Pctechdude,
I appreciate that you made your own warning about over-book loads at the beginning, but the board has a required warning to be inserted in such cases. It's in the sticky at the top of the forum titled:
REQUIRED READ for those posting Extra Heavy Load Information. In this instance I will edit it in for you. Please check stickies for basic forum information where they apply.
A couple of points: You said Federal HST and Winchester Ranger were loaded with BE-86. Did they publish that information somewhere (a Federal contract maybe?) or did a powder company technician provide that information? Usually powder choice is kept proprietary, and you often can't tell based on appearance not only because of appearance similarities among a number of powders, but also because ammunition makers can order lots made with variations not available to the handloader. An example would be Federal's use of special IMR4064 (published in an ATK document) with flash suppressant for the Mk.316 mod.0 sniper ammunition they make for the government. So the fact an ammunition uses a type of powder does not mean it's identical to what we buy for handloading.
The second point is that, as the Alliant tech mentioned, commercial loaders buy bulk grade powder normally (though I am aware of a couple of apparent exceptions) and not the canister grade sold to handloaders. Canister grade is more expensive because it is tweaked to keep burn rates in a narrower lot-to-lot range than bulk powder is kept to (though it can be the same by coincidence at times). This means bulk lots have wider lot-to-lot burn rate variation, and the ammo manufacturers adjust their charges to compensate for that using pressure test guns rather than relying on a recipe. The fact most handloaders don't have pressure test guns is why canister grade burn rates need tighter burn rate tolerances. If they didn't do that, then load manual recipes would be invalidated. Because of the burn rate variation issue, commercial loads can wind up with charge levels that are higher or lower than the canister grade version would need to produce the same peak pressure. Thus, pulling bullets to weigh charges does not necessarily provide a weight suitable for use with the canister grade version of the same powder. It requires validation testing in a pressure gun to know one way or the other.
You may have the above concerns covered, but I mainly don't want other readers to get the idea they can copy commercial loads directly without special instrumentation or validation from a trusted source.
Nick_C_S said:
…I've gotten to just doing a bunch of strings of six (particularly with revolver), and then figuring out the total SD by hand. As long as all the strings are six (or whatever amount), you can simply add up each SD (displayed on the Chrony) and divide by the number of strings - and that'll give you the SD for the entire bunch.
Actually, that doesn't work out quite. It tells you what the average 6-shot SD is. It doesn't take into account that the mean velocity for each set of 6 will be different from the mean velocity for all sets of 6 combined, as would be used to find the overall SD, nor does it consider the higher square root bias the standard SD calculation has in a small sample.
I used Excel to create thirty shots averaging 1000 fps with an SD of 10 fps normally distributed around that mean value of 1000 fps, and divided it into five groups of six. Over 40 trials (got bored and stopped), averaging the five 6-shot SD's gave me results averaging -0.360 smaller than taking the SD of all thirty shots together. Of the 40, the error ranged from -2.23 lower to 0.59 higher, with a standard deviation of 0.56.
You can attack reducing the error a couple of different ways. One is to take the SD of the SD's, square it, then add it to the square of the average SD, then take the square root of that sum. When I did this, it reduced average error to less than +0.1 and the standard deviation of the errors came down from 0.56 to 0.51, with the error spread -1.446 to +0.652.
The other method is to eliminating square root bias from the estimates. To do this, take the 6 shot average SD (or do it for each 6-shot SD before averaging) and divide it by 0.9515. (An Excel formula for the bias factor for different sample sizes is below.) When I used that adjusted average 40 times, I got an average error just over +0.1, with an error standard deviation of 0.49, and an error spread from -1.435 to +0.769.
To try this out in Excel for yourself, the formula to make a cell produce a random number normally distributed around a specified average is:
NORMINV(RAND(),μ,σ)
where μ is the mean and σ is the real standard deviation for your theoretical infinite shot population.
In this case, for an average velocity of 1000 fps and a standard deviation of 10 fps, I used:
=NORMINV(RAND(),1000,10)
in each of thirty cells in a column to get a simultaneous set of 30 velocity variations in a bell curve distribution around 1000 fps.
For the other method, to get rid of small sample bias resulting from the way sample standard deviation is normally calculated, divide the SD from your chronograph by the result of this Excel formula:
(2/(n-1))^0.5*GAMMA(n/2)/GAMMA((n-1)/2)
where n is the number of shots in a sample.
Divide all your six shot SD's by that formula before averaging, or divide their average by it afterward and you will have a more accurate estimate of population standard deviation (that's what sample standard deviations try to be; an estimate of population standard deviation). Due to the standard deviaition in 6-shot mean values, there will still be error that hops around some, randomly, but at least the result will be more accurate on average.