The Limits of Repeatability

We expect that if our scale says a bullet weighs 202.4 grains then that's what it weighs.

But, I expect you already know that's not 100% correct. There's accuracy versus precision and, somewhere in there is also tolerance.

But that's not what interests me at the moment.

Here's what does: If I weigh the same bullet twice, will I get the same answer? Will that 202.4 grain bullet read "202.4" tomorrow? And the day after?

That is repeatability.

I'm interested in this because I want to sort some bullets and, because I have so many to do (3000+), I want to be as efficient as possible on the first attempt. I don't want to have to go back and do it again.

So the question is, how many piles of bullets should I make?

Will the bullets I put in the "200.0 grain" pile today belong in that same pile tomorrow or will some of them get moved to the "200.5" pile?

If my goal is to have bullets that weigh "practically" the same amount for my long-line loads, what is the "practical" range of weight I should look for?

There, in a nutshell, is what I'm after. I want the range of weight, the tolerance, I can expect from one pile.

And it is the repeatability of the scale, its ability to measure a given weight from one day to the next and come up with the same answer, that is the issue.

Strategy

To find out how repeatable my scale is, here's what I decided to do.

I would take ten bullets that weigh slightly different amounts -- the batch of moly-coated 200 grain bullets I've been complaining about would be ideal -- and, one bullet at a time and in random sequence, I would weigh each of them. I would then mix up the 10 bullets and do it again. And then again until I had five weighings and then I would see how much I got for each bullet in each set.

The key question would be whether a given bullet would weigh the same each time or not.

Would the scale repeatedly weigh the same bullet the same each time?

Results

Here are the "raw" results.

 

Table One - Raw Results

	1	2	3	4	5	6	7	8	9	10
Set #1	202.4	200.4	201.8	195.2	197.1	200.1	203.1	198.1	195.4	198.3
Set #2	197.0	201.7	195.4	200.4	195.1	198.1	200.0	197.8	202.5	203.1
Set #3	195.0	195.4	198.0	203.1	202.5	200.1	201.7	198.2	197.2	200.5
Set #4	202.3	194.9	195.3	198.1	201.6	197.9	202.9	200.0	200.4	197.0
Set #5	202.9	200.4	201.6	195.3	197.1	198.0	202.3	197.9	200.0	195.2

 

The first row, Set #1 above, is the first weighings of the ten bullets, recorded from left to right. Remember that I then shuffled the bullets and did it again. That's Set #2. I continued this, shuffling the order of the bullets each time before re-weighing them. I stopped when I had completed five cycles, five sets.

Hence, five rows (separate weighings) of ten bullets (the columns). And because I shuffled the order of the bullets in each set, the weights appear in random order from left to right.

But this doesn't show me how much the same bullet weighed in each set. For that, I need the same bullet lined up from top to bottom over the five sets.

So I sorted each row into increasing weight, left to right. This put the bullets in order by weight.

Here's the result after the sort.

 

Table Two - Results in Bullet Weight Order within Each Row

	1	2	3	4	5	6	7	8	9	10
Set #1	195.2	195.4	197.1	198.1	198.3	200.1	200.4	201.8	202.4	203.1
Set #2	195.1	195.4	197.0	197.8	198.1	200.0	200.4	201.7	202.5	203.1
Set #3	195.0	195.4	197.2	198.0	198.2	200.1	200.5	201.7	202.5	203.1
Set #4	194.9	195.3	197.0	197.9	198.1	200.0	200.4	201.6	202.3	202.9
Set #5	195.2	195.3	197.1	197.9	198.0	200.0	200.4	201.6	202.3	202.9
Min	194.9	195.3	197.0	197.8	198.0	200.0	200.4	201.6	202.3	202.9
Max	195.2	195.4	197.2	198.1	198.3	200.1	200.5	201.8	202.5	203.1
Range	0.3	0.1	0.2	0.3	0.3	0.1	0.1	0.2	0.2	0.2
Variation	0.15%	0.05%	0.10%	0.15%	0.15%	0.05%	0.05%	0.10%	0.10%	0.10%

 

"But wait," you might object, "if the scale is reporting a slightly different weight for a given bullet, isn't it possible that bullet #1 might sometimes weigh heavier than bullet #2 and then sometimes the opposite? That would mean that column 1, for example, might not actually be the same bullet each time!"

