Exterior ballistics question/looking for an old article

pathdoc · May 16, 2013, 05:42 PM

A long, long time ago - probably some time in the mid 1980s, and certainly not after 1988 - a shooting magazine the name of which I've forgotten published an article about exterior ballistics which gave numerous formulae. These, when fed the muzzle velocity, ballistic coefficient (G1, standard BC as listed in the handloading manuals etc.), and I think there might have been one for wind deflection, gave (after much calculator button pushing) remaining velocity, time of flight to range, and bullet drop below axis of bore.

I can remember only one, the remaining velocity equation, which was advertised as being good down to 1400fps. If I recall correctly, it boiled down to:

square root of RV = square root of MV - (0.00863 * R/BC).

Where R was in yards and MV and RV were in feet/second.

Does anyone remember this article? Or better yet, have it? I once had it all programmed into a spreadsheet (there were two values called K and F that had to be derived before the bullet drop could be calculated, so it was a lot of work), but that was ages ago and I no longer have access to that. I also failed to photocopy the relevant pages or even to write down the name of the magazine. Stupid, stupid me, but I was young and foolish at the time. Can anyone help?

jmr40 · May 16, 2013, 06:51 PM

There are better ways to do this today. Just plug in your numbers to any of the many online ballistics programs available. I use this one.

http://www.hornady.com/ballistics-re...ics-calculator

g.willikers · May 17, 2013, 09:56 AM

Yes, run an online version and you won't even need to use your slide rule.

kraigwy · May 17, 2013, 10:12 AM

Quote:

run an online version and you won't even need to use your slide rule

That takes the fun out of it.

Info you are looking at can be found in:

Hatcher's Notebook, by MG Julian Hatcher

Applied Ballistics for the Long Range Shooter, by Bryan Litz of Berger bullets

and the best, but a bit more technical is.

Modern Exterior Ballistics, by Robert McCoy.

pathdoc · May 17, 2013, 05:58 PM

Thanks.

I have Litz's book; I have Hatcher's (shall go back and look); McCoy's is on the way.

I e-mailed Litz. He told me that the equation looks like something Pejsa did, so Pejsa's book (FWIW) is also on its way.

Obviously for practical applications I'd go to a program, but nostalgia is driving me to try to find this article (or the "meat" from which it was derived).

**Unclenick** · May 19, 2013, 08:46 AM

You may need to brush up on your calculus and differential equations for McCoy, but there's no more rigorously detailed examination of all the contributing elements and methodologies for exterior ballistics. I understand a newer printing is coming along (if not there already). I don't know if the errata have been cleaned up in it or not. Unfortunately, Robert McCoy passed away before he could edit the original galleys for his book, so his multitude of understudies have put up corrections on line, here.

Something is amis with your formula for remaining velocity. I have ballistics software (QuickTARGET Unlimited) that includes the BRL measured actual drag function for a 168 grain Sierra Match King, and with respect to which the BC of that bullet will be 1.000. Fired at 2650 fps under U. S. Army Standard Metro conditions, the remaining velocity at 600 yards is 1545 fps using that drag function with the calculator. If I use your formula and Sierra's claimed upper velocity boundary (over 2600 fps) G1 BC of 0.462, I get 2639 fps at 600 yards. If I take away the two zeros after the decimal point in the constant and use 0.863, I get a much closer 1529 fps. If I interpolate Bryan Litz's measured G1 BCs for the 168 grain SMK for 2650 fps (0.447) I get 1492 fps from that formula with the adjusted constant. So it seems any error in BC measurement or degree of exaggeration by the manufacturer is essential to have correct for it to be accurate.

Paul B. · May 19, 2013, 12:22 PM

I remeber something like that. IIRC, it was either an old RIFLE or HANDLOADER Magazine. Some of their early articles were quite technical.
Paul B.

pathdoc · May 19, 2013, 04:56 PM

Unclenick, I take your point about the dodginess of the formula. Please accept my apologies as they may be required - my memory is stretching back twenty-odd years here, and my understanding of ballistics back then was sketchy and naive. I put it up as much to see whether it jogged memories as anything else, and not with any expectation that it represents anything near the currently understood best practice.

