Before getting into improving bullet velocity Standard Deviation, it’s first necessary to understand what it is, and what it isn’t. KEEP READING
I got started on this topic last time, and kind of came in through the side door. Quick backstory: the topic was how to start on solving unsuitably high shot-to-shot velocity inconsistencies. This time we’ll start at the other end of this, and that is taking steps to improve already suitable velocity deviation figures.
Clearly, the first step in getting involved in velocity studies is getting the velocities to study. Of course, that means you need a chronograph. Midsouth Shooters has a selection and there’s a direct link in this article.
Virtually all chronographs are going to be accurate. A well-known manufacturer of shooting-industry electronics once told me that unless a chronograph displays a reading that’s just crazy unrealistic, you can rely on the number. The reason is that the current state of circuitry is pretty well understood and heavily shared. Pay attention, though, to setting up the device according to suggestions in the instructions that will accompany the new chronograph. The more recent Doppler-radar-based units are not technically chronographs, but they function as such. The advantages to those are many! More in another article soon. For now, for here, what matters is getting some numbers.
Point of all that was this: You don’t have to spend up for the best to get a good chronograph. One of the price-point differences in chronographs is how much it will help work with the data it gathers. Most of us any more don’t have to do hands-on calculations. Me? All I want is a number. However, there are a good many that will record, calculate, and print.
Terms and Twists
Speaking of calculations, the most known and probably most used expressed calculation of collected velocity figures is Standard Deviation. SD suggests or reflects the anticipated consistency of bullet velocities (calculated from some number of recorded velocities). “Standard” reflects on a sort of an average of the rounds tested. I know saying “sort of” disturbs folks like my math-major son so here’s more: SD is the square root of the mean of the squares of the deviations.
Standard Deviation calculations did not originate from ballistic research. It’s from statistical analysis and can be applied to a huge number of topics, like population behavior. SD calculation forms a bell curve, familiar to anyone who ever had to take a dreaded Statistics class. 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.
If you have no electronic gadgetry to help: add up all the recorded velocities and divide them by the number of records to get a “mean.” Then subtract that mean value from each single velocity recorded to get a “deviation” from the mean. Then square each of those. Squaring them eliminates any negative numbers that might result from cancelling out and returning a “0.” Add the squares together and find the mean of the squares by dividing again by the number of numbers — minus 1 (divide by n -1; that eliminates a bias toward a misleadingly small result). Then find the square root of that and that’s the Standard Deviation figure, which is “a” Standard Deviation, by the way, not the Standard Deviation.
Knowing a load’s SD allows us to estimate-anticipate how likely it is for “outliers” to show up as we’re shooting one round after another. Based on the distribution based on the curve, if we have an SD of 12, for instance, then a little better than 2 out of 3 shots will be at or closer to the mean than 12 feet per second (fps). The other shots will deviate farther: about 9 out of 10 will be 19 fps, or less, from the mean. 21 out of 22 will be 24 fps closer to the mean. Those numbers represent about 1.00, 1.65, and 2.00 standard deviations.
Now. All that may have ranged from really boring to somewhat helpful, to, at the least, I hope informative.
Mastery of SD calculation and understanding doesn’t necessarily mean smaller groups. It gives a way to, mostly and above all else, tell us, one, the potential of the ammo to deliver consistent elevation impacts, and, two, reflects on both how well we’re doing our job in assembling the ammo and the suitability of our component combination.
I honestly pay zero attention to SD. I go on two other terms, two other numbers. One is “range,” which is the lowest and highest speeds recorded in a session. The one that really matters to me, though, is “extreme spread.” That, misleading on the front end, is defined as the difference between this shot and the next shot, and then that shot and the next shot, and so on. Why? Because that’s how I shoot tournament rounds! This one, then another, and then another. A low extreme spread means that the accuracy of my judgment of my wind call has some support.
Depending on the number of shots and more, SD can be misleading because it gets a little smaller with greater amounts of input. Extreme spread doesn’t. I have yet to calculate an SD that put its single figure greater than my extreme spread records.
