For warp>9, there are many possible variations of a mathematical continuous domain formula that could be approximated. Below is such example of a formula that has the "10/3" exponent growing exponentially with a "w/(10-w)" function, which evidently reach infinity at warp 10. The growth of the exponent is slowed considerably by a Nth root until the warp factor 'wf' approaches 10.

speed/c = wf^( (10/3)^( (wf/(10-wf))^(1/N) ) )
$ speed = wf^{({(\frac{10}{3})}^{({(\frac{wf}{{10-wf}})}^{(\frac{1}{N})})})} c $

For Voyager to do approximately 4 billion miles/s (in VOY, The 37's) at warp 9.9, we would set N=23. If we were to set N=30.35, the 4 billion miles/s would be at warp 9.975.

The people that made TNG, DS9, and Voyager, did not use a formula for WF 9+. As a result there is no formula possible that will fit the examples given across all the stories from that era.
Even in TOS some writers just ignored all formulas and had the ship actually get from one star to another faster than any of the given formulas would reasonably.
MJBurrage(TC) 03:18, June 13, 2010 (UTC)

I've just been playing with a graphing program, using a similar function: $ speed/c = \frac{wf^{\frac{10}{3}}}{(1-(\frac{wf^{N}}{10^{N}}))^{\frac{1}{N}}} $ with N=75. The lower portion here is the tau factor, used in relativity, rescaled for the Warp 10 'wall', and with a higher exponent (in relativity, N=2). This fits the integral warp factors up to warp 9 - not sure how it does for 9+, but it may well be analysable. --Brotherphil 09:28, September 25, 2011 (UTC)

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