Ultrawarp (where v = c * w^5) was in the FASA TNG Officer's Manual and explained how the ENTERPRISE-D could be faster than the Excelsior but use lower warp factor numbers. 

So whilst transwarp allow the Excelsior to do warp 14 that was still using the (old v = c * w^3) TOS warp scale.

The 'WF to UltraWarp' Formula is what I engineered sometime back in 1992-1993

Anyhow this "Ultrawarp" was finally dropped by Paramount later on and used some other scale for Warp 1-10 (Ten max) Its not the TOS Scale.


-Mark_XON 