TL4 to TL5 Cannons and Carronades

[Icelander]

I'm trying to extrapolate more sizes and types of smoothbore, muzzleloading cannon from the selection in Low-Tech and High-Tech.

I'm particularly interested in three things: a) in murderers, falconets and swivel-guns of 1/2-lb to 3-lb chambering, either muzzle- or breech-loading; b) light shipboard cannon of 6-lb to 12-lb; and c) carronades of 6-lb to 36-lb chambering, light enough to be an alternative to full-sized versions of ship's cannon.

It's for a campaign set in TL4; but with access to TL0^ dragonbone, TL1+3 enhanced bronze, TL1^ orichalum, TL3^ mithril, TL4^ adamantine, TL4+1 cast iron and up to TL4+4 steel alloys made in a dragon's forge, I figure that the PCs will be able to come up with any metallurgy they need to match the simpler TL5 cannon designs, such as the carronades.

I can find pretty decent stats for the dimensions, weight, caliber and other numbers that reflect a real-world facts in fairly easily obtainable sources. Even some snippets on relative costs for brass vs. cast iron for a few examples.

But in trying to calculate Dmg and Range numbers, I find myself at a stand. Using Douglas Cole's Ballistics spreadsheet (a version from February 2011) and historical muzzle velocity*, I get much higher Dmg and Range than any of the listed TL4 cannon in Low-Tech. I even get much higher Dmg than the Napoleon 12-pounder in High-Tech.

This is a problem, especially as the main difference between TL5 cannon and carronades is that carronades have a much lower muzzle velocity, to the tune of around 750 fps vs. 1480-1760 fps of ship's cannon in the early 19th century. Obviously, this affects Dmg, but anecdotally, the increased weight of shot for carronades compared to a cannon of the same hundredweight meant that at short ranges, the carronades still did much more damage to ships and men.

In any event, I really need to be able to duplicate the Dmg for those cannon that are listed in HT or LT with the spreadsheet and then play with those numbers by shortening the barrel (enough to really hurt the burn rate), reducing chamber caliber and reducing the pressure to account for a smaller powder charge, resulting in the historical muzzle velocity I want. And if the model is right, that would give me a correct damage for a carronade of the given weight of shot.

I suspect that either my inept data entry or the version I have of Doug's spreadsheet may not be accounting for some factor that Pulver and Hans' damage calcuations include, maybe the large area of impact for a round cannonball compared to a conical bullet, which must spread out the impact energy and reduce penetration. I know that Doug's equations include such things as projectile diameter and aspect ratio, and for all I know may calculate sectional density and/or ballistic coefficient, but I may be failing to adjust some rarely used variable to get correct results with a large round ball.

Does anyone know what factor I should be using to correct the derived Dmg of cannonballs? Why does a 12-lb iron ball just under 112mm in diameter travelling at 1440 fps at the muzzle have Dmg 6dx5 pi++ in GURPS rather than the 6dx7 pi++ that Doug's spreadsheet tells me it should do?

Note, I'm assuming that the High-Tech stats of the Napoleon 12-lb were reality checked to a degree, i.e. that they are, at least to the ballpark, a fair reflection of the penetration capability of a 12-lb cannonball into RHA steel. Which means that the model I'm using or at least the way I'm using it is incorrect and I need to fix this before using it to extrapolate stats.

*Where I can find it.