[Spaceships] Ships of Arbitrary Size WIP

[Langy]

Hopefully it did in the actual calculation. But I'm not sure you're aware of the fundamentals behind how those are supposed to work.

See this post for what's actually in the package. Those things are not simple impactors, and their underlying specs are not available to us.

Yeah, I know - fluff-wise, they're rather complicated. However, they're modeled as if they're just regular Armor-Piercing Hardcore shells. They aren't even as damaging as APHEX rounds. Proximity Detonation mode uses the same rules as for an HE warhead, but does the same damage as if it were a normal kinetic energy round of the same caliber.

If they were sub-impactors, each one would deal significantly less damage than they do as modeled. We're given everything we need to know to find out the kinetic energy of the round - the rounds mass as well as its velocity. We're also given its diameter, which gets us its cross-section. With those three things, we can find out the GURPS damage using this formula from Douglas Cole's article on Interior and Terminal Ballistics for GURPS:

Damage (points) = sqrt(KE^1.04/Xsect^0.314)/13.3926


Well, crap. I distinctly remember doing this before and getting the correct values, but it isn't happening this time. Strange. It all almost works up to about 7cm, but after that it's too far off. Winds up with the 112cm shell in the Spaceships system doing only as much damage as I calculate a 40cm shell should do. Maybe my memory is just playing tricks on me.


The 1.5 dice per CM one works fine for figuring out damage, though, and that's all I was really looking for. Now just need to figure out some way to figure out how heavy a cannon is when given a diameter.




EDIT: I figured out how to go from SM to weapon bore diameter. Unfortunately, it's convoluted, makes no sense, and doesn't fit into a simple formula.

First, find the bore diameter of the weapon sized right below the one you are interested in. This is the part that makes it impossible to fit into a decent, simple formula - I could write one using summations, but since I'm planning on shoving this all into an Excel spreadsheet later on that doesn't help much. Anyways, get the bore diameter of the weapon right below the one you actually want.

Next, find this value:

Step = [SM - ROUNDDOWN(SM)] * 2^ROUNDUP((SM+4)/4-1)
Bore = Smaller Bore + Step
Damage (Dice) = Bore * 1.5

The reason this works is that the progression of bore diameters is completely linear within every 4 size modifiers. For example, between SMs 4 and 8 each weapon increases in bore diameter by 2 centimeters. These are 5 SMs, but only 4 steps (4 to 5, 5 to 6, 6 to 7, 7 to 8). Between SMs 8 and 12 each weapon increases in bore diameter by 4 centimeters, etc. Every 4 SMs, the step size is doubled.



Also, gun shots is relatively simple to calculate:

Shots = 10^((SM+6)/6)
Missile Shots = 10^(SM/6)

Unfortunately, the bullets in a Weapon Battery sometimes completely outmass the Battery itself. This is probably an error in the PDF, so it's possible either the bullet masses or the number of shots is incorrect in the PDF.

[Langy]

After some poking around, I figured out a way to go from ship SM to weapon size, damage, etc. It's very, very close to exact - within a 10% margin of error always, and within 5% most of the time.

The way I figured it was as the SM of a Major Battery increases, its bullet increases in SM every other step - bullets increase in mass half as fast as the weapons battery that fires them.

Gun bore size was figured by noticing that every thirteen steps on the bore size chart, a weapon's bore is increased by roughly 10x. Number of shots just follows the typical 1, 1.5, 2, 3, 5, 7, 10 progression.

For Guns:

Gun Bore Size = 10^((SM+8)/13)
Bullet Mass = 10^((SM-12)/4)
Number of Shots = 10^((SM+6)/6)
dDam (Dice) = Bore * 1.5

For Launchers:

Launcher Bore Size = 10^((SM+12)/13)
Bullet Mass = 10^((SM-8)/4)
Number of Shots = 10^(SM/6)
dDam (Dice) = Bore * 1.5

When using these figures, you find that there are no problems with bullets/missiles taking up all of the mass alloted to a weapon battery - those problems only start at SM+3 or lower. Unfortunately, there's no simple equation to figure out actual weapon mass that fits well with the current figures for number of shots and bullet mass, which makes me sad. I'd think weapon mass should be proportional to the square of the projectile mass, which would mean a constant proportion of weapon battery would be the actual gun no matter the SM, but with the current gun shots count that doesn't work - you'd need to make gun shots be proportional to SM/4 instead of SM/6. I'm not sure if this would be more realistic or not, just that it makes more sense especially for smaller-SM ships.

[Langy]

As an aside, I've developed a (hopefully) more accurate formula for figuring out maximum airspeed. See this post for a long explanation of how I derived it. The formula is as follows:

Velocity = SQRT(Mass^(1/3) * Acceleration * 625000 / Air Density)

Air Density is in percent-of-Earth-sea-level, Acceleration is in Gs, Mass is in Tons, and Velocity is in Miles Per Hour. You can use this table to find the air density figures for altitudes up to 65,000 feet.

[lexington]

Originally Posted by Langy

Mass: 1000

[snip]

Volume: 100000 ft^3

A density of .01 ton per ft^3 is about half that of pure alcohol. I don't know a lot (okay anything) about the density of modern planes or shuttle but that seems low to me.

[Langy]

It's a density of 100 cubic feet per ton, so a cube with 4.6 feet per side masses one ton. This includes air, open space, and vacuum, not just the metal of the ship.

Yes, it's low compared to a lot of things (like water), but water's heavy (compared to empty space).

[malloyd]

Originally Posted by Langy

It's a density of 100 cubic feet per ton, so a cube with 4.6 feet per side masses one ton. This includes air, open space, and vacuum, not just the metal of the ship.

Yes, it's low compared to a lot of things (like water), but water's heavy (compared to empty space).

It's about right, cargo is usually estimated in the 20 to 50 lb/cubic foot, or 40 to 100 cubic feet per ton range. Yeah OK if you are carrying something really dense or space filling - a liquid, or crushed ore, it's heavier, but it's not a bad approximation.