Home Forums Reloading Big Game Rifles Hey Denton and Mathman

Why don'r some of us with numbers training look into what we might contribute by instead of looking at group size we look at POI as a vector from POA?

I can see a few very worthwhile uses for that, not least of which is that it could well provide a basis for computer programming to analyze what we got and what we accomplish as we work it up.

When I was doing a lot more shooting a couple of years ago I was using mean radius of ten or even twenty shot groups at 300 yards. Along with that scalar quantity I was eyeballing the "shape of the cloud" for any trends I could discern. Unlike what Denton would have done, I didn't get into rigorous statistical analysis.

I've often wondered about the usefulness of tracking and compiling data on POI changes from one shot to the next. Maybe there's valuable information there, but I just can't imagine that it would really be more meaningful than measuring a ten-shot group center-to-center like we have always done.

I'm not sure I really understand the intent of the original question. Maybe the following will be helpful:

We usually divide the issue of putting bullets right where we want them into two parts, that we deal with independently. One is how far the center of a group is from where we wanted it to be (accuracy) and the other is how spread out the group is around its center (precision).

We do deal with accuracy as a vector. That is, our bullets are, on average, 2" low and to the left, so we move the sights to move the center 2" higher and to the right. Quantity plus direction = vector.

Usually, we use the mean of the group as the center. There are some advantages to using median, and I've worked out a little field-friendly way to do that. I'm not sure there is a lot of interest in that, but it's easy to do with no computation.

There are, by actual count, 18,492 different ways people measure spread. All but 14 of these were made up by shooters. If you are dealing with small groups, say 5 shots, then standard deviation, mean deviation, root mean square deviation, mean radius, and group size all contain the same information and are convertible from one to the other. Which you use is just a matter of preference. The standard deviation of the distance of shots from the center of the group is the easiest to handle mathematically, and it contains all the information about dispersion, but it's not field-friendly. But for a group of 5, group size has 90% of the information content of standard deviation, and it is field-friendly.

As groups contain more and more shots, the power of group size as a measure gets worse. You'll get a lot more information out of three 5-shot groups than out of one group of 15.

If a group of 5 is at least 3X as long as it is wide, then you have evidence of stringing.

Denton,

I am thinking more along the lines of using vector analysis as a tool to gain insight into rifles that are not grouping well. I can see it providing some different, maybe better looks at problems.

Getting a more clear picture of what's going on would be a good thing. I'm not quite sure how that would work, though.

Basic vector analysis is usually just resolving vectors into components, and then adding them back up, or taking the cross product. I can still do that, just fine. And I might be able to do the gradient of a scalar field with some effort. Beyond that, if you want the divergence or curl.... my head hurts already... again.

One thing that I did work out a while back is that the amount of lateral velocity that can be imparted to a bullet by barrel whip is probably not negligible. It's not just which direction the barrel is pointing, it's also how much lateral velocity the barrel imparts. Fortunately, this effect is minimized at the same point that direction error is minimized.

Denton,

My thoughts are that there is probably some correlation between barrel stability and accuracy that can be shown by analyzing groups as vectors.

Some barrels are just easy. They to shoot well without a great deal of change related to bullet weight or charge weight. There are barrels that shoot well once everything is right for them but they may have very specific requirements and when those are met, they may shoot exceptionally well, maybe much better than the easy barrels. I have little to no expectation of the analysis solving anything, but, it might provide insight into the problem. That insight may suggest places to look for a solution

I'm not sure that the divergence or curl of the 2-dimensional vector field would tell you much, but it might with the correct vector analysis. It's an interesting idea, however, to investigate the vector sum of 10-shot groups with various rifles that display different grouping tendencies, and see if there is a correlation between the normalized net-sum vector and the grouping tendency/mechanical setup of the particular rifle.