help me understand something about cartridge length and seating depth

[labnoti]

I want to better understand how cartridge length and bullet seating depth affect internal ballistics.

I understand that shortening OAL and seating a bullet deeper in the case reduces the case volume and increases the maximum pressure that will be reached after ignition. Some other factors are the bullet's resistance due to mass, diameter, composition, crimping, and how close it is to the lands, and the powder's burn rate.

Independent of those other variables, how would you describe what happens when a bullet is seated farther from the base so that OAL is increased? Two practical examples I've encountered are a shot load or ball in a smoothbore muzzleloader, and the .38 special/.357 magnum in a smoothbore revolver cylinder.

If a ball or load of shot in a smoothbore migrates down the barrel prior to ignition (possibly because of recoil produced by a double-barrel's other barrel firing), the result is a long tube containing powder closed at one end by the breech and the other end by the load. Some people have described the similarities to a pipe-bomb.

Now consider the .357 magnum. Although it's very close to the same diameter as 9mm, the case length is much greater due to the parent .38 Special's black-powder origin, and the desire to make it even longer to establish incompatibility with .38 chambers suitable for no more than 17,000 psi. The .357's SAAMI pressure limit is 35,000 psi, the same as the 9x19mm SAAMI limit.

It is well established that .357 magnum is capable of greater ballistic performance than 9x19mm, but it's obviously not because it can be loaded to higher chamber pressure. So while the case is "bigger," it's not as simple as allowing for a greater charge of powder since the .357 magnum has practically the same pressure limit. In fact, I can't see how it can be anything other than the fact .357 magnum can have the bullet seated farther away and more empty space in the case. They way I imagine that working is that it somehow allows for greater area under the pressure curve, but what other variables are needed to effect that, I'm not sure I understand.

One of the apparent advantages of .357 magnum is the versatility in bullet mass. 158, even 180 grain bullets are popular in .357 magnum, whereas the 9mm is rarely loaded over 147 grains. The greater case length and being insensitive to length with respect to magazines and feeding provide for that. But even when comparing the ballistics of cartridges using the same bullet mass (or 124 gr. vs 125 gr.), and similar or same barrel lengths, the .357 magnum tends to demonstrate unquestionably superior velocity even with the loss of some pressure from a barrel to cylinder gap.

As far as I can tell, reduced case capacity such as found in the 9x19mm tends to limit the use of high speed powders more than low speed powders. In other words, if I'm using a high burn rate powder and seating my bullet deeply, I get into overpressure condition sooner than when using a slower rate powder. I might be mistaken about this, but if this is true, then one advantage of a large case like .357 magnum would be the ability to better handle high burn rate powders. But .357 magnum tends to achieve the highest velocities with slow burn rate powders.

So given the same bullet mass, does .357 have an advantage because of the type of powders that can be utilized? Or is it just the extra case length? And how does that relate to the "pipe bomb" I described?

 

[Ireload2]

Velocity is determined by the average pressure under the time pressure curve.
If you assume the peak pressure is the same, the cartridge with the longer peak pressure will produce higher velocity.

The way you can get a longer peak pressure is by using more of a slower burning powder.

 

[labnoti]

Since slow burning powders could be used in both long and short cases, how does the longer case of a .357 or seating the bullet farther away contribute to more effective use of slow burning powders, or more area under the time/pressure curve?

Is it simply because there's more space for a greater volume of a slow burning powder? If I use a maximum charge of a relatively slow burning powder (slower than what's typically used in 9mm) in a .357 case, it still might only be 50% full. But if I seat the bullet deeper, the max pressure is exceeded. So the advantage from a .357 case is the ability to use a greater bulk of slow burning powders that won't exceed maximum pressure because there's a lot of case volume for expansion, and yet they will produce more area under the time/pressure curve?

 

[.308 Norma]

Velocity is determined by the average pressure under the time pressure curve.

Very well put Ireload2.
Good questions labnoti, and I'm not sure I can answer them. But it seems to me like you're not considering the fact that the "time/pressure curve" doesn't just happen while the bullet is still in the case; it's still going on as the bullet is traveling down the barrel. If all of the "internal ballistics" occurred within confines of the cartridge case, there's no way I could push a 158gr Hornady bullet from my 357 Magnum carbine out at 1600fps, while I can only push the same bullet out at around 1200fps from my 4" 357 Magnum revolver, even though both cartridges contain 15.5grs of 296 and magnum primers.
I'll admit, there is some pressure loss through the barrel/cylinder gap of my 4" 357 Magnum revolver. But that only backs up what I'm saying - not all of the "time/pressure curve" occurs within the confines of the cartridge case.

