Let’s talk load development

[Unclenick]

TL,

After a bit of thought, I reconciled the distribution issue. The bivariate normal distribution I described is a two-dimensional distribution, just like the holes appear on a sheet of target paper. Your Rayleigh distribution is a one-dimensional distribution of the hole radii. So, if I take a two-dimensional distribution of holes on the paper and sweep a radial line from the group center through 360°, collecting all the holes along the way on that line, the hole density then would, indeed, be a Rayleigh distribution from the center outward.

Happily, regardless of which distribution you start with, the radial standard deviation is the same for both. Thus, you can use the radial SD value to compare groups or estimate the future performance of the shooting system.


All,

The reason the radial standard deviation is superior to the mean radius as a group evaluator is that the mean value of any two holes in the target has its location determined by both holes equally. This is regardless of whether one of those holes is in a high-probability impact location, with a high chance of recurring in future groups, or is in a low-probability impact location and less likely to recur, such as an outlier would be. The radial standard deviation's value is more influenced by high-probability impact locations and is less influenced by outliers. That makes it a more probable predictor of future groups because the high probability locations are more likely to get holes in future groups, while outliers don't show up at all in some groups.

The above is also the reason extreme spread is a poor group evaluator. Not only is it comprised of the influence of just two holes while ignoring what the others are telling you, but one or both of those holes are the ones furthest from the center, so, among all the holes in the paper, they have the lowest probability of having holes recur at their locations, making them the poorest possible predictors of future groups size and scores of all the holes there. As Geoffrey Kolbe shows, if you use ES to evaluate groups, you need to shoot a bunch of groups and combine them statistically to get a good prediction of future performance.

It is hard to give up the ES because one is usually trying to determine if all one's shots will stay inside a minute of deer, or within a certain target scoring range. This is the fallacy of saying "I have a half-moa rifle," or a "one-moa rifle," or whatever. It may perform that well some of the time, but often does not do so all of the time, and the shooter tends to blame himself, right or wrong, for outliers that may actually be occurring at a normal rate for the shooting system when the groups are larger than he expects.

What the radial standard deviation gives you is a much more realistic evaluation of your shooting system's expected performance. If you measure the radial standard deviation in moa instead of inches or centimeters, and you shoot a group of large enough sample size (30 is a nice number), then two times the radial standard deviation is how many moa your rifle's future shots are expected to stay inside of 68% of the time (assuming you shoot the same load in the same conditions). Four times the radial standard deviation is how many moa your rifle's future shots are expected to stay inside of 95% of the time. Six times the radial standard deviation is how many moa your rifle's future shots are expected to be inside of 99.7% of the time. Another way to put it is that about seven out of ten shots will be inside a two-SD diameter circle, 19 out of 20 are expected to be inside a four-SD diameter circle, and only about one in 370 are expected to be outside a six-SD diameter circle. You get to decide how much certainty you need before deciding what shots to take.

[tangolima]

Unclenick. Very cool we come to the conclusion. I work in radio communication industry. We use Rayleigh distribution to model signal fading. I made the connection to shot dispersion when I looked at its formulation. Turned out it had been done long before.

Rayleigh distribution is interesting that all its statistical parameters, mean, standard deviation, pdf, cdf, quantile function etc, are related to one parameter sigma. In that sense, mean is as good as standard deviation.

Mean = 1.253*sigma

Standard deviation = 0.665*sigma

Median = Q(0.5) = 1.18*sigma

90% radius = Q(0.9) = 2.15*sigma

...

-TL

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[Metal god]

extreme spread is a poor group evaluator. Not only is it comprised of the influence of just two holes while ignoring what the others are telling you, but one or both of those holes are the ones furthest from the center, so, among all the holes in the paper, they have the lowest probability of having holes recur at their locations, making them the poorest possible predictors of future groups size and scores of all the holes there.

When looking at extreme spread, I never looked at it as a most probable impact spot My bullets would hit. I look at extreme spread as it’s the worst I was going to do with that load . I’ve never worked up loads thinking competition and points. I’m thinking first shot hits at a given distance and the hits don’t have to be in the 10 ring , nine’s or eights are just as good as 10 because they’re all considered hits that will do the job intended .

Can you use extreme spread that way or am I misunderstanding what extreme spread can be used for?

[stagpanther]

Thanks for that excellent explanation and formula for expected distribution of shots Unclenick--going into my reference notes.

[stagpanther]

Shot my last charge weight for the 300 accubonds out of my 375 ruger patriot this afternoon at what QL says is a bit over max pressure. Several published max charges for this combination of powder and bullet I've seen go well over what QL says; but I've learned to be pretty confident in what QL predicts so I'm stopping here.

Winds were quite strong, a base of about 18 mph and gusting to 25 +/- in a quartering headwind. Despite that, because I was shooting down in a quarry cut into the lee side of a hill, I think I was in a good wind shadow for much of the way--though just like the water behind a rock in a rushing brook--there were back eddies of wind.

Just like the last two charge weight groups, the first three shots grouped very close to the point of aim. I can't tell whether the subsequent shots that hit higher are normal deviation to be expected--or perhaps the result of the barrel characteristics changing after the first few shots. I didn't call any shots as a "user-induced goof." My impression is that the Patriot likes em big and fast. I think I might try doing what tango suggests and just shoot a few small groups over different sessions and then combine them.





Thanks are due to Taylor1--he was the one who tipped me off to the great deal on the Oryx chassis for Patriot rifles--a significant improvement to the OEM stock.

[georgehwbush]

target shooting is one thing, live targets are another.
https://www.snipershide.com/shooting...k-story.33679/

that ^ is why i always look at every shot as if it were the only shot.

[stagpanther]

I'm a big fan of Carlos Hathcock and agree--the first cold clean bore shot in a critical situation is the one that counts the most. Target shooting is all I do these days; and considering a cartridge like the 375 Ruger really has no practical purpose other than hunting large/dangerous game at fairly close range --target groups mean little if the shooter doesn't have what it takes to put the bullet where it needs to go in a stress situation. Although I probably will never see the day where I need to get a shot off like that--at least not without a professional guide with back-up weapon --I've always been interested in where the very first "fouler" shot(s) go in relationship to the rest of the group.

Here is where it gets interesting (for me anyway)--in the last 3 latest groups using the big accubonds shot with warm charges--the first cold clean bore shot has hit almost dead-on at the POA and the next 2 or 3 shots very close as well. I haven't seen that too often with other cartridges or with the smaller 375 bullets. Could be pure coincidence, or just this particular barrel, I don't know. I'm not really that interested in going out and shooting big groups of the 375 ruger day after day; it's expensive and after a while that pounding of the shoulder and loud report does take its toll.

[Rimfire5]

Stagpanther,

I have noticed that, as I grew older and lost a lot of weight, that heavier recoiling rifles have moved me out of my shooting position a lot more. With a really heavy recoil, it gets harder and harder to get precisely back into my shooting position exactly where I was when I first set up. And I shoot from a bench with a lot more stable set-up.

Your first three shots show you had recoil under control exceptionally well.

I have an old .270 Winchester with a thin hunting barrel that puts the first two touching, like your first three, but then proceeds to put the next three out at 2 0'clock in increasing 1/2 inch steps. As you said, hunting calibers are meant to be accurate for cold barrel shots since you rarely get a second chance when hunting. That old .270 was fine for hunting, but never was intended for shooting groups.

By the way, I love the Oryx chassis. I now have three of them and they perform beautifully from the bench in my heavy, target barreled .223, 6.5mm CM, and .308.

[stagpanther]

I have noticed that, as I grew older and lost a lot of weight, that heavier recoiling rifles have moved me out of my shooting position a lot more. With a really heavy recoil, it gets harder and harder to get precisely back into my shooting position exactly where I was when I first set up. And I shoot from a bench with a lot more stable set-up.

Your first three shots show you had recoil under control exceptionally well.

I have an old .270 Winchester with a thin hunting barrel that puts the first two touching, like your first three, but then proceeds to put the next three out at 2 0'clock in increasing 1/2 inch steps. As you said, hunting calibers are meant to be accurate for cold barrel shots since you rarely get a second chance when hunting. That old .270 was fine for hunting, but never was intended for shooting groups.

By the way, I love the Oryx chassis. I now have three of them and they perform beautifully from the bench in my heavy, target barreled .223, 6.5mm CM, and .308.

Thanks, I think that's a good way to describe it, shots are very dependent on keeping the set-up the same through all the shots. With a fairly light weight heavy recoiling rifle it's further complicated by the need (I think) to hold the rifle firmly down and back--more work than with just a heavy rifle with little more than finger on the trigger. What makes chassis like MDT's and others like it so good IMO is that they generally have their neutral balance point right about where the barrier block notch is--and the Oryx has that too. I'm big on the thumb rests too which aid in reducing side pull when pulling (squeezing) the trigger.

As george bush seems to allude to above--none of that is going to matter when standing freehand and facing a charging bear or rhino inside of 100 yards; I doubt I could shoot with precision accuracy in that situation (except possibly within an Abrams tank).

[pete2]

Originally Posted by tangolima

With scales available to most of us, 0.05gr is a struggle, and 0.02gr is very hard.

I do 1% steps. .243 load is around 35gr, so 0.4gr step. 5.56 load is around 25gr, so 0.2gr step. That basically gives me 10 ish steps between min and max. Good enough for my need.

-TL

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Sorry. meant .5 and .2 gr.

[Metal god]

I have two different lots ( same head stamp ) of brass that have a very close IMO average case volume . Can /should I just mix them . I use bushing dies and I haven’t checked neck wall thickness yet though so ….. maybe I should do that

On a side note . Now that I’ve been looking at mean radius , I’m not sure what is good . Ok the lower the better I assume but where is the line of good and maybe you should work on the load more . ES is pretty easy to make that call but mean idk ?

Most of my groups right now seem to be getting me a 1/3 mean of ES what does that “mean”

Edit: so I’ve been looking at all my recent groups and like I said almost all have the mean about 1/3 the size of ES regardless of 5 shot or 10 shot groups . Which may answer my question . Although most of those groups seem pretty good looking on paper I’ve only been happy with one . I guess that means 1/3 of ES is not that good and I should keep working on them all

[tangolima]

There are no benefit of mixing the brass. The sum of 2 random variables always have variance higher than each individual random variable. We tend to have illusion of "averaging things out". But that needs to applied to relevant context.

Mean radius (Mu) vs extreme spread (ES). When I fire a shot, I want to know how likely I will hit the target. Those are the 2 tools to estimate the likelihood. Mu is better than ES for reasons that we have discussed.

How to interpret or make use of Mu? Fundamentally it is similar to, or same as, ES. With Mu, one can calculate hit probability for a given target size. I like 50% and 90% group sizes. In particular

90% group diameter = 3.4*Mu

For a regular group with small # of shots, without funky flyers, it is very close to ES, which you have noticed.

There are other secondary interpretations. The YouTuber Preston has AZED (a zone equivalent distance). It is the distance within which his load can hit an a zone target with 50% probability. Mine is TED (torso equivalent distance). Similar idea with larger 18"x20" target with 90% probability and 10% degradation in group size every 100yd.

-TL



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[Savvy_Jack]

I as well. What is important to me, shooting there older cartridges, is knowing where that first shot will place, then the second, then the third through tenth.....then were the hot shots will group after that!

I see a lot of 6 or 7 three shot group targets....but when you overlay them all together....they groups is bigger than they care to admit!