RELOADERS CORNER: SD — what it matters and why

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Getting a handle on improving long-range accuracy has a lot of to do with understanding the importance of consistent bullet velocities. Here’s a start toward that…

Glen Zediker

There’s one more thing (seemingly, there’s always one more thing…) that’s important to accuracy at extended distance. I’ll say “extended distance” is anything over 300 yards. That is bullet velocity consistency.

I’ve said in these pages before that a good shooter will lose more points to elevation than to wind. This next explains that a might more.

First, and the first step, is getting and using a chronograph. It doesn’t have to be a zoot-capri model, and nowadays that’s a fortunate bonus because there are a number of inexpensive chronographs available that are entirely accurate.

PACT chronograph.
A chronograph is essential, well, at least for all this here. There are a lot of good ones. I’m partial to PACT.

Check Misdouth offerings HERE

magnetospeed chronograph
The newer barrel-mounted electro-magnetic chronographs make it really easy. I like the idea of being able to chronograph from shooting position, not just from a benchrest. This is a MagnetoSpeed.

“Standard deviation” (SD) is probably the most commonly used measure of bullet velocity consistency. SD reflects on the consistency of velocity readings taken over a number of shots. “Standard” reflects on a sort of an average of the rounds tested.

[Math folks don’t use phrases like “sort of” when describing numbers and can provide tickier definitions of SD and the means to calculate it. Here it is: it’s the square root of the mean of the squares of the deviations. Actually harder to say than it is to calculate.]

Steady Wins the Race
Standard deviation is not the only measure, and I don’t even think it’s the right one, let alone the most important, but it’s no doubt the most popular way to talk about ballistically consistent bullet performance. I don’t think standard deviation is near as important as is the “range,” which is the lowest and highest speeds recorded. Some who write and talk about it call that “extreme spread,” but if we want to get picky over terms (and ballisticians, card-carrying and self-styled, tend to get right touchy over such formalities) extreme spread is the difference between this shot and the next shot.

I watch the speed on every shot. I compare this one to the next one and to the last one, and, as said, find the highest and the lowest.

There is no saying that a load that exhibits low standard deviation is going to group small, just because of that. Any Benchrest competitor will tell of experiences whereby “screamer” groups came with high SDs and hideous groups with low SDs (“high” and “hideous” by their standards, still pretty small for the most of us). But, at 100 yards the bullet’s time of flight and speed loss are both so relatively small that variation in bullet velocities isn’t going to harm a group, and, yes, not even the tiny groups it takes to be competitive in that sport. On downrange, though, there is going to be a relatively greater effect on shot placement, right? Yes and no. Drift and drop are influenced. There is a relatively greater effect in ultimate displacement of elevation, more next. Based on drift allowance it probably does not.

To put an example on it, let’s say we’re shooting a Sierra® 190gr .308 MatchKing. Its 2600 fps muzzle velocity becomes 2450 at 100 yards and 1750 at 600 yards. (All these numbers are rounded examples, and examples only.)

If we’re working with a truly hideous inconsistency of 100 fps, say, that means one bullet goes out at 2550 and the next leaves at 2650 in a worst-case event. The first bullet tracks across about 28 inches (constant full-value 10-mph wind to keep it simple) and the next moves sideways 26 inches. Figuring drift on 2600 fps means it’s two inches off, one inch per shot.

Drop, which means elevation, is a (the) factor, and here’s where poor SDs bite. With this Sierra® 190, drop amounts over a 100 fps range are about three times as great as drift amounts. A vertically-centered bullet at 2600 fps hits about 5-6 inches higher or lower at each 50 fps muzzle velocity difference. That’s enough to blow up a score to elevation. And it gets way, way on worse at 1000. Keep always in mind that velocity-induced errors are compounding “normal” group dispersion. And, in reality and as discussed before, it’s unusual in a competitive shooting venue for a wind to be full-value, so the on-target lateral displacement is even relatively less — but the elevation displacement is consistent.

The next-to-the-bottom line, then, is that poor SDs don’t hurt in the wind as much as they do on the elevation. The bottom-line, then, is back to the start: don’t shoot a load with inconsistent speeds. It’s flat not (ever) necessary.

