Warp Scales

= 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 sub-dimensional 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 di-lithium 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 sub-dimensional 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.
	
 
 
 
 
 From Earth,
 
 
 
 
 
 1 ly in
 
 
 6 mon
 
 
 1 year
 
 
 2 years
 
 
 days to
 
 
 days to
 
 
 
 
 Speed 
 
 
 Times c
 
 
 n days
 
 
 radius
 
 
 radius
 
 
 radius
 
 
 Centauri
 
 
 Vulcan
 
 
 
 
 Wf 1
 
 
 1
 
 
 365. days
 
 
 .5 
 
 
 1
 
 
 2
 
 
 1,497 
 
 
 5,840
 
 
 
 
 
 Wf 2
 
 
 4 
 
 
 91.25 days
 
 
 1.97
 
 
 3.94
 
 
 7.89
 
 
 374
 
 
 1460
 
 
 
 
 
 Wf 3
 
 
 9 
 
 
 40.5 days
 
 
 4.4
 
 
 8.8
 
 
 17.7
 
 
 166
 
 
 648
 
 
 
 
 
 Wf 4
 
 
 16 
 
 
 22.8 days
 
 
 7.89
 
 
 15.78
 
 
 31.57
 
 
 93.48
 
 
 364.8
 
 
 
 
 
 Wf 5
 
 
 25 
 
 
 14.2 days
 
 
 12.67
 
 
 25.35
 
 
 50.7
 
 
 58.22 
 
 
 227.2
 
 
 
 
 
 Wf 6
 
 
 36 
 
 
 10. days
 
 
 18
 
 
 36 
 
 
 72 
 
 
 41 
 
 
 160
 
 
 
 
 
 Wf 7
 
 
 49 
 
 
 7.44 days
 
 
 24.2
 
 
 48.4
 
 
 96.7
 
 
 30.5 
 
 
 119
 
 
 
 
 
 Wf 8
 
 
 64 
 
 
 5. days
 
 
 36.5
 
 
 73
 
 
 146
 
 
 21 
 
 
 80
 
 
 
 
 
 Wf 9
 
 
 81
 
 
 4.5 days
 
 
 40
 
 
 80
 
 
 160
 
 
 18.5
 
 
 72
 
 
 
 
===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.
 
 
 
 
 
 From Earth,
 
 
 
 
 
 1 ly in
 
 
 6 mon
 
 
 1 year
 
 
 2 years
 
 
 days to
 
 
 days to
 
 
 
 
 Speed 
 
 
 Times c
 
 
 n days
 
 
 radius
 
 
 radius
 
 
 radius
 
 
 Centauri
 
 
 Vulcan
 
 
 
 
 Wf 1
 
 
 1
 
 
 365. days
 
 
 0.5
 
 
 1
 
 
 2
 
 
 1,497 
 
 
 5,840
 
 
 
 
 Wf 2 
 
 
 8 
 
 
 45. days
 
 
 4
 
 
 8 
 
 
 16
 
 
 185
 
 
 720
 
 
 
 
 Wf 3
 
 
 27
 
 
 13. days
 
 
 14
 
 
 28
 
 
 56
 
 
 54
 
 
 208
 
 
 
 
 Wf 4
 
 
 64
 
 
 5. days
 
 
 36.5
 
 
 73
 
 
 146
 
 
 21
 
 
 80
 
 
 
 
 Wf 5
 
 
 125
 
 
 3. days
 
 
 60.8
 
 
 122
 
 
 243
 
 
 12 
 
 
 48
 
 
 
 
 Wf 6
 
 
 216
 
 
 1.6 days
 
 
 114
 
 
 228
 
 
 458
 
 
 6.5
 
 
 25.6
 
 
 
 
 Wf 7
 
 
 343
 
 
 1.06 days
 
 
 172
 
 
 344
 
 
 688
 
 
 4.3 
 
 
 17
 
 
 
 
 Wf 8
 
 
 512
 
 
 0.7 days
 
 
 260
 
 
 520
 
 
 1,040
 
 
 2.87
 
 
 11.2
 
 
 
 
 Wf 9
 
 
 729
 
 
 0.5 days 
 
 
 365
 
 
 730
 
 
 1,460
 
 
 2
 
 
 8 
 
 
 
 
 Wf 10
 
 
 1,000
 
 
 0.365 days
 
 
 500
 
 
 1,000
 
 
 2,000
 
 
 1.5
 
 
 5.8
 
 
 
===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.
 
