Where s is the design stress, PA is the internal atmospheric pressure, G is the additional load for other contents, and a is the length to radius ratio of the cylinder. A typical a, used here, is 10. [12] derives a requirement for 50.8 kPa internal atmosphere, and use a G equal to 16% PA. Since the total area of the structure is:
One can directly solve for the structure radius where the shell is 5000 kg/m2. Using MNT materials, the structure will be 461 km in radius. For comparison, the equivalent number for titanium is 6.6 km, or for a titanium shell is at its ultimate tensile strength with no safety factor, 11 km.
A 461 km radius cylinder with endcaps, with a 4610 km long cylinder portion, has a surface area on that cylinder portion of 1.22 x 1012 m2., half of which would be available for habitation (the other half being taken up with windows). The [12] requirement of 87 m2 land area per person (including land for agriculture) yields a possible population for this structure of 76 billion people. The stressed shell masses 8.0 x 1016 kg of carbon.
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