Mean Radius vs. Group Size

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mtngun
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Mean Radius vs. Group Size

Postby mtngun » Tue Feb 24, 2015 9:47 pm

I'm in the process of converting my load testing over to mean radius rather than group size.

The mean radius method is nothing new, it's been the standard procedure for military ammo for ages. But it is rarely used by civilians because it's a pain in the butt. :lol:
Image

So why use mean radius, if it is a pain in the butt? Because I try to PROVE things, and it's tough to prove a statistically significant difference using conventional group shooting. Three groups won't do it. Six groups are marginal. You really need at least 10 groups to prove statistical significance. That's a lot of shooting. :x

Group shooting gives you only one data point for every group, but mean radius gives you one data point for every shot.

For example, if I shoot four 5 shot groups, that gives me 4 data points, not enough to prove anything. But if I take the same 20 cartridges and shoot two 10 shot groups and calculate mean radius, I get 20 data points, which is often enough to prove statistical significance.

Here's a link to a good explanation of mean radius. It's also discussed in Hatcher's notebook.

There is no exact formula to convert between mean radius and group size, but in practice, a 10 shot group tends to be 3 to 4 times the mean radius. For example, a recent session with a TC 357 rifle produced a 0.55" mean radius and 10-shot groups averaged 2.03", or 3.68 times the mean radius. If that ratio held constant, I'd need a 0.27" mean radius to shoot an MOA 10-shot group.

FYI I measure the coordinates of each bullet hole the old fashioned way (it helps if your target has a grid background) and then use a spreadsheet to crunch the numbers. I'm still tweaking the spreadsheet but if I ever get it perfected I'll share it, or perhaps convert it to a web page so everyone can use it. You can also buy software to help you measure mean radius.

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Re: Mean Radius vs. Group Size

Postby mtngun » Sat Feb 28, 2015 10:01 pm

Here's an article that claims radial standard deviation is the best predictor of an accurate load..

Based on this chart:
Image

So I'll try to start posting both mean radius and radial standard deviation.

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Re: Mean Radius vs. Group Size

Postby mtngun » Sat Jul 25, 2015 9:23 am

Free target analysis website: Taran.

I've read through the examples but haven't actually used it yet. The neat thing is that you can upload a photo of your target(s) and it will analyze it for you. But ..... the bullet holes must be distinct, so one ragged hole won't work. That's a serious limitation, because even my not-so-great groups often throw several shots into one ragged hole. :|

I'll post a review if I ever find time to give it a whirl.

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Re: Mean Radius vs. Group Size

Postby mtngun » Mon Aug 03, 2015 7:18 pm

OK, so I had a chance to use Taran. I like that I didn't have to install anything, it just runs on the Taran website.

I took a photo of my target, taking care to be far enough away to avoid severe distortion in the photo. Taran uploaded my photo, and it was easy to set the scale (just use the long edge of the paper target as a scale) and then click on each bullet hole. That's all you have to do !
Image

Then Taran crunched the numbers. I like that it overlayed the two targets. :)

The numbers may look like Greek but the Taran manual explains what they mean. Today I only shot the one load but eventually I'll use Taran to compare different loads.
Image

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Re: Mean Radius vs. Group Size

Postby mtngun » Thu Aug 06, 2015 5:39 pm

Today I ran into a situation that creates problems for Taran. Here are 3 groups shot with the same load. The scope settings were not changed between groups, yet the point of impact climbed as more shots were fired. Possibly the POI changed because of fouling, or because of the barrel getting warmer.
Image
Normally the Taran anaylsis would combine the three 10-shot groups into one 30-shot group, overlaying them with the bullseye as the reference point. That works fine as long as the POI remains constant. But if the POI shifts, too bad, Taran does not take that into account. :cry:

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Re: Mean Radius vs. Group Size

Postby mtngun » Sun Nov 01, 2015 6:18 pm

I asked the author of Taran about the possibility of adding Radial Standard Deviation to Taran. Here is his reply:

I did consider RSD as a measure of precision (as, by the way, everything else published at ballistipedia -- excellent resource indeed).
There is, however, a slight problem -- RSD considers vertical and horizontal axis independently to get SD (and then provides an aggregate measure). While, strictly speaking, this is more accurate (the biggest approximation error of Taran calculations comes from the assumption of circularity), I have finally chosen the circular Mean Radius / Rayleigh model for the following reasons:
- mean radius is easy to understand intuitively; RSD is not
- Rayleigh makes it way easier to estimate error margins and confidence levels, and understand what they mean (mind you -- the confidence levels are probably the reason of being of the app, the rest is just callipers with attitude).
- circular approximation allows to establish direct comparisons with common group size measures (5 and 10-shot max spread)
- the information/number-of-shots ratio of Rayleigh is only very marginally inferior to RSD

This being said, for the average point of impact there were no such limitations (requirements of comparability with circular measures and single error margin) -- I have used the independent X and Y axis measures, and established separate confidence levels for vertical and horizontal values.

