Reloading to Meet Power Factor with Confidence!

[jwhittin]

I had a chance to run some numbers. The graph below plots the Normal distribution and the T-distribution. The graph is the cumulative distribution function so the Y axis is the probability (p) that a random variable X is less than or equal to a specific value x written as P(X ≤ x) = p.

So it’s easy to compare the two now. As you can see, using the Normal dist for x=-2, P(X ≤ -2) = 2.74 % but using the T-dist it is 14.8%. In our case, we want to know P(X ≥ x) = q which is simply 1- p. So using the Normal dist you get P(X ≥ 2) = 1 - .0274 = 97.3% compared to 1 - 0.14758 = 85.2% using the t-dist.

This means, that until now, there was no way to relate the measurements we take at the range with the results from the 3 samples used for the official PF determination. Using the values of Z I provided in the table at the top of this post and using 8 samples when you chronograph your ammo allows us to now relate the two.

Edited February 25, 2016 by jwhittin

[Foxbat]

"What do you mean this is Cleveland? My math says this is Hiroshima!"

[cnote]

Bump

[johnbu]

I don't see where you are accounting for bullet weight variation. I reloaded yesterday and on a whim weighed each bullet. Most were 124-125gr, but the low was 122.7 the high was 128.2. About 1/10 was under 124 by some amount, even if only 0.1gr.

Should we calculate pf with the minimum measured bullet?

[ChuckS]

I don't see where you are accounting for bullet weight variation. I reloaded yesterday and on a whim weighed each bullet. Most were 124-125gr, but the low was 122.7 the high was 128.2. About 1/10 was under 124 by some amount, even if only 0.1gr.

Should we calculate pf with the minimum measured bullet?

Weigh some bullets and find the SD for them. Then use nominal-3SD as the weight for further calculations.

[jwhittin]

Johnbu,

My method does not account for variations in bullet weight. Mainly because a 1 or 2 gn change in weight doesn't impact PF much. So if you are adding 2 to 3 times your standard deviation of your velocity, you don't have to worry about the weight. If you are concerned, stay in the 2.5 to 3*SD range. You can check worst case bullet weight but even at 3 or 4 gns you should have good margin.

[cnote]

Springtime chrono reminder

[Got2beshooting]

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.

I saw this when I went to optics nationals. I shoot 133 PF in Michigan (50 degrees 800ft above sea level) and when I went to the match I dropped 2 PF (80+ degrees 100ft above sea level). I personally thought my PF would have been higher in Florida. But Someone once told me that TG goes slower at warmer temps. Not sure how accurate that is though. Last years Michigan sectional I shot a the same PF the test before the match. So the change in the geographical area may have made a difference.


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[GeneBray]

Good discussion. I would like to bring up some points and see what the general comments are.

 

As to some of my background, I shoot USPSA/IPSC and reload. More decades ago than I care to count I earned an undergraduate degree in mathematics. And, more recently (but still measured in decades), a MS Systems Management. The degree contained approximately equal parts of management courses, and math focusing on statistical analysis, time value of money, and other areas necessary the technical analysis and management of manufacturing and systems procurement.

 

For the following, lets assume for the sake of discussion we control the following with the degree our measurement systems allow 1) cases volume, 2) powder charge, 3) bullet weight and dimensions, and loaded ammo COL. Basically, doing the best one can to eliminate variables in test results.

 

Two variables we cannot control, in most cases are relative humidity, to which the powder is exposed, and temperature (OAT and ammunition temperature) at the time of testing. Also, OAT, humidy, and density altitude all affect bullet velocity. I suspect, but do not know, how much affect it would have at 10’ when chronographing.

 

Lets say for discussion we are testing 9mm Luger using a 125 gr bullet. We want at 130 PF so the velocity should be 1,040 fps. Holding everything constant except for bullet weight which we will very by 0.1 gr and then chronograph the loads. What are the velocity changes as the weight changes? After 20 years of reloading for competition, I honestly don’t know except that it is small.

