The generally accepted formula for calculating TNG warp velocities is:
Vc=(Wf^3*Wf^1/3)c; for velocities warp 1 to 9, inclusive. Velocities rise asymptotically from 9 to 10, which is regarded as infinite velocity under this system.
Graham Kennedy
Vc=(Wf^4*Wf^1/3)c.
Apparently, the only species with this form of drive is the Voth. (the Borg uses transwarp Conduits, which manifests itself differently).
Now, simply going through the warp10 barrier is not feasible, lest you want to become a giant salamander, so some way of bypassing W10 must be found. I say this becayse Starfleet is apparently unable to sustain long-term TW conduits or Quantum Slipstreams.
I have two possible solutions:
1.At warp 9 create a Transwar conduit and/or Quantum Slipstream which would accelerate you to warp 11 at the exit apeture.
2.engineer some kind of "Inter-warp Drive" which exists only between warp 9 and 11:
Vc=(Wf^4/Wf^1/4)c
Do you have any viable alternatives?
