Reaching 50% the speed of light using a centrifuge

Question

I've seen ideas and previously asked questions for reaching the speed of light through a long bar rotating at some high RPM for the tip to reach $c$. However it seems impossible, so I'm concerned is it impossible still to reach like $c/2$ and if not what fraction through this method is realistic?

Answer 1

The real answer to your question is to direct you to the concept of specific strength which is the concept that is directly applicable to your question. This is the limit where a bar (or strand) of material will break under its own mass. It matters little how lightweight your payload is (even just a sail), because it's the bar's own limits that matter.

Many commenters mentioned that the limit for this is when the tangential velocity exceeds the speed of sound in the material. This was used to resolve the Ehnrenfest paradox in relativity. Long story short, when you approach a tangential speed equal to the speed of sound in that medium, you must also have centrifugal pressures that exceed the specific strength of the material and it rips itself to shreds.

So what's realistic? That's not really an easy question to answer, because we have to question what level of technology you consider "realistic." The most directly applicable answer would be to point to SpinLaunch, a space launch company whose entire business model is basically to implement your idea as best as can be done with modern technology. At the present, they reach 2.1 km/s. So if you want "realistic using modern technology," the state of the art is 0.000007c.

You are welcome to play games with the materials. SpinLaunch uses carbon fiber. I do not know what carbon fiber they use (it is likely proprietary), but Wikipedia's page pegs the best carbon fiber on their list at a specific strength of 7GPa. Its theorized that carbon nanotubes could get up to 300GPa, so in theory one could shave a few zeros off of of that -- almost 2 zeros to be precise.

There is an ultimate limit to specific strength, thanks to relativity. Interestingly enough, if you treat magnetic field lines as "tethers," they achieve this ultimate limit. So maybe the more realistic approach is to ditch the bar entirely, and just rely on electromagnetic attractions to do the trick.

I didn't do the math myself, but based on what I saw, I have suspicions that this ultimate limit would indeed be c, so there would be no fundamental force preventing any fraction of c using electromagnetic tethers. Of course there will be practical limits, but nothing fundamental.