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Old September 24, 2000, 01:30 PM   #1
TGS
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Whether shooting rifle or pistol, I would look in the book make my first loads about mid then load +.5 and -.5 and see what grouped the best and adjust accordingly.
Then I bought a Chronograph......ahhhhhhhhhh.
But its really a big help in keeping reloading costs down and getting where your going much quicker.
My question. Is there a general rule of thumb about s.d.? The lowere the better?
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Old September 24, 2000, 03:04 PM   #2
saands
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My wife tells me that I can never give a simple answer ... just to prove her wrong, I will: Yes lower s.d. is better.
Now ... to show that she really IS right, here's the long answer, just in case you are interested:
S.D. (or standard deviation) is an estimate of the variability of the measurements you are making. A reasonable rule is that if you multiply the s.d. by 6 you will have a pretty good idea of the total range of the measurements. Normally the readings will be close to the average, but you should expect to get readings as far as 3 standard deviations above and below the average. An example would be helpful here:
Suppose you load a .40S&W and get an average velocity of 1350 with a s.d. of 8.0 ...
This means that you should get some rounds travelling as fast as 1350+(3 x 8.0) or 1374 fps.
You will probably also see some rounds travelling as slowly as 1350-(3 x 8.0) or 1326 fps. These extremes will be pretty rare, but you can expect to see them on occasion. You might even see a few lower or higher but the number should be really small ... about 3 rounds every 1000 and they should still be really close to the limit. Keep in mind that this all assumes that you don't change anything in your loading process! Breaking down and re-setting your powder measure might bring about more variation than you got within the lot you measured.

Hope I didn't bore you with the answer.
Be safe,
Bill
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Old September 24, 2000, 03:25 PM   #3
Zach Vonler
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In case it wasn't clear from Bill's post, the primary reason you want low standard deviation is so that each shot has as close as possible to the same trajectory. If doing long range shooting, you'll see a pretty big difference in POI between a 2650fps load and a 2550fps one.
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Old September 25, 2000, 09:25 PM   #4
TGS
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and so it is! my avg. 3479.5 fps, s.d 1.80, min vol. was 3477 & max vol was 3482. 3 x 1.80 plus and minus ='ed 3474.1 min and max 3484.9. All samples (10) were within the prediction. The group was .2559 center to center. this was using a 55gr hpbt and 34 grs of 3031. when I added .3 grs of powder the s.d went up to 28.36 and the range went from 5 fps to 56 fps and the group went to .4724. the average vel. went to 3558, min was 3502 and max was 3519. using +/- 3sd they should have fallen within 3433.92 to 3604 and so they were! so im thinking that if this weekend I drop to 33.7 grains of powder and if the weather is the same it could get worse or better?
Ive been doing this with (4) different calibers. this particular one was #1 ruger .220 swift.(100yds)
Ive worked up loads for my .45acp and the s.d ive quite at was 4.27 and about 1.78" (at 100 ft.) thats as good as I could get it, various powders, 200grswc. etc.
My 454 casull 11.34s.d / .95", but I had a weird thing happen. the first ten as just mentioned the second ten the s.d. went to 22. 26 and the sample grouped no greater than the first group. but wouldnt the increase in s.d yeild a larger group? no changes in anything, just shot two groups of ten (I havent calculated them all togeather, but I will check that out.
I have some loads i've worked up for my .375 H/H. and I'll run them this weekend too.
When using a chronograph ive been placing it at 10' from the muzzle. what could I expect if I were to place it at the target (100yds).
for sure the vel. would go down but would the s.d go up? say for the swift. the range across the sample size would be the same? or not?
So as i get the variation out of the loads the s.d. directly reflects that reduction. I had the chrono at 6' from the muzzle which worked ok for the .45acp but the .454 muzzle blast knocked it over tripod and all!
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Old September 25, 2000, 11:10 PM   #5
saands
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Well ... you got a smile out of me ... Great to see that you are finding the statistics useful. Let me take a stab at the questions ... but I will state up front that I'm better with statistics than I am with reloading. First real question : 454 doesn't reflect the greater s.d. with a larger spread? Well ... I don't know how steadily you hold your .454, but I bet it isn't as steady as your .220 Swift! The contribution of velocity to group size due to trajectory is probably pretty small, so whatever is causing the big groups (shooter, defect in barrel, heating of barrel, lock-up of the action, etc.) is probably more important than the velocity. I'm assuming that the distance is much shorter (.95" at 100 yds would be truly impressive for a pistol ) so the velocity component might truly be tiny not just small.
What if you put the chrono at 100 yds? I would place my money on larger standard deviations and their associated wider ranges in velocities because every bullet is just ever so slightly different and all those differences can't help but add up to a velocity change as they go downrange. A slight burr on one will bleed energy faster, etc. The farther it flies before the measurement is taken, the larger these little effects will become. The effects might be small if the component quality is high, but the ranges should increase. This might be a way to increase your sensitivity if you are trying to rank bullet manufacturers? You will also see some changes from group to group anyway, but assuming you loaded them all the same, the averages for groups of 10 shots should fall in a range of:
R = (6 * s.d.)/3.16
3.16 is the square root of 10 (the number of observations in the group). If an average falls out of that range then something changed!
Enough statistical nonsense ...
Have fun ... I think I might need to get myself one of those chronos. Do they work indoors? ... do indoor ranges let you use them?
Take care,
Bill

[This message has been edited by saands (edited September 26, 2000).]
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Old September 26, 2000, 02:49 PM   #6
Long Path
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What are y'all calling "Match Level" S.D.? If I'm getting an S.D. of below +/- 19 fps at rifle velocities, I'm pretty happy. Shoot, I'm even happier with pistol, come to think of it; I don't prepare the brass as carefully, nor do I usually weigh charges.

Come to think of it, I haven't loaded much at all this year, have I, Johnny?



L.P.
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Old September 26, 2000, 04:41 PM   #7
WESHOOT2
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Fact:

If the group is good what concern about SD?
(...given we are talking target not defense.)

------------------
"All my ammo is factory ammo"

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Old September 28, 2000, 12:36 PM   #8
TGS
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s.d. saves you money!!!! s.d. makes you money! Get the variation out of the process and take it to the bank!

Chronos indoors? The one im using is a Beta Chrono, about the middle of the line. The book says florescent lighting will cause errors. They supply (an option)a special light for indoor shooting. The indoor range I used to shoot at was well lit over the target and the bench but it was dark in-between and you could set up with the optional light. If its a well lighted range with the flouresent probably not. I havent approached any indoor ranges for a longe time so youd have to talk to them about it. At the time I was shooting indoors a chrono waseven something I was thinking about but I remember the conditions were right.
Even out doors on a dark and cloudy day the lack of light can cause errors without the screens in place. they cause the shadow that starts and stops the timer. I thought the wires you see in the picture had some sort of electrical magnetic field or something and the bullet interrupted etc. Nope. The wires you see hold the "umbrella" above the eye, being white, the bullet then causes a shawdow as it passes under it and over the eye. hummmmmm, works but are "light sensitive".
In an old gunsmithing text book of mine I saw an Ohler that the scrrens had to be exactly 20' apart and did use a magnetic field that the bullet interrupted, starting and stopping the clock.
I like the idea better but the 20' thing makes them less portable. I like the Beta im using. it has memory for 6 strings of ten. the upgrades can provide for much more dat but for what I do a sample of 60 seems to meet my needs. Would like to build my own indoor range out back but for now and some time in the future, its outdoors.
tom
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Old September 28, 2000, 01:41 PM   #9
Kernel
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When comparing loads I find Correlation far more useful than Standard Deviation in predicting accuracy. Correlation is calculated by dividing the Standard Deviation by the Average (SD/AVE) and multiplying by 100 (since it's a percentage). For example if your AVE velocity is 3500 fps and your SD is 31 then your Correlation is 0.89%. Conventional wisdom says any load with a Correlation of 1% or less has good potential for accuracy.

The beauty of the "1% Correlation" is it's universal... it holds true for light bullets, heavy bullets, min loads, max loads, handguns, rifles, muzzleloaders, fast balls, BB guns, wrist rockets, etc.

Say you're developing .223 loads for your AR. You got some 40gr varmint loads that have a AVE velocity of 3825fps and a SD of 38.2, and some 69gr target loads that AVE 2455fps and a SD of 24.6. Apples to oranges, how do you evaluate these? The 69gr load is more accurate since it's got a lower SD, right? Not necessarily, they both have a Correlation of 1%, statically they both have equal potential for accuracy. Maybe not the best example but you get the idea.

SD and AVE velocity on their own each tell only half the story. Correlation ties these two findings together resulting in a more meaningful and useful term. -- Kernel
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Old September 30, 2000, 11:20 AM   #10
TGS
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Mr. Kernal,
good info. I think this has been an informative pursuit. I know there was something else missing in the whole picture but didnt have a clue what. Ill look back in some of my text books and see what I can find out about correlation. Ive used it in manufacturing to compare. Ex. A supplier reports a certain result after measuring his product for me but my technicians report different results hence "NO CORRELATION". the the chase is on. Most often the question being who is right and who is wrong when in essence the question is as you have explained what is the degree of accuracy and does the product really meet engineerng requirements. I can see where this could be a real time saver ($$$) to. Im going to dig into this a little more and see what I can come up with.
Appreciate the info. Right now Im going out and shoot. got some .454 loads to try out.
thanks
tgs
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Old October 1, 2000, 12:43 AM   #11
saands
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Correlation? Well, the word threw me off at first. The idea of adjusting the standard deviation for the actual magnitude of the measurements is certainly valid ... and appropriate. If I'm not mistaken, the correct term would be normalization or in the case of the resulting value "Normalized standard deviation." Correlation typically refers to the degree to which two variables are related. Just semantics ... the normalizing process that Kernel describes is quite reasonable. Kernel's rule of thumb, put another way, says that if your total range is less than 6% (+/- 3%)of your velocity, then your accuracy will be pretty good. This seemed a little too high to me, so I ran some numbers for a .308 at 100 and 200 yards. I was quite surprised to find that at 100 yards, +/- 3% variation in velocity contributes to a vertical range of just over .25 inches ... accurate enough for me! At 200 yards the contribution gets up to 1.25 inches ... but still pretty acceptable. Although the contribution due to velocity is increasing as the distance gets longer, even at 300 yards it is only about 3 inches of vertical variation. Just to see where it goes in the extreme, I looked at the 600 yard scenario: the same "normalized std dev" of 1% will contribute to 15.8 inches of vertical dispersion. The bottom line is that the "s.d." should be a LOT more important to the long range shooters than it is to those of us who keep things a little closer in.

TGS ... Thanks for the interesting post.
Bill
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Old October 1, 2000, 08:37 PM   #12
TGS
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I've written a small spreadsheet and have been plugging in the data and now with another "view" of the values to plug in things are taking on some real interesting comparison. I've also added Energy (avg. vel x avg. vel x bullet weight / 450240). Im using the Kernals 1% formula but im still not sure how to write the formula you were using. Should I be looking at the % of change from min to max vel.? Ex. Min= 3477fps, Max= 3482 @ 8' from the muzzle. Avg. is 3479.5, s.d.1.80, now...what do I do? (b-a)/a*100 ? lets see. 3482-3477=5fps/3477=.0014*100=.1438 % of change. would that be +/- .1438%? considerably less than +/- 3%. nope...lets see my range is 5 fps. 6% of the avg vel. is 208.77 fps... (the group i shot was .2555). How did you work it out?
dont these amatures drive ya nuts! If you can show me the formula I'll plug it in and send you a copy of the spreadsheet. Its real interesting when you sort.
tgs
tgs
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Old October 1, 2000, 11:11 PM   #13
saands
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First of all ... No one that asks questions drives me nuts! My +/- 3% was to test the idea that a normalized s.d. of 1% was good. If the normalized s.d. is 1% then the values should all fall in the +/- 3 s.d range or +/- 3%. Your range of 5 fps at 3477 is phenomenally small ... nowhere near +/- 3%!! You are playing in the +/- .43% field. I didn't want to use the space to go through the whole calculation unless someone was interested. I used the ballistics program found at: http://www.norma.cc/htm_files/javapagee.htm
and defined my own bullet using the same ballistic coefficients and weight of an existing bullet. Defining your own allows you to input your own muzzle velocity. Then I looked at the time it takes the bullet in question to travel the distance of interest. This time can then be multiplied by:
1 - (3*normalized sd) to get the fastest time to impact ... let's call that Tf.
The original time can then be multiplied by:
1 + (3*normalized sd) to get the slowest time to impact ... let's call that Ts. I don't think that this is perfectly accurate, but the results are extremely close if the sd's don't get bigger than 3% ... if the range of muzzle velocities got really big then the faster bullets would be slowing down faster than the slower bullets ... but we can keep it relatively simple and go with the version above and just agree not to have 1000 fps ranges in our loads!
Ts - Tf gives us the difference in flight times. This difference is what causes the vertical spread associated with variations in velocity because any object in a free-fall will accelerate downward ... with more time to accelerate downward it falls farther (it doesn't matter that it is also moving forward ... unless it is a wing!). Although the difference is important, it isn't what we use for the calcultation ... for that we'll stay with the actual times Ts and Tf. What we'll do is calculate how far the bullet drops during the fastest and slowest travel times and the difference in drop will be the contribution to variation that we can expect from velocities. On to the calculation:
Drop (measured in inches) = (193.2)*T*T
193.2 comes from the acceleration due to gravity (32.2 feet per second squared) converted to inches and divided by 2.
Have at it!
Bill

[This message has been edited by saands (edited October 02, 2000).]
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Old October 1, 2000, 11:14 PM   #14
Kernel
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The EXCEL spreadsheet formula would look something like this: =100*SD/AVE

Where SD is the Standard Deviation and AVE is the Average Velocity. These two number are calculated for you by the Chrony.

Verbally, "One Hundred times Standard Deviation divided by the Average Velocity."

I use EXCEL to further crunch my numbers as well. I've got the Shooting Chrony Gamma Master that ports directly to my PC, it work's pretty slick. It's nice cuz I can then format everything on to a 8 1/2 x 11 paper for my notebook with all the handload details, shot strings, statistics, firearm info, weather, comments, etc and save everything to my hardisk.

The term "Correlation" and the formula used to calculated I got from a statistics book a few years back after I got my Chrony and was looking for ways to better interpret the numbers. It's not the same thing as "Correlation Coefficient" which is another statistical term, the value of which is always between 1 and -1.

In retrospect I think the more common term for 100*SD/AVE may be Percent Deviation or %SD. But that might be wrong too, it's been awhile since I had a statistic class in school and all my old college text books are still in boxes in the basement since I moved a few months ago (however, all my gun books are unpacked and neatly arranged on several large book shelves in my living room ). Call it what you want, even if the term is wrong the "One Percent Rule" is still a valid benchmark. -- Kernel
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Old October 2, 2000, 03:39 PM   #15
Dave McMillan
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Statistics can give you a headache if used too often. I agree on the use of the word "correlation" as a shortening of "Correlation Coefficient". I'll just stick to Kernal correction.

Another often misunderstood concept is accuracy versus precision. Gunwriters typically refer to a firearm that shoots small groups as "accurate" when in fact it is precise. Accuracy is hitting what you aim at, precision is how closely your hits are to one another.

Those biostatistic courses I took come in handy for shooting too.
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Old October 4, 2000, 09:44 PM   #16
TGS
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This has really been great. I appreciate all the time ya'll have put into this information and I apologize for having to take probably the better part of the rest of my life to absorb it all but I shall.
...and the reminder that there is a difference between accuracy and precision. Remembering back to Metrology 101...we are talking about precision when were refering to group size. so long ago.
Ive got to go take a Excedrin. Make that 2.
latter ya'll
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Old October 5, 2000, 11:19 AM   #17
Bogie
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I no longer worry about S.D. for loading - Why?

A buddy was shooting his PPC, and he decided to find the best SD load... He worked up slowly, found a load that had little standard deviation, etc.

That load wouldn't shoot worth a darn. Lots of vertical dispersion. A little more wrenching on the powder measure, and he was there... Not optimal as far as SD was concerned, but hey...

A chrony will tell you what's going on, but don't build your load around one... Shoot what's accurate, not what looks good in theory.

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Old October 7, 2000, 05:02 AM   #18
Hard Cast 44
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Read an interesting article reguarding SD tonight. See http://www.reloadammo.com/rel-sped.htm. MD did a test useing the 45 colt and the relation of the powder location in the case to SD. Tipping the gun toward the air before firing, and then tipping the gun toward the ground, and then firing with the same loads. Mostly using Accurate powders. The pointing to the air rounds gave an average of between 145 fps and 210 fps faster bullet speeds. Very interesting reading and it gave me reason to question not using strictly group sizes in comparing loads. If some of you Chrono Nerds can check it out and let us know what you results are it would be great. TED
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