Please note that the Greenhill formula was calculated for cast bullets, and a velocity near 1500 fps. If you are shooting them at a much different velocity you need to know this fact, and make an adjustment to get optimum performance.
The multiplier- 150 - in the formula correlates to that 1500 fps velocity.
If you were shooting a cast bullet at 1800 fps, change that multiplier from "150" to " 180 ". Run both formulas and you will see that even this change does not require much difference, if any, to the length of the bullet. That is why the typically pubhished Greenhill formula uses the 150 as the multiplier, without this other information.
Note, however, that with some of the larger caliber " Sharps " rifles, reaching even 1500 fps with a black powder load and some of the long bullets is next to impossible, and many of these guns generate velocities in the 1200 fps range or less. Because of the recoil, trying to get more velocity is abusive to the shooters. IN the old days, ( 19th century) " Express " Cartridges gave these Black Powder bullets more velocity by adding a bit of length to the casing, AND reducing the weight of the bullet.
For instance: The .45-90 was considered the " Express " version of the .45-70 cartridge. The .45-90 had more powder, but shot a 300 or 350 grain bullet. The .45-70 shot less powder, and either a 500 grain, or 405 grain bullet in its factory loadings. Both cartridges were fired from rifles with a 1:22 ROT, so the Greenhill formula was pretty much ignorred in using those shorter, lighter bullets in the Express versions. The Express cartridges were not sold as better long range target ammo: instead, they were sold like " magnums " are today- reputed to have greater " knock down " power!! :shocked2: :rotf: :surrender: :thumbsup: