Maximum Diameter Solid Rotor for Power Loop

The rotor on the launch loop is constrained by heat dissipation and track surface area. The rotor is heated by payload passage, and the maximum operation rate is constrained by the black body radiation heat emission rate. This suggests a thin, large area, hollow rotor. On the other hand, the rotor is contained in a larger diameter evacuated tube, buffeted by wind in the atmosphere. A smaller diameter tube minimizes wind buffeting. Ultimately, wind buffeting limits launch rate.

Power storage loop rotors stay cool, and are not buffeted by wind. They do need to be supported against gravity, earthquake acceleration, and high acceleration turns. The maximum magnetic force limits the surface pressure, which in turn limits the acceleration forces.

Assume iron, and a maximum magnetic field of one Tesla over 25% of the surface area. The magnetic pressure will be 0.25 \times B^2 / 2 \mu_0 or 100,000 pascals. The density of iron is 7900 kg/m3, so the needed support force per square meter is the thickness times the density times the acceleration. At 1 gee, the magnetic pressure can support 1.28 meters ( 100K / 7900*9.81 ) of iron. A 1.28 meter diameter rotor has a cross section of 1.29 m2 and masses 10,000 kg per meter. At 10 gees, the thickness drops to 12.8 centimeters and the mas drops to 100 kg per meter.

One tunnel in the ground can contain many rotors and associated support structures, so this is not a limit on the total rotor mass per tunnel. However, until the systems become very reliable, we may limit the number of rotors per tunnel to minimize fratricide.

Ocean tunnels will have gentler constraints. They will be in floating tubes, anchored to the sea floor with adaptive cables much like a launch loop. Oceans have enormous inertia - the largest abrupt disturbance might be a nearby landslide, triggering a tsunami. However, tsunami waves have deep ocean swells of a fraction of a meter, with 30 minute periods - the accelerations will be almost undetectably small unless the disturbance is very close by. The main effect will be disturbance of the anchor cables. If we can anticipate sea floor movement with distant sensors, we can keep the sideways accelerations on the tube and track very small.