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Old March 14, 2000, 06:39 PM   #1
Gopher a 45
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It's just an academic question but how are these two values derived? I was curious as to how you could use this info to reduce drag for bullets. Also, do you have to test the bullets to find out these values or can you figure them out mathematically before the bullet is even made. I know there's no substitute for actual testing, but can you get a ballpark figure so you can tell if you're on the right track design-wise?

John
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Old March 14, 2000, 11:57 PM   #2
Bud Helms
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BC = w/i(d*2)

BC = weight of the bullet divided by the product of the diameter of the bullet squared and the coefficient of form

i = ? Ah, now we get to it. Coefficient of form is usually given. Hell, BC is usually given.

There is a chart which was published by E.I.Du Pont De Nemours & Co., which was prepared by Wallace H. Coxe and Edgar Beugless, Ballistics Engineers (and principal investigators) of the Smokeless Powder Dept at DuPont's Burnside Laboratory in Wilmington, Delaware, in 1936. Actually it is one in a group of ten charts that were part of an extensive publication on ballistics.

Chart No. 1 is for determining Coefficient of Bullet Form. Chart No 2 is for determining Ballistic Coefficient. And so on.

Without the chart, I don't know how to do it. It is an estimate even with the chart. The ogive of the bullet is determined by comparison with a set of drawn examples which are numbered. That value is taken to a table and a selection is made which yields another value. That number is Coefficient of Form (i). There is not enough information in the table to empirically derive a relationship which can be expressed mathematically.

So, the BC in the reloading manual is usually taken as the truth because computing it is a pain in the arse! I came into the charts when I purchased P.O. Ackley's Handbook for Shooters and Reloaders, Vol. I and II.

Reloading books published by bullet mfgs always (these days) include the BC for every bullet listed. Not so in reloading books by powder mfgs. They treat the bullet as a mass with inertia and assume nominal values. That's not incorrect, it's just incomplete.

As I understand it, Coxe and Beugless based some of their work on results of testing and earlier ballistics-related computations taken from Krupp Industries in Deutschland. Krupp was the foremost military and heavy weapon maker of the 19th and early 20th Centuries.

[This message has been edited by sensop (edited March 15, 2000).]
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Old March 15, 2000, 02:56 AM   #3
Ricciardelli
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It is a number, assigned to a hypothetical perfect bullet, under ideal and constant atmospheric conditions, at a constant velocity. There are three major considerations that we MUST look at here. "Perfect", "Ideal", "Constant". None of these apply to any man or environment know to man, or at least inhabited by man.

First, what is the "perfect" bullet? It is a bullet which is three-calibers long, and ogival head of two-calibers radius, and of homogenous construction with equal and concentricity of the mass around the center from tip to butt. Got that? Name one bullet that meets those specifications!

This bullet must be fired from a source that will establish and guarantee that a constant velocity of that bullet will remain from the moment of launch until the moment of impact. Got that? Name one projectile that meets that requirement!

In addition, all this MUST take place at exactly sea level, at a temperature or 59-degrees F., 29.58-inches of mercury barometric pressure and 78% humidity. Oh, and absolutely no movement of the air... Name one place on earth that has those qualifications, 24-hours-per-day, 7-days-per-week, 52-weeks-per-year... Can't, can ya!

Now if we could find that "perfect" bullet, and launch it and maintain it at the "constant" velocity, under the "ideal" conditions, we would be able to assign a ballistic coefficient of 1.000 to that bullet. That's a hell of a lot of work to get a rating of "1"!
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Old March 15, 2000, 12:56 PM   #4
Gopher a 45
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Sensop,

