Does anyone have a formula for calculating lead alloy bullet weight? For example, I have two .400” bullets each 0.900” long. One is pure lead and weighs 278 grains. The other weighs 228 grains, and I’d like to figure out its likely lead alloy content.
Math was never my strong suit, so forgive me if the formula for solving this is easy.
Thank you math geniuses in advance

You have to know what the other constituent metal was, otherwise all you can say is one is more dense than the other.

If, for example, one component was tin, and for all intents and purposes the only other component was lead, then you could figure out the percentage of each in the alloy pretty easily. Because we know the density of tin, and we know the density of lead.

It’s what is called a weighted average.

But it gets considerably harder, if there are multiple alloying components.

ClapperZapper is correct. It is very simple to calculate the volume of your bullet, knowing how much it weighs when cast of pure lead. But there are so many alloys used as bullet metal, that you would need to have an assay done to know the exact composition of your unknown alloy.

But you may find what you are looking for here:

http://castboolits.gunloads.com/showthread.php?105952-Lead-alloy-calculators

yes, it is easily done IF it is just lead and tin. But in all likelihood you probably have antimony in there too and that means you have 3 unknowns and only two independent equations. In other words, "What ClapperZapper said".


I calculate lead-tin ratios for casting all the time and have a spreadsheet set up for it to make it simpler, but it's only good on PB/SN alloys.

For what it’s worth, with three variables, especially knowing that antimony never gets whst? above 6%? You could actually do the calculation using antimony as a fixed 4%, and could very easily come within one or 2% on the actual alloy if you knew that the alloy was only lead and tin.

Certain variables dominate the equation.In other words, in terms of their overall effect within a weighted average, they behave as though they are fixed. Or at least contribute so little, that you can treat them as though they are fixed.

Calculations assume perfect casting. If that light bullet can be sacrificed, it may have a void in it.

Probably obviously harder or softer if the alloys are so different as well

The easy way, take it to a friend who buys and sells gold.
Ask him to run it through his mass spec
Then you will know



Mike

Thank you. I am going to have to assume that tin alone was used as the alloying metal with the lead

Thanks, Keith. That lead me down a deep and dark rabbit hole, but it was filled with a lot of interesting information. Surely useful to someone better at math than I...

It is an original 1880s paper patched lead bullet that I am guessing was swaged and not cast. Probably missing the void that my wonderful cast bullets have

Care to share your spreadsheet, Brent? I am 99% confident the 1880s bullet is lead and tin only, and does not contain antimony or mercury. Thank you very much

50/50 ratio by volume

Pure Pb bullet is 1.59cm3, unknown bullet is same volume

50% Pb by volume in unknown mix is .795cm3 x 175.03gr/cm3 = 139.14gr
50% Sn by volume in unknown mix is .795cm3 x 112.12gr/cm3 = 89.13gr

Pb + Sn = 228.27gr for approx same volume bullet

pamtnman,
I'd be happy to send you a copy. I just need your email. I do not see one listed for you.

However, it will not exactly fit your specific needs. It was made for casting bullets and moving between different Pb/Sn alloys. Volume is not a fixed variable, which is what you are looking for. I could pencil it out for you however. These are two identically shaped bullets, right? From the same swage die or mould?

Losing 50 grs from a 278 gr bullet by just adding tin to the mix - seems like a lot. May not be possible.

I'll sharpen my pencil in a minute. Gotta feed ponies first.

I appreciate it, Brent. Hi to the ponies. When i was a kid we had a pony in a corral next to the house.

Well, it's is doable.

I pencil it out to be a 1.52 to 1; lead to tin ratio. That's a heck of a lot tin! What we consider to be hard bullets is 16:1 alloy and some folk will go as hard as 12:1. No one goes even close to 1.5:1.

Bullet hardness is what matters, not weight. Hardness increases with a decreasing ratio of Lead:Tin. However, it is a diminishing relationship such that little if any hardness is gained once you cross something like 12:1. If you want harder, you jump to antimony or something else (copper, silver, ...?). Tin is also very expensive relative to Lead. So that makes me think that something else is an issue here. I doubt that bullet is really 1.5:1 lead/tin and nothing else, but it is possible.