So what’s a tolerable SD? 12. That’s the SD that “doesn’t matter” to accuracy. More later…

SD bell curve
Standard deviation calculation forms a bell curve. The steeper and narrower the apex of the bell, the more level and narrower the fluctuations were. But there’s always a bell to a bell curve and the greatest deviations from desired standard are reflected in this portion of the plot. Depending on the number of shots that went into the SD calculation, these deviations may be more or less notable than the SD figure suggests. So? Watch each shot. That’s the way to know how a load performs with respect to velocity consistency. Each and every speed collected for each and every shot fired in a test. More next time…

MATH: For Them That Wants It
If you have no electronic gadgetry to help, calculate SD like so: add all the velocities recorded together and divide them by however many there were to get a mean. Subtract that mean number from each single velocity recorded to get a deviation from the mean. Square each of those (eliminates the negative numbers that ultimately would cancel out and return a “0”). Add the squares together and find the mean of the squares by dividing again by the number of numbers. Then find the square root of that and that’s the standard deviation figure, which is “a” standard deviation, by the way.

This article is adapted from Glen’s book, Handloading For Competition, available at Midsouth HERE. For more information on that and other books by Glen, visit ZedikerPublishing.com

 

 

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6 thoughts on “RELOADERS CORNER: SD — what it matters and why”

  1. 1. Best chrono is the millimeter microwave $600 unit. Good enough for HDY engineers.
    2. Speed test is used more as an analog to chamber press. for
    home reloaders.
    3. Accuracy sweet spot is typically below max speed.
    4. If powder is compressed, maxed out, still no satisfactory speed, change powders, get longer barrel, change bullet or some of each.

  2. A comment and a correction:

    The reason sample standard deviation (SD) is to extreme spread (ES) is that average ES value always grows with sample size, while average SD value stays constant with change in sampler size (if you calculate them correctly; see below). For samples of 3 shots, extreme spread averages about 1.7 times bigger than population standard deviation. For samples of 5 shots ES tends to average about 2.3 times bigger than SD. For samples of 10 shots it tends to be about 3 times bigger. For samples of 25 ES averages almost 4 times bigger. Only SD will tend to have consistent average values with those different sample sizes.

    If you want a good estimate of average ES for a particular sample size—say, you always shoot 10 shot groups for record and want to know what the average 10-shot ES will be—you will get a more accurate average value prediction multiplying your SD by 3 (for nine or ten shot samples) than you will by looking at a single measured SD. The reason is the SD takes the influence of all the shots in your string into account, while the ES number only looks at the two most extreme values that happened to show up. Don’t get me wrong. This is better than just firing two shots because you have given the other chances in between to get there. It just won’t have the same average value across different string sizes.

    Further, SD allows you to estimate how likely it is for outliers to show up. If you have a standard deviation of 12 fps, then slightly over 2 out of 3 of your shots will be at or closer to the mean than 12 fps, while the other shots will deviate further. About 9 out of ten shots will be 19 fps from the mean or less. About 21 out of 22 shots will be 24 fps or closer to the mean. Those numbers represent about 1, 1.65 and 2 standard deviations from the mean.

    The description of how to calculate standard deviation at the end of Mr. Zediker’s article tells how to calculate what is called population standard deviation (sigma, σ). What your chronograph gives you is what is called sample standard deviation (SD). The difference is that for SD the average square of the deviations is not divided directly by the number of velocities measured (the “number of numbers”), but rather by that value, less one. Where the number of measurements is “n”, then you want to divide by n-1 to get SD.

    The reason for that different calculation method is to eliminate a bias toward a misleadingly small result. It must be understood that sample values are never exact population values except by extraordinarily improbable happenstance. But they do serve us as estimates of the population values (the values your future shots will center around). However, small samples don’t “roll the dice” enough times to give less probable values and outliers much chance to show up, so they tend to underestimate what sigma will be. Dividing by n-1 instead of by n fixes most of that bias toward producing an underestimate.

    1. THANK YOU VERY MUCH! I am sharing this addition to the article next issue. As you can probably tell… I’m no mathematician. I have to rely on inputs and sometimes there’s more to a formula than what I receive as feedback looking for help in explaining something.

  3. If you have MS Excel or another spreadsheet program, you can enter each velocity in a separate cell then use the “SD” function of the program to calculate the SD across those cells.

  4. Wow! I got lost going around “Kelsey’s Barn”. Without calculator assistance, squaring and square rooting only eliminates the negative effect of reducing the positive from the average. Assume all differences from the average are the same sign. Then average the variances.

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