Does Velocity Standard Deviation Mean Anything?

[RonAKA]

One issue I struggle with is the meaning of numbers. Just because we can measure things like weight, length, velocity, concentricity, and even statistical derivations of these, does it really give us useful information? Like many others I set up my chronograph and measure the velocity of all my shots. Later when I get home I calculate standard deviation, and dutifully enter it into my records. But, because we have numbers and data, does it contribute anything to our real knowledge of what is happening?

Since I started shooting groups with my Savage 6BR I've recorded group size (average of three, 3 shot groups), as well as the standard deviation of velocity of the same 9 shots. One would expect there would be a relationship between standard deviation, and the group size. But is there? There is a complicated mathematical calculation that can be done with sets of data to determine if there is a relationship between two variables, that even a guy like me can do, if I have the right software and a computer. The number you calculate is called the coefficient of determination or R2. Zero means there is no relationship, and 1 means perfect relationship.

So, I did this with all the groups I shot with this gun and compared group size to the velocity standard deviation, and then calculated the R2 factor. Here is the graphical results and the R2 factor.

The calculation suggests there is essentially zero relationship between standard deviation of velocity and group size.

What do you think? Could it be that my groups are too large to show the effect of velocity variation? Or, did I select sweet spots so well that velocity becomes a non factor? Or is velocity standard deviation calculation just a waste of time?

 

[bozo699]

RonAka,
Are you still working on them berger 62s-68s and 69s ? Ron I personally don't think there is to much to sd and es untill you get to at least 300 yards. 600 yards and past for sure. I know its flustrating isn't it?
Wayne.

 

[RonAKA]

Wayne, the Berger 62's were not included in this graph. They are brutal in my gun for reasons I don't understand. I did not think it fair to distort these stats with the groups for the 62's. There is something else much more significant going on there than velocity differences.

The best group I have is with the Berger 68, and the second best from a Bart's Ultra 68. The standard deviation of velocity, for the Berger 68 was higher at 22, and the Bart's lower at 12. The data also includes Berger 69 which place third, and Berger 80, which are fourth.

 

[TonyR]

Ron. I think you might find a stronger correlation between SD and accuracy if you just measured the vertical dimension of the group because the wind just adds noise in the horizontal direction and the normal sort of variation in MV has almost no effect on wind drift compared to the wind itself. I did some testing a few years back where I shot each shot so I could measure its own vertical from point of aim ignoring the wind. I found that I could explain over 90% of the variation in vertical with variation in MV. I used EXBAL to estimate the expected drops at each velocity and compared them to the actual. I also found that these effects are very hard to measure unless you test at at least 300 yards and some ranges do produce vertical from wind at times. Statistics aside, when I shoot a ladder test, the best ES and SD in the ladder rarely coincides with the best vertical but there is a tendency for the ES to narrow when the load is in the vicinity of a node then open up again away from the nodes. So I think there is a relationship between variation in MV and something that can be observed on the target, but SD by itself may not be the best way to measure it.

 

[minnesota]

i would have to agree with bozo and tony. Look at your manuals or a ballistics program and look how much 50 fps would play a role at 300 to 600 yards and you will see what they are talking about. The point of impact will be higher for a bullet starting at 3000fps than a bullet starting at 2900fps,2950fps, and so on. When you are looking at this at 100 yards you are not getting enough vertical displacement. If you were at 600 yards you would have a lot different vertical patterns, and groups would reflect it better.

 

[bigedp51]

First forgive me I do not shoot in bench rest competition, I just reload my sporter weight rifles and my milsurps.

Any variation or deviation can effect accuracy depending on barrel type, weight, diameter, bedding and up pressure at the fore end tip of the stock.

Below is factory loaded Winchester ammunition with average, extreme variation and standard deviation.

Below is reloaded ammunition in the same rifle showing "LOWER" extreme variation and standard deviation.

Any variation or deviation will effect barrel vibrations and group size.

Below is a 50 yard group fired from a 57 year old No.4 .303 British Enfield rifle by a 60 year old man using the rifles aperture sight. As you can see this group had two flyers caused by deviation.