 

I ran numbers based assuming the only variable was bullet weight which varied by 0.1 grain over a range from 124.0 to 126.0 grains, and then changed velocities by 1 to 5 fps per 0.1 grain a weight and calculated PF. Not until you reach 5 fps do you drop below a 125 PF. I am certain that 9mm velocities do not vary 5 fps per 0.1 grain variance in bullet weight. My assumption was the only variable is bullet weight and that lighter bullets result in higher velocity and the converse as the weight goes up. It may well be just the opposite, but reversing the velocity change doesn’t change the result except as whether the change is at the light or heavy end of the data.

 

Most (if not all) modern smokeless powders are hydroscopic means they absorb water and do so readily. Water affect the powder density which affects it burn rate and volume of gas produced. My guess both affect the the chamber pressure meaning there is a direct affect on velocity. There is a reason most powder and press manufacturers say don’t leave powder in the press. Reload, empty and store in a seal container. But, every time you open a jug of powder you are changing the humidity of the air in the container. Seems sort of like a “no way to win”. Also, nitroglycerin is very temperature sensitive. It becomes more reactive as temperature goes up. I believe most, if not all double based powders, use some type of nitroglycerin in their formulation.

 

In practice no one (I suspect) checks case volume for several thousand case to find 300-600 that are the same with in a range. Nor, do most shooters weight bullets to get 300-600 within a few tenths of a grain of each other. (I am certain some may.) So, no matter what press you use there will be some variation in case volume, bullet weight and dimensions, powder charge, powder humidity with affects it density, and COL, and all affect the velocity.

 

My approach has been to always chronograph 10 rounds at a time. I have a load which veryconsistent with regard to chronographing for over 10 years. And, that is chronoing using my visible light CED and chronographing over dual IR CEDs at major matches. I check the chrono using that load to ensure I am getting good readings. The test ammo varies ~10 fps over a temperature range of ~40 degrees to 85 degrees, and is typically single digit SD for 10 rounds.It is Titegroup if anyone cares. 

 

When I analyze the data I always look at the first three rounds and the 10 rnd. string. I ensure both consistently give me the required PF for the load/gun. Ten days out I start monitoring weather for temperatures. Based on forecast I may adjust the load 0.1 to 0.2 grains up or down. And, almost never do I adjust down. Always make power PF in 9mm and .40 S&W. Several years ago, I had problems twice with .45 ACP and went minor. To this date, I cannot identify a problem that caused low velocities. The major difference between the calibers is I use coated lead bullets in .45 ACP, and jacketed for the others. I do knowthere is more variation in bullet weight and dimensions with lead bullets than jacketed. And, I see larger extreme spreads in velocity with lead than jacketed. It is to be expected without a lot of weighing tocontrol variables.

 

I do weight anywhere between 50 to 200 bullets to get weight stats for match bullets. I keep the numbers with me for 1, 2, and 3 standard deviations and will check the bullet weight from chrono to decide what to do if I ever get to “weight it or shoot it.”

 

I hope some can comment and expand on this. Maybe my comments will be helpful for some one.

[cnote]

good stuff, thanks

[cnote]

always a good reminder

[bwikel]

I don't get stuck in the details as long as I have a repeatable SD of 10 or less. Take that out 3 SD's and you have a process with a very high confidence of success. 

[jwhittin]

On 5/21/2019 at 9:14 AM, bwikel said:

I don't get stuck in the details as long as I have a repeatable SD of 10 or less. Take that out 3 SD's and you have a process with a very high confidence of success. 

 

Finally! Some who understands. This is EXACTLY how my process is supposed to be used!!!  

[cnote]

spring bump

[usmc1974]

Hummm, are people really worried about making power factor today? Even after it's been lowered?

   Kind of funny, I never gave power factor a second thought all the time I was shootingIPSC /USPSA starting back in 1982 or 3 can't quite remember. Back then I knew 5.2 grains red dot and 200 grain semi wadcutter gave me about 900 feet per second.Hummm. just asking.