Tom McKendree came the conclusion that an O'Neill-style cylinder constructed with carbon nanotubes could have a radius of approximately 461 km.

Quoting the above (footnotes omitted):

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

 

$$R < \frac{HoopStress}{gG}$$

 

Where R is the radius, g is the acceleration of pseudo-gravity at the rim, and G is the density. [Molecular nanotechnology (MNT)] offers a 5 x 10$^{10}$ Pa tensile strength. Using the design rule of 50% safety factors for O'Neill style colonies, a 3.3 x 10$^{10}$ Pa design tensile strength is reasonable. The associated material density is 3.51 x 10$^3$ kg/m$^3$. One goal of the architecture is for g to equal 9.8 m/s$^2$. This all gives a possible space station radius of 9.6 x 10$^5$ 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 10$^5$ 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.

In the section immediately following, McKendree arrives at a radius of 461 km when atmosphere and fixtures are accounted for:

One can directly solve for the structure radius where the shell is 5000 kg/m$^2$. 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.

Tom McKendree came the conclusion that an O'Neill-style cylinder constructed with carbon nanotubes could have a radius of approximately 461 km.

Quoting the above (footnotes omitted):

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

$$R < \frac{HoopStress}{gG}$$

Where R is the radius, g is the acceleration of pseudo-gravity at the rim, and G is the density. [Molecular nanotechnology (MNT)] offers a 5 x 10$^{10}$ Pa tensile strength. Using the design rule of 50% safety factors for O'Neill style colonies, a 3.3 x 10$^{10}$ Pa design tensile strength is reasonable. The associated material density is 3.51 x 10$^3$ kg/m$^3$. One goal of the architecture is for g to equal 9.8 m/s$^2$. This all gives a possible space station radius of 9.6 x 10$^5$ 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 10$^5$ 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.

In the section immediately following, McKendree arrives at a radius of 461 km when atmosphere and fixtures are accounted for:

One can directly solve for the structure radius where the shell is 5000 kg/m$^2$. 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.

Tom McKendree came the conclusion that an O'Neill-style cylinder constructed with carbon nanotubes could have a radius of approximately 461 km.

Quoting the above (footnotes omitted):

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

$$R < \frac{HoopStress}{gG}$$

Where R is the radius, g is the acceleration of pseudo-gravity at the rim, and G is the density. [Molecular nanotechnology (MNT)] offers a 5 x 10$^{10}$ Pa tensile strength. Using the design rule of 50% safety factors for O'Neill style colonies, a 3.3 x 10$^{10}$ Pa design tensile strength is reasonable. The associated material density is 3.51 103 kg/m$^3$. One goal of the architecture is for g to equal 9.8 m/s$^2$. 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.

In the section immediately following, McKendree arrives at a radius of 461 km when atmosphere and fixtures are accounted for:

One can directly solve for the structure radius where the shell is 5000 kg/m$^2$. 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.

Tom McKendree came the conclusion that an O'Neill-style cylinder constructed with carbon nanotubes could have a radius of approximately 461 km.

Quoting the above (footnotes omitted):

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

$$R < \frac{HoopStress}{gG}$$

Where R is the radius, g is the acceleration of pseudo-gravity at the rim, and G is the density. [Molecular nanotechnology (MNT)] offers a 5 x 10$^{10}$ Pa tensile strength. Using the design rule of 50% safety factors for O'Neill style colonies, a 3.3 x 10$^{10}$ Pa design tensile strength is reasonable. The associated material density is 3.51 x 10$^3$ kg/m$^3$. One goal of the architecture is for g to equal 9.8 m/s$^2$. This all gives a possible space station radius of 9.6 x 10$^5$ 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 10$^5$ 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.

In the section immediately following, McKendree arrives at a radius of 461 km when atmosphere and fixtures are accounted for:

One can directly solve for the structure radius where the shell is 5000 kg/m$^2$. 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.