Well thank you for contributing to this, Brent. I think you were interested in the old historic paper patched bullet I pulled a couple months ago. It weighs the proper 228 grains (450-400 BPE), and Mike Rowe had said he expected it to be a 12:1 alloy. Well, I had an adjustable mold made, and the same length pure lead bullets come out at 278 grains, so I suspect like you that something else is at play. One thing I noticed when i went back and looked is the original bullet has the copper peg in the tip, which must displace 5-10 grains of lead weight. So the actual poured pure lead bullet is heavier than the original because of the solid nose. Still, if the original was 240 grains with the solid nose, we still have a disparity of 38 grains, which is hard to achieve with just tin alone.

Check your math.

What do you come up with?

Clap, please lead us forward on this. my experience with math is it is taught by people who love math to people who either love math or who are interested in it enough to pay attention and try to learn it. the other 95% of the human population remains fully functional day to day without math, beyond a few basic calculations here and there. math is taught in ways that are impractical for daily use, so that even people who could be interested are driven from it like wildebeests wildly fleeing a mob of hungry lions. thus are requests for help with what may be basic math born
Sincerely and with appreciation,
-scared wildebeest

SOOOOO
What metals are in the bullet?
How do you know?

[spoiler][/spoiler]Guys, I put everything you need to know in my post.

I put the density of lead and tin in their grains per cubic centimeter, I provided the volume of the bullet in cubic centimeters and did the math for you.

I don’t think any of you read my post that showed that the bullet in question is a 50-50 mix of lead and tin by volume.

There is the small possibility, that because of the shape of the lead atom that the tin atom might be able to hide within the matrix to some degree, resulting in a decrease in volume with a mixture of the alloy, But I don’t think so.

It is a good question, and I still assume it is some lead/tin alloy, but I have inquired of a friend who is in the jewelry business. Hopefully she knows someone local with a mass spec machine who will be willing to analyze the bullet

I did read it, but it seemed so improbable that what little math skill I have was stuck in an endless loop of what-the-h..... And yes I do appreciate your contribution. Mike Rowe wrote here last year that these 1880s-1890s bullets were usually 12:1 alloy. I am chasing down the mass spec machine, because it seems the only way to really resolve this question.

Gentlemen,
Are we not missing the known unknown?

Pamtnman in his post on 10th February says the “original bullet has the copper peg in the tip”.

If, as I take it the bullet is for a British black powder express rifle, the “peg” is likely to be the closed top end of a copper tube, extending perhaps half way down the bullet and filled with air (or perhaps fulminate?) to promote sudden and violent expansion on impact.

In case it is fulminate I would suggest not trying to dismantle it.

The hollow is likely to be at least the volume of a 40 grain .22 bullet (perhaps narrower but longer) and would easily account for the difference.

CZ,
The 1.52:1 ratio was by weight as that is how casting is done, but you are right that the problem has to be solved by volume given what we had to work with. I'm happy with my math.

But the copper peg issue kills it and if the bullets are not cast in the same mould or die, then this all becomes even more pointless. Subtle differences that are very hard to detect via "hairy eyeball" can make huge differences in final weight of the bullet.

The reason I ask what elements
is that my cast alloys may contain, lead, tin, antimony,
silver, arsenic, and other trace stuff

Mike

fun reading

https://oregontrailbullets.com/xcart/laser-cast-lead-bullets.html

I don’t know where the other data came from.

I just took the information that the original poster posted, and did the math.

Two seemingly identical bullets, one is lighter. Why? Because the alloy is less dense.

I took his post to mean he acquired some bullets that were different, and couldn’t figure out why. And wanted to know what the mix might be.

Never saw, or read anything other than his first request for help before I grabbed a pen and a napkin.

Composing a reply that would defang the peanut gallery took longer than solving the equation.

I think Parabola has the answer, you first need to know the volume and weight of the copper tube before proceeding. Once you know the tubes weight and volume it can be subtracted from that of the bullet and at that point you can begin to figure out the composition of the bullet alloy.

Backing up, if it was known to be a paper patch bullet and suspected to be swayed, it is likely a softer alloy and specific percentages may not matter quite as much. The size of the copper tube void(?) can probably be calculated. But, to make it shoot, is it better to get the length of the bullet close or the weight, for the same shape?

I think much of it depends on the rifle and what you are trying to accomplish. I take it this is a double rifle so it may likely have been made to shoot more than one bullet weight. The rate of twist must be fast enough to stabilize the bullet, for hunting accuracy a bit faster twist will not be an issue. Many other factors go in to getting a black powder double to regulate such as powder charge, wadding, bullet lube etc.

I would be interested in what the mass spec machine shows.