ETA and slightly off-topic: Speaking of the magazines mentioned, a bit of googling shows me that the entirety of both magazines are available on DVD from the publishers, in full text, up to the end of last year. At steep prices, true, but available. I am tempted, but I've heard there's a point where Handloader stopped being mostly technical and started picking up a distinct trend towards sales & advertising. Can anyone clarify? Would anyone here do it, cash no object?

**Unclenick** · May 20, 2013, 08:06 AM

No problem. It was an opportunity to see the limitations of simplifying calculations, and to show the limitations of BC's taken with respect to reference projectiles that poorly match the shape of your bullet.

Re Handloader, Dave Scovill had to do what was necessary to keep Handloader alive. It turns out that means two things in the modern world: One is that the source of articles must be nearly free. What an editor can afford to pay a writer is a fraction, in dollars, much less in constant dollars, of what it was fifty years ago. Outside of full time employment by a gun rag publisher, the day when someone could make a living as a gun writer is dead. There will be no new Jack O'Connor (who quit teaching English to be a full-time outdoor writer because, in the 1940's, he could). Gun rag editors now depend a good deal on persons doing something for their own purposes to be willing to write it up and illustrate it for less than their time is worth at almost any other job. Almost certainly less than minimum wage, unless they can write really fast and fill most of the part of a page not jammed with ads with photos instead of writing.

Second, TV and Internet sources, like You Tube and even this kind of forum, have hit all print media hard by competing successfully for reader's leisure time and attention span limits. Modern readers often are those who grew up accustomed to communication consisting of pictures and superficial descriptions comprised of TV news vocabularies (about 5,000 words). Curiously, this means they've developed what I find to be an astounding tolerance for bad writing and video monologues that are run-on, hesitating, include wandering digressions, are accompanied by gratuitous narcissistic images of their authors shooting guns, and are, to me, flat out too boring to finish viewing. But they don't seem to exhibit the same tolerance for dry, but concise, technical writing. I don't know why; habit, perhaps. I just hope there are enough young people with enough curiosity about the technical minutiae to become the next generation of innovators.

The bottom line is, a gun rag editor has to publish superficial information with lots of pretty pictures. That's why Precision Shooting died. Handloader has not died, but not long ago I took a look at one of their two-article free issue previews. It consisted of one article extolling the virtues of the 6.5×55, with lots of photos and lots more advertising, and exactly one paragraph mentioning handloading for it, plus a very small table of load data. The second article was on .22 Rimfire rifles. .22 Rimfire? For a magazine called "Handloading"? Really? Obviously there was no handloading information there, either. But apparently that keeps the lights on.

pathdoc · May 20, 2013, 05:39 PM

Unclenick, thank you for your reply and your perspective on Handloader. I understand completely.

Your point about YouTube videos is well made. They range from the professional and confidence-inspiring to the positively hair-raising (as in how is this guy not blowing bits of himself off?) and some of them promise much and deliver little. If I'm looking for a review on a firearm I'm considering buying, for example, I don't need a description of how many rails I can attach and gizmos I can hang off it, coupled with video of the owner blazing away at whatever; I want to know how it's performed over hundreds or thousands of loaded rounds and/or many years' use. Sure, if it's something rare and interesting then watching it being loaded, cycled and fired is of value if you're considering collecting one yourself. But otherwise it's just gun p*rn.

And for all the guys (mostly) who do serious reviews (or at least entertaining historical vignettes) of firearms before treating the viewer to an orgy of soda-can blasting, there are some I have to say I wouldn't care to be around when they're handling a loaded gun.

Some of the professional reloading manuals are IMO little better. Sure, it helps knowing that the bullet does its job downrange well, but it's a book about putting ammunition together and quite frankly I'd rather read two pages of dry technical tips and potential pitfalls the lab people discovered than a glowing testimonial or account of a memorable hunting trip shot through with superlatives.

kraigwy · May 20, 2013, 07:19 PM

It's a shame, no one wants to read anymore. They'd rather get instant gratification from the internet or TV.

