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Old 10-07-2016, 05:16 AM   #1
Icelander
 
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Default TL4 to TL5 Cannons and Carronades

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.
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Old 10-07-2016, 11:56 AM   #2
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Default Re: TL4 to TL5 Cannons and Carronades

Aside from the ones with stone balls (which I didn't check), some work I've done previously indicates that most of values you get using 3e Vehicles matches up pretty well with TL4 cannon, although I can't quite recall how much time I spent on that comparison (my interest being more in personal arms). If you have that book, you might want to use it for designing your weapons. I'll also note that you can simplify things greatly simply by holding TL constant (and then adding in a modifier if higher/lower TL stuff is available). Also, the multiplier for length scales linearly with the length of the barrel, so in my case I replaced that table lookup with a variable for length in calibers.

Exotic materials for the barrel are simply going to influence its weight and durability to attack - a P of 1 I believe represents the fastest the explosive used can accelerate the projectile. Exotic explosives, however, are going to influence damage (and possibly range and Malf). I think it's appropriate to scale P (and thus damage) by the square root of REF. So, if you're making TL 4 firearms, the corned powder from that time period is REF 0.4. If your firearms are instead using REF 0.8 smokepowder*, that's going to multiply P by x1.4, increasing both damage and weapon weight.

*No clue what smokepowder's actual REF is supposed to be, although I recall hearing that it was higher than gunpowder's.
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Old 10-07-2016, 12:52 PM   #3
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Default Re: TL4 to TL5 Cannons and Carronades

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Originally Posted by Icelander View Post
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.
...
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?
Doug's calculator has a number of assumptions built into contemporary small arms. Significantly it assumes rifling, not smoothbore and nitrocelluose, not serpentine. Rifled barrels, and much faster and cleaner burns are both going to have significant impacts on muzzle velocity and projectile stability.
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Old 10-07-2016, 01:01 PM   #4
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Default Re: TL4 to TL5 Cannons and Carronades

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.
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Old 10-07-2016, 01:40 PM   #5
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Default Re: TL4 to TL5 Cannons and Carronades

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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.
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Old 10-07-2016, 03:34 PM   #6
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Default Re: TL4 to TL5 Cannons and Carronades

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Originally Posted by Varyon View Post
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.
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Old 10-07-2016, 04:29 PM   #7
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Default Re: TL4 to TL5 Cannons and Carronades

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Originally Posted by Varyon View Post
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).
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Old 10-07-2016, 06:15 PM   #8
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Default Re: TL4 to TL5 Cannons and Carronades

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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).
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Old 10-07-2016, 06:54 PM   #9
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Default Re: TL4 to TL5 Cannons and Carronades

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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.
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Old 10-07-2016, 07:24 PM   #10
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Default Re: TL4 to TL5 Cannons and Carronades

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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.
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