FFS Hull Size Observation

[Libris]

Just doing the maths for FFS Hull Volume (I was trying to accurately interpolate between two Hull Sizes) and I noticed that the MV values on the Hull Size table (p11) don't actually work out for the area of a sphere and the Chassis Size MV (p17) don't work out for a 1.67 x 1 x 2.5 ratio cuboid. Or I should say don't appear to work. Or else my maths is crap; a distinct possibility.

Yes I realise that the volume of a 1cm thick skin on a sphere is actually equal to the Volume of sphere of radius r - the volume of a sphere of radius r - 1, if r is in cm. Of course using this formula means that smaller vehicles' armour increases in weight quicker than big vehicles' and doubling the AV doesn't quite double the volume of armour.

 

[far-trader]

Yeah, I think it was all pretty ballpark math, though a reasonable approximation. I expect the numbers (like other parts of the design rules) work best for the averages. Wouldn't want to make FF&S too complicated now

 

[Libris]

For surface areas the following two formulae are very close. And you can use it for any volume.

Sphere Area = 4.84 x (Volume) ^ (2/3)

Chassis Area = 6.44 x (Volume) ^ (2/3)

It's actually more of a pain to use the original tables than the formula if using a spreadsheet.

 

[TheDS]

I think the simplification that was used is: figure out the surface area, then decide the thickness of the armor and multiply the two together. A very good simplification, as long as the armor isn't about 1/8 the thickness of the object or so. Then it starts getting dramatically inaccurate. However, most large designs shouldn't notice a big difference.

I don't know about you, but I don't think I want to spend half an hour on one calculation when a much simpler approximation will do in 10 seconds.

 

[robject]

John, have you gathered all your tweaks and changes and adds into a webpage, perhaps, so that others may partake?

 

[aramis]

Real way to do it (But not the FF&S way):

Figure out the volume of the solid, then of one 2x the armor thickness less in all dimensions, which subtracts from the volume of the first to find the volume!

 

[TheDS]

So in other words, say you have a cube 15 cm at each direction, and you want 1 cm of armor for it all around. So you must subtract twice the armor thickness from each dimension, which would be a cube of 13 cm to a side.

Next, take the volume of the smaller from the larger, and the remainder is the armor volume. So in our example, 15cubed - 13cubed = 1178 cc out of 3375. About 1/3 of the total!

The method I suggested would be, 15squared x 6 = 1350. But remember, I did warn about when the armor got to be about 1/8 (maybe shoulda said 1/10th) of the total thickness, and here you see that the difference is significant. The reason my method is simpler, though, is because the book TELLS you the surface area, but unless your ship has a regularized shape, you cannot otherwise compute the exact surface area from the given dimensions. So you might be able to break your design down into its component shapes and figure it all out, but really, who wants to do all that work for no real gain?

 

[aramis]

Which is why, for standard design shapes, use the formulae provided, and scale that. Now, lets compare the 2x1x4 slab configuration:

a 1m baseline with 1cm, vs a 10m with a 1cm armor:
8kL - 7.529kL =0.470464kL, approx 1/16th
8ML, less 7995.200954994kL = 4.79904006kL, approx 1/200th...

and then ignore any irregularities. (BTW< a 1x2x4 slap is short busses, delivery vans, sports cars.