If you have any leads as how average 5- and 10-shot group spread relate to specific values of RSD, and how to establish error margins on RSD measurements -- I would very much appreciate if you could share this, I'd love to learn new things, and then maybe Taran 2.0 may come up.

On the other hand, I recently had contact with the author of shotGroups package for R (Web version here -- https://dwoll.shinyapps.io/shotGroupsApp/ ), which goes well beyond the basic stats provided by Taran's interface. The idea is to leave Taran as it is (dumb and simple), but make the output directly compatible with shotGroups, where extensive statistical analysis can be done by those who really want to push the limits of knowledge.

Cheers,
Alexandre

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Re: Mean Radius vs. Group Size

Postby PG1 » Sat May 27, 2017 7:24 pm

Hi,

just registered for the forum and was interested in a number of the topics, including this post on shot statistics.

I have been using a program called OnTarget PC (https://ontargetshooting.com/ontarget-pc) which is only $10 and facilitates doing complex statistics starting with bullet holes in paper targets. OnTarget will directly grab an image from a flatbed scanner, and with the mouse the user can locate the centers of the shots, as well as Point of Aim on the target. The data is exported as a .csv file for analysis in Excel.

I use an Excel template from Ballistipedia (http://ballistipedia.com/index.php?titl ... y:Examples) which calculates the x-and y-standard deviations of the shot group, and then performs an estimate of Radial Standard Deviation together with user-adjustable confidence limits and correction for sample size.

It is easy to manually aggregate an arbitrary number of shot groups into one large virtual group using Excel, simply by referencing individual shot x-y deviations to its own group center rather than referencing to POI. This avoids the problem of shifting POI as you illustrated in a later post. Of course, it is also possible to calculate deviation from POI to see how POI drifts over the course of shooting a number of groups.

I have been analyzing my RSD with a given rifle and bullet combination to see if there are significant changes due to powder charge/powder type, bullet design and so on. The RSD has been remarkably consistent if the bullet is not changed. For example, 0.3 MOA RSD at 100 m with 175gn Sierra Match Kings in a .308 Win cartridge, 1 in 10" twist. This RSD is pretty constant for a powder charge from 43 to 44gn of IMR 4064, although POI will move by about 1 MOA up and down.

I appreciate your engineering approach to shooting related subjects -- the BHN testing thread was very informative -- as well as home-built equipment.

Although I do not cast bullets, being busy with other pursuits, I do find the information here very interesting.

regards,

Paul

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Re: Mean Radius vs. Group Size

Postby mtngun » Sat May 27, 2017 8:49 pm

Interesting that you are getting very consistent results with RSD. Thanks for that insight, Paul. :)

I went with Taran rather than OnTarget simply because I run Linux. Plus, I like being able to run Taran through a website without the hassle of installing it on my computer.

That said, lately I have abandoned mean radius measurements and gone back to group size for the simple reason that you can't measure mean radius when the group starts to form one ragged hole, which generally happens any time a 10 shot group is less than 1.25 inches at 100 yards. However, that's the kind of problem I want to have! :lol:

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Re: Mean Radius vs. Group Size

Postby PG1 » Thu Jun 01, 2017 5:37 am

Sure, the ragged hole is a good problem to have :D

The common way of handling this is to shoot a small number of shots, say 2 each at 5 targets, and then combine them into one 10-shot group using software. I do that with 4 or 5-shot groups to get an aggregate of 20 and run the RSD algorithm on the aggregate.

This showed me that one brand of .308 bullet had RSD of 0.6 MOA vs. the Sierras which are at 0.3 MOA, a 2x difference. The difference was obvious from looking at the groups, but I like to have the statistical measure for quantitative comparison.

Anyway, people have different goals and preferences. Mine is for numerical comparison :)


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