MASTER WARP TABLE COMPARISON James Dixon
9408
This is the ONLY warp chart you'll ever need!
-------------W A R P--F A C T O R S-------------
Theoretical
/TRANSWARP\ JACKILL'S
TNG FASA FANDOM TMS TOS MULTIPLES OF THE
(2360s) (2360s) (2280s) (2270s) (2260s) SPEED OF LIGHT
Wf^(10/3) Wf^5 Wf^4 Wf^3+ Wf^3 x299,781 km/sec.
~~~~~~~~~ ~~~~~~~ ~~~~~~~ ~~~~~~~~ ~~~~~~~ ~~~~~~~~~~~~~~~~
1 1 1 1 1 1
1.866 1.516 1.682 2 2 8
2 1.587 1.782 2.16 2.16 10.079
2.297 1.741 2 2.52 2.52 16
2.688 1.933 2.279 3 3 27
2.828 2 2.378 3.175 3.175 32
3 2.08 2.498 3.389 3.389 38.941
3.482 2.297 2.828 4 4 64
3.737 2.408 3 4.327 4.327 81
4 2.52 3.175 4.666 4.666 101.593
4.257 2.627 3.344 5 5 125
5 2.924 3.824 5.979 5.979 213.747
5.016 2.93 3.834 6 6 216
5.196 3 3.948 6.24 6.24 243
5.278 3.031 4 6.35 6.35 256
5.762 3.214 4.304 7 7 343
6 3.302 4.451 7.322 7.322 392.498
6.498 3.484 4.757 8 8 513
6.899 3.624 5 8.55 8.55 625
7 3.659 5.061 8.69 8.69 656.135
7.225 3.737 5.196 9 9 729
7.33 3.773 5.259 9.1 9.146 765.055
7.403 3.798 5.303 9.2 9.246 790.555
7.475 3.822 5.346 9.3 9.347 816.615
7.547 3.848 5.389 9.4 9.448 843.242
7.619 3.872 5.432 9.5 9.548 870.441
7.692 3.897 5.475 9.6 9.649 898.219
7.943 3.981 5.623 9.6? 10 1000
7.968 3.989 5.638 9.7 10.034 1010.245
8 4 5.657 9.7? 10.079 1024
8.398 4.132 5.891 9.8 10.638 1203.979
8.586 4.193 6 9.8? 10.903 1296
8.655 4.215 6.040 9.8? 11 1331
9 4.327 6.240 9.8? 11.489 1516.381
9.173 4.383 6.342 9.9 11.739 1617.612
9.2 4.4 6.372 9.9? 11.814 1649
9.3 4.441 6.447 9.91? 12 1728
9.6 4.531 6.61 9.93? 12.405 1908.912
9.? 4.66 6.846 9.95? 13 2197
9.? 4.743 7 9.96? 13.391 2401
9.? 4.872 7.238 9.97? 14 2744
9.9 4.977 7.433 9.98? 14.069 3052.975
9.9? 5 7.477 9.98? 14.62 3125
9.9? 5.078 7.622 9.98? 15 3375
9.9? 5.278 8 9.992 16 4096
9.9? 5.474 8.372 9.996 17 4913
9.9? 5.665 8.739 9.997 18 5832
9.9? 5.8 9 9.998 18.721 6561
9.9? 5.851 9.1 9.998 19 6859
9.9? 6 9.391 9.999 19.812 7776
9.99 6.02 9.431 9.999 19.927 7912.349
9.99? 6.034 9.457 9.999 20 8000
9.99? 6.31 10 9.999 21.544 10000
9.99? 7 11.386 9.999 25.615 16807
9.99? 8 13.454 9.999 32 32768
9.99? 9 15.588 9.999 38.941 59049
9.99? 10 17.783 9.999 46.416 100000
9.9999 11.376 20.893 9.999 57.543 190536.012
10 UNATTAINABLE? 10 INFINITE VELOCITY?
NOTES (From Left-most Column to Right-most Column)
--
0. Warp 1 on all scales is lightspeed. ? indicates a missing digit not a
questionable number.
1. For TNG warp factors the general equation is Wf^3.33 up through warp
factor
afterwards an asymptotic curve comes into play with Warp 10 supposedly an
unreachable "infinite" speed. Various formulas have been created to compute
relative lightspeed velocities though all have been unsatisfactory...
From RIME net I got this simple formula which holds up for TNG warp factors
above and below warp 9: V=Wf^(10/3)*(1+(Wf/9)^100/18323/(10-Wf)^1.25).
The values produced are fairly close to that in the TNG Technical Manual.
A text file called Not The Technical Manual provides this short and sweet
formula: V=Wf^(10/3)+(10-Wf)^(-11/3). Warp factors under 9 give us a slight
problem here: they're all slightly above the plain and accepted Wf^(10/3)
values. Yet otherwise this formula is the simplest next to the Writer's
Technical Guide (which is more a rule of thumb than a formula).
Finally, a man named Kraschinski tackled the problem from a different angle.
He drew strictly upon given warp values above warp 9 in the various
publication
yielding a most complex equation, though one he claims yields very accurate
values: 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. Long, messy, but it works and quite well.
