[Spaceships] Ships of Arbitrary Size WIP - Page 3

Langy · 08-17-2009, 06:34 PM

This is a work-in-progress. This not only provides some rules for ships of arbitrary size, but also discusses how I came to these values and formulae. After I’m finished, I will simplify everything and cut out the extraneous discussion.

I have been attempting to reverse-engineer the Spaceships design system in order to design space craft of some arbitrary mass - ships that are between the Size Modifiers, for example a ship that masses 2,000 Tons. This doesn't appear to be that difficult - just time-consuming. Most ship systems are priced by their mass, but some appear to be priced by surface area. The capabilities of systems are usually dependent on their mass - for example, a fuel tank or cargo hold is rated in the number of tons of storage, but some are more complicated - especially weapon mounts. Unfortunately, designing Major Batteries for any arbitrary ship size is slightly difficult - instead I'm simply going to go with the weapons and weapon sizes already presented in Spaceships, with no new weapon sizes available. Some systems are dependent on ship surface area instead of mass, while others take into consideration both surface area and mass - armor is the typical example of the latter.

First, here is an extension of the Hull Size Table:

SM: +5 Mass: 30 Length: 45 ft dST/HP: 20 Hnd/SR: 0/4 Surface Area: 1000 ft^2 Volume: 3000 ft^3
SM: +6 Mass: 100 Length: 60 ft dST/HP: 30 Hnd/SR: 0/4 Surface Area: 2500 ft^2 Volume: 10000 ft^3
SM: +7 Mass: 300 Length: 90 ft dST/HP: 50 Hnd/SR: -1/5 Surface Area: 5000 ft^2 Volume: 30000 ft^3
SM: +8 Mass: 1000 Length: 150 ft dST/HP: 70 Hnd/SR: -1/5 Surface Area: 10000 ft^2 Volume: 100000 ft^3

The table continues on from there. The important bits to note are the Surface Area and Volume bits - they're extensions of the original table that were not provided in the book. Both Surface Area and Volume follow these progressions through the rest of the table – Surface Area follows the 10, 25, 50, 100 progression, while Volume follows the 10, 30, 100 progression. Volume is simply 100 times the tonnage of the ship, since Spaceships assumes that all components have a density of 100 cubic feet per ton. Coincidentally, this makes a 7.5 ton Habitat cabin a roughly 10x10x7 foot room. Surface area is slightly more complicated - I'll explain how I calculated it shortly.

In order to have ships of arbitrary size, we need to be able to find values for each of the bits in that hull size table.

SM: SM is easy enough if we find Length - just find the entry on the Size and Speed/Range Table on page 550 of the Basic Set that matches the ship's calculated Length value. Remember to round up.

Mass: The simplest value to find - this is the one you choose arbitrarily. This can be anything, so long as it's over 10 tons, which is the minimum size of a ship in the Spaceships system. You might want to simplify to two significant figures and round the second one to either 5 or 0 to keep things consistent.

Length: I reverse-engineered a formula that works well for the ship progression listed in Spaceships. Remember that the Lengths listed in the Spaceships book are all exactly the same as those in the Speed/Range Table – they were defined as such. Ship masses are very, very close to a square root of ten progression – a ship of one SM larger than another has a mass equal to the smaller ship’s mass multiplied by the square root of ten, which is roughly 3.16. I mention these things because the formula I came up with does not follow the Spaceships Length progression exactly unless you round all the odd Size Modifier ship masses up to a power of the square root of ten. Specifically, there’s a problem at the Length 45 foot, 450 foot, etc. size modifiers – they round down to 40, 400, etc., respectively. Still, it works for the most part. Luckily, Length doesn’t matter in the Spaceships design process except when assigning a Size Modifier to the ship.

In any case, the formula works by finding out the size of the ship as if it were a sphere. We can easily find the volume of a ship by multiplying the mass by one hundred cubic feet per ton, which is the assumed density of a ship in Spaceships. From the volume, we find the radius of a sphere of the same size – the formula for volume of a sphere of radius R is V = 4/3*PI*R^3, so after some simple algebra we get the equation:

R = [V/(4/3*PI)]^(1/3)

This gives you the radius of a sphere of the same volume as your ship. However, the default assumption is that ships are not sphere-shaped. After doing some calculations, I found that Spaceships assumes ships are roughly 4.7 times longer than a sphere of the same volume’s radius. My formula for a ship’s length is thus:

Length = [Mass (Tons) * 100 Cubic Feet/Ton / (4/3*PI)]^(1/3) * 4.673

You then simplify to two significant figures and round the second one to either 5 or 0 for display, though the actual unrounded length is used further on.

dST/HP: This is slightly complicated. I’m not sure if it’s intentional or an error, but David Pulver didn’t use the normal rules for figuring out an unliving object’s hitpoints. Instead, all spaceships have the hitpoints that the formula would give a ship one size modifier larger than themselves. The actual formula used in the books, therefore, is as follows:

dST/HP: 4 * [Mass (Tons) * 2000 Pounds per Ton * SQRT(10)] ^ (1/3)

You then simplify to two significant figures and round the second one to either 5 or 0.

Hnd/SR: If you’re making a ship between two SMs in size, just use the Hnd of the larger SM and the SR of the smaller SM. This is a pessimistic assumption – taking the Hnd of the smaller SM and the SR of the larger SM is also viable, as is rounding to the closest SM and treating it as that SM for Hnd/SR purposes.

