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jwhittin

Reloading to Meet Power Factor with Confidence!

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I still see a lot of people wondering why they fail to meet PF at a match. If you just add a few extra power factor points, now you know what can happen. The bottom line is that velocity is random in nature and the BEST way to understand and manage it is to use statistics. You don’t need to have any special math skills. This post provides the simple steps to follow. For the why and more details, see Frontsight Magazine, Jan/Feb 2015 Edition, Pg. 70.

The standard deviation (STD) measures the amount of variation (uncertainty) around the average velocity and it should always be used when reloading. The table below maps the chance of failing an official USPSA PF check to the variable Z. Use Z for reloading by simply multiplying the value of Z by your STD (measured using 8 rounds with your chronograph) and add the result to the required velocity to make major or minor PF for your bullet weight. The result is your desired load velocity.

Values of Z are shown from 0 to 3 to illustrate the tradeoff between Z and the chance of failure. My guidance is to use values of Z in the 2 to 2.5 range. Note that if you use the STD (i.e., Z=1), which I’m sure some people do, the chance of failing PF is a whopping 44%.

Z Chance of failing PF (per USPSA rules)

3.0 3%

2.5 5%

2.0 10%

1.5 21%

1.0 44%

Assume a shooter’s standard deviation for a load with a 155 gain bullet is 15 ft/second (chronographed using 8 rounds). An average velocity of at least 1065 ft/sec is needed to make major power factor. To limit the risk of failure to no more than about 10%, use Z = 2.0 and simply add 30 ft/sec (Z*STD=2*15) to the required velocity to meet PF. Thus the desired load velocity would be 1065+30 =1095 ft/sec. It’s that easy!

In our example above, if we “just add a few PF points” and loaded to say 168 PF, this is equivalent to Z=1.26 and the result is a 1 out of 3 or 33% chance of failure. If instead we use the measured extreme spread (which can typically run 60 fps or higher) and load to 1065+60 =1125 fps, it is equivalent to 4*STD or a 186 PF and we needlessly incur excessive recoil and higher cost.

If you always load to say a PF=170 (1097 fps), your chance of passing is okay so long as your STD remains below 16 fps (1097-1065)/2. However, if your STD is actually 23 fps, Z drops from just above 2 down to 1.4 (i.e., 32/23) and your chance of failure more than doubles going from below 10% up to 26%. This is why you should measure and use the STD.

Shoot with any comments or questions!

Edited by jwhittin

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Yeah and don't forget velocity is a function of air temperature, humidty, and barometric pressure. What you chrono at 100 degrees in Florida at 90% humidity at sea level will not be the same in Colorado at 6000 feet 40 degrees and 15% humidity.

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Or, without doing the math… Chrono 8 rounds and if ANY are below your minimum power factor, increase your load so that all 8 are above the desired bullet speed. That will provide 100% confidence that you will make PF :)

Sent from my iPhone using Tapatalk

Edited by bradsteimel

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Chrono 8 rounds and if ANY are below your minimum power factor, increase your load so that all 8 are above the desired bullet speed.

I chrono 20 rounds, and make sure that ALL 20 are at or above PF. :cheers:

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Or, without doing the math… Chrono 8 rounds and if ANY are below your minimum power factor, increase your load so that all 8 are above the desired bullet speed. That will provide 100% confidence that you will make PF :)

Sent from my iPhone using Tapatalk

Actually, statistically speaking, all you know for 100% confidence is that the 8 rounds that you shot made PF. :devil:

Edited by ChuckS

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Chrono 8 rounds and if ANY are below your minimum power factor, increase your load

Actually, statistically speaking, all you know with 100% confidence is that the 8 rounds that you shot made PF. :devil:

Lies, large lies, and statistics. :devil:

As mentioned above, many other factors involved and I personally feel much more

confident shooting 20 rounds rather than 8 over the chrono. :cheers:

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I just wish the OP would stop calling it STD! :)

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Great question rev1911! I’m glad you asked.

We are using a few samples to estimate parameters such as average velocity and variance. We use these sample estimates to make inferences (judgements) about a much larger population; in this case, the population is all our reloads of the same bullet profile, weight, powder, OAL, primer, etc. It has long been established that for most applications that follow the Normal distribution (such as velocity) only about 8 samples are needed to provide good results when using the sampled estimates to make inferences about the population. Bad results are produced as the sample size goes below about 8 samples and in fact the Normal distribution can no longer be used. Going above 8 samples is not necessary and thus a waste of time and material. The chance of failure given in the table above corresponds to 8 samples.

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Yeah and don't forget velocity is a function of air temperature, humidty, and barometric pressure. What you chrono at 100 degrees in Florida at 90% humidity at sea level will not be the same in Colorado at 6000 feet 40 degrees and 15% humidity.

Do people see that significant of variation for the typical handgun rounds we use at 10ft from the muzzle? I can't see anything but temperature that affects powder burn being of consequence. I would think your advice runs better with longer distance rifle shooting.

Edited by PKT1106

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"Lies, large lies, and statistics. :devil:" LOL.

