While it's easy to calculate the ballistics for factory produced center fire cartridges - they blend their powder in gigantic lots, use computerized machines to control just about the entire loading process, you might think that applying the same calculations to black powder will yield similar results - it just won't.
And as others have noted, my own chrono shows that the black powder ballistics tables are at best "a rough guess" at what you might expect to see.
Black powder shooting is primitive. If you use a fixed powder measure you could be off a few grains compared to what you think you are loading.
Then, table "a" might be assuming you are shooting a 42" barrel with a 1:66 twist with 70 grains of Goex 3F produced in 1977 from batch AB2343 - if none of that applies, even with the same amount of powder, in the same caliber of rifle you could be looking at a 10% variance.
But if you are just looking for "generalizations" books such as the Lyman manual can give you an "idea" of what you might see in comparison.
For example, it shows that with a 50 cal, with a 1:48 twist, 28" barrel (read Lyman Trade Rifle) you might expect to get the following results when shooting a .490 roundball:
70gr of Goex FF and an Ox Yoke .015" prelubed patch and a CCI #11 primer = 1471 fps/muzzle
go with 70gr of Goex FFF, all else the same and you get 1657 fps/muzzle
now swap the Goex for Elephant FF and your muzzle velocity is 1505 fps or 1569 fps if you use their FFF
The different formulations of Pyrodex yielded results in the 1540-1580 fps range.
In this one case there is a dramatic increase between Goex FF and FFF (180'ish fps) but if you look at their numbers for the Great Plains Rifle - so 1:60 twist 32" barrel the same powders results in much "tamer" differences.
70 grains of Goex FF gives you 1627 fps/muzzle. Going with FFF gives you 1655 fps/muzzle - only 28 more fps.
So if you had of looked at the 1:48/28" numbers you would "expect" significant gains moving from FF to FFF - but if you were shooting a GPR instead of a Trade Rifle a couple degrees of temperature change could result in exactly the same chrono results from "either" powder.
Convoluted, but I hope you get the point I'm trying to make - no two rifles, powder, caps, twist rates, weather conditions etc etc etc will be precise enough that you can use some "table" to figure your ballistics.
You need to chrono your gun, the way you load and shoot it, in the conditions that you shoot to determine it's ballistics.
Or forget trying to shoot "mathematically" - find an accurate load and use it without worrying whether it's 1650 fps or 1580 fps. Most game animals don't carry "speed guns" anyhow and I have never seen the "chrono season" listed in the hunting regs :rotf:
And if you want to know where it will impact at 50, 100, 150 and 200 yards - you are going to have to shoot those distances - you can't shoot at 50 and then extrapolate with a paper chart the way you can with a box of Hornady Premiere Sierra 180 gr 30.06 custom ammunition..
(all numbers in the above were taken from the Lyman Black Powder Handbook - 2nd edition)