Typical Pistol velocity St. Dev. & Extreme Spread

[DirtyHarold]

I recently got a chrono and was testing factory ammo through some revolvers. I got SD up to 30 and ES up to 90 on just one cylinder worth of data.

SD would of course get smaller with more data, but that ES seems large to me. With revolvers, is velocity variation typically ammo related or firearm related? I was using quality ammo.

Thanks

[reddog81]

Assuming you're using a quality revolver with consistent throats most of the variation should be from the ammo.

Last November I was shooting my new Python and testing out some loads with with various wadcutters and charge weights. The worst load got an ES of 67 FPS and SD of 26. The best load had an ES of 12 and SD of 5 FPS. The best load was 2.8 grains of Bullseye with a homecast 148 grain wadcutter. This is a well known and classic load for a reason...

If a gun is capable of such low number with one load it should be capable of such low numbers with other loads.

[FlyFish]

Standard deviation of a sample will not necessarily get smaller with more data (i.e., with a larger sample), although it will presumably become a better estimate of the [usually unknown] population standard deviation. ES, of course, can only get larger.

[Shadow9mm]

6in gp100 38spl 158gswc hand loads, 6 shots, avg 866fps, sd 9.4, es 26.

[Nick_C_S]

I got SD up to 30 and ES up to 90 on just one cylinder worth of data.

I've done a lot of revolver chronographing over the years. This ^ doesn't raise my eyebrows. Especially if you're talking magnum ammo.

What caliber of ammo are we talking about here? What gun? What barrel length (longer barrels tend to "smooth out" high SD's and ES')?

[74A95]

It depends on the cartridge and the powder. In most instances with handguns used at common distances, SD and ES aren't meaningful and can be ignored.

[jmr40]

You have six different chambers, 6 different sets of data. Number the chambers and keep up with them individually. I bet all of the data from the same chamber will be much closer and I bet you see significant differences between some of them.

[std7mag]

Define "quality ammo".

High priced, factory ammo?
Or handloads?

Second, if your shooting under 300 yards, ES/SD wouldn't make too much difference.
Unless your trying to shoot some form of competition with it.

I only use my chrono for pistol to ensure i have enough velocity for hollow points to expand reliably.

[44 AMP]

If a gun is capable of such low number with one load it should be capable of such low numbers with other loads.

Its not the gun, its the ammo.

You're looking at variations between individual rounds. The gun isn't changing between shots (or at least not in any significant way).

And as already mentioned, revolvers are virtually 6 different "guns" firing down the same barrel. No matter how much effort is made to make them as identical as possible, variations do happen.

Another point, usually not an issue, but possible, chronograph reading can be screwed up by the "shadow" of the powder gas, or even bits of unburnt powder, if they are too close to the muzzle.

One question I usually don't see answered when someone is asking about ES and SD numbers is, "how did it shoot?"

If your gun shoots acceptable groups with ammo that has "large" variations in velocity spread between rounds, is it really something to be concerned about??

If it gives you "patterns" with a load that has large ES and nice tight groups with one with a low ES, (what we normally expect) that's one thing. If the gun groups acceptably well with large ES is that really a problem?

[Jim Watson]

Looking back through my notebook, I only have one .38 factory load chronograph record; 110 gr PMC Starfire, and it was that bad.
Most of my reloads have been substantially better.
My PhD friend took an interest and concluded that "match grade" called for a Coefficient of Variation (the Standard Deviation as a percentage of the Mean) of 1%.

[rclark]

I consider under 50fps ES for 15 shots 'acceptable' for revolvers. That's just me though. I like consistency. If I find a nice load with ES in the teens, low 20s even better. For a 'meaningful' SD statistically you need at least 10 shots, and more is better of course. As you see above, SD is usually about 1/3 of the ES, so I concern myself more with ES and what my groups look like downrange. Normal handgun distances to me is out to 100 yards. I don't know about semi-autos (what is normal ES) as I mostly avoid that class of handgun.

[DMY]

A few years ago when I was recovering from a knee injury, I took advantage of the free loaner chronograph at my gun club. Velocities were interesting, but I couldn't find a relationship between low ES, low SD, and accuracy. My best groups had ES-s in the high double-digits and SD-s between 25 -50. I tried eliminating some variables, but ultimately stopped obsessing about ES and SD. I'd rather have accuracy.

[Unclenick]

If I take a bullet with a G1 BC of 1.5 and shoot it at 750 fps and 850 fps at 25 yards, the difference in drop is about half an inch. If your groups are not that small, you probably can't see that 100 fps spread at that range. At 50 yards it grows to 1.7" and some of the very best shots might notice. At 100 yards it is about 7 inches, and that would be noticed.

What determines your best accuracy is likely to be something else.

Because of chamber variation, revolver accuracy smiths typically ream the chamber throats to the maximum SAAMI diameter as the first step toward accuracy. They will tune the alignment of the chambers with the barrel by shimming or replacing the cylinder bolt. They make sure the cylinder latching mechanism is tight. Indeed, some custom gun makers have gone so far as to under-bore the chambers, then use a special boring tool that centers in the barrel to take the pilot cuts for the chamber reamer, ensuring alignment at each position. All this is considered important to get the most out of your ammunition.

Regarding ES and SD, as FlyFish mentioned, SD can get smaller or larger with sample size. It is an estimate of population standard deviation (sigma, σ), so whether it grows or shrinks with additional events increasing the size of the sample just depends on whether the initial sample has over or underestimated σ. Board member Statshooter teaches statistics for a living, and he doesn't trust a sample smaller than 30 for getting a good estimate of population SD.

ES grows with sample size. This is because a larger sample includes more opportunities for less likely wider-spread data to be included. On average, over many samples, you will find ES is a multiple of the SD. And, indeed, for a sample size of 2-7 or smaller, dividing the ES by the expected ratio of ES to σ, ξ(n), results in a more accurate estimate of σ than the sample standard deviation computation by your chronograph does. This is due to bias that exists in the standard sample SD calculation. You can look at unbiased estimation of standard deviation in Wikipedia as a starting point if you are interested in the subject. But in the meanwhile, the expected ratio of ES to σ has these values:

Sample Size   ξ(n) (ES to SD ratio, on average)
      
      2           1.128
      3           1.693
      4           2.059
      5           2.326
      6           2.534
      7           2.704
      8           2.847
      9           2.970
     10           3.078
     15           3.472
     20           3.735
     30           4.086

[74A95]

These mathematical models of SD might be of interest to mathematicians, but 99.99% of shooters don't care. We use them to give us a clue of how consistent our velocities are, but it ends there.

We aren't interested about how well the SD estimates the population standard deviation. Not at all. Our goal when collecting chrono data is not, "I wonder what the population standard deviation is for this load". We. Don't. Care. At. All.

Chrono data tells us the average speed. We might be interested in SD or ES to tell us how consistent the speed is. And we might want to know that if we're using the data to make sure we make power factor for some types of competition.

But when it comes to accuracy, SD and ES mean nothing compared to what the target tells us. It's group size that matters. Your target will tell you which loads are best.

Some folks assume that a wider SD/ES means bigger groups. It might if you're shooting at 1,000 yards, but it doesn't matter for the typical handgun at typical handgun distances. The issue has been tested, and there is no correlation between group size and SD/ES:

https://americanhandgunner.com/handg...city-accuracy/

[Unclenick]

I don't know what poll gave you that 99.99% number, but between Bryan Litz's books and multiple articles on stats for shooters over the last few years, more people are indicating interest in shooting stats than was the case even a decade ago. The growing interest in long-range shooting has a lot to do with it.

In this particular instance, the OP made a statement indicating some misunderstanding of the nature of SD, as Flyfish first observed, but the OP's statement also suggests he is paying attention to the stats for his purposes, so it seemed reasonable to offer some explanation of the misunderstanding. As I illustrated in my first paragraph, until you are at least beyond 25 yards and 50 yards for many, it isn't going to be a factor for most handgun shooting.

And as always, of course, readers are free to ignore what doesn't interest them. Every post is not required to speak to every reader.

[74A95]

You're right. 99.99% is probably wrong. It's probably 99.999%. Probably more than that.

[Shadow9mm]

Wow, I feel exclusive, I'm part of the 0.001% !!! If I am going to the trouble to work a load up, consistency in all areas in important to me. And consistency in velocity is definitely part of that for me. And you need to understand what you are measuring to do that. ES is easy enough, SD is a bit harder, but it is not beyond the grasp of most shooters.

[rclark]

Sounds like I am in the 0.001 exclusive club too . I do care... 1/2" at 25 yards or 1.7" at 50 yards can be the difference of actually hitting the pest or say a tin can or not..... At 100 yards 7" would be a clean miss from shot to shot.

[jetinteriorguy]

My hats off to you if you can actually see and hit a tin can at 100yds with a pistol. When I was younger I could routinely hit a paper plate at 100yds with my .41 mag about 60% of the time and figured I was a pretty decent shot with that gun. I was deadly on gophers with my Ruger MKII with a 5” bull barrel out to 50yds, or head shots on raccoons that my hounds had treed. But boy are those days long gone.

