"I was told there'd be no math."
"You were misinformed."
While kibitzing in the other thread about starship design, I mentioned the FF&S hull table.
The math is described in the descriptions, and it's straightforward.
The issue is that there were, um, liberties taken with what's actually in the chart.
So, the Hull Size Table has 4 columns: Rate, Vol, MV, L
Rate is the "rating", this is basically dTons.
Volume is the volume in m^3.
MV is the Material Volume (how much volume does the hull take).
L is the length of the hull.
In the notes, we find that a dTon is 14 m^3, so Volume is simply rate *14. MV, material volume, is "the volume of material required to enclose the hull in a shell 1cm thick". Length is the length of the hull in meters that is also the diameter of a spherical hull (Aha!).
So, we're dealing with spheres here and everything else works from that.
The volume of a sphere is 4/3 pi r^3. We need the radius for a given volume.
radius = cube_root(.75 * v / pi)
Diameter is radius * 2, so L = 2 * cube_root(.75 * v / pi).
Next, the material volume. Here we take the radius of the given volume, subtract 1cm from the radius, compute the new volume, and take the difference from the original volume and the new volume. Here we're looking at (4/3 * pi * r^3) - (4/3 * pi * (r - 0.01)^3).
Actually, there's a bit of pedantry here. The text says "1cm shell enclosing the hull" which I read as "1cm shell enclosing the volume". In that we should be ADDING 1cm to the radius (so the entirety of the volume is enclosed), not subtracting. BUT hull volume in the end reduces the total available volume of the hull. So, a spherical hull of a 1000 ton ship consumes 28 m^3 of the ship (2 dTons). So, since it's "inside", I subtract the cm. Heresy, I know.
So, how does that compute out?
In contrast to the book:
There's also the differences in MV and L from the book and the math.
It's clear there's just some "eyeball rounding" going on here to make the numbers "look good".
In the end, the number differences have little impact, but I will say that between 1 and 10 tons, the numbers can be pretty different. For example, for a 10 ton ship, the table has an MV of 1.9, but the math comes out to 1.3, 30% difference. All of the table numbers are high in the range. For the range, they're high by 17-33%.
"You were misinformed."
While kibitzing in the other thread about starship design, I mentioned the FF&S hull table.
The math is described in the descriptions, and it's straightforward.
The issue is that there were, um, liberties taken with what's actually in the chart.
So, the Hull Size Table has 4 columns: Rate, Vol, MV, L
Rate is the "rating", this is basically dTons.
Volume is the volume in m^3.
MV is the Material Volume (how much volume does the hull take).
L is the length of the hull.
In the notes, we find that a dTon is 14 m^3, so Volume is simply rate *14. MV, material volume, is "the volume of material required to enclose the hull in a shell 1cm thick". Length is the length of the hull in meters that is also the diameter of a spherical hull (Aha!).
So, we're dealing with spheres here and everything else works from that.
The volume of a sphere is 4/3 pi r^3. We need the radius for a given volume.
radius = cube_root(.75 * v / pi)
Diameter is radius * 2, so L = 2 * cube_root(.75 * v / pi).
Next, the material volume. Here we take the radius of the given volume, subtract 1cm from the radius, compute the new volume, and take the difference from the original volume and the new volume. Here we're looking at (4/3 * pi * r^3) - (4/3 * pi * (r - 0.01)^3).
Actually, there's a bit of pedantry here. The text says "1cm shell enclosing the hull" which I read as "1cm shell enclosing the volume". In that we should be ADDING 1cm to the radius (so the entirety of the volume is enclosed), not subtracting. BUT hull volume in the end reduces the total available volume of the hull. So, a spherical hull of a 1000 ton ship consumes 28 m^3 of the ship (2 dTons). So, since it's "inside", I subtract the cm. Heresy, I know.
So, how does that compute out?
| Rate | Volume | MV | L |
| 1000 | 14000 | 28.07 | 29.90 |
| 2000 | 28000 | 44.57 | 37.67 |
| 3000 | 42000 | 58.40 | 43.13 |
| 4000 | 56000 | 70.76 | 47.47 |
| 5000 | 70000 | 82.11 | 51.13 |
| 6000 | 84000 | 92.72 | 54.34 |
| 7000 | 98000 | 102.76 | 57.20 |
| 8000 | 112000 | 112.33 | 59.81 |
| 9000 | 126000 | 121.50 | 62.20 |
In contrast to the book:
| Rate | Volume | MV | L | dMV | dL |
| 1000 | 14000 | 28 | 30 | -0.07 | 0.10 |
| 2000 | 28000 | 43 | 36 | -1.57 | -1.37 |
| 3000 | 42000 | 57 | 42 | -1.40 | -1.13 |
| 4000 | 56000 | 70 | 47 | -0.76 | -0.47 |
| 5000 | 70000 | 80 | 51 | -2.11 | -0.13 |
| 6000 | 84000 | 90 | 53 | -2.72 | -1.34 |
| 7000 | 98000 | 100 | 57 | -2.76 | -0.20 |
| 8000 | 112000 | 110 | 60 | -2.33 | 0.19 |
| 9000 | 126000 | 120 | 62 | -1.50 | -0.20 |
There's also the differences in MV and L from the book and the math.
It's clear there's just some "eyeball rounding" going on here to make the numbers "look good".
In the end, the number differences have little impact, but I will say that between 1 and 10 tons, the numbers can be pretty different. For example, for a 10 ton ship, the table has an MV of 1.9, but the math comes out to 1.3, 30% difference. All of the table numbers are high in the range. For the range, they're high by 17-33%.