 
 
 
 From Earth,
 
 
 
 
 
 1 ly in
 
 
 6 mon
 
 
 1 year
 
 
 2 years
 
 
 days to
 
 
 days to
 
 
 
 
 Speed 
 
 
 Times c
 
 
 n days
 
 
 radius
 
 
 radius
 
 
 radius
 
 
 Centauri
 
 
 Vulcan
 
 
 
 
 Wf 1
 
 
 1
 
 
 365
 
 
 0.5
 
 
 1
 
 
 2
 
 
 1,497
 
 
 5,840
 
 
 
 
 Wf 2
 
 
 10
 
 
 36.21 
 
 
 5
 
 
 0
 
 
 20
 
 
 148
 
 
 579
 
 
 
 
 Wf 3
 
 
 39
 
 
 9.3
 
 
 20
 
 
 39 
 
 
 78
 
 
 38
 
 
 149
 
 
 
 
 Wf 4
 
 
 102
 
 
 3.58
 
 
 51
 
 
 102
 
 
 204
 
 
 15
 
 
 57
 
 
 
 
 Wf 5
 
 
 214
 
 
 1.7
 
 
 107
 
 
 215
 
 
 429
 
 
 7
 
 
 27 
 
 
 
 
 Wf 6
 
 
 393
 
 
 0.93
 
 
 196
 
 
 392
 
 
 785
 
 
 4
 
 
 15
 
 
 
 
 Wf 7
 
 
 656
 
 
 0.55
 
 
 331
 
 
 664
 
 
 1,327
 
 
 2
 
 
 9
 
 
 
 
 Wf 8 
 
 
 1,024
 
 
 0.35
 
 
 513
 
 
 1,025
 
 
 2,051
 
 
 1.5
 
 
 5.6
 
 
 
 
 Wf 9
 
 
 1,516
 
 
 0.24
 
 
 760
 
 
 1,520
 
 
 3,041
 
 
 1 
 
 
 4
 
 
 
 
 Wf 9.1
 
 
 1,684
 
 
 0.22
 
 
 830
 
 
 1,659
 
 
 3,318
 
 
 0.9
 
 
 3.52
 
 
 
 
 Wf 9.2 
 
 
 1,853
 
 
 0.196 
 
 
 931
 
 
 1,862
 
 
 3,724
 
 
 0.8
 
 
 3.1 
 
 
 
 
 Wf 9.3 
 
 
 2,021
 
 
 0.18
 
 
 1,013
 
 
 2,027
 
 
 4,055
 
 
 0.7
 
 
 4 3
 
 
 
 
 Wf 9.4 
 
 
 2,190
 
 
 0.16
 
 
 1,140
 
 
 2,281
 
 
 4,562 
 
 
 0.65
 
 
 2.5
 
 
 
 
 Wf 9.5
 
 
 2,358
 
 
 0.154
 
 
 1,185
 
 
 2,370
 
 
 4,740
 
 
 0.63
 
 
 2.46
 
 
 
 
 Wf 9.6 
 
 
 2,527
 
 
 0.144
 
 
 1,267
 
 
 2,535
 
 
 5,069
 
 
 0.59
 
 
 2.3
 
 
 
 
 Wf 9.7
 
 
 2,695
 
 
 0.135
 
 
 1,352
 
 
 2,704
 
 
 5,407
 
 
 0.55
 
 
 2.16
 
 
 
 
 Wf 9.8 
 
 
 2,864
 
 
 0.127 
 
 
 1,437
 
 
 2,874
 
 
 5,748
 
 
 0.52 
 
 
 2
 
 
 
 
 Wf 9.9 
 
 
 3,032
 
 
 0.12 
 
 
 1,520 
 
 
 3,041
 
 
 6,083
 
 
 0.49
 
 
 1.92
 
 
 
 
 Wf 9.91
 
 
 3,369
 
 
 0.108
 
 
 1,690 
 
 
 3,379
 
 
 6,759
 
 
 0.44
 
 
 1.72
 
 
 
 
 Wf 9.92 
 
 
 3,706
 
 
 0.0984
 
 
 1,855
 
 
 3,709
 
 
 7,419
 
 
 0.4
 
 
 1.57
 
 
 
 
 Wf 9.93 
 
 
 4,043
 
 
 0.09 
 
 
 2,027 
 
 
 4,055
 
 
 8,111
 
 
 0.369
 
 
 1.44
 
 
 
 
 Wf 9.94
 
 
 4,380
 
 
 0.083
 
 
 2,198
 
 
 4,397
 
 
 8,795
 
 
 0.34
 
 
 1.32
 
 
 
 
 Wf 9.95
 
 
 4,716
 
 
 0.077
 
 
 2,370 
 
 
 4,740
 
 
 9,480
 
 
 0.31
 
 
 1.23
 
 
 
 
 Wf 9.96 
 
 
 5,053
 
 
 0.072
 
 
 2,534
 
 
 5,069
 
 
 10,138
 
 
 0.29
 
 
 1.15
 
 
 
 
 Wf 9.97
 
 
 5,390
 
 
 0.067
 
 
 2,723
 
 
 5,448
 
 
 10,895 
 
 
 0.27
 
 
 1.07
 
 
 
 
 Wf 9.98
 
 
 5,727
 
 
 0.063
 
 
 2,896
 
 
 5,794
 
 
 11,587
 
 
 0.258
 
 
 1
 
 
 
 
 Wf 9.99
 
 
 6,064
 
 
 0.06 
 
 
 3,041
 
 
 6,083
 
 
 12,166
 
 
 0.246 
 
 
 0.96 
 
 
 
 
 Wf 9.999
 
 
 12,128
 
 
 0.03
 
 
 6,083 
 
 
 12,166 
 
 
 24,333
 
 
 0.123
 
 
 0.48
 
 
 
 
 Wf 9.9999 
 
 
 24,256
 
 
 0.015
 
 
 12,166
 
 
 24,333 
 
 
 48,666 
 
 
 0.06
 
 
 0.24
 
 
 
 
 Wf 9.99999
 
 
 48,512
 
 
 0.0075
 
 
 24,333
 
 
 48,666
 
 
 97,333
 
 
 0.03
 
 
 0.12
 
 
 
===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.
 From Earth, 1 ly in1 LY in
6 mon1 year2 yearsdays todays toSpeed Times cn daysN Hours
radiusradiusradiusCentauriVulcanWf 11365. days8760.5121,4975,840 Wf 21622.8 days547.57.8915.7831.5793.5364.8 Wf 3814.5 days108.15408016018.572 Wf 42561.42 days34.22126.7253.55075.822.7 Wf 56250.58 days14310.3620.61241.32.389.28 Wf 612960.28 days6.76642.81285.72571.41.154.5 Wf 724010.15 days3.651200240048000.6152.4 Wf 840960.089 days2.152022.44044.98089.80.3531.424 Wf 965610.055 days1.343272.76545.41309.90.22550.88 
===Dipotassium "New Scale" (power of 5)===
This scale I first saw in the "technical" write up for the Enterprise-D 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.
 
 
 
 
 From Earth,
 
 
 
 
 
 1 ly in
 
 
 6 mon
 
 
 1 year
 
 
 2 years
 
 
 days to
 
 
 days to
 
 
 
 
 Speed 
 
 
 Times c
 
 
 n days
 
 
 radius
 
 
 radius
 
 
 radius
 
 
 Centauri
 
 
 Vulcan
 
 
 
 
 Wf 1
 
 
 1
 
 
 365
 
 
 0.5
 
 
 1
 
 
 2
 
 
 1,497
 
 
 5,840
 
 
 
 
 Wf 2 
 
 
 32
 
 
 11.4
 
 
 16
 
 
 32
 
 
 64
 
 
 46.7
 
 
 182.4
 
 
 
 
 Wf 3
 
 
 243
 
 
 1.46
 
 
 250
 
 
 500
 
 
 1,000
 
 
 5.9
 
 
 23.36
 
 
 
 
 Wf 4
 
 
 1,024
 
 
 0.35
 
 
 521
 
 
 1,042
 
 
 2,084
 
 
 1.43
 
 
 5.6
 
 
 
 
 Wf 5
 
 
 3,125
 
 
 0.1168
 
 
 1,562
 
 
 3,125
 
 
 6,250
 
 
 0.47
 
 
 1.86
 
 
 
 
 Wf 6
 
 
 7,776
 
 
 0.046
 
 
 3,967
 
 
 7,935
 
 
 15,859
 
 
 0.18
 
 
 0.736
 
 
 
 
 Wf 7
 
 
 16,807
 
 
 0.0217
 
 
 8,410
 
 
 16,820
 
 
 33,640
 
 
 0.088
 
 
 0.347
 
 
 
 
 Wf 8
 
 
 32,768
 
 
 0.011
 
 
 16,591
 
 
 33,182
 
 
 66,363
 
 
 0.045
 
 
 0.176
 
 
 
 
 Wf 9
 
 
 52,049
 
 
 0.007
 
 
 26,071
 
 
 52,143
 
 
 104,286
 
 
 0.028
 
 
 0.112
 
 
 
 
 Wf 10
 
 
 100,000
 
 
 0.00365
 
 
 50,000
 
 
 100,000
 
 
 200,000
 
 
 0.014
 
 
 0.056
 
 
 
===Other===
A few more figures to place some relevance on the numbers above.<BR>
0.1 days = 2 hours 24 minutes<BR>
0.01 days = 14 minutes, 24 seconds<BR>
0.001 days = 1 minute, 2.42 seconds 
Distance to Centauri is assumed to be 4.1 ly<BR>
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.
<CENTER>"A journey of a thousand miles, begins with a single step."<BR>
-- Confusian Proverb--</CENTER>
Category:TreknicalCategory:Epiphany Trek