Warp Factors: Eras and Ranges
Epiphany Trek
How fast is fast? A question that has caused endless debates in fan circles. At least for my stories, these are the scales.
Warp power is made possible by the leverage of a series of "second state" elements first discovered by Dr. Long du Hoc in 2052. These elements are necessary to control the energy flow in warp drive engines. The subdimensional Group 1A (Group 1A^2) elements are the most efficient for use in warp drives. Properly hydrogen^2, lithium^2, sodium^2, potassium^2, rubidium^2, cesium^2, and francium^2. The terminology "Dihydrogen" was popularized in the press at the time of discovery and has unfortunately made it back into the technical journals. Dihydrogen can be produced in the laboratory, and is relatively stable in use. Dilithium, the current element of choice. Disodium is a fragile and difficult element to find. As of yet only enough for a few elementary tests has been located. Elements further up the chart have not been identified under scientific conditions.
Each jump in the element used renders a more efficient use of the energy produced to greater powers of the warp factor. The formula s=wf^x*c is used to figure the resulting speed for the use of a given element in the system. Differences in technology can vary this exact formula. Starfeet vessels currently using dilithium are achieving wf^(10/3)c due to improvements in warp coils and drive controls.
Warp factors are produced in nine ideal energy levels. Speeds between the ideal levels can be achieved, but with a greater drain on the ships resources. Warp 10, represents total efficiency and is technically unachievable. It is mistakenly referred to as "infinite speed". It is actually an energy use plateau that cannot be reached. A ship with a powerful drive can attain and pass what on the warp factor scale would be "warp ten", but not find the energy plateau. The practice of indicating the ship's speed in warp factors above 9 has been discontinued.
A further group of subdimensional elements has been discovered. The Group 1a^3 series element have not proved exact analogs of the Group 1A, and Group 1A^2 elements. Attempts to use Trihydrogen or the even rarer Trilithium in starship drives have proven failures.
OK, enough of the technobabble. See, I can do it too.
Dihydrogen Warp Scale (power of 2)
The following warp scale is the diHydrogen scale. I had not figured it out before the Romulan War Series. I might go back and correct them.


































































































DiLithium (TOS) Warp Scale (power of 3)
This is the old and accepted scale for warp factors given in days gone by. Star Trek TOS never took it seriously, and the stories had them gallivanting all over the place regardless of how long or where the star or place was located. The 10,000 odd light years to the "edge" of the Galaxy from Earth would have taken a whopping 16,000 days or almost 44 years to accomplish. In short, consistency never got in the way of a good tale.
Contrary to some fan notions this scale is in the Star Trek Writer's Guide, and not Fanon cooked up after the fact.

































































































DiLithium Modified (TNG) (V=Wf*(10/3) to warp 9)
The TNG table is the only one I have included the "nines" on. It's the only one where it matters or anyone really uses them
I rounded a few figures, and changed the under explained asymptotic curve. My chart does not stay with the "explained" speeds passed warp 9.99, and then it is rounded off a bit to the slower side. I found a simple and workable solution to the 9s to infinity problem. Every time you add a decimal place, double the speed from the last full decimal place. I.E. If Wf 9 is 600c, then Wf 9.9 is 1200c and Wf 9.99 is 2400c etc. For the decimal warp factors between them divide the "9" factor by 9 and add it to each consecutively. This is not strictly a curve, but a series of arithmetic additions between geometric increases. It's ugly, but it functions. These are not the figures used "officially", but it should be workable. I don't know if these figures are anywhere close to what the show's technical writers had in mind, but they do not require a math degree to figure out or understand. This formula also works for any of the other warp scales for Warp Factors above Warp Factor 9.
Warp factor 10 is not infinitely fast. It is an energy plateau that is never reached.

































































































































































































































































Disodium Warp Table (Power of 4)
The DiSodium table. The numbers quickly pile up, but at this stage of the game the Federation (and anyone else) could really use the boost in technology.
This is the case in Epiphany Trek. A source of diSodium has been located and the current generation of Starfleet vessel are taking advantage of the technology.


































































































Dipotassium "New Scale" (power of 5)
This scale I first saw in the "technical" write up for the EnterpriseD model. Who ever thought this up didn't have a clue as to how the math would work out and how big the Galaxy was. It is presented as an interesting proposition. It does fit with DiPotassium. Such cultures as the Builders have ships that move at this scale.

































































































Other
A few more figures to place some relevance on the numbers above.
0.1 days = 2 hours 24 minutes
0.01 days = 14 minutes, 24 seconds
0.001 days = 1 minute, 2.42 seconds
Distance to Centauri is assumed to be 4.1 ly
Distance to Vulcan is assumed to be 16 ly
The Speed of Light in a vacuum is 186,262 miles per second (299,792km/sec). There are 31,536,000 seconds in the year. My little pocket calculator will not handle that equation. However, long hand still works. For those that like mind bogglers that will be: 5.886,938,432,000 miles a year, five trillion, eight hundred and eighty six billion, nine hundred and thirty eight million, four hundred and thirty two thousand miles.
 Confusian Proverb