Thought Experiment, need Math Wiz

Crosswind

Crosswind

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Hello, just a shot in the dark to see if there's anybody here that has an obsession with consistency.

My question is, if you documented and calculated the means, modes, standard deviations, etc. for the components of your cartridges; is there a way to calculate the means, modes, and standard deviations for the completed cartridges without have to directly measure and record each cartridge?

For example, let's say you measured and recorded accurate weights for 100 casings, bullets, primers, and powder loads. And you did your math to find the standard deviations for this particular batch of casings, bullets, primers, and powder loads. Is there a way you can calculate the standard deviation of the total cartridge weight without having to weigh all 100 completed cartridges all over again?

My first thought was to simply add the standard deviations of the individual parts; but then I thought that wouldn't seem right, since if I were to deduce the range of total cartridge weight, it's highly unlikely that I would assemble a cartridge made of the lightest (or heaviest) parts of each group of components. In other words, an overly heavy casing could be balanced out when combined with a underweight powder load.

If I lost you at 'standard deviation' please don't be offended; I'm just curious about how to ensure ammo consistency. In terms of shooting, won't make a lick of difference with my skills. I'm concerned with cycling reliability, because it seems that people that shoot reloads always seemed to have malfunctions or jams, way more than what I accustomed to, and that number is zero. ;)

Anyways, Thanks for reading.
 
id really like to help and i think i could but im kinda confused ill try anyway find the avg(mean - all items added together then divided by the total number of items) of all the individual components add those together and that should give you the approximate avg of the whole round. and to speed things up its generally accepted in statistics to only measure/survey 10% you dont need the standard deviation or the mode or median but if your using high quality components no matter what of these four numbers (mode, median, mean, standard deviation) you use the number SHOULD be the same or so similar its negligable
 
If one that reloads full length size instead of neck sizing only and don't get too silly with this
crimping process, stuck, jamming and fail to eject shouldn't be much of a problem.
And not getting too silly with excessive pressures either.
Unless your shooting stick has problems.
 
Jamming is usually not a quality control issue. It is a dimensional issue.

Cases may not be sufficiently FL sized.

The OAL may be too long (or too short).

Not enough powder (or too much).

measuring all the components or the completed rounds won't tell you much. Shooting the ammo and then figuring out the correct variables to adjust is the answer.
 
OP, what you're suggesting is nearly impossible. You can get very close but that's about it.

Every time you buy a new can of powder, even with the same nomenclature from the same manufacturer, each lot has a slightly different burn rate. Same goes for primers as well as the make up of the brass casings and bullets.

Far to many variables to bother.

The components we use to assemble our hand loads are made under a commercial plan to make a profit. They also know they can't guarantee their products, other than to keep them regulated between plus or minus parameters. They test heavily to make sure they meet these parameters for safety reasons and of course litigation reasons.

Good luck with your endeavors, even if you do figure it all out, it will only happen for one batch of powder/primers/ weighed bullets/weighed cases.
 
Crosswind said:
Hello, just a shot in the dark to see if there's anybody here that has an obsession with consistency.

My question is, if you documented and calculated the means, modes, standard deviations, etc. for the components of your cartridges; is there a way to calculate the means, modes, and standard deviations for the completed cartridges without have to directly measure and record each cartridge?
Click to expand...

To directly answer the question you pose: yes, you can calculate standard deviations for the completed cartridges

This is a straightforward statistics problem (this is just a reloading-specific example). In fact, this is one of the reasons that standard deviations are used in statistics (rather than extreme spreads etc).


For example, let's say you measured and recorded accurate weights for 100 casings, bullets, primers, and powder loads. And you did your math to find the standard deviations for this particular batch of casings, bullets, primers, and powder loads. Is there a way you can calculate the standard deviation of the total cartridge weight without having to weigh all 100 completed cartridges all over again?

My first thought was to simply add the standard deviations of the individual parts; but then I thought that wouldn't seem right, since if I were to deduce the range of total cartridge weight, it's highly unlikely that I would assemble a cartridge made of the lightest (or heaviest) parts of each group of components. In other words, an overly heavy casing could be balanced out when combined with a underweight powder load.
Click to expand...

You don't add the standard deviations of the component weights. You take the square root of the sum of the squares of the component weight standard deviations. Like this:

SDcase is the standard deviation of your case weights
SDprimer is the standard deviation of your primer weights
SDpowder is the standard deviation of your powder charge weights
SDbullet is the standard deviation of your bullet weights

Here's how you add the standard deviations:

SDcartridge = SQRT[ SDcase^2 + SDprimer^2 + SDpowder^2 + SDbullet^2 ]

(where SDcartridge is the standard deviation of the weight of the assembled cartridges)
 
rnbra-shooter said:
To directly answer the question you pose: yes, you can calculate standard deviations for the completed cartridges

This is a straightforward statistics problem (this is just a reloading-specific example). In fact, this is one of the reasons that standard deviations are used in statistics (rather than extreme spreads etc).




You don't add the standard deviations of the component weights. You take the square root of the sum of the squares of the component weight standard deviations. Like this:

SDcase is the standard deviation of your case weights
SDprimer is the standard deviation of your primer weights
SDpowder is the standard deviation of your powder charge weights
SDbullet is the standard deviation of your bullet weights

Here's how you add the standard deviations:

SDcartridge = SQRT[ SDcase^2 + SDprimer^2 + SDpowder^2 + SDbullet^2 ]

(where SDcartridge is the standard deviation of the weight of the assembled cartridges)
Click to expand...

Well done and Bob's your uncle.

Graydog
 
Other than squibs almost all jams in repeaters will be either gun/magazine problem, or improperly sized ammo (case). The weight, charge etc etc might help with mass produced match ammo accuracy but won't likely affect cycling in a 1911 or M14 etc.
 
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