Understanding Load Development and Precision with Michael. 

It lowers the stiffness of the barrel material, which will change the bending mode frequencies. It also causes expansion of the material, which could cause warping and/or expansion/contraction of the bore.

Been there, done that. It works.

@ShootingInTheWind another vote for “OnTarget TDS” for an excellent program that gives you precise (X,Y) measurements.

Great tip. This is exactly the type of characterization described in the video. Thanks!

Yes, for two reasons. First, it demonstrates the concepts at the available ranges (100 and less). Second, 22lr is used for various competitions. Accuracy and precision might not what we expect from a CF rifle, but it is still important to those that compete with it.

22lr is relatively economical and time efficient to shoot hundreds of rounds with, plus with little to no recoil it doesn't fatigue the shooter nearly as much. It would be interesting to repeat the test with a centerfire rifle and see if the trends or conclusions are different.

If you're working in mean radius instead of group size, the metric can get better with more shots. This is where the topic starts to turn more into how do you compare two different populations, ie when you change a variable and gather data on the new set, how do you assess if it's significantly different or not. I use the t test to do this, which takes into account the number of samples and the variance in the samples. Working from your example, say you are comparing two loads with mean radii 0.25 and 0.375, a 50% difference. The number of samples you need to tell these apart will depend on how large the variance within each set of samples is. If the standard deviation in radius is large, say 25%, you might have trouble saying confidently that one is really worse than the other without more samples because the tails of those populations overlap quite a bit. If the standard deviation is small, say 10%, you might have better luck with fewer samples because the populations are more isolated.

@@solarshooter Yeah, When I want to compare sets of groups with different fixed variables I use a two tailed T-TEST that I setup in google sheets. I have mine set at 90% confidence level. However, I was just giving an example on setting upper boundaries. You can't use distance from POI when you're testing powder/seating depth because they are all going to naturally land different distances from your POA(mean radius obviously still works). Distance from POI is great once you want to verify an established load where the variables aren't changing. Or your skill level in varying conditions(you'd expect POI distance to increase with the severity of wind/mirage etc).

@@MMBRM If you first calculate the relative center of each group, you can use mean radius even as your group poi shifts. Plus this gives you a precise measurement of group to group poi shift to assess the harmonic trend.

Once you have x,y coordinates of each shot, you can calculate the radius from center for each point. Then you can compute mean and standard deviation of that set of data. This is probably as far as you need to go in order to characterize your rifle. Just keep adding to the list of shots that you log and add to the calculation of mean and sd radius. And keep in mind that as you get more and more shots those numbers will become more and more confident. If you wanted to go farther, to generate the same sort of "funnel chart" presented in this video, you would need to take that list of shot radii, calculate the running average, randomize the list, repeat, and so on until you build the chart that shows your "funnel of error". Then you could determine for your particular rifle/ammo how much error/confidence your mean and sd radius has.

Using the term 'DoE' around reloading will get your mouth washed out with soap! The "scientific method" begins and ends with the classic one-factor-at-a-time (aka OFAT) everyone learned in grade-school science class. Anything else is heresy 🤣 Just in case it didn't come through, yes, I am joking. Kind of. I would love it if *anyone* in the shooting community would even dabble in DoE... but it's hard enough to get people to use mean radius rather than extreme spread 🤷‍♂

Positive compensation is an interesting topic, and one Bryan Litz also explored in his book. He did find some kernel of truth to it, though it was not conclusive. I look forward to seeing further study on the topic. The way to test it is to set up multiple targets on the same flightpath, so you can log the dispersion of the same shots at multiple ranges. I would expect that wind, mv, and bc dispersions, which are a nonlinear effect with range, will cause your group to grow with range. This is what I have observed in my tests at different ranges.

@@solarshooter It's what barrel harmonics are. You're making shots leave at different angles according to their speed, even if you don't know it. Play with a ballistics calculator. Punch in a 1000-yard zero and a 2800 fps shot vs a 2820 fps shot. Look at the drop at 100 yards for each one. When using a 1000-yard zero the difference in drop at 1000 yards will naturally be zero, as that's your intended target distance. But since the two bullets have different speedds they will be at different heights at every other distance. They must be in order to hit the same spot at 1000 yards. The difference in drop at 100 yards for a 1000-yard zero with a delta of just 20 fps might be a little surprising. Then do the same for a 100-yard zero and compare the drop at 1000 yards. The figures you see for drop at the other distance is how much vertical you would see on target at that distance when using a zero at the other distance. This is what I'm talking about when I say you will not see the same results at a distance ABC when you are testing/tuning at distance XYZ. When you do that you are trying to optimize the compensated departure angles to reduce group size, but when you go to shoot for score at the other distance you've unintentionally ensured you'll have larger groups at that for-score distance. You'll always get better results testing/tuning at your for-score distance. For some reason quite a large group of people are skeptical of positive compensation, when I can see no other reason to explain shot behaviour. Positive compensation is barrel harmonics, it's just that you're trying to coax a specific desirable amount of harmonic to help you get better results. You can calculate how quickly you need the barrel to be swinging upwards in order to provide the necessary amount of compensation in the angle of departure for a given distance. You can then calculate whether or not your barrel can be swinging upwards near the speed required in order to approach that amount of compensation with regard to a given load. Then if you have a barrel contour that swings upwards a little too fast you can add mass (a barrel tuner) to it in order to slow it down to it lives in the sweet spot and provides just enough compensation to shrink your groups at your desired target distance. I had a rather unusual barrel built for a 22 rimfire benchrest gun, following Varmint Al's FEA design. Go to Varmint Al's website and to his page titled "22 LR rifle & tuner" and go about halfway down the page to the section titled "Two-Flats Barrel Contour with Vertical Flexibility and Greater Horizontal Stiffness" and you'll see what he came up with in the FEA software for a 50-yard barrel. He never did go to the trouble of actually building one. So I did. Hehe. Yes, it looks crazy. Yes, it works. It is just slightly too fast in its upwards swing for 50 yards. And only needed a very, very light tuner to bring it into the sweet spot. So far I've determined that it needs to be in the 31-32 gram region, but I'm still playing to find out exactly how much. Small changes can make quite a difference.