If it is a paper patched bullet, lead/tin alloy is critically important to best accuracy, especially if it has a long nose. Swaging 16:1 is something I have done by hand for many thousands of rounds. Harder alloy can be done with the right equipment, so those bullets could be anything. But I'm extremely doubtful that the two bullets are even from the same die or mould.

As for which is more important to get it to shoot, length or weight? Well, yes. Both are. If skeettx really wants to figure this out, we need a whole bunch more information.

I know many things have been done and are possible, but with what we know, there may not be the need for match ammo prep. I would guess that the new mold is an attempt to replicate that didn't translate as would be hoped.

I would almost universally lean towards softer alloys for antiques assuming I'll get whatever bump up that was needed. How many mold weights and designs, and alloys are worth pursuing? Maybe, get some mileage on that first mold out at the range, minute of pie plate is honest and reasonable. I bet the second mold, if ever wanted, will hit the goals better after some experience with the rifle.

craig I don't know what you mean by softer, but we shoot 16:1 in any gun without a problem, from Rigbys to Ballards, Sharps, trapdoors, etc. Some guys mess with antimony and wheel weights. I don't bother with them, but they do work. If skeettx is serious about it, he will get back to us with a lot more information and then it will be pretty trivial to find a bullet mould or design one for whatever purpose. This is not rocket science (though that can be helpful).

You are comparing the weights of a solid bullet and an express bullet. Of course the weights are going to be different.
It's usually about 25 grains for the 400 and 40 for the 450. The bullets are the same length.
This is being made way more complicated than it needs to be.

Ok, having kicked this hornet’s nest, and being so very very appreciative of everyone’s best effort here, I have helpful information and an update:

A) The helpful information: The ledger entry for this Lancaster 450/400 double oval bore rifle calls for two projectiles. A 225-grain bullet, and a 230-grain “shell.” I took the 230-grain shell to be an explosive shell. But that’s supposition. That others here made the same conclusion about this particular bullet is interesting.

Additionally, I pulled the antique paper patched bullet from an 1880s loaded shell. It is in pretty much the same shape it was when it was in situ.The copper plug is going to be pulled. The SECOND bullet was cast of pure lead in a new adjustable Brooks mold made to accommodate different bullet weights and sizes, as needed.

B) Update: Tomorrow morning, McCreath Labs here in Harrisburg PA are conducting a hand-held mass spectrometer test for free. If that test provides improbable results, then the bullet will be subjected to a full mass spec test that results in the destruction of the projectile. For those lamenting the loss of this rare bullet, I hear you. But I have another nine loaded antique rounds in perfect shape, and this one was pulled precisely to inform us of the bullet’s character.

Thank you for all your ideas, suggestions, math tutoring, and insights. I’m doing my best

It all sounds interesting so I'm eager to hear more.

Is it possible that the copper may have an explosive charge in it? I have not encountered anything like it. Be careful.

Also, measure the twist rate on your rifle. That will help a bit also.

Brent, measuring the twist rate in a black powder oval bore is just about the same as measuring the twist rate in a shotgun barrel. It’s difficult. Plenty of slips.

I can't see why it would be hard. But bump up a bullet to engrave in the "rifling" and have at it. I've measured a belted ball gun. I would not expect it to be too much different.

Was the original bullet oval from the mould/swage?

"I took the 230-grain shell to be an explosive shell." -- Why?

British rifle ammunition for the 450/400 3 1/4" cartridge was made primarily (and perhaps exclusively) by Kynoch and Eley.
Their early 20th Century catalogs make no mention of an "explosive shell" nor does Fleming in "British Sporting Rifle Cartridges."

Can anyone cite a source for explosive bullets in British commercial metallic sporting rifle ammunition?

Explosive bullets are historically associated with Sir Samuel Baker and George Fosbery. In Baker's case, his bullets were being
launched from a 4-bore barrel. A detailed study of explosive rifle bullets used in the Civil War can be found in the journal of
the American Society of Arms Collectors. They were used to shoot at observation balloons in WWI and Germany experimented
with the B-Patron in WWII. If they were ever practical - as bullet size decreased, they became impractical.

Pantaman - suggested topic for your next investigation. Weight of the priming compound in the No.40 Berdan primer.

This particular antique sacrifice/ study bullet is from a factory Eley round. Its diameter is .400" and I am hoping, after failing with some other diameter bullets in this Lancaster rifle, that I can get its alloy figured out and thereby cast something close in the Brooks mold. Unless they had their own mold etc with the gun, Lancaster oval bores generally shot whatever was standard for caliber. This Eley round is very much what was the market standard for the 450/400, and I want to replicate it, having failed with others.