The Writer's Technical Guide gives this formula: V=(Wf^X)C where V is
Velocity,
Wf is the warp factor and X is the (series dependent) exponent. X is 10/3
for
warps 1 through 9, above this the following is substituted for X:
Warp 9.6 X = 3.34
Warp 9.9 X = 3.5
Warp 9.99 X = 3.9
Warp 9.9999 X = 5.28
And these values I have used for the TNG scale above. Rounded off, they
match
up with those in the Star Trek Encyclopedia of Okuda's, with the exception of
Warp factor 9 (199,516) which I'm considering erroneous.
None of the above approaches to the TNG warp asymptote values give identical
results. Generally, the closer to warp 10 one gets, the further the values
deviate. For this reason I have not used any one of the above save for the
Writer's Guide approach and values...
2. According to the Writer's Guides and such, the "Galaxy" class "Enterprise"
has a maximum safe cruising speed of warp 6 (392c), a maximum speed of warp
9.2
(1649c), a maximum rated speed of warp 9.6 (1909c) maintainable for 12 hours,
and warp 9.9 (3053c) results in automatic shutdown of the engines after 10
minutes. However, after "Force of Nature" the Federation-wide speed limit,
regardless of engine capabilities, was set at warp factor 5 (214c). We are
als
told in the TNG Technical Manual that subspace radio travels at a maximum
speed
of warp 9.9999 (190536c).
3. According to these same reference books, warp 10 is an unattainable
"infinite" speed on the TNG warp scale. For a ship to reach warp 10 would
mean
that it would occupy all points in the universe simultaneously and travel
time
would be meaningless. To reach warp 10 requires infinite energy. Now the
problem with this is that onscreen information says otherwise.
"Where No One Has Gone Before": involves the "Enterprise" traveling faster
than
warp 10, along with the discussion of a new "Kosinksi" warp scale for above-
warp-10 speeds.
"Time Squared": brings up the discussion of time travel. Riker tells Picard
that theoretically traveling faster than warp 10 would result in time warp.
This suggests that warp 10 is a barrier--a barrier which can be surpassed.
Otherwise, how would one travel faster than "infinite speed"?
"All Good Things...": The future "Enterprise" and "Pasteur" retreat at warp
13.
It has been suggested that this could be another warp scale. Maybe, maybe
not.
The TNG Technical Manual says that this is bunk, that warp 10 is infinite
speed
and that the "Enterprise" really traveled at warp factor 9.9999999996 in the
episode "Where No One Has Gone Before." But I think the onscreen information
weighs a lot more in favor of warp 10 being more akin to the sound barrier,
not
some "infinite" speed atop of an asymptote, simply an unreachable velocity.
4. There are two Transwarp Factor columns. The first was developed and
used by
the FASA roleplaying game, simply taking the warp factor to the 5th power to
yield relative lightspeed velocity. This has always been considered to be
"too fast" to be realistic. The 2nd column is the more popularly accepted
Wf^4
Transwarp system used by more serious Technical Fandom publications (although
the FASA system has been carelessly substituted at times!). It has its
origins
in the erroneous old Spaceflight Chronology book and the theoretical
"superwarp
drive which apparently evolved into Transwarp. Either scale is open-ended
with
no upper limits and no asymptotes (at least there's absolutely nothing to
suggest otherwise).
5. Jackill's warp scale comes from the two Jackill's Reference Manuals
publishe
apparently in the late 2270s. These two booklets are the Only sources which
employ such a scale and it is included here for the same reason the outmoded
FASA Transwarp scale is: for completeness. It is identical to the classic
warp
scale (Wf^3) up until around warp factor 9. Afterwards, as with the TNG warp
scale, the factors go asymptotic until warp 10 is an unreachable "infinite"
speed. The obvious problem with this scale is evident above warp 17 (classic
scale): it takes 5 digits to give a meaningful velocity! For this reason it
was probably phased out in no time at all, with the classic warp scale re-
instituted...
6. The 5th column is the classic V=Wf^3 warp scale. The easiest to calculate
and the longest one in use. Star Trek Maps states it was instituted back in
2161 with the development of the Quantum II Time Warp drive variant.
Probably
during the first century of warp drive, faster than light velocities were
simply expressed as multiples of lightspeed. Warp factor was originally
known
as Time Warp Factor and trimmed down over the years. The scale has no
asymptote
and is used throughout the 23rd Century (it's still uncertain as to when
the TNG
scale went into use). It wasn't until 2243 (ST Maps) that the "Time
Barrier" of
warp 4 was broken by intermix improvements. Although there are records of
ship
reaching as high as warp 10 years earlier, this apparently applies to time
dilation effects experienced above warp 4. Warp 6 (216c) was the cruising
speed
of "Constitution" class heavy cruisers, warp 8 (513c) was the emergency
speed.
These values also generally applied to most other Class I ships of the line,
up until the development of linear warp drive in the late 2260s which bumped
up the cruising speed and maximum speed to warp 8 and 12 (1728c) respectively
for "Enterprise" class heavy cruisers. Even before engine upgrade, however,
the "Enterprise" had already achieved a staggering warp 14.1 (2803c) when her
matter-antimatter integrator was fused ("That Which Survives")! The upgraded
"Enterprise (II)" class heavy cruisers reportedly had cruising velocities of
warp 9 (729c) and maximum velocities of warp 13 (2197c)--other reports state
as high as warp 18.6 (6435c)! Refinement continued until around 2290 when
specially designed perimeter action ships could achieve speeds in excess of
war
21 (9261c) during absolute battle emergency conditions. Why ships in TNG's
time
can't match these velocities is unknown. Perhaps a matter of the larger
hulls/
additional drag? