The Firing Line Forums Calculating Velocity
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 September 4, 2012, 09:52 PM #26 culpeper Junior Member   Join Date: September 4, 2012 Posts: 3 Google led me here I read this article and found it interesting but the author is a little aloof on his actual methodology like his table is, "an application of the familiar...'method of least squares'." But I can't find anything in the form related to least square regression and I can't replicate what he is doing using the data analysis tool in Excel. Maybe somebody can shed some light on what is actually going on with his calculations. The author is apparently writing this stuff for all audiences but I'm a little more than curious. Thanks in advance http://www.24hourcampfire.com/chronograph.html Last edited by culpeper; September 4, 2012 at 10:00 PM.
 September 5, 2012, 07:46 PM #27 tac_driver Member   Join Date: April 14, 2008 Location: North Carolina Posts: 61 __________________ http://home.roadrunner.com/~cuttingedgz/ 22/45 Ruger S&W 640 Glock 21SF,S&W 67 Combat,Colt series 80 Combat,Glock 19
 September 5, 2012, 09:43 PM #28 mrawesome22 Senior Member   Join Date: November 9, 2005 Location: Ohio, Appalachia's foothills. Posts: 3,779 Too many variables. First post had it. Buy a chronograph. sudo passwd root
 September 6, 2012, 08:32 AM #29 culpeper Junior Member   Join Date: September 4, 2012 Posts: 3 I figured it out. Take the 1-R Square variable to estimate your overall average based on what is going on in the article. The article is about using your chronograph and some simple math to save some ammo or at least give you a solid starting point before collecting and using range data.
 September 6, 2012, 11:39 AM #30 Unclenick Staff   Join Date: March 4, 2005 Location: Ohio Posts: 14,964 Interesting article. I would take issue with his method, though. He finds an expected average velocity for a 54 grain charge then divides it by 54 grains to get the velocity per grain of powder. He then uses that to find expected velocities for each of the other charges from which he takes his deviations from the actual results. While fps/grain is pretty linear it isn't perfectly linear, so I would at least have used the average of his first column of difference numbers divided by the number of grains per charge increment (2 grs) to get 52.75 fps/gr as being more representative in his pressure and velocity range. Doing that lowers the SD of the resulting expected values. If I go sophisticated and do an actual linear regression by the method of least squares, the slope is a slightly larger 54.25 fps/gr, and it changes the expected 54 grain velocity to 2638.8 fps. Substituting that in and finding the expected values for other charges gets me a still lower SD, indicating it is a still more accurate reflection of reality. I note Howell's admission and other indications in the piece that he doesn't really understand how the math is working, so my surmise is that he is copying a method by analogy without understanding how well it actually applies. His assertion that the information he gleans from five shots is as good as firing five ten shot groups fails to consider the confidence limits of a five shot sample size. I would take the whole thing with a grain of salt. Board member Denton Bramwell does statistical analysis for a living. If he sees this he can better comment on it than I can, or perhaps set me straight on what I think I'm seeing. __________________ Gunsite Orange Hat Family Member CMP Certified GSM Master Instructor NRA Certified Rifle Instructor NRA Benefactor Member and Golden Eagle Last edited by Unclenick; September 7, 2012 at 09:06 AM. Reason: clarification
 September 6, 2012, 01:08 PM #31 Edward429451 Junior member   Join Date: November 12, 2000 Location: Colorado Springs, Colorado Posts: 9,494 Who'd of thought there'd be so much math in shooting guns?! I'm glad I have a chronograph and a calculator. That and a target tells me all I'll need to know. This is some interesting stuff though.
September 6, 2012, 01:31 PM   #32
Wyoredman
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Join Date: September 6, 2011
Location: Wyoming
Posts: 1,320
Here is an actual velocity test I did for my .223 using CFE223. As you can see, the velocities are not quite linear, and are quite a bit faster than listed int the Hodgdon 2012 reloading magazine. Also notice the differance in mag vs. std primers.

The only way to tell is to spend a \$100 on a chrony.
Attached Files
 cfe223[1].pdf (145.9 KB, 11 views)
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 September 6, 2012, 06:51 PM #33 Unclenick Staff   Join Date: March 4, 2005 Location: Ohio Posts: 14,964 No surprise there. Charles Petty tested about all the small rifle primers there are with the same charge of Reloader 10X and 55 grain V-max bullets in 2006. He got 3150 to 3300 fps, in round numbers. Primers can make quite a difference. __________________ Gunsite Orange Hat Family Member CMP Certified GSM Master Instructor NRA Certified Rifle Instructor NRA Benefactor Member and Golden Eagle
 September 6, 2012, 09:27 PM #34 culpeper Junior Member   Join Date: September 4, 2012 Posts: 3 I too went the regression route and came up with the same thing. Even just using the XY Scatter chart you can come up with the least squares formula. I don't really know for sure though what the author means that his half looking bell curve is an application of the least squares method. This is basically statistical sampling so we really don't know the true value but can only come close because there is yet to be a universe created. How close? The author doesn't state. I have tested his method and it works as far as initial zero loads for an unfamiliar rifle. I've tested on two different rifles (.300 H&H Ruger and a custom bolt action .300 H&H). In each case I was able to determine the nearest safe max load as well as accuracy load once you create a scatter chart. The rest was up to the range work and didn't have to make any load changes after verification. Too bad he never followed up on his article on how the chronograph can help estimate pressure as well.
September 8, 2012, 09:39 PM   #35
Bart B.
Senior Member

Join Date: February 15, 2009
Posts: 6,318
wncchester claims:
Quote:
 The velocities in factory ballistics charts and our loading manuals are often so far off reality that any efforts to 'calculate' a speed has nothing to start from.
I disagree. The numbers the factory got are just as real as the numbers anybody else gets. If you don't understand why, then go measure a bunch of barrel's bore, groove and chamber dimensions. Next, go measure the velocity spreads several lots of the same powder produce with the same case, primer, powder charge weight in the same barrel. And finally, give the same rifle and ammo to several people and have them chronograph that load in that rifle. The issue of different neck tension's effect on muzzle velocity is a whole different matter.

You may well not believe the muzzle velocity spreads this simple and real test of components, barrels and people get.

We all choose different barrels, powder lots, primer lots and probably shooting positions than the factory did. Therefore, we should not expect to get the same muzzle velocity they do. We don't use the same "stuff" the factory did.

Plotting a graph is a good way to get an idea of what might happen.

 September 9, 2012, 09:09 AM #36 WESHOOT2 Senior Member   Join Date: February 20, 1999 Location: home on the range; Vermont (Caspian country) Posts: 14,270 here's my proven formula The chronograph calculates velocity; every other 'method' is best labeled "guessing" And that's the fact. __________________ . "all my ammo is mostly retired factory ammo"

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