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Reloading Corner

RELOADERS CORNER: Standard Deviation

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Improving longer-range accuracy has a lot to with consistent bullet velocities. First comes understanding it! Here’s a start on it… KEEP READING

chronograph

Glen Zediker

It’s springtime (finally) and one of the things on your list might be working up a load for a new rifle, or new bullet. I’ve talked about testing processes and procedures, and also some about those bullets, and especially those with higher ballistic coefficients. The more aerodynamic bullet, by itself, is no guarantee of a smaller group (and whether you’re shooting one shot or 20 shots, you’re always shooting a group…).

To make the “magic” of a high-BC bullet come to life, they all need to be arriving at the destination at really close to the same speed. On target, that’s all about elevation consistency. It’s pretty commonly accepted among long-range competitive shooters that points losses come more from errant high and low impacts than from missed wind calls. High-BC bullets traveling at more consistent speeds reduces dispersions in all directions. But only if they’re traveling at consistent velocities!

The first step to improving velocity consistency is getting a good way to measure it. That there would be a chronograph. Nowadays especially, there are a number of simple-to-use and inexpensive chronographs available, that are accurate. Some have more features, which mostly revolve around providing printouts, digital records, and calculations, but what matters most (to me at least) is one that lets me easily read the velocity of each shot.

Check Misdouth offerings HERE

MagnetoSpeed
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.

So. What’s next is understanding the terms associated with this area of data-gathering.

“Standard deviation” (SD) is the most common measure of shot-to-shot consistency. It reflects on the SD reflects on the anticipated consistency of bullet velocities (some number of recorded velocities). The “standard” part reflects on a sort of an average of the rounds tested.

[Phrases like “sort of” upset mathematically-oriented folks, so here’s the actual definition: SD is the square root of the mean of the squares of the deviations. More in a bit.]

I pay less attention than many to standard deviation because: I don’t think standard deviation is near as important as is the “range,” which is the lowest and highest speeds recorded. Another that matters is “extreme spread,” which, by definition, is the difference between this shot and the next shot. I watch the speed on each shot. I compare this one to the next one and to the last one, and, as said, find the highest and the lowest.

Why? Well because that’s how I shoot tournament rounds. This one, then another, and another. A low velocity difference means that the accuracy of my judgment of my own wind call has some support.

standard deviation
Standard deviation calculation forms a bell curve. The steeper and narrower the apex of the bell, the 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. SD allows you to estimate how likely it is for “outliers” to show up.

A load that exhibits a low SD is not automatically going to group small, just because a low SD. I’ve had Benchrest competitors tell me that sometimes their best groups don’t come with a low-SD load, but do not apply that to greater distance! At 100 yards a bullet’s time of flight and speed loss are both so relatively small that even what some might call a big variation in bullet velocities (+/-25 fps or so) isn’t going to harm a group, not even the tiny groups it takes to be competitive in that sport. On downrange, though, it really starts to matter. (And keep in mind that “it” is a reference to velocity consistency, whether denoted by SD or otherwise.)

For an example from my notes: Sierra 190gr .308 MatchKing. Its 2600 fps muzzle velocity becomes 2450 at 100 yards and 1750 at 600 yards. (These numbers are rounded but serve for a example.)

If we’re working with a just awful 100 fps muzzle velocity change, that means one bullet goes out at 2550 and the next leaves at 2650, in the worst-case. The first drifts about 28 inches (let’s make it a constant full-value 10-mph wind to keep it simple) and the next slides 26 inches. But! Drop… That is THE factor, and here’s where inconsistent velocities really hurt. With this 190, drop amounts over a 100 fps range are about three times as great as drift amounts. This bullet at 2600 muzzle velocity hits 5-6 inches higher or lower for each 50 fps muzzle velocity difference. That’s going to cost on target, big time. And it gets way, way (way) worse at 1000 yards. Velocity-caused errors compound on top of “normal” group dispersion (which would be group size given perfect velocity consistency). Now, it’s unusual for a wind to be full-value and dead constant, so on-target left and right displacement is even relatively less — but elevation displacement is consistent regardless.

So, my 100 fps example is extreme, but half of that, or a quarter of that, still blows up a score, or an important hit on a target.

propellant charge consistency
This is probably the most influential factor in improving SD: consistent propellant charge. It’s not only that each case has an identical powder load, though, because primer factors, and finding the right combination ultimately is why we do all the testing…

So what’s a tolerable SD? 12. There have been, rest assured, much calculation to lead  up to that answer. That’s the SD that “doesn’t matter” to accuracy, meaning it’s not going to be the leading factor in a miss. It’s more than I’ll accept for a tournament load, but for those I’m looking for an extreme spread never more than 10 fps (the range might be higher, but now we’re just mincing terms). More later…

The information in this article is from Glen’s newest book, Top-Grade Ammo, available HERE at Midsouth. Also check HERE for more information about this and other publications from Zediker Publishing.

Reloading Corner

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