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How can we make the next leap in drive tech in the form of creating a viable transwarp drive?

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 states an unexplored "Transwarp Domain" exists beyond warp10, the formula is:

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?

Seven should be able to help SF, if they give her the stuff she needs and keeps S31 from taking her.

Any "transwarp" drive, of course, would disprove the notion that Warp 10 = Infinite Speed. Otherwise, it'd just be Warp 9.9999999... whatever.

SPOOFE wrote:Any "transwarp" drive, of course, would disprove the notion that Warp 10 = Infinite Speed. Otherwise, it'd just be Warp 9.9999999... whatever.

But in Voyager we see that Warp 10 = Butchery of Science Speed.

So how it would disprove it? Or chalk it up to another stupid continuity error.