ChuckS is exactly right!

Are you feeling the power of statistics yet!

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is the original article supposing only shooting 3 rounds? or the 7 that you actually get to shoot (if needed)?

My empirical testing has only been a handful of big matches (maybe 10 chrono visits total), but everyone of them was withing 1 or 2 pf of my averages at home. And I never had to go past the original 3 shots either.

Looking at the numbers above, one would expect that I would at least have had some close calls, and likely failed a few times, so either I am lucky, or something is fishy. ( load 5-7 above pf and typically see SD's in the 15-ish range).

I typically chrono 6 or so rounds at least twice on separate occasions before a major match, and it seems like they average pf is always within 1 or 2 of what I've gotten in the past. So I don't worry too much about the chrono.

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I never had to go past the original 3 shots.

I've gone to the fourth shot :sick:

With some reloads I bought from a local shooter. :ph34r:

Never again - now it's 20 shots over the chrono, and ALL MUST go PF at least. :cheers:

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Yeah and don't forget velocity is a function of air temperature, humidty, and barometric pressure. What you chrono at 100 degrees in Florida at 90% humidity at sea level will not be the same in Colorado at 6000 feet 40 degrees and 15% humidity.

Do people see that significant of variation for the typical handgun rounds we use at 10ft from the muzzle? I can't see anything but temperature that affects powder burn being of consequence. I would think your advice runs better with longer distance rifle shooting.

I don't see any difference. Last year at Area 1 (4700') I chronoed at exactly the same velocity as I do at home (250'), but I don't load close to minimum (136 for minor, 172 for major) so I've never even come close to failing chrono.

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I never had to go past the original 3 shots.

I've gone to the fourth shot :sick:

With some reloads I bought from a local shooter. :ph34r:

Never again - now it's 20 shots over the chrono, and ALL MUST go PF at least. :cheers:

nothing wrong with that. it's easier than learning math.

just plugging my ballpark numbers into bell curve calculator (132 pf which is around 898 fps with a 147 gr bullet, SD of 15), there is only a tiny area (less than 1% as a guess) of the curve that is below 850 fps. The chances of having 5 or 6 shots come out of that tiny percentage seems vanishingly small. Loading to z=3 or thereabouts I should have a 3% chance of failing, but just looking at that curve, 3% seems wildly high.

Admittedly it's been a while since college, but I majored in applied math and statistics, so understand the fundamental concepts.

bellcurve_zpsa5cqcgbb.png

Edited by motosapiens

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Motosapiens,

In your case, using PF=132 is equivalent to Z=3.2 which provides a high confidence level. As I mentioned above, you can’t use the Normal distribution in this case. It is not accurate for small sample sizes. Take a look at the T-distribution and you will see the tails are much higher.

How did you insert the png file? I can show you the T-dist.

Edited by jwhittin

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Motosapiens,

In your case, using PF=132 is equivalent to Z=3.2 which provides a high confidence level. As I mentioned above, you can’t use the Normal distribution in this case. It is not accurate for small sample sizes. Take a look at the T-distribution and you will see the tails are much higher.

How did you insert the png file? I can show you the T-dist.

i just saved the image to my photobucket account and linked to it here with the insert image button.

Anecdotally speaking, it appears that the normal distribution with tiny tails fits my experience better. There appears to be no chance short of something bizarre happening (like a reloading equipment failure) of not passing chrono. I'm not sure I've ever even had 1 shot of my match ammo chrono under pf (in my own tests, or at majors), so it's hard to imagine I could get at least 4 and probably 5 of them of under pf at a match. Even if I did get 5 under pf, as long as they were reasonably close (124 or so), a 6th typical shot of 132 pf would save me.

Are you including shots 5-6 (and possibly 7) if necessary in your calculations? or only going on the initial 3 shots?

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Mark, the confidence levels I calculated are only based on the first 3 rounds. My point is that you can't use the Normal distribution at all. You have to integrate the area under the t-dist for the statistic under evaluation. You can clearly see that the tails of the t-dist are much larger than the Normal dist. I'll run some numbers when I have time to show you the difference.

Trying to add a plot I generated.

post-42675-0-45299300-1455990239_thumb.j

Edited by jwhittin

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I've always said that if you load for 172-173PF or more your chance of going Minor is almost zero, and it doesn't take statistics of formulas to figure that out. Anything lower and you might wind up unhappy, or at least down to the last round at the chrono.

I had a batch of ammo loaded for several majors a few years ago that went (going off memory) 173PF at two different majors, then 166.1PF at Nationals. The same lot of bullets, primers, new cases, etc, etc....all loaded as one big batch with a chrono test before and after giving me the same numbers. I came home and ran some over the chronograph because it was so unusual, and got my normal 173PF or so out of them. I can only guess that I just happened to get three in a row that were on the very low end of the ES for that batch.

People that go Minor are often heard saying "but it was consistently 167-168 back home" and there's a lesson in that.

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Sure, once you get closer to 10 points over, you are probably fine. Better to be high than not high enough.

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