Ladder test question

[turtlehead]

I normally shoot at Ben Avery and Table Mesa. Will have to look at Rio Salado.

I can just load for the ARs for now and wait for the weather to cool off.

[Unclenick]

Originally Posted by T'Oheir

A ladder test...Tells you nothing about the accuracy of any load out of your rifle.

Benchrest shooter Creighton Audette came up with his version of the ladder exactly for that purpose. What it identifies is a narrow range of loads that get bullets clear of the muzzle when the muzzle is at a phase in its recoil-induced swinging motion that causes the least stringing. By putting loads in the middle of that range, normal shot-to-shot pressure and velocity variations contribute less to stringing than at any other muzzle swing phase, resulting in smaller groups. Read the results in the second link I have in my previous post to see how this works out.


Turtlehead,

CEP was invented by the military to help with artillery targeting, and in declassified military documents you can find more than one level of complexity in how to calculate it, some including things like the gun mount position repeatability and other factors. I've run CEP calculations with randomly generated targets before and saw no significant difference between how much it varies and how much either the radial standard deviation or the mean radius, as described by FlyFish, vary. Mean radius is used by the military to define and determine ammunition lot accuracy, and it's good enough as a single point of comparison. Radial standard deviation is what you want if you need to predict what portion of future groups fired with the same ammo will be outside some group size limit.

[Clark]

20 years ago I read about the 1" 5 shot group at 100 yards on usenet rec.guns.
19 years ago I read about Bart's 3.25" 20 shot group at 800 yards on usenet.
But I was still trying to get the 1" group. Every range I visited, no one got anything close to a 1" group. I bought lots of guns. The AR15s would shoot 1.1" groups.
14 years ago I bought (3) Lothar Walther light varmint 257 barrels and chambered them in 257RAI.
They would shoot 1/2" 5 shot groups at 100 yards.
This allowed me to work backwards and determine what was not needed for accuracy. I came up with a list of common gun culture accuracy rituals that were worth it, and a list that I could determine no benefit.

The worthless list included many of the internet suggestions I got to to help me get a 1" group.
I understand polishing a flash hole may be common for benchrest competitors, but some guy with a surplus bolt action does not need that kind of suggestion to reduce his 6" groups. The suggestion if implemented just wasted his time, money, and enthusiasm.

I occasionally posted my lists of helpful and waste of time accuracy rituals.

10 years ago at work I designed an amplifier with ~ 100 components that affected gain. The components had specified accuracy tolerances. I wrote some equations and used a spreadsheet to see if the amplifier in production would meet gain specification or if I needed a select in test to tweak the amp. The amplifier gain needed to be between 20 and 30. If all the parts came in one way, it might be minus 10 or plus 1000. They built 100 amplifiers and there was statistical feedback to me from auto test. They were all between 24 and 26 in a narrow Gaussian distribution. Other guys said to me, "Oh yeah, you need to R.M.S. those errors or Monte Carlo them."

This was a shock to me. Errors cancelled errors so well they were almost gone. I complained about my shock to other engineers and they said i needed to build a million or 10 million amplifiers to see the extremes.

I wondered if this could explain how I could get great groups while ignoring most of the accuracy rituals.

[Unclenick]

Or vice versa.

What throws people off is that all the error elements preventing them from shooting bugholes have a normal distribution of some kind. A group is a bivariate normal distribution. When the groups are round, you can place the axes conveniently at horizontal and vertical. When the group is oblong, you place them perpendicular to one another along the narrow and long axes. Each axis then has its own bell curve.

Consider the round group to have the convenience of placing the perpendicular axes wherever we want them, and so make them horizontal and vertical to have the familiar Cartesian coordinates. Each hole location's distance from the center is the hypotenuse of a triangle whose right sides are the horizontal and vertical errors present for that shot. By Pythagoras, the length of that hypotenuse is the square root of the sum of the squares of the two right sides, or the horizontal and vertical errors in this case. Thus, you see the way two independent standard deviations add is as the square root of the sum of their squares. This turns out to be true even when the standard deviations being added are along the same axis, because there are times they will add and times they will subtract from one another, and, assuming normal distributions, they will tend add from close to the center more often than they add at extreme deviations.

So, suppose we play the SD addition game with independent sources of error. If you have two independent normally distributed random sources of error, each of which opens a bughole rifle's groups by one moa by itself, and you incur both sources of error at once, you wind up with a group size that is not 2 moa. You wind up with √(1²+1²) or √2 or a group 1.414 inches.

Now suppose you introduce another 1 moa error source. Now you have √(1²+1²+1²) or √(3) or a group of 1.732 inches. The first 1 moa source made a 1 moa group. Adding the second only grew the group 41.4%. Adding the third only grew it 22.5%, and fourth 1" source would add 15.5% to that, and, BTW, it has taken all four 1 moa error sources combined to double the group size. The same would apply if we worked with ½moa error sources, except it would take four of them to get to a 1 moa group. Whatever sources of random error you add up, their effect on group size diminishes as the number of other sources of random error are increased.

But most shooters come at this from the other direction. They have a big group that already is comprised of multiple different random error sources and many of them are not as big as others, so they affect the total group size even less than in the previous example when I add them to the pot. They could be anything from crown imperfections to inadvertent stock contact points, to uneven bolt lug contact, to out of square bolt faces and off-bore-axis chambers, to miscellaneous recoil moments due to asymmetries, to bad ammo with imbalanced bullets, to sights that have their adjustments jiggle around slightly under recoil, etc.

Example: Suppose all the random error sources in your gun combine to give you an average 1.5 moa group size. Now you remove enough average bullet runout from your handloads to eliminate what would be an average of 0.5 moa of error if it were the only error source you had. The effect on that 1.5 moa combined error source group will be to reduce it to:

√(1.5²-0.5²) = √(2.25-0.25 = √2 = 1.414 moa

So, you took 0.086 moa off the group size by removing a 0.5 moa independent error source. Given how much your group sizes already vary around the 1.5 moa average, could you tell the difference was real? You would probably have to shoot some inconveniently large groups to tell. You could use Student's T-test to work how how confident you could be that your 1.414 moa group was really smaller than your 1.5 moa group and not just a randomly smaller result due to normal group variation, but the confidence wouldn't be very high if the groups were only 5 rounds each.

Note that ammo is only one of the possible sources. And its own error will be a collection of sources, like primer seating errors, flash hole burrs, wall runout, axial runout of the loaded round, charge errors, bullet quality, etc. So, is it any wonder that when you remove just one of those sources of ammo error the effect is so small that you can't see it in your overall group size amid the variation they already have? Indeed, something as small as deburring a flash hole might not make a visible improvement until you had eliminated all the other error sources and had only that last 0.1 or 0.2 moa left to remove.

What I'm getting at with all this is, just because an accuracy step that eliminates a source of error makes no obvious improvement in group size, doesn't mean it didn't make an improvement. Indeed, you may well have to eliminate several error sources before the group starts shrinking to an obvious degree.

Instead, what many folks do is try eliminating different sources of error, then cease eliminating them when they move on to eliminate the next one, trying to keep the variables independent. They repeat until they remove one error source that makes an obvious improvement, then in the future continue to ignore everything they tried that didn't make an obvious improvement in the original group. But what they've actually done is try different things until they happen to fix one of the larger error sources in their shooting system, so the improvement effect was visible. Instead of blowing off all the other techniques, they would then need to go back and try them again to see if this time they make a visible improvement to the now-smaller group. The smaller the group gets, the more apparent the effect of removing small sources of error will be.

[turtlehead]

Hippopotamus of a triangle. Got it.

It all makes more sense now.

[308Loader]

Wow, clicked on this post expecting to read a bunch of stuff I've heard before. Must say it's got me thinking a little deeper on the subject. Lots of great info here, thanks all.