TL4 to TL5 Cannons and Carronades

[Varyon]

Originally Posted by Anthony

I suspect the problem is that the HT values are empirically determined while Doug's spreadsheet is a formula (I don't have a link to it so I don't know what that is). Realistically, the curve for how penetration varies with velocity is not linear or even particularly consistent, and can even be negative at some points.

According to the July 30, 2013 version of Doug's spreadsheet, base penetration damage is ((K^1.04)/(X^0.314))/13.3926, with K as kinetic energy in Joules and X as cross-section of the bullet in square meters. So, it's roughly kinetic energy divided by the cube root of cross section.

[The_Ryujin]

Originally Posted by Varyon

According to the July 30, 2013 version of Doug's spreadsheet, base penetration damage is ((K^1.04)/(X^0.314))/13.3926, with K as kinetic energy in Joules and X as cross-section of the bullet in square meters. So, it's roughly kinetic energy divided by the cube root of cross section.

Anthony is talking about real life here, not how GURPS handles things. GURPS formula does work reasonably well for small arms but at higher and lower velocities things get... complicated heh.

[Anthony]

Originally Posted by Varyon

According to the July 30, 2013 version of Doug's spreadsheet, base penetration damage is ((K^1.04)/(X^0.314))/13.3926, with K as kinetic energy in Joules and X as cross-section of the bullet in square meters. So, it's roughly kinetic energy divided by the cube root of cross section.

Actually, just found it, it's ROUND(SQRT((K12^1.04)/(I17^0.314))/13.3926,1); K12 is KE and I17 is cross-section. If we clean up all the math, we wind up with KE^0.52 * (pi/4*B^2)^-0.157 / 13.3926, or KE^0.52 * B^-0.314 * 0.077554 (KE in J, B in meters, penetration in points of DR).

This is the sort of function that comes from applying a curve-fitting tool to a bunch of data points, it's grossly unlikely to have any physical basis. If it disagrees with some other source, I would simply assume that the formula is wrong. Note that there are fairly strong theoretical reasons to assert that, given constant projectile velocity, density, and shape, penetration should be linear in projectile diameter, and Doug's formula puts the exponent at 1.246 (however, many historical formulas are not precisely linear).

[Anaraxes]

Originally Posted by Anthony

This is the sort of function that comes from applying a curve-fitting tool to a bunch of data points

Doug will no doubt be along to speak for himself -- but wasn't his original purpose exactly to fit a curve to the existing GURPS small arms values, so that other reasonable values could be calculated while retaining compatibility with the original stats? So while the basic form of the equation might have a physical basis (or not), the exact coefficients and even powers would be empirical, designed to get GURPS numbers rated in dice and adds (not the most common engineering unit of measure).

[Anthony]

Originally Posted by Anaraxes

Doug will no doubt be along to speak for himself -- but wasn't his original purpose exactly to fit a curve to the existing GURPS small arms values, so that other reasonable values could be calculated while retaining compatibility with the original stats?

Yes, but this means it should be taken with a medium to large grain of salt if applied to anything outside the range of TL 6-8 small arms with 5-15mm bore sizes.

[sir_pudding]

Originally Posted by Anthony

Yes, but this means it should be taken with a medium to large grain of salt if applied to anything outside the range of TL 6-8 small arms with 5-15mm bore sizes.

Especially, as I said, smoothbore cannon using serpentine or corned powder, since it should be obvious that both rifling and nitrocellulose propellants have significant effect on firearm performance.

[Anaraxes]

Originally Posted by Anthony

it should be taken with a medium to large grain of salt if applied to anything outside the range of TL 6-8 small arms

Originally Posted by sir_pudding

Especially, as I said, smoothbore cannon using serpentine or corned powder

Agreed on both. Also should a question arise about real-world effects, since the fundamental starting point, and point of compatibility, was pre-existing GURPS stats. Those might well be accurate, or they might not. Regardless, Doug's spreadsheet isn't meant to be a physical simulation of kinetic energy penetrators from first principles.

[Anthony]

Originally Posted by Anaraxes

Regardless, Doug's spreadsheet isn't meant to be a physical simulation of kinetic energy penetrators from first principles.

If you're interested in that, Luke Campbell poked at that.

[Icelander]

Originally Posted by Anthony

Yes, but this means it should be taken with a medium to large grain of salt if applied to anything outside the range of TL 6-8 small arms with 5-15mm bore sizes.

Originally Posted by sir_pudding

Especially, as I said, smoothbore cannon using serpentine or corned powder, since it should be obvious that both rifling and nitrocellulose propellants have significant effect on firearm performance.

Originally Posted by Anaraxes

Agreed on both. Also should a question arise about real-world effects, since the fundamental starting point, and point of compatibility, was pre-existing GURPS stats. Those might well be accurate, or they might not. Regardless, Doug's spreadsheet isn't meant to be a physical simulation of kinetic energy penetrators from first principles.

Does anyone have an idea about what factors in Doug's calculations specifically account for rifling and/or nitrocelluse propellants?

Or what to change when modelling smoothbores and an equivalent to black powder?

In any case, Doug's spreadsheet produces results that appear to be in the ballpark for High-Tech's black-power, smoothbore muzzleloading personal firearms of .45 caliber to 8-bore. If anything, Doug's spreadsheet is slightly less optimistic in terms of Max Range (and more optimistic in terms of 1/2D Range), but still within an acceptable margin of error from the published stats when I input what muzzle velocities I can find, a few from period sources, but mainly from reenactor and amateur black powder shooter sources.

It's when I get to cannon that the stats generated by the spreadsheet and the published ones stop being in the same ballpark. To some extent, of course, Low-Tech might be assuming very low velocities for its cannon, due to inferior powder, but as noted above, even the TL5 12-pounder Napoleon gets a significantly higher Dmg (6dx7 pi++) in the spreadsheet than is actually the fact in High-Tech (6dx5 pi++).

As far as I can determine, Doug's formula accounts for the diameter of the projectile and aspect ratio 1 of a round ball, and thus the comparatively larger impact area than if it were a conical ball or spitzer bullet.

Is there some other factor that makes larger and heavier round balls exhibit less of a gain in penetration than one would naively assume?

I remember that by the standard GURPS damage equation, going from .600 NE to .700 NE didn't really produce much of a performance increase. I think Hans explained it as the increase in bullet cross-section almost counteracting the higher energy. Could this be a similar issue?