.22 RF Muzzle Velocity Data

[gitano]

It's not exactly "me" you are disagreeing with - it's Euclid and Pythagoras. :)

My first reaction is ifva gun groups one inch at a hundred yards and you have a three inch circle to hit you should basically hit it every time.

I understand your thinking, but what's going on here is kind of an 'apples and oranges' issue.

Let me start by putting it this way:
I'm going to let you shoot 5 shots from your rifle at a target at 25 yards away.
The "Max Spread" of those shots is 0.25", and therefore you theorize that at 100 yards, you should be able to put ALL of your shots in a 1" circle. I am willing to "take that bet", but only if I get to choose the wager; I choose that you must give your house, farm, and all your worldly possessions to me if even ONE IN A HUNDRED of the bullets goes outside that 1" circle. Now how CONFIDENT are you about the size of that 1" circle?

Instead, I take the STANDARD DEVIATION of the windage and elevation of the the group of 5 shots you took at 25 yards. I multiply those values by 2.574 (the "t" value for n=5), and add and subtract them from the average value (the mathematical center of the group). The results are the 95% CONFIDENCE INTERVAL in windage and elevation. If the max spread of the group is 0.25", the 95% CI WILL be larger than 0.25". The 95% CI is that interval in which one can be CONFIDENT that 95 out of 100 (or 950 out of 1000, etc.) new "samples" will fall. Now expand those values by 4 to get the windage and elevation 95% CIs at 100 yd. The CIs WILL be greater than 1".

Let's say for this discussion that based on the SDs of the sample that the 100-yd windage and elevation CIs are THREE inches. I would NOT "take that bet" if you then said "I bet my house, farm, and all my worldly possessions that I can keep 95 out of the next hundred shots in a 3" circle at 100 yards." The reason is that the statistics of the distribution of the sample make the PROBABILITY of 95% of them falling INSIDE the 3" circle "too close to bet". That - prediction WHEN THE OUTCOME MATTERS - is the point of statistics.

Now let me address the "square" issue. The simplest way is with actual numbers from the examples we have in hand. I'll use the example of the Remington Golden bullet from the 10/22 with Volquartsen barrel (1:9 twist rate).

The windage SD is 0.15" and the elevation SD is 0.24". (For arithmetic simplicity, I'm going to set the mathematical center of the group at x,y coordinates of "0,0".) If we calculate the LINEAR value of the 95% CI for each we get 0.15*2.574 = 0.39" for the windage, and 0.24*2.574 = 0.62". The formula for the area of a circle is pi * r^2, or in words, pi times the radius squared. The formula for the area of an ellipse - an ellipse is just a "special" circle - is pi * r1 * r2, or in words, pi times the long axis radius times the short axis radius. If the "long" axis radius and the "short" axis radius are equal, we have r*r (radius times radius) which equals r^2 (r squared) which is a circle.

So our ellipse has an elevation axis length (diameter) of 2*0.62" (the positive side of the center point + the negative side of the center point), or 1.24". The windage axis length is 2*0.39" or 0.78". Since we need only the radii for calculating area, we use the 0.62 and 0.39 values. (Diameter = 2*r, or r = diameter /2). So the area of our 95% CE = 3.14 * 0.62 * 0.39 = 0.76 SQUARE inches. That "makes sense" if you think about a rectangle with sides 1.24" and 0.78". The area of that rectangle would be 1.24*.78 = 0.97 square inches. Since an ellipse with those axes (1.24" and 0.78") fits INSIDE a rectangle with those sides, the ellipse must have a slightly smaller area. 0.76 square inches (area of the ellipse) is 'slightly' smaller than 0.97 square inches (the area of the rectangle).

Now let's move that out to 100 yards. To do that, we multiply each SD by 4. (Maybe it's clear now, but I'll finish the arithmetic.) So the windage SD for 100 yd become 4*.15=0.6 and for the elevation becomes 4*.24=0.96. Now we again multiply the SDs by the "t" value - 2.574 and get 1.52 and 2.47 respectively. Those are now our 100 yard radii. The area of an ellipse with radii 1.54 and 2.47 is 11.99 square inches. 11.99 divided by 0.76 = 15.77. The reason it doesn't equal 16 (4 squared) is because I rounded the numbers to two decimal places.

I'll put this in mathematical terms of the area of a ellipse:
pi * r1 * r2 (ellipse)

To expand to 100 yards (multiply by 4):
pi * (r1*4) * (r2*4) - you square the "rs" and you square their multipliers.

So to get the area of the 100-yard 95% CE when you have the area of the 25-yd CE, simply multiply the area of the 25-yd CE by 16. 0.76 * 16 = 12.16 square inches.

Paul

[gitano]

I appreciate you taking the time to read this thread, farmboy, AND taking the trouble to 'think about' what I am writing. Lotsa folks get 'glassy-eyed' PDQ on most of this stuff. But a personal "law" unto myself has long been, "Don't fool yourself". (Since my earliest days in college, over 50 years ago.) Wishful thinking and "wanting" a tool to be "good" can lead one to 'look the other way' or 'fool oneself'. All of these statistics keep 'optimism' and desire from causing me to believe that a tool of mine (a rifle) is better than it actually is.

Paul

[gitano]

So I thought maybe a picture would help understanding.

There are such things as "random number generators". Some of them generate a series of random numbers from a specific distribution. The common distributions are "Uniform" and "Gaussian". The uniform distribution looks like a rectangle. All of the numbers between the upper and lower limits you set - say between 0 and 1 - are equally likely to be generated. The Gaussian distribution is the classic "bell curve" (AKA "normal" curve), and the numbers generated are based on the average value and the standard deviation of the distribution. Unless you have information to the contrary, there is no reason to assume that a two-dimensional Gaussian distribution represents the shots  on a target at a specific point. By putting the average value in and the standard deviations, a Gaussian random number generator will generate a sample of numbers (like 100 of them) that have the same average and standard deviation that you specified.

I specified an average of 0 (meaning that the group is centered around the point of aim), and standard deviations of 0.12 for both windage and elevation. I told it to generate 100 random x,y pairs from a Gaussian distribution with a mean (average) of 0 and a standard deviation of 0.12. I then created an ellipse using the methods I presented above using standard deviations of 0.12 and 0.12. (This represents the 5-shot group from the 10/22 and the SSS bullet.) Here is a graph of that distribution of 100 "shots".



You will notice that 6 of them fall outside the 95% confidence ellipse. That's not "strange" or "special". That is what statistics predicts will happen when the data have a Gaussian distribution and those SDs. If I did it again, the result might be 4 'out of bounds'. But if I did 1000, very close to 50 would be 'out'. Maybe 48 to 52.

You will also notice that "most" of them are WELL within the 95% ellipse. This is the 'truth' to farmboy's comment: " ifva gun groups one inch at a hundred yards and you have a three inch circle to hit you should basically hit it every time."

Let me emphasize that there is no hand-waving, smoke-blowing, or 'mirrors' involved here. The random number generator is just the first one I came to on the internet. I didn't "make" this work out. I could generate 100 different random numbers 100 times and while all the little black dots would be in different places, 95% of them would fall within the lines of the CE. "It's the law."

So unless "you" can suggest (and prove) that the distribution of bullet holes around a point of aim on a target are NOT Gaussian distributed, (and "you" can't, because they are), the statistics, math, and arithmetic I have presented represents ESTIMATES of "reality". I can't tell you where all of the rest of your bullets will hit, but I CAN describe an ellipse within which I am confident that 95% of them WILL fall relative to a specific point of aim. And I'd be willing to bet BIG money on the ACCURACY of that estimate/bet.

This is REAL description of the precision of a rifle/ammo/shooter. "Max spread" and "MoA"s are quick and dirty AND OPTIMISTIC ESTIMATES of a rifle/ammo/shooter system. I prefer reality to "looking" good. The truth is, the only difference between the way I am presenting the ESTIMATES of the future bullet hits, is the rigor with which I am presenting it. A 1" group at 100 yd is a 1" group no how you 'slice' it statistically. The issue is do you want to have a realistic predictor of your rifle's precision so you can hit what you're aiming at, or do you want to impress your friends (that don't know the statistics of what they are doing), or make a rifle or ammo manufacturer that is "doing you favors" look good? I prefer the former. Gunwriters (ptooey) and other ne'er-do-wells prefer the latter.

Paul

[Alboy]

" Lotsa folks get 'glassy-eyed' PDQ on most of this stuff."

Amen, not that I do not believe but just get lost. So over the years I have used what ever I had and generally leaned to the philosophy of aim small miss small, practice at a level of difficulty considerably above your expected performance in the field.

When I carried a pistol for duty use I warmed up at 25 yards and got plenty of practiced in at 100 with the 357 and 4" or 6 1/2" barrel, expecting most need distances to be 5' to 25 yards. Rifles varied widely but 22RF expected use for me is around 30 yards, practice at 100 was a standard.

It just builds muscle memory so thinking is not real necessary all the time.

[gitano]

aim small miss small

AMEN!

Quick and dirty stuff that you can do in the field or with minimal effort has value as long as you understand their limitations. Gunwriters (ptooey) have all the resources needed to perform all of the basic math I have presented here (and elsewhere). They don't, because 1) they're too lazy to, 2) they haven't taken the 'afternoon' it would take to understand it, and most importantly, 3) REAL parameterization removes the ability to LIE about the results AND 4) MAKE the performance of a firearm look better than it is. (Another way of saying LIE.)

I'm not suggesting ANYONE "do the math" that I do. I know how to do it, I understand the theory and mechanics, and I enjoy doing it. My primary reason for going to the trouble to present this stuff here is so that 1) folks can see what gunwriters (ptooey) have hidden for decades (maybe over a century), 2) they can 'qualify' their field measurements of "max spread", 3) that some "newby" might get exposed to something other than the lies and drivel of gunwriters (ptooey), and finally, 4) that it might actually help someone make a decision on 'to shoot or not to shoot'.

It is very difficult to follow written explanations about ANYTHING, let alone math. I try to keep mine as simple and short as possible. There is a catch to "short and simple" though; it's much easier to get lost in "short an simple" than it is in "long and thorough". The problem of 'long and thorough' is 'boring'. You really gotta wanna.

What I would like folks to take away from this besides the specific MV data, are the comparisons. There is some interesting stuff here if you look. After I post the data for the 10/22 with the "standard", 1:16-twist barrel, I'll point out some of the things I have noticed in these data.

Paul

PS - The barrel on the second 10/22 was NOT 1:16 twist. It was 1:9.

Paul

[gitano]

Here is the data for the other 10/22 I have, with the standard 1:16-twist barrel.

The Remington Golden Bullet data:


The CCI Mini Mag data:


The Aguila Interceptor data:


The SSS data:


The Federal #712 data:


The Winchester 36-grain HP data:


The data from the "Unknown" manufacturer:


The group size data are interesting, but look at the actual targets from the SSS, and the Unknown ammo. Then look at the targets from the 1:9-twist barrel and specifically the targets from Mini Mag, Interceptor,  Federal, and SSS. Notice anything? In each of those groups the first bullet is significantly away from the other four. In ALL of those cases, that is the first shot of the group.

Normally, we 'blame' those shots on "cold barrel", or "clean barrel". That does not work here. The barrel was neither "cold" or "clean" for those shots. I scratched my head about that a little and then it dawned on me: Those are the shots in which the autoloading operation of the action did NOT chamber the round. I started "dropping" a SECOND time, turning it loose from as far rearward as I could. You can see that doing that reduced the "First shot" anomaly (but did not eliminate it), in the second 10/22. Some of those groups that exclude that first shot are very nice.

Another 'thing' I'm seeing, is that the variance in MV has almost ZERO to do with group size. In other words, even when the variance (SD) is high, the group can be small, and conversely, when the variance is low, the group can be large.

I would also add that I forgot to mention when I shot the CBs in the 1:9-twist gun that I could see the bullets about 5 yd before they hit the target. Here's the "wierd" thing: They were spiraling down-range. And I mean BIG spiral, like maybe 4". It looked weird to see it.

Let's compare (side by side) the values for each bullet type from the three rifles so far shot.

Remington Golden Bullet:
Krico - - - - -  1242 f/s
10/22-1:9 - - 1292 f/s
10/22-1:16 - 1292 f/s

CCI Mini Mag:
Krico - - - - -  1188 f/s
10/22-1:9 - - 1207 f/s
10/22-1:16 - 1232 f/s

Aguila SSS:
Krico - - - - -  846 f/s
10/22-1:9 - - N/A f/s
10/22-1:16 - N/A f/s

Agiula Interceptor:
Krico - - - - -  1453 f/s
10/22-1:9 - - 1443 f/s
10/22-1:16 - 1499 f/s

Federal Hi Power #712:
Krico - - - - -  1158 f/s
10/22-1:9 - - 1181 f/s
10/22-1:16 - 1249 f/s

Wincheser 36-grain HP:
Krico - - - - -  1218 f/s
10/22-1:9 - - 1235 f/s
10/22-1:16 - 1256 f/s

Unknown:
Krico - - - - -  N/A f/s
10/22-1:9 - - 1265 f/s
10/22-1:16 - 1346 f/s

Remingtons are exactly the same in the two 10/22s.
Krico seems a bit slower than the 10/22s except the Interceptor is faster in the Krico that the 1:9 10/22.
The Interceptor is clearly the fastest and in the 1:9 10/22 looks like if the "first shot" phenomenon were accounted for, might actually produce an acceptable group. Maybe.
Winchester groups look good, especially when the "First shot" is ignored.
Federal produces some good groups in the 10/22s again when "First shot" is ignored.
The "Unknown" ammo (might be Yellow Jacket, I used to have a brick of that), doesn't do too badly. Good velocity. Groups are mediocre at best.
Notice how the Mini Mag shoots "sideways" from all three rifles. I find that VERY interesting. It produces VERY small variations in elevation.

All for now. I haven't decide on what the next rifle(s) will be. Maybe the Anschutz with the competition stock.

Paul

[gitano]

Here are pictures of the whole, real targets:
Krico:


10/22 1:9 barrel:


10/22 1:16 twist barrel:


Paul

[j0e_bl0ggs (deceased)]

Loads to digest here...

I get it.

Paul

[j0e_bl0ggs (deceased)]

A little light relief from the number crunching, care to test these Paul?





A friend dropped them in my lap this morning!



Bet they are 'collectable' one of the Remington boxes is still unopened...

[farmboy]

Several conclusions, number one the rabbit is quite safe at head shots at 100 yards as I see it only one gun and load that is making one biger hole at 25. Number two no wonder why I sold the 10 22 I had years ago shoot it at paper get not bad groups take it to the field and not hit much first shot flier everytime interesting I don't carry guns loaded in the chamber so every first shot is off.number three CCI mini mags have a great reputation around here for accurate shot placement animals are most times longer than tall so if you hit the animal it was a good shot and if the groups vary by length not hieght it would seem like in the field they are better than they are. Next why I don't like head shots never thought I was good enough perhaps it just statically not very good target too small. Also tells you why I dislike 22lrs not much good on bodyshots in the way of knock down power. And lastly (and I cannot help myself with this one lol) not sure I can trust old Greeks and math look at there banking system economy today!

[farmboy]

I do understand where you got to on your further explanation. Also why I never care for statistics it is a guess not an actual. What in mean by that is where are the other five percent? It gets to be like the fly and the train. If a fly is flying south at ten miles per hour and a train is running north at forty miles per hour and the fly hits the windshield of the train. The fly stops for a very short period of time before it is traveling north at forty miles per hour. So does the train stop for a short period of time? The amount of time difference would be the percentage difference in weight.

[gitano]

In classic Clintonese; That depends on how you define "train".

The train as a whole doesn't stop. Molecules on the train's windshield stop, causing it to 'flex' or 'give' very slightly at the molecular level. It's called the law of conservation of momentum. It is not the "guideline" of conservation of momentum. :) There just ain't no magic.

The other 5% are out of the 95% CE.

I won't belabor this any more than the following: The math is a tool to use to predict the future. That's what we humans like to do. We look at the observed information (data, shots fired, etc.) and try to predict what will happen the next time(s) we perform the same task- in this case, shoot the rifle - basing our prognostication on past performance.

If the outcome of the future event is non-critical, i.e. I don't hit the gopher, then "betting" on the "max spread" has no real consequence. (Except to the gopher.) If on the other hand, a human life depends on whether or not the bullet hits a target of a given size - say the apple on top of one's child's head - at 100 yd, then knowing the characteristics (history) of it's performance, you can choose to "take the bet" and shoot - or not.

I wouldn't want to be the child with a PLUM on my head and my dad saying "This rifle ALWAYS shoots 1" groups at 100 yds so I am willing to bet my child's life that the max spread I measure is a true representation of what this rifle/ammo will shoot EVERY TIME. I am unconcerned about  variation in any component of the ammo; no variation in the charge, no variation in the bullet, no variation in the case, no variation in the primer, no variation in the wind, no variation in the humidity, no variation in the temperature, no variation in the altitude, no variation in the shooter's mental state." You and William Tell are more confident in 'max spread' than I am.

Paul

[gitano]

I wouldn't hesitate one microsecond to shoot that old ammo. Other than hesitation about preserving it for historical reasons.

Paul

[sakorick]

I would shoot that old ammo with a big grin! I have some old WWII 303 ammo that shoots great......got to clean it like right now, however.

[j0e_bl0ggs (deceased)]

gonna take some cleaning the oxide under the wax is pretty tough...