Ex-News Junkie
Relativistic Centrifuge Concept - Back-of-the-envelope math
Wed Oct 25, 2017 8:11pm
2001:1970:5c22:6100:5d4b:d822:4c29:ea20

Radius = 100 meters
Tangential velocity = c-1 = 299792457 m/s
Vt/c = 0.99999999666
Lorentz Factor = 12243

As before the centrifuge is spinning with a rim speed of c-1 m/s, that is just 1 m/s slower than the speed of light. The resulting time dilation (Lorentz Factor) means that for every minute that passes in the centrifuge, 8.5 days passes in the outside world.

Distance to Alpha Centauri = 4.132E+16 meters
New Horizons speed = 16260 m/s
Outside world travel time = 80581 years
Relativistic travel time = 6.6 years

Therefore the fastest man-made spacecraft would take 80581 years to travel to Alpha Centauri. Onboard an interstellar transport moving at the same speed, only 6.6 years would be experienced by passengers inside a relativistic centrifuge. For full-time ship crew, this time could be broken up into a 5-day work week spent maintaining various ship systems, carrying out inspections & repairs, capped off with a 2-day weekend spent inside the relativistic centrifuge, replenishing their food supplies and chillin' with the rest of the passengers. At the start of the work week, they would exit the centrifuge with at least a week's worth of supplies - through a staged entry/exit system perhaps. The first order of business would be to review the list of problems & repairs made by other ship crews over the 67-year "weekend" they spent in the centrifuge.

Relativistic weekends (2 day intervals) = 1201
2-days-inside/5-days-outside time = 23 years
Outside world time passed per 2-days inside = 67 years
Number of rotating crews needed for continuous outside manning = 3498
Number of people per crew = 15
Total number of people on rotating shifts for 23 years = 52470

Due to the time dilation of the relativistic centrifuge, the average distance covered by the ship per unit time would seem to be a significant fraction of the speed of light, even though the actual speed of the ship is no faster than any other man-made spacecraft.

Outside distance traveled per week toward Alpha C = 3.44E+13 meters
Average apparent velocity toward Alpha C = 56878463 m/s (19% light speed)

The relativistic centrifuge would work by balancing the centrifugal forces with diamagnetic levitation acting on every atom & molecule in the passenger's bodies. Despite centrifugal acceleration equivalent to trillions of gees, they would feel nothing. This would require a very high magnetic field in the relativistic centrifuge.

Earth-normal gravity = 9.81 m/s^2
Centripetal acceleration = 9.16E+13 g's
Magnetic permeability of free space = 4*PI*10^(-7) Henries/meter
Average Density of materials being levitated = 3000 kg/m^3
Molecular susceptibility for diamagnetic materials = 10^(-5)
Radial Field Gradient = 8.23E+8 Teslas (not sure if I did this correctly)

source

As I understand it, the magnetic field lines have to be parallel to the applied force vector, so that diamagnetism can directly oppose it. For example, at the link above the samples (frogs, etc) are levitated in the vertical bore of a powerful Bitter-type solenoid magnet because that way the magnetic field lines are aligned with the downward force of gravity. For this to work in a space-based centrifuge, the field lines would have to be aligned radially against the centrifugal force. This might (conceptually) be accomplished with an inner cylinder representing magnetic north, and an outer cylinder representing magnetic south. The field lines would then be straight radial lines spanning the gap between the two cylindrical walls. The cylinders should be stators, not moving and therefore not required to support excessive g-forces. A yet-to-be-conceptualized diamagnetic system to compel levitated objects to spin around the centrifuge would be needed. The rotor of the centrifuge would therefore be a diamagnetically levitated volume of, for example, water, which would provide a more-or-less uniform mass and eliminate vibration. The whole system would have to be designed to last for thousands of years without maintenance - all very speculative. As for the strength of the field that would be required: that is a fun idea.


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