08-17-2009, 06:34 PM	#1
Langy Join Date: May 2008 Location: CA	[Spaceships] Ships of Arbitrary Size WIP This is a work-in-progress. This not only provides some rules for ships of arbitrary size, but also discusses how I came to these values and formulae. After I’m finished, I will simplify everything and cut out the extraneous discussion. I have been attempting to reverse-engineer the Spaceships design system in order to design space craft of some arbitrary mass - ships that are between the Size Modifiers, for example a ship that masses 2,000 Tons. This doesn't appear to be that difficult - just time-consuming. Most ship systems are priced by their mass, but some appear to be priced by surface area. The capabilities of systems are usually dependent on their mass - for example, a fuel tank or cargo hold is rated in the number of tons of storage, but some are more complicated - especially weapon mounts. Unfortunately, designing Major Batteries for any arbitrary ship size is slightly difficult - instead I'm simply going to go with the weapons and weapon sizes already presented in Spaceships, with no new weapon sizes available. Some systems are dependent on ship surface area instead of mass, while others take into consideration both surface area and mass - armor is the typical example of the latter. First, here is an extension of the Hull Size Table: SM: +5 Mass: 30 Length: 45 ft dST/HP: 20 Hnd/SR: 0/4 Surface Area: 1000 ft^2 Volume: 3000 ft^3 SM: +6 Mass: 100 Length: 60 ft dST/HP: 30 Hnd/SR: 0/4 Surface Area: 2500 ft^2 Volume: 10000 ft^3 SM: +7 Mass: 300 Length: 90 ft dST/HP: 50 Hnd/SR: -1/5 Surface Area: 5000 ft^2 Volume: 30000 ft^3 SM: +8 Mass: 1000 Length: 150 ft dST/HP: 70 Hnd/SR: -1/5 Surface Area: 10000 ft^2 Volume: 100000 ft^3 The table continues on from there. The important bits to note are the Surface Area and Volume bits - they're extensions of the original table that were not provided in the book. Both Surface Area and Volume follow these progressions through the rest of the table – Surface Area follows the 10, 25, 50, 100 progression, while Volume follows the 10, 30, 100 progression. Volume is simply 100 times the tonnage of the ship, since Spaceships assumes that all components have a density of 100 cubic feet per ton. Coincidentally, this makes a 7.5 ton Habitat cabin a roughly 10x10x7 foot room. Surface area is slightly more complicated - I'll explain how I calculated it shortly. In order to have ships of arbitrary size, we need to be able to find values for each of the bits in that hull size table. SM: SM is easy enough if we find Length - just find the entry on the Size and Speed/Range Table on page 550 of the Basic Set that matches the ship's calculated Length value. Remember to round up. Mass: The simplest value to find - this is the one you choose arbitrarily. This can be anything, so long as it's over 10 tons, which is the minimum size of a ship in the Spaceships system. You might want to simplify to two significant figures and round the second one to either 5 or 0 to keep things consistent. Length: I reverse-engineered a formula that works well for the ship progression listed in Spaceships. Remember that the Lengths listed in the Spaceships book are all exactly the same as those in the Speed/Range Table – they were defined as such. Ship masses are very, very close to a square root of ten progression – a ship of one SM larger than another has a mass equal to the smaller ship’s mass multiplied by the square root of ten, which is roughly 3.16. I mention these things because the formula I came up with does not follow the Spaceships Length progression exactly unless you round all the odd Size Modifier ship masses up to a power of the square root of ten. Specifically, there’s a problem at the Length 45 foot, 450 foot, etc. size modifiers – they round down to 40, 400, etc., respectively. Still, it works for the most part. Luckily, Length doesn’t matter in the Spaceships design process except when assigning a Size Modifier to the ship. In any case, the formula works by finding out the size of the ship as if it were a sphere. We can easily find the volume of a ship by multiplying the mass by one hundred cubic feet per ton, which is the assumed density of a ship in Spaceships. From the volume, we find the radius of a sphere of the same size – the formula for volume of a sphere of radius R is V = 4/3PIR^3, so after some simple algebra we get the equation: R = [V/(4/3PI)]^(1/3) This gives you the radius of a sphere of the same volume as your ship. However, the default assumption is that ships are not sphere-shaped. After doing some calculations, I found that Spaceships assumes ships are roughly 4.7 times longer than a sphere of the same volume’s radius. My formula for a ship’s length is thus: Length = [Mass (Tons) 100 Cubic Feet/Ton / (4/3PI)]^(1/3) 4.673 You then simplify to two significant figures and round the second one to either 5 or 0 for display, though the actual unrounded length is used further on. dST/HP: This is slightly complicated. I’m not sure if it’s intentional or an error, but David Pulver didn’t use the normal rules for figuring out an unliving object’s hitpoints. Instead, all spaceships have the hitpoints that the formula would give a ship one size modifier larger than themselves. The actual formula used in the books, therefore, is as follows: dST/HP: 4 * [Mass (Tons) * 2000 Pounds per Ton * SQRT(10)] ^ (1/3) You then simplify to two significant figures and round the second one to either 5 or 0. Hnd/SR: If you’re making a ship between two SMs in size, just use the Hnd of the larger SM and the SR of the smaller SM. This is a pessimistic assumption – taking the Hnd of the smaller SM and the SR of the larger SM is also viable, as is rounding to the closest SM and treating it as that SM for Hnd/SR purposes.