[rclark]

Note that I didn't say I routinely shoot out to 100 yards (or more). Most of my range distance shooting is less than 75 yards.... But if I 'choose' to take that shot at a pest/game animal (or milk jug, tin can, or whatever), I would have 7" of 'slop' of where the bullet could end up. However if my ES was much tighter (0 would be the ultimate of course!!) , I would have a much greater chance of hitting what I am aiming at long distances. So when you find an accurate load with a low ES, it is a keeper. And a 1/2" can mean difference of nicking the tin can or missing (my bullets rarely go 'perfectly' where I want 'em ) . As for the eyes ... ya, I am beginning to notice some differences now that I am in my later 50s....

[Unclenick]

Well, you have a possible 7" of slop. The thing the ballistics programs do is assume a perfectly rigid barrel. With the actually gun, the faster loads will recoil slightly harder, but the bullet will also leave faster. With a revolver or a straight blow-back-operated pistol, I find this influence tends to exaggerate drop (hotter load impacts slightly higher, even at short ranges). With a pistol that has a barrel that locks up, the muzzle rise doesn't usually amount to much until after the bullet is gone, so it behaves a little more like the rigid barrel.

I used to shoot paper plates at 100 with the 1911. The trick was just to pick out a stone or other ground feature about a foot above the plate and then aim at that feature. Elmer Keith did it differently. He put horizontal lines on his front sights to mark how high the top edge of the rear sight blade should be at different ranges, and by keeping that blade level with the appropriate line, could hold the front sight directly on the target.

This series on stats at the Precision Rifle Blog maybe something some find useful.

[zeke]

With the advent of automatically generated numbers from chrono's, lots of people became more interested in sd and es. IMO, you do not get valid es/sd from six shots out of a revolver and the numbers with so few data points is statistically irrelevant. Am more interested in av velocity, or a wide variation of velocity from an individual round.

As an experiment once loaded some 257 wby cartridges with very tight necks and heavily crimped. The velocity variations were within 3 fps for 5 shots. The accuracy was extremely poor.

And while sd/es can be important considerations in some shooting, am still picking the combination with best accuracy.

[Shadow9mm]

Originally Posted by zeke

With the advent of automatically generated numbers from chrono's, lots of people became more interested in sd and es. IMO, you do not get valid es/sd from six shots out of a revolver and the numbers with so few data points is statistically irrelevant. Am more interested in av velocity, or a wide variation of velocity from an individual round.

As an experiment once loaded some 257 wby cartridges with very tight necks and heavily crimped. The velocity variations were within 3 fps for 5 shots. The accuracy was extremely poor.

And while sd/es can be important considerations in some shooting, am still picking the combination with best accuracy.

While I agree, sd is mighty suspect with only 6rnds, es should be reasonably reliable.

For accuracy I don't care what the charge weight is, as long as it has a reasonable avg and low sd/es. I get my accuracy from tweaking the seating depth, not the charge weight.

[Unclenick]

Zeke,

You probably changed the barrel time with the tight crimp. You may also have distorted the bullet with it. Either one can throw accuracy off. That's not the fault of the ES.

Small samples, assuming the vertical and horizontal distributions are normal, have predictable confidence levels. For 95% confidence, you can expect the means point of impact to vary. The SD of the variation in the average is a statistic called the standard error. You get it by dividing the population standard deviation by the square root of the sample size. In most instances, we don't know the population standard deviation, so we use the SD, which is an estimate of the population standard deviation.

Error to 95% confidence in group diameter:

Shots      Upper   Lower  Standard Error
 2	+346.63% -77.61% SD × 0.71
 3	+146.49% -59.43% SD × 0.58
 4	+77.22%	 -43.57% SD × 0.50
 5	+53.31%	 -34.77% SD × 0.45
 6	+41.44%	 -29.30% SD × 0.41
 7	+34.21%	 -25.49% SD × 0.38
 8	+29.36%	 -22.70% SD × 0.35
 9	+25.89%	 -20.57% SD × 0.33
10	+23.23%	 -18.85% SD × 0.32
15	+15.96%	 -13.76% SD × 0.26
20	+12.53%	 -11.13% SD × 0.22
30	 +9.12%	  -8.36% SD × 0.18

In other words, repeatability and the accuracy with which you can find the center of the mean increases with shots per group.

You can also combine smaller groups. The SD's add as the square root of the sum of their squares. SE is just that number times the square root of the total shot count for all the targets. ES you can find by overlapping the targets.

[tangolima]

SD or ES without MV has little meaning. SD of 50fps for 1000fps and 3000fps are two rather different concepts. It is ratio SD/MV that matters. I'd like to keep this below 1% for my loads.

It is easier to achieve in rifle than in pistol loads. 0.1gr uncertainty produces more error in a 10gr load than a 50gr load. It is unreasonable to expect a rifle accuracy from a pistol. Even at short pistol target range, a change in MV produces POI shift more than ballistics calculator predicts. Different MV leads to different muzzle rise.

Good group may happen with a load with higher SD. It is because the MV hits the sweet spot. The group will improve further if the SD is improved.

-TL

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