As a rough guide, see here. 3" is a pretty common shaft size really.

So say a 3" shaft, 46" long will have a critical speed around 8200rpm. You CANNOT run the shaft to this rpm, it must be below it. Mine is an overall length of 57" and when I had a 1 piece I could only do 120mph before horrific vibrations came into the car ( before I knew about critical speed, and shaft supplier never even mentioned the fucking thing when I was ordering, nor when I complained about the vibrations ! ), so as strong as it may have been it was totally and utterly useless.
Custom 2 piece shaft and it's been spun to close to 10krpm smoothly


http://www.markwilliams.com/driveshafttech.aspx