Minimum "foot pounds of energy" is really not valid. You see, a 223 has almost the same FPE at 100 yards (925) as a 45-70 does (1000)
But the old black powder 45-70 is the single most successful round in US history for killing buffalo followed by the 44-77 sharps. Most hits on buffalo with 430 to 500 grain bullets would exit the other side, and when they didn't they were found on the off-side skin.
I don't think many men here would place much money of the likelihood of a standard 22-250 doing that.
But with that said, I do agree that for elk, a 50 cal is probably minimum if you shoot balls.
Not because of any mathematical theory. But because I have seen it done, and have killed elk myself, and I have been into muzzleloaders now for most of my life. At 60 years old and having started to hunt with muzzleloaders when i was 13, I have some background in the subject.
If we were talking about hand made barrels in the old "weird" calibers maybe a 48 or a 49 would be just as good. But today the jump is made from 45 to 50 cal, and that's a pretty large jump. The 45 fores balls of about 125 grains to 128 grains depending on allow and exact diameter. The 50 fores balls of about 177 to 180 grains So there is a fairly large jump in weight as well as the diameter of the wound channel. The 50 will go through an elk if the ball is hard. A 45? I don't know for sure, but I doubt it.
I have been on hunts with men who killed deer with 45s and many if not most recovered their balls from the animals. So that makes me thing penetration may not be all we'd want on an elk.
The best sources to learn from is simply the writings of the old timers. When flintlock muzzleloaders were the "assault rifles" of the day, men would shoot anything that presented itself, with anything they had in their hands. Reading those old letters we do see a lot of wounded game that got away from a lot of shooters and if you look at the rifles they carried you get a very good idea of what was effective most of the time, and what was not.
I have been a muzzleloading hunter for most of my life, but if I look at the old timers, many of them killed more deer and elk in a month than I will in my life. Most didn't keep technical notes, but some did. Those that did are a gold mine of info.
As a rule what was considered to be "elk rifle" in the early m800s fired balls of "40 to the pound" I have read that number from about 6 old hunters. Well there are 7000 grains in a pound. 7000 divided by 40 =175 grains. That's about 49-50 caliber. So it was then. So it is now.
As TerryK said, you can kill elk with a 22, but that doesn't mean it's a good choice for your elk rifle.
I have read more such reports from hunters in India and Africa then in America, but an 800 pound animal in a different location still weight 800 pounds. If the balls are doing the job and going clear through I think that will show us about what to expect.
I own and shoot 2 flintlock for my hunting. One is a 50 and the other is a 62. The 62 has put a lot of game in the freezer. I killed one moose with it, and after breaking both upper leg bones it still exited. I doubt the FPE would have been impressive to someone shooting a 338 ultra mag, but the moose seemed to be VERY impressed.
Boom and down.
Get my knife out.
I shoot hard .605" balls ( about 326 grains)with 140 gr of 3F Goex. The chronograph says I am getting 1800 FPS + or - about 15.
I killed that moose at about 80 yards. I don't know how fast the ball was going when it hit the moose, but I can tell you faithfully, it was fast enough.
