Alternative Warp Scale

[John Wain]

I've been thinking a lot about the warp scale used in TNG and thought it could have been much better.
The "speed=warp_factor^3" used for TOS is very straightforward and works well given the small speeds that Star Trek ships travel at. Actually the Sovereign's speed of warp 9.99 (on the TNG scale) corresponds to just a little below TOS warp 20 - a very manageable number.
What I do not understand however is why Roddenberry did not come with a proper formula for TNG scale, if he really wanted a revision of the old scale - OK, we do have a "speed=warp_factor^(10/3)" up to warp 9, but what happens between 9 and 10 is bogus, and the increase in speed is defined by nothing more than a drawing.

To cut a long story short, I came up with my own warp scale (I'll take the liberty to call it the "JohnWain warp scale" or JWW in short ) which goes between 1 and 100.
JWW 1 = 1x speed of light
JWW 100 = infinite speed

The formula I have used is the following:

S(c) = (W^4 * 100 - 1)/(100-W)

where:
S(c) - multiples of speed of light
w - warp factor

It is clear that the larger the warp chosen, the smaller the denominator will be. At warp 100, the denominator is 0 and so the resulting speed is infinite. In the numerator, it was necessary to have the (-1) in order to obtain equivalence at warp 1 (the fraction for warp 1 is 99/99 = 1x speed of light). This formula allows for consistent results throughout the scale, and can plot any speed. (As an aside note, TNG 9.99 = JWW 9.203. However, other TV shows use much higher speeds for their ships. For example, in Stargate Atlantis, the City Ship travelled 3 million light years in a few hours (Enemy at the Gate episode). It is unclear exactly how long the journey took, but I would put the City Ship's speed between JWW 96-98, which makes this scale very comprehensive).

I have created a calculator in Excel for the scale. I will post a print screen here (my monitor resolution is 1366x768, which imposed the layout of the document):


You can download it and play with it. I have hosted it on MEGA. The file is virus free. It has two pages, the one print-screened above and one with several warp factor graphs (called Comparisons).
WarpFactor.xlsx

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[McAvoy]

Stargate series though early in the series showed Trek speeds or lower (Teal'c once said Goa'uld ships went only ten times the speed of light) it started to become consistent with many ships have intergalactic speed to cross the Milky Way in days or even hours. Then they have the ones that can cross the distance between galaxies in two and half weeks or 18days without a Zpm. The Asgard has shown to have speed to cross that distance within minutes.

[Tinadrin Chelnor]

It looks like you've put a lot of work into that.
I have an obsession with numbers and formulae. I've borrowed it for a little play

[John Wain]

Stargate series though early in the series showed Trek speeds or lower (Teal'c once said Goa'uld ships went only ten times the speed of light) it started to become consistent with many ships have intergalactic speed to cross the Milky Way in days or even hours. Then they have the ones that can cross the distance between galaxies in two and half weeks or 18days without a Zpm. The Asgard has shown to have speed to cross that distance within minutes.

I know. I was quite surprised when Teal'c quoted the 10c speed (with the journey to Earth stated by Carter to be one year from their position), but I think the show needed to increase the speeds in order to get the Goa'uld somewhere.

And when it comes to Star Trek, the warp scale was just technobabble anyway - seeing that the captain throws in an almost random number whenever he wants to go somewhere, and the inconsistencies in ship speeds abound throughout the series.

@Tinadrin Chelnor: I am very pleased if my work can serve its purpose. Go ahead, have fun!

[Coalition]

It looks like you have a similar issue between warp 90 and 100, as the TNG warp between 9 and 10. Both effectively climb to infinity.

From one of the older warp charts, the warp 2, 3, 4, 5, aso were locations where the power needed to reach that speed dropped (like a higher gear in cars). You would have cases where it cost more to go Warp Factor N-.1, than it cost to go warp factor N (for N<10). When you reach Warp 9, there are no more higher gears.

I'd just refer to ship speeds as multipliers of c. Otherwise once you get to warp 99, and start adding 9's after the decimal, you might count wrong and go the wrong speed.

[Graham Kennedy]

The whole idea of making a scale where warp 10 was infinite speed struck me as idiotic from the first days of watching TNG. I read somewhere (can't remember where) that the idea behind it was that TOS had several times resorted to the Enterprise going at some impossibly high warp factor as a way to generate a sense of danger - most notable in The Which Survives when they topped out at Warp 14.1, IIRC. Gene didn't like that and so he wanted to "cap" warp speeds at Warp 10 to make it impossible.

