Ever wonder how fast the ships in Star Trek actually are? How about relative to one another? I remember from somewhere that the cube of the Warp Speed was the multiple of the speed of light that the ship moved at.
So, for example, a Warp 6 ship would travel at 6x6x6 times the speed of light (216 times in this case). Having even a 0.1 increase in Warp Speed would still add several multiples of light speed (c) to the ship's velocity.
EC Henry puts the various Enterprises through their speed paces in the above video, showing how they compare in performance to one another. While the speed cubed formula seems to apply to TOS and pre-TOS era ships, a different formula is in use for TNG-era ships, resulting in much higher multiples of the speed of light.
The video doesn't cover anomalies, which is a shame, because it misses when the NCC-1701 travels at Warp 14.1 (2803c) in the TOS episode That Which Survives, the NCC-1701 traveling at Warp 22 (10648c) in the animated episode The Counter-Clock Incident, The NCC-1701D travelling super fast in the Where No man Has Gone Before episode and the Cochrane shuttle of Voyager crossing the Warp 10 threshold, causing Tom Paris to evolve in reverse into a reptile.
In addition, in TOS episode The Changeling, a bolt of energy is reported as travelling at Warp 15 (3375c) and also in the animated episode The Counter-Clock Incident, the Enterprise encounters a ship travelling at Warp 36 (46656c).
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