Some custom rifles beyond "the Baby" fired explosive bullets, made up by the shooter with the tools and materials that accompanied the rifle. A number have been paraded in DGJ over the years. I think Frank Findlow wrote an article about a .577 that had some explosive compounds and hollow tips; Ross Seyfriend for sure did. I know I have seen some for sale over the years. What do you suppose this gun's ledger entry means? Why the distinction between a 225 grain bullet and 230 grain "shell"? While zero tools accompanied this gun, it was made in 1894 for a maharaja who liked it so much the Lancaster ledgers show he had another exact same one made the next year. The maharajas could order anything, and get exactly what they ordered. If he wanted an exploding shell for his 450/400, he could get it. Incidentally, I recently finished reading Baker's Rifle & Hound in Ceylon, Wild Animals and Their Ways, and The Nile Tributaries of Abyssinia. He really did use the exploding shells in hippos, rhinos and elephants. I think some buffalo, too.

Mike Rowe, I agree with you this is complicated, but what else is to be done? The other bullets I either cast or bought did not work as expected. I felt fortunate to locate some original antique 450/400 Eley rounds that were surely the industry standard, and which the Lancaster probably shot very well. So I am trying to replicate that Eley bullet. Having failed to come up with the correct formula for comparing the factory bullet to one cast of pure lead and getting the Eley bullet's alloy mix, the mass spectrometer is the only way to definitively answer the question of what the Eley bullet is made of. And no, my lead tester did not work, because the copper tube in the nose squished down and the slight cup in the base interfered with the tester. So, maybe this is too complicated, but no one here knows how else to get the bullet's actual alloy. You said it was likely 12:1, and you are probably right. Hopefully we find out tomorrow.

Finally, Steve, I did as you requested, and arrived at the average Berdan primer compound weight of between 1.112 grains and 1.159 grains per primer. But as I was increasing the N to get a more robust confidence in such a huge variation, I noticed the tips of my fingers were disappearing from exposure to the fulminate. So I had to stop, because my thumbs were unable to manipulate those tiny primers very well.

More tomorrow!

This is definitely not that hard or complicated. Just set the mould for the same length as the original and cast in a few different alloys from 16:1 to 40:1. I doubt you will be able to tell the difference, but pick up and read the paper patches to confirm what is working.

I seriously doubt that "shells" refer to anything explosive. All my life I have heard people refer to both cases and cartridges as shells. Nothing to do with explosive projectiles whatsoever.

I
Brent, I hear ya. It ain't me making this distinction, it is in the 1894 ledger entry for the gun. Why the gun manufacturer distinguished between a 225-grain bullet and a 230-grain "shell" is mystery, but they for sure did it for a distinct reason with a real purpose in mind. I am sure a five grain difference in bullet weight does not matter in a black powder gun, so it must have meant something important to them at that time. And your advice is good. The only thing is the Brooks mold is one of those adjustable nose-pours, that even experienced casters are occasionally challenged by. So I am trying to keep my casting time with this mold to a minimum. The more I experiment, the much much longer the project will take. If Mike Rowe is correct, and the 12:1 alloy is standard (in this Eley bullet), and that little cup on the bottom is sufficient for spreading the heel into the rifling, then that is the alloy mix I will try first. A regular base-pour mold is not intimidating; this one is.

A few grains of bullet weight either way doesn't make a darn bit of difference to an Express rifle. Nor does the bullet alloy if it's anywhere from 1 in 12 to 1 in 20 or so. So long as it's a lead/tin mix. The cup on the base does little, if anything, for obturation. The bullet fore shortening does that - and black powder does a fine job of it.

Personally, I think 12:1 is too far, but whatever. Better to make some bullets and get them airborne than beat the issue to death without ever launching one.

I've cast many a nose pour. Why are you finding it intimidating? In so far as casting goes, it is all pretty much the same to me. I have two nose pours that I use. One I use a lot. It's as easy as any. More important will be bullet diameter, paper thickness, and bullet seating depth. And what did you find between the bullet and the powder? That will be more important than alloy.

I would love to see photos of the original cartridges you have and some dimensions for them. I've spent 25+ yrs shooting paper patches with blackpowder for hunting and competition. It's the only rifle shooting that is very interesting to me.

First - the 12 to 1 theory is not mine.

I assume that there are two reasons why Eley or Kynoch wouldn't want the bullets to be any harder than necessary -
expansion in the target is one and the other is cost (tin being more expensive than lead).

The "cup" in the base of the bullet should be for the twisted end of the paper patch.

