I just literally re-used the TNG era formula for backwards compatibility, I didn't change anything other than after Warp 9.I don't know if the .3333333 part is necessary, though. Just extrapolate the original v = w^3 instead. Or, to allow for higher speeds as the 25th century approaches and transwarp engines are perfected, go to v = w^4. Warp 4 is now 256c, warp 8 is 4096c, and warp 11 is a blazing 14,641c. Just have the top speed be warp 13.6 or something, and no I'm not going to multiply it out.
So, that's my take =D
Then I did estimations on where all the advanced FTL things fell on the scale post Warp 9.
So, on my scale, we have different categories of Warp like you have different categories of Warp Speed just like you have different categories of Speed within Atmosphere.
Speed Travel in Atmosphere here on Earth.
Sub-Sonic: Mach < 0.8
Trans-Sonic: Mach 0.8-1.2
Super-Sonic: Mach 1.2–5.0
Hyper-Sonic: Mach 5.0-10.0
High Hyper-Sonic: Mach 10.0–25.0
Atmospheric Re-Entry Speeds: Mach > 25.0
My UFP categorization:
Basic Warp Factors: 1 - 9.x
Deca Warp Factors: 10 - 99.x
Trans Warp Factors: 100 - 999.x
Super Warp Factors: 1,000 - 9,999.x
Hyper Warp Factors: 10,000 - 99,999.x
Ultra Warp Factors: 100,000 - 999,999.x
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