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
^{(T•C)}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)