However, for TNG it is more illusive.
At Warp 1, warp^3 is right on.
At Warp 2, it is off by 25%
At Warp 3, it is off by 44%
At Warp 4, it is off by 60%
At Warp 5, it is off by 71%
At Warp 6, it is off by 81%
At Warp 7, it is off by 91%
At Warp 8, it is off by 100% Warp 8 is exactly Warp^3*2
At Warp 9, it is off by 108%
It looks like the formula just might be Warp^3*n, where n grow larger as Warp increases.

Using Warp^(10/3) as Been suggests:
At Warp 1, it is right on.
At Warp 2, it is right on.
At Warp 3, it is off by 00.001%. I'd call that right on.
At Warp 4, it is off by 00.004%.
At Warp 5, it is off by 00.001%
At Warp 6, it is off by 00.001%, this time short instead of over.
At Warp 7, it is right on.
At Warp 8, it is right on.
At Warp 9, it is right on.

This one's promising.

At Warp 9.2, it is off by 00.01%
At Warp 9.6, it is off by 00.02%
At Warp 9.9, it is off by 46.54%. The formula breaks down about here.
At Warp 9.99, it is off by 368.47%
At Warp 9.9999, it is off by 9261%
At Warp 10, where speed should be infinite, warp^(10/3) yields 2154, which is less than Warp 9.9.

we're onto something.

Then Been Said: I HAVE CLOSE, AFTER WARP NINE USE THE EQUATION

SPEED=-658.39*LN (1-WF/10)

IT�S NOT PERFECT, THE SPEED BELOW 9.6 ARE AS MUCH AS TEN PERCENT OUT AND ABOVE ARE RIGHT OUT BUT FOR NOW THEY ARE THE CLOSEST I CAN GET.

Frankly, I don't remember what "LN()" does.

Then Gaunt_Man said:
This is a formula I found in a file by James Dixon, I haven't tested it, but according to Jimmy D, it yields very accurate results:

V=X^Y, Where: Y=(10/3)+A+B+C+D
A=(((X-9.5)/2)+ABS((X-9.5)/2))/(((10-X)/2)+ABS((10-X)/2))*M*X
B=(((X-9.7)/2)+ABS((X-9.7)/2))/(((10-X)/2)+ABS((10-X)/2))*N*X
C=(((X-9.8)/2)+ABS((X-9.8)/2))/(((10-X)/2)+ABS((10-X)/2))*O*X
D=(((X-9.9997)/2)+ABS((X-9.9997)/2))/(((10-X)/2)+ABS((10-X)/2))*P*X
M=2.482070812522956*(10^-2)
N=-2.47992326011683*(10^-2)
O=-2.459507883040688*(10^-2)
P=-1.71893747069059813*(10^-1)
That's it in pseudo-BASIC.

As you can see, it's HIGHLY complex (which is why I haven't tried it), so someone who is mathematically inclined, please try it and tell us the results.

I tried it out, and here are the results:
This Warp Formula works fine up to Warp Nine.
At Warp 9.2, it is off by 1%
At Warp 9.6, it is off by 12.7%
At Warp 9.9, it is off by 20.6%
At Warp 9.99, it is off by 46.23%
At Warp 9.9999, it is off by 2.02%
Not bad. Gotta fix that Warp 9.99 thing. If anyone wants it, I have a basic program that executes this formula for known Warp Factors, and am working on one to do any warp factor as well as reverse calculation.

Reverse calculation is turning out to be harder than it seemed.

I am soliciting thoughts and improvements.

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You're a Starfleet Officer. "Weird" is part of the job.

The latest formula is a good compromise between simplicity and accuracy, while the one before manages to nail every factor pretty close.

A comment about the "deviations" from W^(10/3) - I'd argue that the formula is perfect from 1-9 and that the speed numbers in the Encyclopedia are simply a result of rounding. Try dividing some of the larger distances (to the Andromeda Galaxy, across the Federation and similar) by the travel times given in the table, and you'll see that the W^(10/3) relationship holds perfectly from 1 to 9.

After that, the curve was hand-drawn by Okuda, that's why there is no easy formula to match.

Boris

Oh, and spyone, LN means 'natural logarithm' (sp?). Every scientific calculator has the LN button. I can recommend you the CASIO fx-82.
[this message has no commercial intentions; and I don't work for CASIO]

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You're a Starfleet Officer. "Weird" is part of the job.

Also, Martin Shields' warp formula and warp calculator can be accessed via a link on the page mentioned above.

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You're a Starfleet Officer. "Weird" is part of the job.

http://www-personal.usyd.edu.au/~mshields/TV/