gloger's Rule- Animals in warm/moist climates have darker coloration than those of the same species in cold/dry climates.

As I remember the hawk laws... the size distributions were thought to be East-West (open space-tight cover) rather than North-South and balanced by wingloading that showed only that the stronger winds and longer stoops were best served by longer wings and a bit more weight... ie; Allen's rule.

But that gets beyond my memory of such things <img src="/ubbthreads/images/graemlins/blush.gif" alt="" /> <img src="/ubbthreads/images/graemlins/blush.gif" alt="" /> <img src="/ubbthreads/images/graemlins/blush.gif" alt="" /> it has been many moons since I actually looked at any of this stuff...
art

Sitka-

Thanks. I don't remember if there was a law or not regarding the raptors or if it's just a 'freak of nature'.

I was aware of the laws, but couldn't remember the names, regarding size/extremities but had heard the one on color. Then again I did a liberal arts undergrad, so I dealt more with pre-med sorta stuff than that.

A question on coloration. Whitetails, and I've noticed to a lesser extent mule deer, are 'Red' during the spring/summer. I've heard it hypothesized that this is because red and green appear the same shade of gray in a black/white spectrum. This would in effect give them 'camo' from predators during the green times of year. Sorta why you can use an orange throw dummy to train retrievers. Any thoughts?

Ok, ok, wait a minute. Can't expansion ration be expressed in the following simple formula?

Expansion ratio = (volume of chamber + volume of bore) / volume of chamber

You guys are probably saying the same thing, but my simple mind requires absolutes. <img src="/ubbthreads/images/graemlins/help.gif" alt="" />

If I put 1/2 gr Bullseye in a 45/70 and a .454" lead ball over wads.....

a) Seated in the case mouth, the fired ball bounces off wood.

b) Seated deep in the case to compress the powder, the fired ball penetrates an inch of wood.

Both loads make the same pellet gun like sound from the muzzle, but the seconds load makes a much louder sound when it hits the wood.

The difference between the two loadings can be though of as expansion ratio.

Every time a gas doubles in volume, the pressure drops in half.

The second load starts with a much higher pressure, but both loads result in the same muzzle pressure ~ 1 atmosphere above ambient... the threshold of supersonic gas escapement.


Here you see Hawk has defined expansion ratio as = expanded / compressed.

http://en.wikipedia.org/wiki/Expansion_ratio
Here you see the chemists have defined expansion ratio as = compressed / expanded


http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/diesel.html
In diesel engines, expansion ratio is = expanded / compressed


http://www.frfrogspad.com/intballi.htm
Here you can see expansion ratio = powder fill ratio
Maybe they made a mistake.

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.