It's less about shooting out the aim point on the target, and more about losing the actual x,y coordinates of the shots inside the big hole. Yes the total group size will be a more accurate number, but you won't be able to characterize the distribution of shots inside that group, which is really what tells you about the precision of the system.

2 shots is a very small sample to try and determine true average point of impact, especially when you are making such small changes in powder. You are trying to assess a small delta with a small number of samples, which will likely not result in a meaningful answer. It might be better to do slightly more shots per charge, say 3-5, and use larger steps in charge. Your total number of shots won't change, but you'll be able to characterize the same harmonic pattern with higher confidence. Also make sure to accurately calculate average POI for each charge. After you get this initial sweep, you can focus on a particular range with finer increments just as you are currently doing, but you should also increase the number of shots per charge, say 10, when you do this.

I have tried the "one shot at one bull" before, and found greater dispersion in mean radius than taking 5 shots per bull. My theory on why is that I'm constantly shifting my rest to hit all the different aim points, and that it's harder to pace myself and manage the heat since I don't have the obvious 5 shot breaks. Both could be mitigated easily however so I see the merit here.

@@solarshooter A rest that has windage and elevation adjustments is golden.

This was a practical demonstration of the theoretical concepts presented in that video. It does agree with some of their conclusions, just as their video agreed with Bryan Litz's conclusions. However the takeaways regarding focusing on shot radius, the efficacy of testing with small groups, and the importance of long term characterization with data vs. constant tuning are valuable.

Stiffness and density are the key values. They are pretty similar for those two materials, probably not hugely significant.

X,Y coordinates for each shot is all that's needed, everything else is handled downstream. Thanks for the tip!

@@solarshooter lol well it doesn't do that. Not sure if you could mess with some CAD/CAM software to make that part easier or not. CAD/CAM is the only thing I know of that spits out X and Y. Either way, keep up the good work and keep sharing with the community.

​@@solarshooterHey, I just found a target analysis app that does X and Y of each individual shot. Hornady's 4DOF app. The target analysis part is $5 one time fee. I'd show you if I had a way to share screen shots, but I thought you'd be excited to have an app to do the X and Y of each individual shot for you! Keep up the good work Sir.

The plot at 6:16 shows my results for the distribution of group size, and yes I was also surprised by this result. I think Litz presented real group data, but I think the Hornady folks generated their data via simulation (might be wrong about that). This looks more like a "log normal" distribution to me, but again I'm out of my depth here. I doubt I would start to see a normal at 50 groups that I couldn't see at 38, especially since they would all have to be extremely small to "fill in" the missing part of a normal distribution. If you look at the scatter plot of all 190 shots (9:31), it does look like it's centered about 0 with a "normal-ish" distribution but I did not try to assess that here. Perhaps this is yet another emergent trait of sampling a larger true group with small 5 shot sets - it skews the answer from reality. I didn't get a chance to show the mean radius distribution plot but it has a Rayleigh shape to it (MLE = 0.159), which would be expected when combining a 2d problem (x,y coordinate) where each variable is normally distributed and uncorrelated into a 1d metric (radius). This indicates that what I said above is probably true, and that vertical vs horizontal dispersion may be uncorrelated. If I had tested at different range, this might change, since different types of dispersion affect each axis differently.

@@solarshooter I’m pretty sure that hornady said that the data for a group, not groups, is normally distributed and that 50 shots was enough to clearly establish the normal distribution. What they did not explain is how are you putting 2D data into a normal distribution! I asked after watching their small sample size podcast, and they said that the data being presented was from actual groups fired in their test rig.

Does someone have a source for machine rests and related information? Thanks.

True! I didn’t think of that either. Kiss method

Harold Vaughn, Rifle Accuracy Facts. There is a copy online for free.

@@solarshooter Thank You

I haven't watched it yet. Was it good?

Yes its very similar to what you have been saying.

@@winninginthewind We've got a bunch of podcasts that may interest you. Thanks for looking!

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-QwumAGRmz2I.html

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-6yZyXwy40JM.html

In some circles that's probably true, but it is rarely discussed in the mainstream of recreational shooting.

@@solarshooter it has been mentioned a bit over the years at Accurate Shooter, but clearly has not made an impression on many folks.

@@charlesking8542 Part of the issue with forums, is a lot of good info is hidden in a thread with a title or preamble that wouldn't lead a person to look at it for given reason. Or it is so far down in the thread that people have quit reading before they get near it. Found a few like that over the years, such as one on the Campfire that in the back part of a big thread, had people like Ken Oehler participating on internal ballistics, and a few others who worked in test labs. Or others that someone had put up a link to something by someone who really could speak on the subject, or a study on it.

Thank you!

You would have to try it to see if it works for you.

@@winninginthewind thank you!