Warp Factors: Eras and Ranges

       How fast is fast? A question that has caused endless debates in fan circles. At least for my sotries, 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 "Di-hydrogen" was popularized in the press at the time of discovery and has unfortunately made it back into the technical journals. Di-hydrogen can be produced in the laboratory, and is relatively stable in use. Di-lithium, the current element of choice. Di-sodium 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 efficency and is technically unachievable. It is mistakenly referred to as "infinite speed". It is actually a 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 element 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 Tri-hydrogen or the even rarer Tri-lithium in starship drives have proven failures.

       OK, enough of the technobabble. See I can do it too. The following at the warp scale is the di-hydrogen scale. I had not figued it out before the Romulan War Series. I might go back and correct them.

Di-hydrogen Warp Scale (power of 2)

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

       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 as to 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.

Di-lithium (TOS) Warp Scale (power of 3)

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

       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 Di-potassium. However finding enough of that for a ship is impossible.

Di-potassium "New Scale" (power of 5)

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

       The TNG table is the only one I have included the "nines" on. It's the only one where it matters or anyone really ues 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 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.
       A note to the Voyager bunnies. My figures are slightly slower than the given figures for Wf 9.97, the Voyager cruising speed as given. However, if you do the math (70,000/5448=12.848751) you will note that Voyager is on a 13 year trip, not a 70 year trip. Still pretty long, but you think the guys doing the series could have looked at their own materiel, and used a pocket calculator. One of many large holes in the Voyager premise that makes me say Beman has no clue.

Di-lithium Modified (TNG) (V=Wf*(10/3) to warp 9)

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
Wf 10
Infinity
0
0
0
0
0
0

       And just for completenesses sake the Di-sodium 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.

Di-sodium Warp Table (Power of 4)

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
16
22.8 days
7.89
15.78
31.57
93.5
364.8
Wf 3
81
4.5 days
40
80
160
18.5
72
Wf 4
256
1.42 days
126.7
253.5
507
5.8
22.7
Wf 5
625
0.58 days
310.3
620.6
1241.3
2.38
9.28
Wf 6
1296
0.28 days
642.8
1285.7
2571.4
1.15
4.5
Wf 7
2401
0.15 days
1200
2400
4800
0.615
2.4
Wf 8
4096
0.089 days
2022.4
4044.9
8089.8
0.353
1.424
Wf 9
6561
0.055 days
3272.7
6545.4
1309.9
0.2255
0.88


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.


"A journey of a thousand miles, begins with a single step."
-- Confusian Proverb--


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The above is a work of fiction. All scientific facts are fictional, any resemblance to scientific facts living or dead is coincidental.

Copyright Garry Stahl: November 2000. All rights reserved, re-print only with permission.


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