They don't realize what they are missing by not taking an evening with McCoy, a few bullets, a mic, and slide rule or calculator.

Seems anymore that if you can't do it without batteries, it can't be done.

pathdoc · June 9, 2013, 06:27 PM

I've got Pejsa's little red book and it's definitely his formula - at least the construction of it. Strictly speaking, above 1400fps and using the US .30cal M2 bullet as its reference projectile, it breaks down to:

r = 332 (sqrt(MV) - sqrt(V1))

...which rearranges to:

sqrt(V1) = sqrt (MV) - r/332

...with r in FEET.

If you do R in yards and change the fraction into a decimal, you do actually get sqrt (V1) = sqrt (MV) - 0.00904 R. Now the BC doesn't actually figure in this at all, at least if you use the M2 shape without modification. Dividing 0.00904 by 0.00863 gives about 1.047 (the reciprocal is about 0.955), which makes me wonder if there hasn't been some sort of correction for form factor put in, to relate the M2 projectile back to the typically-published G1 coefficients. I honestly don't know.

I recall that the formulae were given in the magazine article "as is", with none of the attempts at derivation which Pejsa gives in his book. That makes me more certain that this IS Pejsa's formula as above, but presented for ease of use by everyday hunters and target shooters who want to just plug in the numbers they know (range, MV, BC) and get out an answer they can then insert into further calculations (deriving K, F, etc. and using them to plug into the drop, TOF and other equations; in effect, going the other direction from the line Pejsa's book takes).

This is looking more and more likely the more I consider it.

May 16, 2013, 05:42 PM	#1
pathdoc Senior Member Join Date: February 12, 2013 Posts: 669	Exterior ballistics question/looking for an old article A long, long time ago - probably some time in the mid 1980s, and certainly not after 1988 - a shooting magazine the name of which I've forgotten published an article about exterior ballistics which gave numerous formulae. These, when fed the muzzle velocity, ballistic coefficient (G1, standard BC as listed in the handloading manuals etc.), and I think there might have been one for wind deflection, gave (after much calculator button pushing) remaining velocity, time of flight to range, and bullet drop below axis of bore. I can remember only one, the remaining velocity equation, which was advertised as being good down to 1400fps. If I recall correctly, it boiled down to: square root of RV = square root of MV - (0.00863 * R/BC). Where R was in yards and MV and RV were in feet/second. Does anyone remember this article? Or better yet, have it? I once had it all programmed into a spreadsheet (there were two values called K and F that had to be derived before the bullet drop could be calculated, so it was a lot of work), but that was ages ago and I no longer have access to that. I also failed to photocopy the relevant pages or even to write down the name of the magazine. Stupid, stupid me, but I was young and foolish at the time. Can anyone help?

May 17, 2013, 09:56 AM	#3
g.willikers Senior Member Join Date: September 28, 2008 Posts: 10,442	Yes, run an online version and you won't even need to use your slide rule. __________________ Walt Kelly, alias Pogo, sez: “Don't take life so serious, son, it ain't nohow permanent.”

May 19, 2013, 08:46 AM	#6
Unclenick Staff Join Date: March 4, 2005 Location: Ohio Posts: 21,063	You may need to brush up on your calculus and differential equations for McCoy, but there's no more rigorously detailed examination of all the contributing elements and methodologies for exterior ballistics. I understand a newer printing is coming along (if not there already). I don't know if the errata have been cleaned up in it or not. Unfortunately, Robert McCoy passed away before he could edit the original galleys for his book, so his multitude of understudies have put up corrections on line, here. Something is amis with your formula for remaining velocity. I have ballistics software (QuickTARGET Unlimited) that includes the BRL measured actual drag function for a 168 grain Sierra Match King, and with respect to which the BC of that bullet will be 1.000. Fired at 2650 fps under U. S. Army Standard Metro conditions, the remaining velocity at 600 yards is 1545 fps using that drag function with the calculator. If I use your formula and Sierra's claimed upper velocity boundary (over 2600 fps) G1 BC of 0.462, I get 2639 fps at 600 yards. If I take away the two zeros after the decimal point in the constant and use 0.863, I get a much closer 1529 fps. If I interpolate Bryan Litz's measured G1 BCs for the 168 grain SMK for 2650 fps (0.447) I get 1492 fps from that formula with the adjusted constant. So it seems any error in BC measurement or degree of exaggeration by the manufacturer is essential to have correct for it to be accurate. __________________ Gunsite Orange Hat Family Member CMP Certified GSM Master Instructor NRA Certified Rifle Instructor NRA Benefactor Member and Golden Eagle

May 19, 2013, 12:22 PM	#7
Paul B. Senior Member Join Date: March 28, 1999 Location: Tucson, AZ Posts: 3,802	I remeber something like that. IIRC, it was either an old RIFLE or HANDLOADER Magazine. Some of their early articles were quite technical. Paul B. __________________ COMPROMISE IS NOT AN OPTION!

May 19, 2013, 04:56 PM	#8
pathdoc Senior Member Join Date: February 12, 2013 Posts: 669	Unclenick, I take your point about the dodginess of the formula. Please accept my apologies as they may be required - my memory is stretching back twenty-odd years here, and my understanding of ballistics back then was sketchy and naive. I put it up as much to see whether it jogged memories as anything else, and not with any expectation that it represents anything near the currently understood best practice. ETA and slightly off-topic: Speaking of the magazines mentioned, a bit of googling shows me that the entirety of both magazines are available on DVD from the publishers, in full text, up to the end of last year. At steep prices, true, but available. I am tempted, but I've heard there's a point where Handloader stopped being mostly technical and started picking up a distinct trend towards sales & advertising. Can anyone clarify? Would anyone here do it, cash no object? Last edited by pathdoc; May 19, 2013 at 06:04 PM.

May 16, 2013, 06:51 PM	#2
jmr40 Senior Member Join Date: June 15, 2008 Location: Georgia Posts: 10,809	There are better ways to do this today. Just plug in your numbers to any of the many online ballistics programs available. I use this one. http://www.hornady.com/ballistics-re...ics-calculator

May 17, 2013, 05:58 PM	#5
pathdoc Senior Member Join Date: February 12, 2013 Posts: 669	Thanks. I have Litz's book; I have Hatcher's (shall go back and look); McCoy's is on the way. I e-mailed Litz. He told me that the equation looks like something Pejsa did, so Pejsa's book (FWIW) is also on its way. Obviously for practical applications I'd go to a program, but nostalgia is driving me to try to find this article (or the "meat" from which it was derived).

May 20, 2013, 08:06 AM	#9
Unclenick Staff Join Date: March 4, 2005 Location: Ohio Posts: 21,063	No problem. It was an opportunity to see the limitations of simplifying calculations, and to show the limitations of BC's taken with respect to reference projectiles that poorly match the shape of your bullet. Re Handloader, Dave Scovill had to do what was necessary to keep Handloader alive. It turns out that means two things in the modern world: One is that the source of articles must be nearly free. What an editor can afford to pay a writer is a fraction, in dollars, much less in constant dollars, of what it was fifty years ago. Outside of full time employment by a gun rag publisher, the day when someone could make a living as a gun writer is dead. There will be no new Jack O'Connor (who quit teaching English to be a full-time outdoor writer because, in the 1940's, he could). Gun rag editors now depend a good deal on persons doing something for their own purposes to be willing to write it up and illustrate it for less than their time is worth at almost any other job. Almost certainly less than minimum wage, unless they can write really fast and fill most of the part of a page not jammed with ads with photos instead of writing. Second, TV and Internet sources, like You Tube and even this kind of forum, have hit all print media hard by competing successfully for reader's leisure time and attention span limits. Modern readers often are those who grew up accustomed to communication consisting of pictures and superficial descriptions comprised of TV news vocabularies (about 5,000 words). Curiously, this means they've developed what I find to be an astounding tolerance for bad writing and video monologues that are run-on, hesitating, include wandering digressions, are accompanied by gratuitous narcissistic images of their authors shooting guns, and are, to me, flat out too boring to finish viewing. But they don't seem to exhibit the same tolerance for dry, but concise, technical writing. I don't know why; habit, perhaps. I just hope there are enough young people with enough curiosity about the technical minutiae to become the next generation of innovators. The bottom line is, a gun rag editor has to publish superficial information with lots of pretty pictures. That's why Precision Shooting died. Handloader has not died, but not long ago I took a look at one of their two-article free issue previews. It consisted of one article extolling the virtues of the 6.5×55, with lots of photos and lots more advertising, and exactly one paragraph mentioning handloading for it, plus a very small table of load data. The second article was on .22 Rimfire rifles. .22 Rimfire? For a magazine called "Handloading"? Really? Obviously there was no handloading information there, either. But apparently that keeps the lights on. __________________ Gunsite Orange Hat Family Member CMP Certified GSM Master Instructor NRA Certified Rifle Instructor NRA Benefactor Member and Golden Eagle Last edited by Unclenick; May 20, 2013 at 08:12 AM.

