Volume in Ultimate Base

[Armitage]

I'm looking at the Size Comparisons table on p. 8 of The Ultimate Base and the numbers seem a little off. I want to make sure I'm not missing something.

 

The Size Comparisons table lists volumes in cubic kilometers, but the Base Size table on pp. 10-11 lists volumes in cubic meters, which is a difference of a factor of 1,000,000,000.

 

e.g.

The volume of the Moon is listed as 22 billion cubic kilometers, Size 38. But 22 billion cubic kilometers is 22 quintillion cubic meters, Size 58 on the Base Size Table.

 

Earth: 1.08 trillion cubic kilometers, Size 43. 1.08 sextillion cubic meters is Size 63.

 

Jupiter: 1.43 quintillion cubic kilometers, Size 53. 1.43 octillion cubic meters is Size 84.

 

I also now see that starting at Size 19 all three Base dimensions double while the Volume only doubles instead of octupling.

Size 18: 500m x 250 m x 250 m = 32 million cubic meters.

Size 19 1 km x 500 m x 500 m = 250 million cubic meters, while the table lists 64 million.

[Matt Holck]

Re: Volume in Ultimate Base

 

to error is human

to exponentially error is heroic

[dmjalund]

Re: Volume in Ultimate Base

 

also - according to the table, it seems to cost more to have the base covering the surface of a planet than it does to have the base completely fill the planet

[Bodkins Odds]

Re: Volume in Ultimate Base

 

That is very odd, even if I do say so myself. ;D

[Blue Jogger]

Re: Volume in Ultimate Base

 

A little algebra can fix this problem. Size N can be calculated from looking at Size N-3 and doubling each dimension and octupling the volume.

 

Extrapolating from the table on 6E2, page 189:

 

Size 18, 500 m, 250 m, 250 m, 32 million cubic meters (from 6E2, page 189)

Size 19, 640 m, 320 m, 320 m, 64 million cubic meters (double each dimension of Size 16)

Size 20, 800 m, 400 m, 400 m, 120 million cubic meters (double each dimension of Size 17)

Size 21, 1 km, 500 m, 500 m, 250 million cubic meters (double each dimension of Size 18)

Size 22, 500 million cubic meters

Size 23, 1 cubic kilometer

 

Now, we can use a trick that 10 doublings is roughly 1000 (2^10=1024).

 

Size 33, 1000 cubic kilometers

Size 43, 1 million cubic kilometers

Size 53, 1 billion cubic kilometers

Size 58, 32 billion cubic kilometers, Moon (by Volume)

Size 63, 1 trillion cubic kilometers, Earth (by Volume)

Size 73, 1 quadrillion cubic kilometers, Jupiter (by Volume)

[Matt Holck]

Re: Volume in Ultimate Base

 

Okay

1 cubic km should cover the inner pod of Cobrina's low orbital bio-engineered photosynthetic base named Hydra.

 

But I should consider the length of it's root

that sweeps through the stratosphere collecting water and nutrients

15 km above the ground .

 

A reasonable low orbit would be at 300 km so the root would have to be 285 km long

The width of the root is 6 m diameter so the area would be

PI*r^2 = 9Pi approximately 28 square meters * 10^(-6) (km^2/m^2)

Volume = length*width = 285*28*10^(-6)=0.00798 km^3

0.00798 km^3 is the volume of the root stretching to the Earth's stratosphere.

Not a significant volume of the base.

base size 1 cubic km 23 points

 

There is also 3 km of photosynthetic petals growing around the base

Those are bought to be grounds at x8 volume +3.

 

So Cobrina's base size + grounds cost would be 26 points.

[Matt Holck]

Re: Volume in Ultimate Base

 

some one brought up tension

which is a big issue in the beanstalk concepts

how would the 285 km thread hang without breaking apart ?