Hornady Method

[Unclenick]

The groups result from a Gaussian bivariate distribution of random numbers with equal standard deviations on both axes. It is the combining of two bell curve distributions (the "normal distribution"; the most common kind in nature) on axes that are at 90° to each other, with the random values along each axis being normalized to the Gaussian distribution probability, but found independently of one another. The location of each hole just uses the resulting normalized random values as cartesian coordinates. Using the same standard deviation for both bell curves makes the group shape round on average rather than oval. This means it assumes all error sources contributing to the size of the groups are also round or else that their contributions to shot deviation combine to result in a round group. So it's sort of like firing from a machine rest in zero wind.

More on that statistical approach is in the Ballistipedia, here.

You are correct that real shooting often has non-random variables, though they are usually actually biased random variables. For example, the general direction of a flinch is usually predictable, even though the exact magnitudes and exact angles away from POA of individual flinched shots have random variations among themselves, so its effect can be modeled as an additional pair of bell curves along and perpendicular to the general flinch axis with the center being offset in the direction of the flinch and the two curves having different standard deviations so the effect of the flinch is to produce an elongated ellipse combined with the rest of the target. The reason bell curves are still involved is that nerve firing and muscle twitching both have noise that is random.

The other complicating factor is that random error sources don't add directly. Two random error sources can subtract from each other's errors just as easily as they can add together in any given shot. Similarly, the direction of each error can be at right angles to one another and thus neither add nor subtract along each other's axes. So how do you allow for this? Because the angle of error away from the POA is random, going all the way around the clock, the average direction is halfway between and is thus at a right angle, so the contribution act as the cartesian X and Y coordinates, with the combined effect being a distance from the center that you find by the Pythagorian rule, the resulting distance from center being, on average, the square root of the sum of the squares of the two contributing error distances from the mean. Thus, if I have one source of error that makes one-inch holes when it is acting alone and another that also makes one-inch holes when it is acting alone, and I then combine the two, the resulting average group size will be the square root of two inches, or 1.414... inches. The brain is tempted to say it will be two inches, but to get a two-inch group, the two sources of error have to act with maximum amplitude in the same direction for each of the two shots that define the extreme spread. It's actually a highly improbable coincidence. It will happen once in a while, but not on average.

Where the above becomes important is when you look at fine-tuning steps. Suppose, for example, you have a source of error like bad bedding that produces one-inch groups when acting alone and another source of error, like uneven neck wall thickness that produces 0.1" groups when acting alone. So you combine those two errors by the Pythagorian rule, and you get:

Group size = √(1²+0.1²) = √1.01 = 1.005"

That means if you start outside turning your necks to eliminate your 0.1" source of error, your average group will only shrink by 0.005"! You basically won't be able to measure that you've made any difference unless you shoot really huge group samples and are likely to conclude outside neck turning does nothing.

The bottom line is that a lot of fine-tuning people do becomes invisible due to larger error sources covering them up. So you could be doing some good with your extra measures but not see any obvious effect, even though, every once in a while, you'll get an extra point on a target due to that 0.005" being just enough to bring you a scratch of the next higher scoring ring.

[zeke]

It would certainly makes sense to increase your number of shots in a group to improve the accuracy and reliability of a statistical analysis. This may be the reason i do not depend on a statistical analysis to steer my handloading direction. Am still using 3 shot groups in .2 grain powder increments. This after a test load to see if the loads might behave as expected.

After getting a "good" load, it is then shot repeatedly at differing ranges/conditions. If it regulary performs as expected, it gets produced in a greater quantity. If the load fulfills my need in one firearm, it gets tried in others. If the basics of the load produce the desired results in several firearms, it gets mass produced.

Am simply not resourced enough to shoot enough for a statistically reliable group. And, imo, shooting a large data group from a firearm in one sitting introduces any number of factors (outside of the handload) to increase group size that may not be present under the circumstances am loading for.

And of course that is only an opinion, as others certainly will differ. Especially a powder or bullet company testing their bullets or powder.

[Unclenick]

Originally Posted by zeke

After getting a "good" load, it is then shot repeatedly at differing ranges/conditions. If it regularly performs as expected, it gets produced in a greater quantity. If the load fulfills my need in one firearm, it gets tried in others. If the basics of the load produce the desired results in several firearms, it gets mass-produced.

This is basically the same as shooting large groups. There is nothing in the statistical rules to suggest you need to fire a whole sample in one sitting. Indeed, part of the value of the On Target TDS software is it lets you combine different small groups into one big group, so you don't have so many holes in one target that you can no longer identify where some of their centers are.

You can also do that manually. The next time you shoot sets of three, use identical targets and keep them. After you have several, lay one over a page of paper and mark the hole centers with a pencil. Then lay the next over that same page and do it again, and so on, until you have as many hole centers accumulated as you want; then, the paper will show you what the collective group size looks like. Nothing wrong with doing that.

[zeke]

Originally Posted by Unclenick

This is basically the same as shooting large groups. There is nothing in the statistical rules to suggest you need to fire a whole sample in one sitting. Indeed, part of the value of the On Target TDS software is it lets you combine different small groups into one big group, so you don't have so many holes in one target that you can no longer identify where some of their centers are.

You can also do that manually. The next time you shoot sets of three, use identical targets and keep them. After you have several, lay one over a page of paper and mark the hole centers with a pencil. Then lay the next over that same page and do it again, and so on, until you have as many hole centers accumulated as you want; then, the paper will show you what the collective group size looks like. Nothing wrong with doing that.

Gonna take ya on your knowledge statistically. Am simply basic on the matter. Never believed in large groups in a single sitting due to the other factors like shooters ability, range conditions or the specific firearm involved.

And when i describe how i do things doesn't mean it is the best or correct way, it's just how i do them. Sometimes it's just habit and too old to change.

[cdoc42]

If you are loading for competitive sports, it's a bit different than hunting. I asked this question on the "net": "What is the size of the lethal target on a whitetail deer?"

I got this answer:

"The average size whitetail deer has a kill zone of about 10 inches for a perfect shot. This is a much smaller kill zone compared to an elk that has a kill zone of 22 inches by 17 inches."

So technically, if your 3-shot group is 2.5" at 100 yards, it will be 5" at 200 and 10" at 300. Any need to get smaller to start (and I am one of those) just gives some more room for error.

[Nathan]

Originally Posted by cdoc42

So technically, if your 3-shot group is 2.5" at 100 yards, it will be 5" at 200……Any need to get smaller to start (and I am one of those) just gives some more room for error.

This demonstrates Hornady’s logic perfectly. A gun shooting 2.5” 3 shot groups at 100yds will normally be impossible to hit a 8” steel at 300 yds. Why?

It is the small group theory. Normally, a 3 shot group does not represent the rifles capability well. Group is too small. If you shoot 17 more, maybe it is a 4in group at 100. That will have ~12-14” capability at 300yds. So many rounds will be off the 8” plate by dispersion alone.

[Unclenick]

Statistically, with a 3-shot group, you can have 95% confidence your future 3-shot groups will not be more than 2.47 times bigger nor less than 0.41 times smaller than the one you just shot.

Originally Posted by cdoc42

So technically, if your 3-shot group is 2.5" at 100 yards, it will be 5" at 200 and 10" at 300.

Well, actually, not. You have to remember what causes groups to be something other than one-holers, and you have to remember the bullet is slowing down as it travels.

What causes group dispersion is mainly drift. At the time the bullet exits the muzzle, the barrel may be moving laterally (with respect to the boreline: sideways, up, down, or in between) away from its ideal position due to shooter-induced movement or barrel vibration swing. Another cause is an imperfect alignment of the bullet center of mass with the bore axis, imparting lateral drift from the aerodynamic jump when it clears the muzzle, or perhaps it has been given a lateral shove by asymmetric muzzle blast at that time. All these influences impart drift, usually on the order of inches or feet per second. This drift velocity is too slow to create enough lateral air drag to change that velocity significantly during the bullet's short flight, so it is essentially constant all the way to the target.

Because bullets slow down as they fly, each successive 100 yards of bullet travel has a longer time of flight than the previous 100 yards did. So, each successive 100 yards gives the constant lateral drift more time to move the bullet away from the ideal trajectory that would put one hole in the target. If a shoot the Hornady .308 165-grain CX at 2700 fps, the time of flight (TOF) for the first 100 yards is 0.1154s. The second 100 yards takes 0.1246 seconds. The third 100 yards takes 0.1350s. So the second 100 yards gives the bullet 1.08 times more time to drift than the first 100 yards did, and the third 100 yards gives the bullet 1.17 times more time to drift than the first 100 yards did, so the constant drift will grow the MOA by an amount proportional to those numbers at each 100-yard range increment. Specifically, if you line up three targets at 100, 200, and 300 so the same bullets have points of impact on all three, and you ignore the effect of the paper on the bullet trajectory, and your group at 100 yards is 2.50 MOA, then at 200 yards, your expected MOA is:

2.50 MOA × 1.08 = 2.70 MOA


At 300 yards, the expected MOA is the 200 yard moa times the:

2.50 MOA × 1.17 = 2.92 MOA

Bryan Litz did that kind of experiment out to longer ranges and found measured growth in MOA with rang was a little greater than the expected numbers above, but that's the real world with the wind speed and direction perhaps not being perfectly consistent all the way downrange and then the paper impact influence and whatnot. But the expectation figured out that way proved to be a good start and accounted for most of the increase in MOA with range.

[tangolima]

Group size in moa, even without wind, grows 10%-15% for every additional 100yd. It is the rule of thumb I go by. 1" group at 100yd will become >24" at 1000yd. Can it still hit a 16” target at that distance? Yes but with reduced hit probability.

Statistically I would like to have more shots in a group. But deterministically my wallet and my schedule don't agree. I use 3-shot groups to narrow down where the poi inflexes. Then I increase the number of shots to home in the load. I will fire 10 shots to "qualify" a load for keep.

-TL

Sent from my SM-N960U using Tapatalk

[Unclenick]

When you shoot multiple groups without changing anything, no two of them have the exact same center location. When you get close enough, you start chasing the center, meaning additional sight adjustments based on correcting for each additional group never converge on a final setting. You may coincidentally get one that centers where you want and think you've got it, only to have the next one move again.

If I were constrained to using three-shot groups, my strategy would look like this: Shoot one 3-shot group. If that group's center is further from my intended point of impact (POI) than the diameter of the group, make a sight correction and shoot the next group. If it's center is within a diameter of the intended POI impact, shoot two more groups, find their centers, then find their combined center. Draw a line from it to my intended POI and make a sight adjustment to match the length and direction of that line.

For those not familiar with the process, find the center of a 3-shot group by drawing a straight line between hole centers 1 and 2 and another between hole centers 2 and 3. Next, draw a line from the middle of the first line to the center of hole 3, and another from the middle of the second line to the center of hole 1. Where the two lines cross is the group's geometric center.

The way to find the combined center for three groups is to do exactly as above, but connecting the first three centers where lines cross with the lines that went to bullet hole centers in the first description. In other words using the group centers as the hole centers.

[reynolds357]

Originally Posted by Nathan

Anybody listen to the latest Hornady podcast?

They discuss a loading method like:
Pick a load design….bullet, powder, case, primer.
Set an oal to a reasonable value.
Set a charge weight that will get you the minimum velocity you need.
Set your accuracy threshold.
Load up 20.
Start shooting 20 round group. As long as you stay under target, keep shooting until you shoot 20 or exceed your accuracy threshold.

If you exceed your threshold, pull down remaining rounds, change something and build another 20.

Change something is powder, bullet or primer for bigger changes…..oal or charge weight for much smaller.

And Hornady sells what? Surprised they don't recommend 100 shot groups. Gotta be sure you know.

[603Country]

I need to find a good load for my 6.5 Grendel and a different bullet than I’ve been using. I’ll decide on a starting load and COAL. I know the powder I’ll be using. I have my own 100 yard range, with a shooting bench which is 20 yards from my loading bench. I’ll load 3 rounds, shoot them and record the result. If it looks promising I’ll load 2 more for the same group. If it looks bad I’ll move to the next load level. Eventually I’ll usually find a load that I really like. Then I’ll load up for a more extensive test. This usually works for me, and has for many years. I’m sure that if I was a competitive shooter, my approach wouldn’t be good enough. But I’m a hunter and paper puncher, and if I find a load that’ll give me a nice small round group, I’m happy. The Grendel is my pig gun, so groups of about 3/4” will be fine.

[cdoc42]

Expense is, no doubt, the greatest variable. Especially today.

[Nathan]

And Hornady sells what? Surprised they don't recommend 100 shot groups. Gotta be sure you know.

You do realize this method requires fewer shots, right?

[USAF Ret]

I think Hornady wants to sell more bullets and brass. That's a lot of $$$.

[Nathan]

Seems like they will fail then. Shooting smaller groups will lead to inconclusive results. Thus you will need additional groups to prove a load is consistent. Many of those will be lower accuracy recipes. So, small group shooters will need more shots to achieve the same level of confidence.