Limits to muzzle velocity standard deviation

When attempting to get the best long range accuracy there are a number of contributing factors. Some of the are

  • The firearm components including barrel, scope, bedding of the stock, etc.
  • The consistency of the bullet in weight, jacket thickness consistency, and shape
  • The consistency of the primers
  • The consistency of the shell casing
  • The consistency of the powder
  • The consistency of the powder charge

When reloading these last five are the ones you have most under your control. You buy match grade bullets and primers and obtain good brass. You might even weight each piece of brass and turn the necks to be uniform.

The muzzle velocity variation is a major contributor at the longer ranges. Suppose you are shooting a 69 grain Sierra Match King bullet with a BC of 0.301 at a MV of 3000 fps.

Here are the odds of getting a 0.5 MOA result at various ranges assuming everything else is perfect (zero wind, perfect bullets, etc.) with the muzzle velocity variation the only contribution to the inaccuracy (via Modern Ballistics):

MV Stdev \  Range 200 300 400 500
10 fps 100% 100% 100% 99.6%
15 fps 100% 100% 98.7% 80.8%
20 fps 100% 99.8% 84.4% 50.4%

As a reference point on expected standard deviation of MVs, for 55 grain American Eagle FMJ ammo I get from 20 to 25 fps. If I let the default powder measure on the Dillion 550 do the powder charges I sometimes get up to 30 fps. With match ammo from Federal and Blackhills using 10 or more shot samples I typically see 12 to 18 fps with one 10 shot sample giving me 8.3 fps.

As you can see muzzle velocity variation makes a big difference and it’s tough to get it in the range of 10 fps.

The next question is, “How much tight of tolerance on powder mass is required to get the standard deviation into the range of 10 fps?” Or put another way, “What is the MV change per unit mass of powder?”

By measuring the average velocity for powder charges on either side of your chosen load you can get an approximate answer. It’s important to not make the difference be too large from the load in question because the relationship between powder mass and velocity is not linear. And if you make the delta too small you lose your “signal” in the “noise”.

I did this measurement for two different powders for .223 loads. I was a bit surprised to find that for both powders the muzzle velocity sensitivity to powder mass was very close to the same and larger than I expected. For Varget it was 11.10 fps/0.1 grain and for CFE 223 it was 10.14 fps/0.1 grain.

What this means is that having powder masses +/- 0.1 grain can blow your entire muzzle velocity standard deviation budget!

My electronic powder scale only has a resolution of +/- 0.1 grain. Furthermore, I have found that with extruded cylinder powders like Varget three kernels of the powder weigh about 0.1 grain. Hence, if you want to get muzzle velocity standard deviations with a relatively small powder charge into the range of 10 fps you must measure it down to, literally, one or two kernels of powder.

So, how do you do that?

What I did was set my electronic charge dispenser to output 0.1 grains less than my desired charge. I then add the one, two, or three additional kernels of powder and stop when the scale first indicates the correct charge. Using this technique I loaded 15 rounds and measured them with a doppler radar chronograph. I got a standard deviation of 12.5 fps. from a loading that has approximately 11.1 fps delta for each 0.1 grain of powder.

So… what I want to know, is how do factories output 100’s of thousands (millions?) of rounds of match ammo with standard deviations in the range of 10 fps?

18 thoughts on “Limits to muzzle velocity standard deviation

  1. “…how do factories output 100’s of thousands (millions?) of rounds of match ammo with standard deviations in the range of 10 fps?”

    They use a powder that’s not so sensitive to charge weight variations within the requisite pressure range?

    Also I wonder; what is our actual resolution in measuring these things? Sure, our instruments are giving us numbers, but at what resolution are those numbers in doubt? From playing with my electronic and beam scales together, I’d say that the tenth indication is well into the “in doubt” range, even of you go to the extent of placing a cover over the scale for each and every measurement to null out the air currents. If its windy outside, my scales, both types, will be useless. I can’t load indoors during certain weather. The internal air movement, which is otherwise unnoticeable, will throw the scales into a several tenths variation of the exact same charge. I can stand there and watch the beam scale move on its own. If the heater is running, my scales behave differently from when the heater is off.

    And wouldn’t variations in barrel bore surface conditions from shot to shot be more than enough to account for a 10 fps ES? To put it another way, what variation in net average friction would it take to induce such a variation? I’d say very little.

    But there are regulating phenomena. The more force it takes to push the bullet through the bore, the more the average pressure. Being as this is a chemical process; the more the pressure, the hotter and faster the burn. Maybe (OK, total guess) with the right additives for slowing the burn above a certain temperature, I could imagine a load which would have a narrow band in which it is thus self regulating to some extent.

    They also check neck tension (the force required to pull the bullet out of a finished round). How many hand loaders have a way to test neck tension? What is your neck tension standard deviation? In loading new ammo, one would have more control over the brass condition and the bullets in large lots.

    In reloading it’s a very different situation. Every box of bullets I open, I have to readjust the seating die to maintain, cart OAL. So there’s bullet lot issues there too. Do reloaders get the best bullets and all the best powders? Maybe. How would one know?

    • To get repeatable measurements I have to do a number of things.

      1) Turn off the air cleaner on the bench.
      2) Close all windows.
      3) Heating vent in the room is closed.
      4) Stand perfectly still.
      5) Power on the scales a minumum of 10 minutes before making any measurements.
      6) Calibrate the scales if there has been more than just a few degrees of temperature change.
      7) No florescent lights on the same power circuit as the scales.
      8) AC power filtering.
      9) DC power filtering.

      The bullets I’m currently using don’t have an issue with OAL or weight from lot to lot (so far). As long as I don’t have a compressed charge the OAL is +/- 0.002. The bullets weight (sample sizes of 20) on the first box had an extreme spread of 0.1 grains. On the second box, purchased more than a year later, it was 0.2 grains. And this is another one of those “self-regulating” variables.

      • How are you doing your AC power filtering?
        If you are feeding the dc adapter for the scale/dispenser a perfect clean 60hz 115v, why would anything else on the circuit be causing power issues?

        I have to turn off the heater in my apt to get clean power, but am always looking for a better way.

        • Tripp Lite Isotel Ultra. It’s primarily a surge protector but it is supposed to supply some noise protection as well.

          The D.C. can pick up noise. Leave a big loop in the DC cord and bring a heavy draw or high noise AC cord nearby. You can get common mode noise really easy. Differential noise is also possible but more difficult unless you do something stupid.

          I also put the scale and the electronic trickle dispenser on a copper plate which is grounded and there is only a couple of inches from the DC power supply to the copper plate with the cords wrapped up very short so there little chance of creating a loop.

  2. Ever read the Houston warehouse article for accuracy? I seem to remember the guy said the final bit of accuracy was in learning how to prepare the throat of the case so it released the same every time? At these levels that maybe as important as getting the powder to the exact #of kernels necessary. Although a more forgiving powder( one that doesn’t make a pressure/velocity change with a single kernel) maybe the easier way to go

    • I have read Rifle Accuracy Facts. I should go read, or at least scan, it again. But the point of this post was that muzzle velocity variation matters, there are limits to how tight you can hold it, and what those limits might be.

  3. The example you give in the chart is a bullet of relatively poor BC.

    This brings up the concept of, I don’t know what to call it; say, the “optimum practical man-carried” caliber (OPMC) for a long range precision system. It suggests that caliber which results in a reasonably man-carriable firearm, exhibiting reasonable recoil, allows the carrying of plenty of rounds, and which gets you into the best bullet BC range for the above criteria.

    50 BMG is disqualified because it’s heavy, and 223 is disqualified because it’s too light for a good BC for long range. They’re both excellent calibers, but they’re way outside the narrow parameters of OPMC.