With some things a little deviation is a good thing but on my rifles I try and keep deviation to a minimum.

Forget the deviation carts the real question is what is your barrel doing after you pull the trigger.

 

[camac]

I agree with Tony. To understand the difference between ES and SD and how it affects your rifle is quite complicated but should generally be condsidered in the vertical plane. (ignoring you might bump into a scatter node for now).
Now consider this. extreme spread of velocity will ulitmately effect the vertical height dispersion from edge to edge (Group size). Standard deviation is different though and determines the number in the tight bunch. In long range score shooting I would much prefer to have an ES of 20 and SD of 4 than an ES of 20 and SD of 12. The Extreme spreads may both be out in the 9 ring at 1000yards but the tighter SD mean the rest are tightly bunched in the middle of the 10 or X ring (depending on where you shoot). I would prefer to only have the one out there than all.
So Group size is a measurement of extreme spread of bullets (measured from worst two) and thus should be correlated with ES of velocity. and score shooting is more affected by SD and so vice versa. Es and SD of course have there own correlation and tend to come down together.

 

[BoydAllen]

What distance were your groups shot at? The reason that I ask is that at 100 yards variations in velocity, within a given group, are of much less concern than at longer ranges. Another question that I have is what the conditions, were, and what equipment was used (bench, rest/bags, flags, trigger pull weight) when you shot the groups? In order to look at a single variable, one needs to minimize the influence of all other possible variables. You may not have succeeded in doing this, in which case the small differences in group size caused by variations in velocity my have been lost in the noise.

 

[RonAKA]

All these groups were shot at 100 meters off a benchrest, and bag on rear. Wind should not have had a major effect on the majority of the groups, as I schedule my range days when there is no or minimal wind. My take away from the comments is that:

- At 100 meters, velocity variation does not have as big an effect as further out. I agree. At 100 with a 68 grain bullet and considering a plus and minus two standard deviations of 25 fps (3350, 3450), this translates to an elevation difference of 0.10". So if you are shooting 0.1" groups, a big difference, and not so much at a 0.4" size.

- I should really have measured the vertical spread only for this exercise. Good point. I'm now just wondering if I am curious enough to make it worth re-measuring...

I have not considered ES in my analysis, as one point on the graph is only 9 shots. At 9 shots standard deviation is starting to become accurate. However, extreme spread can be all over the map, and is more good luck than an accurate statistic. The standard deviation in my opinion much better estimates the probability of spread, than just ES. But, yes after the fact it is what it is. The other part I wonder about is the repeatability of my basic two plane chronograph, and suspect a significant part of the velocity standard deviation is just the standard deviation of the measurement error.

Thanks for the comments. I will have to think on remeasuring the groups for vertical only. Perhaps I will just scan them first to see if it looks like it may make a significant difference.

 

[BoydAllen]

Your comment about the wind and your range days would make any short range Benchrest shooter laugh, or at least smile broadly. An experienced Benchrest shooter once wrote that it is amazing how putting out wind flags will make a breeze come up. I applaud your pursuit of accuracy. Go to a short range Benchrest match. You will learn a lot. Good luck

 

[RonAKA]

Actually the range has some semi-permanent flags. I do watch them, and attempt to shoot my groups as quickly as possible when the wind seems constant. The range is also quite sheltered, and the majority of my groups have been shot with the flags hanging straight down. I've shot lots of rimfire in lots of wind, so I know what it can do.

No organized competition in my area, but there are some quite serious shooters, which interestingly seem to show up at the range the same days I do -- I guess viewing the same weather reports.

 

[camac]

Ron - I would like to make this point clear again. Even though typically SD and ES are related. ES is what you should measure for group "size". ES of whatever variable you are measuring will determine the extreme points. In measuring groups you are measuring extreme points. SD is how tight the rest of the bunch is together (or average varitation around the mean). But 4 shots within a few fps of each other in one hole and one an inch below due to a big drop in velocity for one shot will show up as a more direct correlation with ES than SD.
ES for velocity should be correlated to ES for vertical dispersion (vertical group size)

 

[RonAKA]

camac,

Yes, I believe I understand what you are saying and agree. A group is an extreme spread measure, and obviously velocity ES is an extreme spread measure. So the correlation between the two should be better, especially if I did the correlation on a group by group basis.