I would have to answer, "Yes, that's quite possible."

"But my goal," I would go on, "is to separate the bullets into different piles in a repeatable manner. If two bullets are so close that their weights shift their order from time to time, that variation would really put them into one pile."

Sorting the weights according to the scale's reading is really what I'm after, not the actual weight of the bullets.

Therefore, in this second table, if we read down each column vertically, we see what the scale said for something close to that weight.

This is where the repeatability, or lack thereof, shows up.

And from the above data, it therefore looks like the scale's repeatability for things weighing about 200 grains is going to be from 0.1 to 0.3 grains.

To make it easier to quantify this, I added rows for minimum, maximum, the range (maximum - minimum) and finally, the percent of variation (range / maximum).

The worst case variation (above) was 0.15%. That means that if I weighed a 200.0 grain bullet but then weighed a bunch of other things before re-weighing that same 200.0 grain bullet a second time, the two readings of the same bullet might vary by 0.3 grains (200 * 0.0015).

That's the number I'm after.

It means that, for 200 grain bullets, a difference of 0.3 grain between two bullets (or the same bullet weighed twice) could be entirely due to the scale.

Conclusion

"So what?"

Good question. Does this really matter?

For the scale I use, sorting to identical readings gives me bullets that are within 0.3 grains of each other.

My equipment won't let me be separate bullet by weight any better than that.

My sorting of the moly-coated bullets, for the first 1000 with 3000 still to go, has been into "whole grain" buckets. There is a 200 grain bucket, a 201 grain bucket, and so forth.

For my next round of testing, I'm going to load and test the bullets in the 200 grain bucket. From the above, I know those bullets vary from 199.85 to 201.15 grains, a range of 1.3 grains and, if they perform well, I'll know "that's good enough." (Actually, I'll know that's "more than good enough.")

But if they don't perform well and I suspect bullet weight variations might still be an issue, then I can sort them down to those that read (on the scale) EXACTLY the same, say 200.5 grains.

But no matter what I do, there's still going to be that 0.3 grains of non-repeatability. Those "identical weight" bullets may actually vary from 200.35 to 200.65 grains. Will that be good enough?

If so, I'll have my answer. I'll know how much weight variation is permissible and, in the future, I can sort bullets accordingly.

And if not, then I'll also have an answer, and that is that at least with some bullets, it doesn't matter how closely you match their weight. Some bullets will still just not perform at the long line.

So, my hope is that I'll discover there is a weight variation that can be tolerated at the long line.

Is "within 1.3 grains" good enough or do I have to go all the way to 0.3 grains?

I hope to find out.

And when I do, I'll know its number.

 

[Phew!] I'm beat.

How about we go and shoot up some targets?

All right!

Bullet Weight Distributions

I weighed 100 samples of each of two different 200 grain bullets. Here are the results and some comments.

Bullet Weight Distributions
(Click for bigger version)

First, let me describe the two bullets.

The Bear Creek -- blue line, the lower and broader of the two -- are labeled as molybdenum-coated 200 grain SWC (Semi-Wad Cutter) bullets with 0.452" diameter. I bought these back when lead was in short supply and almost no one had any bullets for sale. The "price was right" as they say and, from this chart, you can probably see why. They are very inconsistent in weight varying from 193 to 202 grains.

The second bullet, the pink spike, is from X-Caliber Bullets. The box says they are 200 grain LSWC (Lead Semi-Wad Cutter) bullets also with a 0.452" diameter. These are a much later and more expensive purchase. And as the chart clearly shows, their weights are much more consistent; although they range from 195 to 198 grains, in fact only 7 weighed 195 and only 3 weighed 198 grains. The remaining 90 weighed either 196 or 197 grains.