 

[Ireload2]

The larger case takes more powder burned to reach the same pressure.
Even a fast burning powder will develop a higher velocity in a larger case. More powder is required because the larger case has more volume.

If you want to read the gas laws used in chemistry you will find that pressure and volume are inversely related assuming the same amount of gas.
PV = PV
Say if you use the same powder charge in both cases the pressure in the small case will be higher because you are filling a smaller cavity.

Some of these relationships might be easier to see in shot shell loading data.
Light skeet loads develop the same pressures as heavy waterfowl loads. Yet a skeet load might use 18 gr of a very fast powder.
The duck or turkey load might use twice as much powder to boost the heavier shot load to about the same speed.

 

[reddog81]

I imagine the more voluminous case allows for more powder which creates a higher average pressure while maintaining the same peak pressure.

For example my Lyman manual shows a 110 grain 38 special +P load of 6.7 grains of Power Pistol with a velocity of 1098 and pressure at 18,700 CUP (a +P load). While the starting load of 5.9 grains PP in a 9mm case with a 115 grain bullet will do 1102 FPS and creates 27,100 CUP. This demonstrates that you can get identical performance from a 9mm and .38 Special and the .38 Special will generate less pressure while using more powder.

A similar example comparing .357 and 9mm shows a 125 grain jacketed HP with 9 grains vs 5.7 grains Power Pistol with respective velocities of 1107 and 1238. The pressure of the .357 load is listed at 32,100 vs 31,300 for the 9mm. The pressure of the .357 is 2% higher yet the Magnum round got 11% more velocity, however it used 57% more powder. Both notes show the use of a 4" universal receiver.

 

[Blue68f100]

And all this happens in nano-millisecond time frame. Every powder has a unique pressure curve alone with a preferred pressure range. This is one reason fast powders are not normally used for larger capacity rounds. With a small volume round like the 25cal/380cal use faster powders. You can not stuff enough slow powder in them to gain the same velocity.

Rifle loads react a little different when it comes to seating depth and bullet jump.

 

[ray15]

A similar example comparing .357 and 9mm shows a 125 grain jacketed HP with 9 grains vs 5.7 grains Power Pistol with respective velocities of 1107 and 1238. The pressure of the .357 load is listed at 32,100 vs 31,300 for the 9mm. The pressure of the .357 is 2% higher yet the Magnum round got 11% more velocity, however it used 57% more powder. Both notes show the use of a 4" universal receiver.

Due to the difference in case volume .357 never really sings with a powder suitable for use in 9mm. The reason the increase in case capacity is such a game-changer is it that it allows a sufficient quantity of slower burning powder to achieve the same 35,000 PSI pressure level. The full-tilt 125gr. .357 load is 22 grains of H110/W296 which makes an honest 1485fps from a fresh 4" GP100. This is essentially filling the case to where it produces just a bit of compression. And it generate right at 35,000 PSI. If you were to use a powder this slow in 9mm you could not get anything like 22 grains in the case, resulting in far less than 35,000 PSI pressure. Slow powders need pressure to ignite and burn properly, so at a certain point in burn speed they are only useful in large capacity cases.

It is sometimes helpful to take things to the extreme when evaluating such topics. In comparing rifle cartridges to handgun, no one has any confusion about how much more powerful bottleneck rifle is. This is also due primarily to much greater case capacities, which allow large amounts vastly slower powders than applicable to handguns naturally resulting in much more total energy. Many modern rifle rounds operate at pressures beyond most handguns, but even loaded down to 35,000 PSI you are looking at a whole lot more powder/energy even though the burn rate must be slower.

 

[Dudedog]

The reason the increase in case capacity is such a game-changer is it that it allows a sufficient quantity of slower burning powder to achieve the same 35,000 PSI pressure level. /QUOTE]

Exactly


You could not get enough say H110 in a 9mm case to have the same pressure you can get in .357, the larger case gives you room for the larger charge of slower burning powder.
Same sort of thing in say 7mm-8 and 7mm Rem Mag.