Transhuman Space Appendix A helpfully lists hull statistics at the beginning of the design process. I, myself, feel that the design process would be a tad easier if the hull was one of the last things to specify, after deciding on what's required inside the hull.
To that end, I've re-jigged the volume formulae so that one can plug in the volume of all the bits to get the dimensions of the hull. This is easy algebra, but it's nice not to have to work it out from scratch every time.
R = 5 × 3√Vol
R is radius in feet, Vol is volume in spaces, 3√ is the cube root.
Once you have the volume, decide on the length-to-width ratio, then divide the volume by this. Use this new volume in the formula below to find the diameter, W. Then multiply W by the length-to-width ratio to get the Length.
W = 8.5 × 3√Vol
For example, a 1600-space hull with a length-to-width ratio of 8:1.
1600/8 = 200 spaces.
W = 8.5 × 3√200
= 8.5 × 5.85
≅ 50'
L = 50 × 8
= 400'
L = 2.9 × 3√Vol
Decide on the length-to-width-to-height ratio. Multiply these numbers together, then divide the total volume by this. Use this volume in the formula below to find L2. Then re-multiply L2 by the ratio to find length, width and height.
L2 = 7.9 × 3√Vol
For example, a 240-space hull, with a length-to-width-to-height ratio of 5:3:2.
5 × 3 × 2 = 30
240/30 = 8 spaces
L2 = 7.9 × 3√8
= 7.9 × 2
= 15.8'
Length = 5 × 15.8 = 79'
Width = 3 × 15.8 ≅ 47'
Height = 2 × 15.8 = 32'
Decide on the ratio of torus radius to cross-section radius. Divide total volume by this. Use this new volume in the formula below to find r, the cross-section radius. Then multiply r by the ratio to get the torus radius, R.
r = 2.9 × 3√Vol
For example, a 10,000-space hull, torus-to-cross-section ratio 10.
10,000/10 = 1,000 spaces
r = 2.9 × 3√1,000
= 29'
R = 29 × 10
= 290'
This is a new hull shape I thought would be useful. Formulae for surface area are down below.
Decide on the height-to-base-radius ratio. Divide total volume by this. Use this new volume in the formula below to find the base radius, R. Then multiply the ratio by R to get the height, H.
R = 7.8 × 3√Vol
For example, a 500-space cone, with a height-to-base-radius ratio of 4:1.
500/4 = 125 spaces
R = 7.8 × 3√Vol
= 7.8 × 3√125
= 7.8 × 5
= 39'
H = 4 × 39
= 156'
Add base area and side area together for the total area.
Base Area = R2/320
Side Area = R × √(R2 + H2)/320
Where R is the radius of the base and H is the height of the cone.
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This page updated Weds, December 21, 2005, around about 12:00 ish (GMT).