Tony Brong, in Electronic Scales Part II, said that by sorting bullets by weight, you then have "the opportunity to select a group of bullets to be culled solely for the long line; where their near identical weights will assist you in minimizing the potential of vertical stringing."

But how wide a deviation would Tony accept, two grains, one grain, half a grain?

So I called him.

"Tony, this is Ed. How are you?"

And after we exchanged pleasantries I asked, "Just how tight a weight grouping do you look for when making long-line ammunition?"

I was astonished when he said, "Plus or minus 0.1 grains."

Wow, that's tight!

After thanking Tony for sharing his expertise I looked at my two sets of data.

I had not sorted to a tenth of a grain. If I wanted to load the moly-coated bullets for the long line would I need to pick the most populace weight (201 grains) -- they were still in separate baggies, one for either weight -- and re-weigh that group to a tenth of a grain?

Now the old hands probably took one look at the chart and thought, "Forget the molys. They're no good for the long line. Save 'em for guests and fishing lines."

But I'm not that wise, not yet anyway.

Plowing ahead, I reasoned that if I took the 17 bullets that weighed from 201.0 to 201.9 grains and re-weighed looking for the 201.4 to 201.5999 grains (Tony's plus or minus 0.1 grains), I would "probably" get about 3 bullets (one-fifth of 17).

And since I had started with a sample of 100 bullets, that would mean that only 3% on average would fall within that range.

Only 3%?

That's awful!

The old-timers are nodding their heads now.

If the same logic is applied to the X-Caliber bullets, I should net 11% within that same plus-or-minus 0.1 grain weight range.

If you then calculate what I paid for long-line bullets, the higher cost of the box of X-Caliber bullets is multiplied about 9X whereas the cost of the cheaper bullets gets multiplied by a whopping 33X -- all of a sudden those "cheap bullets" leaped out to be way more expensive, for long-line bullets, than the X-Calibers.

That is, if I want to load to the level of precision Tony mentioned, I'd have to set aside 97% of the so-called cheap bullets for something else. With the better quality bullets, I would still be setting aside 89% but notice that I'll be making ammunition with 4X as many of the X-Calibers. That's a much better level of productivity.

While I don't think my shooting will be able to realize the full advantage of ammunition as good as what Tony produces, I do know that if I'm shooting poor ammunition and a shot goes astray, I won't know if it's the ammo or me that messed up.

With good ammo in a good gun, I'll know.

It's me.

 

Revised (11 January 2011)

 

The math (above) has been corrected.

I had erroneously figured the numbers assuming "plus or minus 0.1 grains" gave a range of 0.3, from 201.4 through 201.6 whereas, in fact, it is a range of 0.2, from 201.4 through 201.5999. That means the acceptance rate is worse than I originally wrote, one-fifth of 17 (3+%) instead of one-third (5+%), and similarly for the X-Caliber bullets. This error and the consequent numbers, computed therefrom, have all been corrected in the text.

Last night I began going through my supply of molys and sorting them by weight. That is going to take some time as I have about 3000 on hand.

For the first pass, I am sorting to "whole number of grains". That is, there are twelve buckets on the work table, one for each integral number of grains weight: 192, 193, 194 and so on through 203.

And using the 201 grain bucket (201.0 through 201.9 grains which can also be described as 201.5 plus 0.4 or minus 0.5 grains), I will make some test rounds to see how they perform at 50 yards.

If they perform well, I expect I can probably do the same with the 200 and the 202 grain buckets. (The remaining bullets will go in the recycle bin.)

If they perform less-than-well but show significant promise, then it may be worth an additional sort, to the "plus or minus 0.1 grain" which will then be loaded and tested.

Of course, it's quite possible that the 201.0 through 201.9 grain rounds will not group in which case the whole lot is no better than the dross they may not have been fully separated from.