I did not. I used the average of three groups for group size, and standard deviation was calculated based on all the shots in all the groups. What I was trying to do was find the predictive value of standard deviation on group size. In other words if I make changes to my reloading techniques and improve standard deviation, what are the chances it will produce smaller group sizes.

I am very leery of ES as a predictive value (although I agree it is a perfect after the fact measure). ES in small sample sizes can be all over the map, and ES does not consider probability, while standard deviation does.

Agree about velocity variation mainly affecting the vertical. I probably should go back and measure the groups while isolating the vertical. Now that I have the correlation coefficient based on overall group size, it would be interesting to see if the correlation went up if I just used vertical.

 

[bowslngr]

Here is what standard deviation is useful for: estimating what the extreme spread would be for a very large sample of rounds loaded to the same specifications. In other words, what the worst case would be for your extreme spread when firing a small sample (like 5 shots).
Assuming your sample standard deviation (the one you get from the several rounds you fire and measure) is equal to the overall population standard deviation (what it would be if you measured a very large number of rounds), then you can assume that 99.8 percent of all rounds would have a velocity withing +/- 3 standard deviations of the average. Another way of looking at that is that the worst case extreme spread of any group you fire could be approximated by taking six times the standard deviation.
Perhaps you are comfortable with something a little less certain. Two standard deviations on either side of the average will get you a little over 95% of all potential muzzle velocities. In other words, there is only a one in twenty chance that any given round fired will have a velocity outside two standard deviations.
Of course, the larger the sample size (the more rounds from which you actually measure muzzle velocity) the better predictor of actual population standard deviation is your sample standard deviation. In other words, a standard deviation derived from firing more rounds gives you a more reliable predictor of your actual extreme spread possibilities.

 

[necchi]

I'm with camac,,
SD is really a typically worthless example of scientific notation. Or better said, it's a neat fact of mathmatical equasion that can be logged with little practical use beyond filling a space in a log book and using printer ink.
It's best used by Sociologists and Scientists to prove or disprove a therum, depending upon the view they have.
In light of the current mid-term election, you'll see polls of current canidates;
Canidate 1 is favored by 33%
Canidate 2 is favored by 29%
Yet the poll has a SD of +/-3%,, meaning Canidate 2 could be favored by 2%, ??? :.
With shooters the SD can be discussed after the shooting and scoreing is done, to prove or disprove the shooters load data as being the best it can be. And that's about it's worth,,discusion.

 

[bozo699]

I have read this thread over and over trying to understand? Are you all saying to throw your chronographs away because the info they give is useless to the shooting world? All I know for sure when my Es and Sd were double didgits I couldn't consistantly hit a 16" plate @ 1k now that I have figured out how to get them to single didgit I am in the center of the steel? Maybe the wind is letting up on me a little
Wayne.

 

[Beau]

Mean Radius is a better way of measuring group dispersion than extreme spread too.

 

[jo191145]

Wayne

1000yd shooters live and die by SD and ES, or so I'm told.

For 100-200yd point blank I care very little about those numbers.

Smallest group I ever shot was .048" at 100yds. Es on those five was over 200fps.
This group included no foulers.

This was the culmination of an expieriement I conducted one winter on bore prep procedures.
Gun used was a factory Savage VLP in 204R with over 3500 rds through it. Basically fried.
Its also somewhat repeatable.
Same gun same prep also netted a .098" and .111" in cold bore testing with very high ES.
Not good for much more than five rds before normal bore fouling takes over and groups return to normal.

The prep required is too extensive to use in timed matches.
I also consider it cheating ;D
Never tried it on any other rifle.
I did learn a lot about bore fouling characteristics and they're affect on accuracy.

 

[necchi]

"Are you all saying to throw your chronographs away because the info they give is useless to the shooting world? "

No, not at all.
But when the ES dropped because of your corrective means, the SD simply followed suit.