Lemmeesplain: The shot-to-shot routine is to fire a round. It’s either centered or not. If it’s not centered, calculate the amount of correction to get the next one to center. Put that on the sight. Fire again. If I know that there’s no more than 10 fps between those rounds, that’s no enough to account for (technically it can’t be accounted for with a 1/4-MOA sight) then it’s all on me, and if it’s all on me I know that the input I got from the last shot, applied to the next shot, will be telling. Was I right or wrong? It can’t be the ammo, folks. Then I know better whether the correction is true and correct.
Some might be thinking “what’s the difference?” and it’s small, and so are scoring lines.
A load that calculates to a low SD is not automatically going to group small, just because it has a low SD. Champion Benchrest competitors have told me that their best groups don’t always come with a low-SD load. But that does not apply to shooting greater distance! A bullet’s time of flight and speed loss are both so relatively small at 100 yards that any reasonable variation in bullet velocities (even a 20 SD) isn’t going to open a group, not even the miniscule clusters it takes to be competitive in that sport. On downrange, though, it really starts to matter.
For an example from my notes: Sierra 190gr .308 MatchKing, in a .308 Win. Its 2600 fps muzzle velocity becomes 2450 at 100 yards and 1750 at 600 yards (I rounded these numbers).
If we’re working with a horrid 100 fps muzzle velocity change, that means one bullet could lauch at 2550 and the next might hit 2650, in the extreme. The first drifts about 28 inches (let’s make it a constant full-value 10-mph wind again to keep it simple) and the faster one slides 26 inches. That’s not a huge deal. However! Drop — that is THE factor, and here’s where inconsistent velocities really hurt. With that 190, drop amount differences over a 100 fps range are about 3 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 is going to cost on target. And it gets 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).
This 100 fps example is completely extreme, but half of that, or even a quarter of that, still blows up a score, or creates a miss on an important target.
That all led to this: What is a tolerable SD?
I say 12. There has been much (a huge amount) of calculation that led to that answer. But that’s what I say is the SD that “doesn’t matter” to accuracy. It’s more than I’ll accept for a tournament load, but for those I’m looking for an extreme spread less than 10 fps (the range might be higher, but now we’re just talking terms). More later…
Check out chronographs HERE
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
7 thoughts on “RELOADERS CORNER: Standard Deviation”
Agree, SD means little. To shoot and hunt for small SD’s will get you nowhere. The best is to find what shoots and then use the chronograph to see the velocity. Do not use the machine to find accuracy.
If the computer is doing the algorythm let it go. but for most of us we can somplify the calculation by ignoring the +/- sign and just use the number with out squaring to get rid of the sign. A plus 12 is the same as a minus 12, They are both deviate 12 units from the standard.
I’m not seeing how not using the minus sign helps. You still have to do the square root of the sum of the squares of the differences, then divide by n.
If we have the velocities of 2600, 2610, and 2630 the standard deviation (sample) is 15.3 fps. I’m not seeing the short cut???
There is no magic formula to accuracy. If there where everyone would be one-holing all the time. As far as SD goes, I have had loads run 6 fps SD and shoot 5 inch groups. My experience has taught me that the three most important things in a greatly accurate load are; OAL, OAL and OAL.
I agree that SD doesn’t equate to tight groups. It is a tell that something is going right and something going wrong. If I’m usually getting under 12fps and next trip, get over 12 fps, that tells me my brass needs annealing or had reloading problems. If I’m testing different loads and I get two similar groups, I’ll go with the one with the lower SD. Mo data, mo betta…
If you are interested in calculating the Standard Deviation, it is a snap. Microsoft Excel can be readily programed to calculate the SD, average velocity, extreme spread, high value and low value by just entering your velocity numbers on the spread sheet. No calculator is required!
James, maybe I’m not understanding, but I don’t think that will work. The SD is the square root of the sum of the squares of the differences divided by the number of samples.
Whether you use the minus sign or not, you still have to square the differences, sum them, and then take the square root of the sum and then divide.