If that was his reason (and I may be misremembering it) then it's pretty dumb, IMO. Especially given that the very first episode of TNG repeats that exact type of scene with Q chasing the Enterprise-D - they just count off Warp 9.4, 9.5, 9.6 instead of warp 10, 11, 12.

And of course writers still couldn't resist ever higher warp factors, with Voyager's 9.975 and such. It's just supid.

As for why the scale is a bit wonky, it's in the TNG TM. The idea of speed = warp factor cubed was used in the TOS behind the scenes stuff; they wanted to the new scale to be faster, so they used Speed = warp factor ^ 3.33333 from warp 1 to 9. After 9 the exponent increased, but they just picked random numbers for four or five different warp factors and left it at that.

And for that matter, they very never used any xc speeds in the show, and very rarely gave any distance/time measurements that you could calculate speeds from, either. Though when they did, they usually got them wrong.

All in all, it's the biggest kludge that TNG ever used.

Personally, I'd have done it this way :

All TNG warp drives are transwarp. TNG was made several years after Star Trek III/IV, so this should have been a given.

Transwarp factors work as Speed = Warp Factor^4.

GCS cruise speed = Warp 9, Maximum speed = Warp 11, Emergency "never exceed" speed = Warp 11.8.

That means at cruise speed it's about six and a half hours from one system to another; at maximum more like three, and all out just over two.

But that's just me.

[McAvoy]

I agree. I think there should have been no limit but the limit on the ship itself. A GCS could only go so fast before being ripped apart. Just like planes

It would make much more sense like Graham said in that the E-D could only go 11.8. Maybe by end of TNG she could go 12. Voyager could go 13.1. The Defiant could go in short bursts at 10.3.

[John Wain]

It looks like you have a similar issue between warp 90 and 100, as the TNG warp between 9 and 10. Both effectively climb to infinity.

You have to take into account that the chart is logarithmic. Therefore, even if it looks like the increase in speed is slowing down, and then going up again, this is not so. I have re-plotted the JWW scale between 0-80, in a linear graph. Here is how it looks:



As you can see, the speed goes up pretty fast, and it gains momentum as you approach 100 because of the way the equation is designed.

I'd just refer to ship speeds as multipliers of c. Otherwise once you get to warp 99, and start adding 9's after the decimal, you might count wrong and go the wrong speed.

I agree. This is why the JWW scale is designed such that you would need to travel exceptionally fast before you get to 99.9 (equivalent to ~99.6 billion times the speed of light!) When I invented the scale, I wanted to be able to plot speeds much higher than what Star Trek was quoting (for example, speeds like those of the ships in Stargate).

When you put the TNG scale into perspective, it looks very weird. Here is a plot showing the TOS and TNG scales (with JWW dotted for comparison):



Note that since I could find no generally-agreed formula for TNG between 9-10, I used values quoted here on the DITL calculator page.

Here is the TNG scale again, in more detail (yellow color). I have plotted on the same graph a 1-10 TNG 'variant' scale of my own design. Again, the point I am trying to make is that even if the creators wanted it to stop at Warp 10, they still could have chosen a different formula, one that would accelerate the exponential increase in speed as a ship approached 10, in such a manner that it would have been travelling very fast way before it reached 9.9. It is ridiculous that the Star Trek ships want to 'push off' the scale and they travel at speeds like 9.975 or 9.99! If designed differently, the scale could accommodate much higher speeds without getting within a hair's width of the impossible 10.



The formula used is:
S(c) = (W^5 x 81)/(10-W)^2.
This satisfies Warp 1 = 1c and Warp 10 = infinite velocity

Finally, I took a different approach altogether and came up with the idea of using a 'boosted' TOS scale, where S(c) = W^4. This is just what Graham said above. The advantage is that you have a very straightforward calculation to make in order to derive the actual speed from the warp speed, and it also increases fast enough that by Warp 10 you'd already travel faster than any TNG-era ship, so you'd not need to use high numbers. This graph (plotted logarithmically both on the X and the Y axes) puts all the scales I talked about together. You decide if you have a clear winner out of these.