Calling all OCW experts

[Varminterror]

The "math" Bart is using is basically a rule of thumb for a standard distribution. If you assume all shooter errors are ignored, then there's no predilection for any given particular error contributor to be "non-standard," so most shooters assume assuming a standard distribution is fair. Then a few decimals slide around here or there.

Until you have the data set (or experience a similar data set), there's really no way to know what the set size needs to be to determine the confidence interval.

 

[Bart B.]

Can you post the math you used to derive this number? I'd like to read the analysis. How many shots are needed to establish that any given shot from the same sample has a 90% probability of landing inside a given interval? I think this is a slightly different question. What interval was used for your calculation? Is saying that a certain number of shots are required to establish that one load is without a doubt better than another at a certain confidence level the same as saying that there is no likelihood that useful direction that can be gained from any group of smaller size?

All I did was approximate what these web sites show plus my own observations shooting 20 to 30 shot strings plotting each shot then seeing where those after the first few went to the total composite.

https://thefiringline.com/forums/showpost.php?p=5980841&postcount=25

http://www.the-long-family.com/group_size_analysis.htm

Plus others I now forget. The 'net's full of them; each tailored for different objectives. All based on statistical bell curves for distribution.

My best analogy of group shooting equates to throwing several pairs of dice at once. A 7 with each pair is zero for each variable of rifle, ammo and shorter. A 2 is the limit in one direction, 12 the limit in the opposite. Some directions mostly vertical, others horizontal, but at all hours on the clock.

 

[Bart B.]

Everyone should learn to read signs of pressure on a case.

Having shot a few hundred 7.62 NATO Arsenal proof loads in Garands then showed the fired cases to people, they all said they looked normal for safe max pressure; often just like their own. They had about 67,500 cup while service and match loads have 50,000 cup.

Sorry, but such suggestions are dangerous. There are no established standards for case and primer appearance that correlates precisely to pressure. All the metals used do not have the same properties; they'll deform differently for the same peak pressure. Cases and primers don't come with tarage tables listing defoming dimensions for pressures like copper crushers do.

 

[Gtscotty]

I'm not trying to be snarky but any good statistics text book will provide the answer and math. I'm afraid I remember enough about statistics to be dangerous these days and before retiring, I let the statisticians at my work do the math.

There is not a simple answer but the greater the points in the data set, the more confidence in its results. But the greater number of points, the greater the cost to accumulate the results (time, material, man hours, etc.).

If its simple to prove that 25 shots is some kind of magic number for distinguishing two loads, regardless of the actual characteristics of the groups, then it shouldn't be too hard for someone to post the math up and settle this once and for all. I can't seem to find my old Prob/Stat book, but I did peruse the statistics portion of my MERM today, and really didn't see any elementary way to determine a magic number of shots that creates a relevant group size without knowing anything about the group characteristics... Maybe the statisticians at your work can shed some light on the subject.

 

[Gtscotty]

All I did was approximate what these web sites show plus my own observations shooting 20 to 30 shot strings plotting each shot then seeing where those after the first few went to the total composite.

https://thefiringline.com/forums/showpost.php?p=5980841&postcount=25

http://www.the-long-family.com/group_size_analysis.htm

Plus others I now forget. The 'net's full of them; each tailored for different objectives. All based on statistical bell curves for distribution.

My best analogy of group shooting equates to throwing several pairs of dice at once. A 7 with each pair is zero for each variable of rifle, ammo and shorter. A 2 is the limit in one direction, 12 the limit in the opposite. Some directions mostly vertical, others horizontal, but at all hours on the clock.

I looked at those websites, and didn't really see anything that supports your claim of 25 shots for a 90% probability, perhaps you can clarify the math. It sounds like the 25 shot number is more of a notional number estimated from your experience, where does the 90% probablility claim come from though?

From my quick review of confidence intervals and engineering statistics today, I didn't really see how one could make the blanket statement that 25 shots provides a 90% confidence for all future shots. From what I saw, to determine whether a certain group represents a "better" ammo population than another group, you would need to know the average values and standard deviation of whatever values you are measuring in each group (I would assume radius of each shot in the group from the group center). If you think you can make a blanket statement about when it is possible to determine whether one group represents a better ammo population than another without having all of the information on the shots in the group, I'd like to know how, and what assumptions you've made to get there. I believe that the issue is a little more complex than basic dice probability examples, more along the lines of process variability statistics.

Until you have the data set (or experience a similar data set), there's really no way to know what the set size needs to be to determine the confidence interval.

Exactly what the information I found said.... but again, if someone has another calculation method, I'm interested in learning.