In my 'ill-spent' youth I made explosive Minie balls. They worked.

I am a fan of Baker and have studied him extensively (including corresponding with his great-great grandson who lives in England).
I am convinced he used explosive bullets but his descriptions don't 'add-up.' He described using a 1/2 pound (3500 grains) bullet
with either "10 drachms of powder" in the bullet or as the propelling charge. In my 8-bore, I used 10 drachms (280 grains) of powder
behind a 1605 grain bullet that produced a velocity of 1040 fps. That charge behind a bullet weighing more than twice as much, in a larger
diameter barrel, would produce an anemic velocity. If Baker meant that the 10 drachms was the explosive charge in the bullet, by
volume, it would displace 2000-grains of lead unless the bullet was substantially lengthened. Seems like a great project for "Myth Busters."

On Baker, I took his charge descriptions to be the propellant, not the explosive. He does not describe the explosive bullets in detail. In a couple animals he describes the explosive internal results, which sound right.
Brent, I’m trying to save time on this by researching before casting more bullets, because I have already expended what to me is a great deal of time on this. As anyone who has tried to get a black powder oval bore to shoot right learns, they are an acquired taste. Whatever you believe you know about ballistics, throw it out the window. When the correct round is fired, the oval bore is phenomenal. Finding that correct round is a long road littered with wasted time and unhappy gun owners. It’s a well known story with this rifling. So instead of spending my limited time sending more incorrect rounds down range, I’m hoping to find out for myself what exactly this old Eley round is made of. As for posting pictures here, the process is still clunky. I would like to know what it would cost to make this site like so many others, where posting photos is easier than posting text.

Hopefully we learn all we need this morning at the lab

Well, well, well... isn’t this mass spectrometer result interesting.
The 228-grain Eley 450/400 paper patched copper-tubed bullet is
92% lead
7% tin
1% copper plus other contaminant stuff that was likely all on an individual basis byproducts of the various processes associated with mining and refining lead and tin separately, and then again those processes associated with combining them together.

I think Mike Rowe gets the prize for being right, again. Bravo! If I respected your opinion on these matters before, I really really respect and value it now.

Now, about that C&H #6 gunpowder that was in the Eley case...we also studied this in the mass spectrometer, and obtained some fascinating results. If the readings are correct, then C&H had a secret ingredient that made their powder especially energetic. Their ratios of carbon, sulfur and potassium are also unique. We are going to further study the powder in a destructive way in a mass spectrometer better designed for analyzing the organics inside the black powder. Then we will know for sure what C&H was up to, and why their powders were so highly successful.

Steve, no theory about the 1 in 12 mix. It's on the Kynoch factory's blueprint.

That may be, Mike, but isn’t it satisfying to see the mass spectrometer analysis confirm it absolutely.
I thought the test results would generate more discussion. The C&H #6 results especially. There’s been so much discussion about that central powder

I admit, I’ve had the thought to comment a bit more here and there, but if it were me, I’d be casting it 1:20 simply because that’s what’s in my main pot and the majority of my stash for my preference. I don’t know if changing the alloy will make it shoot much different, but I hope it does.

A comment I had thought to add earlier was that if you have only tried pure lead in the Brooks mold and found it finicky, I’d guess it would cast easier with a tin alloy. If you have good temperature control in the pot, bump the heat up of the melt and preheat the mold? Are you using a bottom pour pot. I think Brooks molds seem easy to get to cast well, but of course I don’t know yours.

Thanks, Craig. With the Lancaster oval bore, it’s best to have a variety of alloys at hand. Generally softer lead is better. This 1894 BPE rifle’s bores are different than the other Lancaster BPE guns I have looked at. They are straight and not tapered. Having already experimented with other alloys and diameters, I’m ready for this rifle to shoot to its best ability. Because Lancasters usually shot whatever was standard for caliber, I’m using the original Eley bullet at hand as my guide for what to cast next. Because it’s a 12:1 alloy, that’s what I’ll be mixing up and casting.
I have trouble with the Brooks mold for two reasons. First, it has more moving parts than a typical bottom pour mold. Second, my hands suffer from an autoimmune disease called rheumatoid disease. It gets worse each year. Hands that once quickly tied size 20 dry flies one after another now struggle to hold a coffee mug without dropping it. So the fewer moving parts in any given procedure, the better for me.

For the record, the secret ingredient in C&H #6 black powder that showed up on the mass spectromeer was...
zinc.
Zinc is an amplifier in black powder.