5.1 Maximum Radius of Space Colonies
The maximum radius of such an O'Neill style colony is limited by the hoop stress of the spinning structure, and the tensile strength to density ratio of the material. The formula is
R = HoopStress/gG
Where R is the radius, g is the acceleration of pseudo-gravity at the rim, and G is the density. MNT offers a 5 x 1010
Pa tensile strength. Using the design rule of 50% safety factors for O'Neill style colonies , a 3.3 x 1010
Pa design tensile strength is reasonable. The associated material density is 3.51 103
. One goal of the architecture is for g to equal 9.8 m/s2
,. This all gives a possible space station radius of 9.6 x 105
m, or nearly 1000 km. For comparison, the corresponding feasible radius for titanium is 14 km, and even at its ultimate tensile strength with no safety factor, the titanium limit would be 23 km.
At the 9.6 x 105
m radius, the entire available strength (at the safety factor) of the MNT-based material is being used to prevent the rotating structure from bursting, and there is no strength left over to hold the space station's contents, including an atmosphere. To do so, a lower radius must be set.