 

[kingmt]

Having shot a few hundred 7.62 NATO Arsenal proof loads in Garands then showed the fired cases to people, they all said they looked normal for safe max pressure; often just like their own. They had about 67,500 cup while service and match loads have 50,000 cup.

Sorry, but such suggestions are dangerous. There are no established standards for case and primer appearance that correlates precisely to pressure. All the metals used do not have the same properties; they'll deform differently for the same peak pressure. Cases and primers don't come with tarage tables listing defoming dimensions for pressures like copper crushers do.

If you can afford & g want the tools to measure pressure with then great. However there is things to look at as your loading. I can't teach you across the web but I can point at what to consider. A case that you could replace the primer, powder, & bullet without sizing is very low. If the primer looks like it's just been pushed out the back & is sitting proud the pressure is to low. Once the primer is seated flush & the neck is sealing the chamber your up to probably enough pressure to start burning right & start looking for a load. When the primers are filling the case & you start getting a shiny spot on the brass around the ejector your likely around max. Once a case head starts flowing it's over a pressure I want to be at.

These signs are going to change depending on your brass hardness but give you an idea along the way even if they don't give you an exact number.

Only fallowing half the insertions in a manual isn't going to give you an exact picture of pressure ether. Likely the numbers are tanted a little from fear of law suit anyhow. But your powder being a different lot, different primers, not the exact same bullet, different col, & so on will all change the pressure given in the book.

I looked at those websites, and didn't really see anything that supports your claim of 25 shots for a 90% probability, perhaps you can clarify the math. It sounds like the 25 shot number is more of a notional number estimated from your experience, where does the 90% probablility claim come from though?

We'll we picked a really big number that we thought would sound good.

The more you shoot the more you know. I'll agree with him on that. 3 shots gives you a guess while 5 could get you interested. Shooting 3 shots of 3 however would be 9 shots & should give you an idea of what your looking at. All of this being my opinion. Personally I can stop anywhere & decide a load isn't worth working with anymore.

 

[Bart B.]

It sounds like the 25 shot number is more of a notional number estimated from your experience, where does the 90% probablility claim come from though?

Here's my experience with what I consider most credible.

Shooting several 100-shot groups noting the shot count when group size didn't increase more than about 10%.

What plotted shot holes in this 270-shot group fired with match ammo were the first 3, 5, 10, 25 and 50 rounds fired?



Inner ring's 1 MOA, outer is 2 MOA.

Does it matter where they were?

 

[Bart B.]

When the primers are filling the case & you start getting a shiny spot on the brass around the ejector your likely around max. Once a case head starts flowing it's over a pressure I want to be at.

You're way past max when case heads extrude back into bolt face cutouts.

Cartridge brass starts flowing back into bolt face ejector holes at about 65,000 to 70,000 cup; way, way higher than safe pressures in the low 50,000 cup range. That's when that shiny spot shows up on case heads.

None of those proof loads I mentioned had shiny spots from the Garands bolt face ejector holes letting case heads expand back into them.

Anytime case heads expand back into round bolt face cutouts evidenced by shiny round spots on case heads, pressure's way over safe specs established by rational entities.

 

[macgrumpy]

Most of the comments on forums are based on limited personal experience and interpreted by amateur scientists and mathematicians (myself included). Misapplying dynamic laws of physics, injecting false assumptions as facts, flat out false claims, etc., is the norm.

For some semi-automatic rifles it's almost impossible to estimate chamber pressure using the standard processes used with a bolt action rifle, by the time you see all that case damage it's too late. I'm not saying that you shouldn't be familiar with the signs of excessive pressure but I am saying that none of these signs are conclusive. Many factors can effect what you see and the simple fact that the yield strength of cartridge brass can vary quite a lot (with a common yield value of around 65,000 PSI), means that you could either be mislead in to believing that an extrusion mark indicated too high of pressure when in fact it wasn't or not see the same extrusion mark until you've exceeded the SAAMI max pressure for your chambering, it's so variable that I wouldn't really depend on that test for any kind of consistency across the board. On the other hand, if you know your firearm very well and you've already proven (through other processes) that extrusion marks indicate a specific pressure limit has been reached then by all means, continue to use that as a valid field expedient. But if you're just starting out then it's just a guess as to what kinds of pressures you're working with. Primers can move because of a worn primer pocket, even with a proper powder charge. Primer cups can flatten differently to the same pressure depending on any coating or wash that was applied by the manufacturer or slight dimensional differences of the firearm. Primer cups are normally made from cartridge brass so the same problems with extrusion applies as mentioned above. Primer sizes (small, large, pistol, rifle) will change how the same pressure effects the look of the fired primer cup. Primers are just another unreliable test that is only reliable if you have proven through some other process that a specific feature indicates that a certain pressure limit with a specific firearm has been reached. But that's very individualistic and each of us have to come up with our own standard for each of our weapons.