    In my research from many years ago, this caliber would be in the 6.5 to 7mm range (6.5, 270 and 280). Things have changed a little bit since then, and so a 30 caliber may qualify, but there you’re getting into more recoil in a heavier rifle and heavier ammunition with a lower round capacity. The OPMC would of course depend on the person doing the carrying, but you get the concept. It’s a balance of all those factors.

    The 223/5.56 would in no way qualify, as the bullets are too light for a high BC. It’s a fine caliber, certainly, but it’s practical range is limited by the BC.

    Hornady has since come up with their new 300 PRC cartridge, which addresses this concept rather thoughtfully. Still I think, in the preponderance of factors, a 6.5 to 7mm is more practical.

    I know a guy who loads the 6.5-284 with what he claims are astounding results. Takes elk with it at far Boomershoot distances. You know him I believe. He’s the guy who runs the optic coating business near UltiMAK.

    Also, for an event similar to Boomershoot to address the concept of the OPMC rifle, it would have to involve carrying your entire setup from place to place, within time constraints, during the event. One way, the event favors the heaviest and most complicated (and therefore the least mobile) setup, and the other way favors mobile and simple.

    • I agree on the example bullet not being optimal. I used it to make the point that MV makes a difference and there are limits as to what you can do at what sound like reasonable distances. I’ll do a different caliber when I have the data.

      Another thing, beside the BC, that enters into the calculations is that if your scale has a resolution/repeatability of 0.1 grains then a 0.1 grain error has a bigger impact on charge weight of 25 grains than on charge weight of 75 grains.

      • “…a 0.1 grain error has a bigger impact on charge weight of 25 grains than on charge weight of 75 grains.”

        Excellent point, and another factor favoring the larger cartridge.

        Similarly, a 10 fps MV SD will be a larger factor with longer flight times, so a higher BC at the same SD and average MV will attain a better hit probably than the same average MV and SD with the lower BC.

        Thus, I know an old former hippie with an off-the-shelf Ruger American chambered in the ubiquitous 270 Win. who’s getting better results with factory ammo than some moderately intensive hand loaders using custom rifles. He’s got himself a 700 yard range not far from here, working on expanding it to 1,000.

    • I just ran the numbers in Modern Ballistics for Match Grade ammo in 300 Win Mag (190 grain SMK bullet with a MV of 2960 fps). It turns out that with a standard deviation of 20 fps (and everything else being perfect) the 50% chance of getting a five shot 0.5 MOA group only moves out to 590 yards from the 500 yards with the .223. At a 10 fps at 500 yards it’s 99.97% chance. The better BC just doesn’t make that much difference.

  4. Thus was the race to create “ball powders”, small spheres that were easy to meter. infusion of chemical “fire dampeners”, directly into the sphere, to control burn rate. rather than kernel size.
    Another way was through “optimum charge weight” loads. it’s been proven that the harmonics of a charge of powder burning, travel up and down the length of the firearm. the trick is to find a charge that puts the vibrations at the back of the firearm as the bullet leaves the muzzle. it works in most firearms, even in different barrel lengths. that “sweet spot”, is well within industry standards now.
    Go look up,”Dave Newberry’s O.C.W. loads”. I’ve been using them for years. especially with my semi-auto systems as exterior case dimension are critical on them. Powder charges can vary.
    Also, bullet length plays a role in that it allows the bullet to enter the lands and grooves while being held straight by the case neck. personally, I believe this one factor is to account for the great success of the 6.5 Creedmore. in regards to accuracy. it’s been entertaining to watch the world wakeup to what the swiss invented a 100 yrs. ago, in the 6.5×55 swiss!
    Just my .02, hope it helps.

  5. Some years back I dabbled in Benchrest, which is the shooting sport for the severely anal retentive and OCD.

    By the time one gets to actually participating in Benchrest one has been thoroughly indoctrinated in the concept of minimizing variance, so BR becomes an exercise in the practical application of variance minimalization. Ex: cases are purchased in huge quantities, or at least as huge as budget allows, and intitially segregated by length and weight before the winners are fire formed in one chamber, then trimmed (including standardizing flash holes) and re-weighed. If external dimensions and weight are identical then so are the internal dimensions, a crucial step toward making powder combustion pressures uniform, and even advanced beginners frequently understand some of the relationship between chamber pressures and velocity, presented as velocity differences causing vertical stringing. Going further, tracing pressure curves from ignition point to bullet barrel exit can provide some insights in how the firearm’s components react physically to such time-related changes in pressure. Many Benchresters have as SOP exactly what Joe mentioned above RE: throwing slightly light charges then using a trickler to add individual powder kernels to get to the ideal charge weight; the really AR and OCD then weigh that charge multiple times on different scales to ensure absolute uniformity (all of which works – I’ve had groups of 20 rounds which display identical FPS figures on each of the two chronographs in simultaneous use; as it turns out, that and a $10 bill will get you coffee at Starbucks, because you can still get beat by the guy reloading the same 5 cases on the firing line with a plastic scoop from a Lee Loader kit).

    Needless to say, no ammunition manufacturer I’m aware of does any of all this with the thousands of rounds they load per hour. Modern manufacturing is based on elimination of variance, but there’s little point in expensively eliminating variance that does not affect performance of the final product.

    I suspect Lyle may be onto something RE: “pressure curve friendly powders,” “pressure curve friendly” defined as “extremely uniform.” I’d like to see (but doubt any of us outside the manufacturer labs ever will) detailed data on the pressure curves of modern mass produced ammunition and the chemical makeup of the powders which provide them.

  6. One thing I look for in the search for a “well behaved” powder is a powder that is a top performer, or near top performer, in a range of different calibers. The problems come in when they don’t necessarily meter well, in which case you’re down to trickling each and every charge, as Joe indicated. For short range pistol the SD isn’t so important, so I look for powders that meter well and choose from among those. If you can find a powder that meters extremely well and also posts good numbers in a range of calibers including yours (hopefully your caliber being near the middle of that range) then you may be on to something.

    Other than having shot up many thousands of rounds of hand loaded 10mm Auto, all that I’ve accomplished in reloading so far is to discover just how problematic it can be. One exception was the 280 Remington using heavy VLDs. I did very quickly stumble upon a terrific load for that, but I practically never shoot 280 Rem. That was for my son’s rifle.

    One must either really love it and have a lot of time to spend on it, or not care too terribly much about the finished product. And therein comes the phrase; “The Perfect is the Enemy of the Good” (if you won’t do it until you can do it perfect, then chances are you’ll never do it).

  7. I’m not sure I can find it but some years ago, Handloader magazine had an article regarding the relative contributions of various components to the accuracy of reloaded ammo. The author did his experimenting with .308 Winchester. My recollection is that the article actually concluded that uniformity of powder charge was not the most important of the various sources of variations. This now motivates me to find that article.

  8. This is why I don’t use Varget for my .223 loads. I found I couldn’t get consistent loads without resorting to single kernel shenanigans. It works great pushing my .308 rounds out of the gun but I use 322? powder for my .223 rounds. Much better consistency even just cylinder charging them on the progressive.

    I imagine big manufacturers do something similar. They’ve got the time and research budget to build a perfect powder for each on of their match grade loads.

    • Yes, and they also do something that’s been an express no-no for us mortals. they blend powder types to get desired results.

  9. If I were a company that was making a lot of ammo that I wanted to be high accuracy, I would focus less on the super accurate metering of powder, and more on the measurement end. Sort the bullets and cases by weight, load them as precisely as you can, but then sort them into groups by identical case/bullet weights and then by overall weight. Chrono and package the group that is the largest as your match grade ammo, recycle the outliers, sell the rest as the regular stuff.

    We have a hard time doing this because we just don’t have the scale that they do. I bet that quickly and accurately weighing solid components is a much easier engineering problem to solve than metering/weighing powder.

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