Regardless, weighing and sorting that many bullets is a real time killer, and boring as the dickens. I did 1000 last night over a couple of hours but it'll take at least two more sessions like that for this first complete pass.

Stay tuned.

Brass Cleaning

Ok, Ok, it's a boring subject, I know. But it's gotta be done so let's get this out'a the way.

First, equipment and supplies.

• Cleaning machine. I've got the small Dillon vibratory cleaner that does up to 500 pieces of brass in about an hour or so. It's well made and does the job and, after several years, I'm still using the original.
  And, yes, it's expensive. But you're not into this hobby because it's affordable ... because it isn't. And you don't reload because it's more economical -- come on, I know better than that. You reload so you can shoot, and you shoot everything you make. If it was "economical", you'd be selling what you've made instead of shooting it up. So stop complaining and go ahead and get a machine you won't have to think about.
• Abrasive for the cleaning machine. Some use ground up corn cobs. Some us ground up walnut shells. Choose whichever is available and least expensive. My pick comes from Harbor Freight and, at roughly $25.00 for 25 pounds, the price will be hard to beat -- I know that contradicts the attitude I espoused in the previous item. Ok, so I'm arbitrary. Or maybe after buying that expensive Dillon cleaner, I feel guilty and compensate by saving money on the abrasive. Ok, I feel guilty. Can we move on now?
  Regardless, beware the shipping charge from Harbor Freight for that 25 pounds. It's an additional $9.00 for me. Instead, if you have one of these stores in town, pay the local sales tax (about $2.00 in Phoenix) and save on the shipping. I replace the media when the brass starts looking "very dusty" after cleaning. I'd guess that's about every 5-10 batches, more or less. At that rate, the 25 pounds of walnut media will last for a long time.

• 
  Manual Timer

  Timer. While you may find a "Turn off the plugged in appliance in two hours" electrical timer somewhere, why bother? Just write yourself a note and leave it where you'll find it. Coffee pot, refrigerator, front door and computer screen are all good places to stick it. I've left brass churning in there for hours and hours with no apparent harm so it's no big deal to run over. (For "noise abatement", put the machine outside and well away from any windows. It does make a racket.)
• Separator. Use this outside -- the "stuff" that floats up is gonna be bad for your lungs. Don't breath it! Again, I have the little Dillon model and it works fine.
  But there are two caveats. First, watch out for the stray 22 shell amongst the 45s. During cleaning, they will "separate" very nicely but when you dump the batch into the separator, they'll sneak back inside a 45 shell and stay there until reloading when it'll make a nasty noise in the deprimer. Inspect the batch carefully and remove any non-45 brass as early as possible.
  And second, tumble and separate thoroughly. Bits of the walnut media may hide in the flash hole and make an odd "scrunch" when you deprime. It's distracting and causes me to pause and look to see what's wrong. Interruptions in reloading lead to errors in reloading, and that can be bad. Avoid it by taking the time to purge any wrong size brass before you start pulling the crank.
• Brass polish (optional). This is dumped into the walnut media (and run empty for about 10 minutes before adding brass) and shines up the brass more than just the walnut shells would've done. In my opinion, this is purely cosmetic -- but there's nothing wrong with "clean and pretty." I use it and, again, it's the Dillon product. (What can I say? Their store is "in town" for me and it's a fun place to lust and drool.)
• Something to store the cleaned brass in -- and it's not from Dillon! I use the quart-size ZipLock baggies and, because I keep my brass separated by head stamp, I also stick in a hand-written 3x5 note so I can see what flavor of brass is in a given bag from a couple of feet away. This week I'm reloading Winchester brass so those are the bags I'm after.
• A place to store things when not in use; one of those annoyingly essential things to figure out. Mine are under the work table and come out from there when in use and then back when done.

 

That's about it -- and I can see by the note taped to my computer screen that the current batch of brass has been in the cleaner for 75 minutes. It should be done.

I'm headed outside to tumble and separate.

See ya!