What are formulae for computing bullet weights?
How do you calculate the weight of a bullet from its dimensions? I have formulae for calculating the weights of: round balls; cylinders; and cones. Therefore, I can "come close" when trying to calculate a pointed boat tail with [unknown] ogive.
I know this calculation can be done -- I refuse to believe bullet companies create bullets of a specific weight by trial-and-error.
If I have a written formula, I will be able to program my database or spreadsheet to calculate on the fly. I run Macintosh computers. PC programs will not be useful; the formula will be.
I know this calculation can be done -- I refuse to believe bullet companies create bullets of a specific weight by trial-and-error.
If I have a written formula, I will be able to program my database or spreadsheet to calculate on the fly. I run Macintosh computers. PC programs will not be useful; the formula will be.
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I think to do that formula is not that hard in pronciple. Every math formula book gives you the formulas. The problem is, that bullets are made out of different materials lead and a copper alloy and by just looking at is you can't figure out how much of it was used.
in a world full of compromise some don't0 -
The parabola of the tip of the bullet varies in different designs. Most lead bullets I use have a copper sheathing (FMJ). The larger calibers tend to have a flattened nose, Some, hollow points, have an indentation. The variations goes on ...
I would conjecture that engineers stamp out the jacket deeper than they need, fill it with molten lead, and trim it until it is the weight they want. Then they decide how deep it must seat within the cartridge. A Wilson mag I just bought describes proper .45 ACP cartridge length for reloads to be 1.24" ~ 1.26" in order to feed correctly (I think these numbers are right; I threw out the literature).
When studying the difference between .380, .40, .45, and 9mm, although I had no examples but the .380, I found an informative site with complete and detailed sketches of bullet and cartridge design. I no longer have the link, and forgot what words I used in my Google search.
I am not an engineer, definitely not an expert by any definition, but the great firearms designers built and tested, built and tested. So I repeat, this is only conjecture; it may be right on the money, and it might be way off.
Why don't you e-mail Federal or Winchester?
I'm sure their tecs. would love to see someone take an interest in armament design.
The world will always need bullet designers.
Heck, I have not a clue how one bullet can travel 100 yds flat and another take it in an arc. Look what engineers have done to the golf ball, and dimpling.
Luck !
p.s. ~ here is some info on makeup of bullets
http://www.redding-reloading.com/pages/bulletweights.html0 -
Lance,
Here is a link to Benchrest Central's bullet page. Listed are several custom bullets makers. All very nice people who make custom bullets one at a time, usually for the benchrest crowd. It might be, that if you asked real nice, that they would walk you through the process and tell you how they arrive at a new bullets weight and shape. I've had a couple of questions in the past and they were very forecoming with information.
Best.
http://benchrest.com/html/bullets.shtml0 -
What you're attempting to do could (in principle) be handled by elementary calculus: you're computing the volume (and, using density, the mass thereby) of a solid of revolution. There are two "tricky parts" to doing this: (1) describing the bullet profile by a single curve, or using a set of curves that join smoothly, and (2) accounting for the apparent "density" of the bullet material if it's a jacketed composite (copper jacket over a lead core, say.) And here's the rub: You'd have to use a DIFFERENT curve to describe the bullet profile for each distinct type of bullet, which means that you'd have to determine a different y = f(x) curve for a spitzer as opposed to a round-nose or flat-nose bullet. Once you had a curve that described the shape---or profile---of the bullet satisfactorily, it would be an easy matter to calculate the volume of the solid resulting from revolving this curve around its axis of symmetry and (mathematically) cutting it into disks, then summing the volumes of the disks by integration. If this seems like a rather abstruse explanation, simply grab a calculus textbook and look up "volume, solids of revolution" for an explanation involving pix and examples.
I suspect, however, that bullet engineers already have these various ogives and shapes plotted and the curves worked out in whatever software they use for bullet design, so you'd probably be better off asking one of them where you could get such data...
It's all a matter of how far you're willing to go in the "do-it-yourself" part of this project.0 -
Should be able to calculate the weight using calculus (volumetric integral across the length/axis of the bullet). The integration would give you the volume. Mass/volume would be available from chemistry texts (or calculated using molecular weights). This should give you a mass for the calculated volume. Convert result (either in lbs or kgs) to grains.
The hard part would be determining the equation that would describe the outside curve of the bullet, and deciding where the inflection points would be along with the change in the equation at those inflection points.
Btw, most companies would use a CAD program to design and build their bullet these days. In the "good ol' days", weight vs. shape was from an imperical (sp?) lookup table.
"Nuke 'em 'til they glow - then shoot 'em in the dark."0 -
No-Stick: There really wouldn't be an "inflection point" to deal with here, since the bullet's profile could be approximated by either a parabola or a catenary-type hyperbolic sine or cosine; there would be no point on the curve where the concavity changes character, like it does on a graph of, say, y = x^3. But we're in harmonious agreement on the GENERAL approach here, and the rest is mere detail... 0 -
Why not solve it the way Archimedes (sp?) would? 0 -
trstone: I included the term "inflection" to include edges and discontinuities in the equation (eg., lips of grooves around the base). A continuous equation typically falls apart at these points.
Personally (doing it the hard way), I would section up the bullet into simpler arc-curves with breakpoints at the discontinuities, performa a volumetric integration via revolution about the axis from breakpoint to breakpoint, then sum the total. Naturally special care would have to be given to the bullet's tip if it's a hollowpoint (equation reflects in on itself about the axis - so the tip would have to be defined to revolve along the y-axis instead of the x).
Doing it the easy way, I'd just fire up one of my CAD programs that supports material analysis.
"Nuke 'em 'til they glow - then shoot 'em in the dark."0 -
I think it'd be a whole lot more useful if one could compute the ballistic coefficient from the shape and composition, wouldn't you agree? And I believe that there is a way to do it which is fairly accurate, though I've never seen it done and I don't know what the relevant formulae are. Saw an ad on the 'Net for software that claimed it calculated BC from shape, so I know it can be done....
I'm darned curious to know how it's done, though.0 -
Get a scale...[xx(] 0
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