May 20, 2013, 05:39 PM	#10
pathdoc Senior Member Join Date: February 12, 2013 Posts: 669	Unclenick, thank you for your reply and your perspective on Handloader. I understand completely. Your point about YouTube videos is well made. They range from the professional and confidence-inspiring to the positively hair-raising (as in how is this guy not blowing bits of himself off?) and some of them promise much and deliver little. If I'm looking for a review on a firearm I'm considering buying, for example, I don't need a description of how many rails I can attach and gizmos I can hang off it, coupled with video of the owner blazing away at whatever; I want to know how it's performed over hundreds or thousands of loaded rounds and/or many years' use. Sure, if it's something rare and interesting then watching it being loaded, cycled and fired is of value if you're considering collecting one yourself. But otherwise it's just gun prn. And for all the guys (mostly) who do serious reviews (or at least entertaining historical vignettes) of firearms before treating the viewer to an orgy of soda-can blasting, there are some I have to say I wouldn't care to be around when they're handling a loaded gun. Some of the professional reloading manuals are IMO little better. Sure, it helps knowing that the bullet does its job downrange well, but it's a book about putting ammunition together* and quite frankly I'd rather read two pages of dry technical tips and potential pitfalls the lab people discovered than a glowing testimonial or account of a memorable hunting trip shot through with superlatives.

May 20, 2013, 07:19 PM	#11
kraigwy Senior Member Join Date: June 16, 2008 Location: Wyoming Posts: 11,061	It's a shame, no one wants to read anymore. They'd rather get instant gratification from the internet or TV. They don't realize what they are missing by not taking an evening with McCoy, a few bullets, a mic, and slide rule or calculator. Seems anymore that if you can't do it without batteries, it can't be done. __________________ Kraig Stuart CPT USAR Ret USAMU Sniper School Distinguished Rifle Badge 1071

June 9, 2013, 06:27 PM	#12
pathdoc Senior Member Join Date: February 12, 2013 Posts: 669	I've got Pejsa's little red book and it's definitely his formula - at least the construction of it. Strictly speaking, above 1400fps and using the US .30cal M2 bullet as its reference projectile, it breaks down to: r = 332 (sqrt(MV) - sqrt(V1)) ...which rearranges to: sqrt(V1) = sqrt (MV) - r/332 ...with r in FEET. If you do R in yards and change the fraction into a decimal, you do actually get sqrt (V1) = sqrt (MV) - 0.00904 R. Now the BC doesn't actually figure in this at all, at least if you use the M2 shape without modification. Dividing 0.00904 by 0.00863 gives about 1.047 (the reciprocal is about 0.955), which makes me wonder if there hasn't been some sort of correction for form factor put in, to relate the M2 projectile back to the typically-published G1 coefficients. I honestly don't know. I recall that the formulae were given in the magazine article "as is", with none of the attempts at derivation which Pejsa gives in his book. That makes me more certain that this IS Pejsa's formula as above, but presented for ease of use by everyday hunters and target shooters who want to just plug in the numbers they know (range, MV, BC) and get out an answer they can then insert into further calculations (deriving K, F, etc. and using them to plug into the drop, TOF and other equations; in effect, going the other direction from the line Pejsa's book takes). This is looking more and more likely the more I consider it.