Thanks for the info. It's just as I suspected. The coefficient of form is a pain to derive! All the reloading manuals sort of give a: "Trust us. The BC is what we say it is" without any elaboration as to how they get an actual figure of say, .269 for a 55g .223FMJ bullet. They're happy to provide the formula for BC, but don't provide the way to get one of the variables, coeff. of form. Undefined variables make me nervous! So I was wondering how they got their numbers. I suppose Speer et al. have got a lot of eggheads working with slide rules and abaci back in the shop somewhere to come up with this stuff! I'll have to look into getting those volumes you mentioned. I assume they're still available? I see now why a 40mm Bofors round at 3200fps has a better BC than a .243 round of the same shape and velocity. It's all about mass! I guess our old friend Newton's at work again. The inertia of the larger round resists velocity loss due to friction much better than the varmint bullet. I guess the corrolary is you've got to use more bang-stuff to get it moving at the same velocity and therfore recoil is greater. Man, there just ain't no such thing as a free lunch when it comes to physics! As an aside, I know the Jerries were into big guns. Didn't Krupp make all the German battleship and railroad guns including that monster Paris gun of WWI? Talk about an exercise in ballistics! I think that's where they discovered the Coriolis effect, since Paris wasn't where they were aiming at by the time the shell had traveled the 75 miles to the target. You know you've got a long-range gun when you have to factor in not only windage but the rotation of the earth! I wonder if anyone makes reloading dies for something like that So, I guess it would be about time to do some new testing if the only tables out there are based on work done 75+ years ago? Of course, physical laws haven't changed since then (as much as Congress tries), so maybe it would be a waste of time.

Ricciardelli,

Sure, I get those conditions here at my range all the time. You mean you don't? And, rocket-assisted projos give a consistent velocity every time (my gyrojet pistol functions flawlessly).
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Old March 15, 2000, 02:40 PM   #5
Bud Helms
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With the new Tungsten 6 mm bullets, VLD bullets of various calibers (mostly 6 mm, I think) and other advances in bullet technology, i.e., materials, which change the composition and therefore the mass properties of the average bullet AND with today's superior instrumentation and data collection methods, I would dearly love to be part of an engineering group to replicate Krupp and DuPont data. Oooooh, I'm salivating.

I'd make sure the Swedish Bofors 40 mm got in on it too! Maybe a single shot version of the Vulcan 20 mm. Hell, might as well test the GAU-8 30 mm too. Here we go!
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Old March 15, 2000, 03:16 PM   #6
Ricciardelli
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My Gyro-Jet didn't have constant velocity. As a matter of fact, you could hold your hand right in front of the "launching ramp" and stop the projectile from exiting...I was more than a little nervous the first time I did that...
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Old March 15, 2000, 03:57 PM   #7
Kenneth L. Walters
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There are probably three dozen plus ballistic tables. The first were done around 1900 and based on earlier work with, if memory serves, one inch diameter cannon shells. The last I ever heard of were done by Winchester just after WWII.

The ballistic coefficient is kind of like trying to do a one dimensional curve fit. Using the Ingalls tables, for example, the ballistic coefficient is an attempt to explain what a new projectile will do in comparison to the one for which all the measurements were made.

In the late 1800's this was high science. Today it isn't. What isn't clear is if it is better than nothing. I know not!
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Old March 15, 2000, 04:40 PM   #8
Gopher a 45
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Oh I'm well aware of the inconsistencies of the gyrojet. Hence, the What happened to the burning propellant while you stopped the rocket with your finger? That might get a bit warm, no?

Um, do we have any Paul Bunyan types out there willing to test a shoulder-fired 30mm GAU-8 single-shot?

I'm rather surprised to see that the last serious ballistic work was done that long ago. Hey, did you know that the Bell X-1 sound barrier rocket plane back in '47 was supposedly designed after the .50 cal boat-tail bullet. They knew the BULLET broke the sound barrier, so they thought they'd scale it up and see if it'd work in a plane. I hope Yeager didn't ever see spent .50 slugs looked like at the range, or he might have reconsidered that little trip!
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Old March 15, 2000, 09:18 PM   #9
Bud Helms
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<BLOCKQUOTE><font size="1" face="Verdana, Arial">quote:</font><HR>... the ballistic coefficient is an attempt to explain what a new projectile will do in comparison to the one for which all the measurements were made.[/quote]

Good answer, Ken.

***************
Gopher,

As I recall, they didn't discover the coriolis effect, it was a known phenomenon, but it was the only thing that fit their problem and they were right!


[This message has been edited by sensop (edited March 15, 2000).]
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