The only way I feel fairly assured of a safe powder load is to stay within factory recommended powder charges and no, lawyers haven't forced Hornady to produce light load recommendations. Powder manufacturers are not the best source of load data, bullet manufacturers are. The guys that produce the bullets usually provide detailed cartridge and test data when they recommend a powder charge along with what specific bullet they used. Powder manufacturers usually provide minimal information about the cartridge, they simply want to tell you how much of their powder you should use. I also use QuickLoad to help develop cartridges but again, it's all about the details, you have to understand a little more than the average shooter about the physics and mathematics involved and you have to be very precise with the inputs. With QuickLoad just knowing that the estimated max pressure is within SAAMI standards isn't enough to tell if the load is safe.

 

[Bart B.]

For some semi-automatic rifles it's almost impossible to estimate chamber pressure using the standard processes used with a bolt action rifle, by the time you see all that case damage it's too late.

Are you suggesting Garand barrels are not good for evaluating basic pressure extremes on their fired cases?

Bullets from them are several feet past the muzzle before the bolt opens. Those 7.62 proof load fired cases had no mutilation from firing or ejecting.

 

[kingmt]

Most of the comments on forums are based on limited personal experience and interpreted by amateur scientists and mathematicians (myself included). Misapplying dynamic laws of physics, injecting false assumptions as facts, flat out false claims, etc., is the norm.

For some semi-automatic rifles it's almost impossible to estimate chamber pressure using the standard processes used with a bolt action rifle, by the time you see all that case damage it's too late. I'm not saying that you shouldn't be familiar with the signs of excessive pressure but I am saying that none of these signs are conclusive. Many factors can effect what you see and the simple fact that the yield strength of cartridge brass can vary quite a lot (with a common yield value of around 65,000 PSI), means that you could either be mislead in to believing that an extrusion mark indicated too high of pressure when in fact it wasn't or not see the same extrusion mark until you've exceeded the SAAMI max pressure for your chambering, it's so variable that I wouldn't really depend on that test for any kind of consistency across the board. On the other hand, if you know your firearm very well and you've already proven (through other processes) that extrusion marks indicate a specific pressure limit has been reached then by all means, continue to use that as a valid field expedient. But if you're just starting out then it's just a guess as to what kinds of pressures you're working with. Primers can move because of a worn primer pocket, even with a proper powder charge. Primer cups can flatten differently to the same pressure depending on any coating or wash that was applied by the manufacturer or slight dimensional differences of the firearm. Primer cups are normally made from cartridge brass so the same problems with extrusion applies as mentioned above. Primer sizes (small, large, pistol, rifle) will change how the same pressure effects the look of the fired primer cup. Primers are just another unreliable test that is only reliable if you have proven through some other process that a specific feature indicates that a certain pressure limit with a specific firearm has been reached. But that's very individualistic and each of us have to come up with our own standard for each of our weapons.

The only way I feel fairly assured of a safe powder load is to stay within factory recommended powder charges and no, lawyers haven't forced Hornady to produce light load recommendations. Powder manufacturers are not the best source of load data, bullet manufacturers are. The guys that produce the bullets usually provide detailed cartridge and test data when they recommend a powder charge along with what specific bullet they used. Powder manufacturers usually provide minimal information about the cartridge, they simply want to tell you how much of their powder you should use. I also use QuickLoad to help develop cartridges but again, it's all about the details, you have to understand a little more than the average shooter about the physics and mathematics involved and you have to be very precise with the inputs. With QuickLoad just knowing that the estimated max pressure is within SAAMI standards isn't enough to tell if the load is safe.

That is well worded. Much better then I put it.

I also agree the signs are harder to see in a automatic but still there.

I bought some factory Federal ammo for the BMG the other day & was surprised to see the head had flowed back into the injector port. I haven't talked to Federal but I assumed the rounds would be about 56K psi. I don't want to load to that hoping my brass last longer.

 

[sugarmaker]

It seems like drawing a curve through only the vertical center of the groups will miss any horizontal dispersion. Maybe find the average radial center relative to the aiming point and plot deviation from that point?

 

[Varminterror]

It seems like drawing a curve through only the vertical center of the groups will miss any horizontal dispersion. Maybe find the average radial center relative to the aiming point and plot deviation from that point?

The first pass in OCW theory is vertical dispersion. Limiting vertical through powder band typically leaves a pretty simple fix for horizontal, so the test only worries about vertical in the first.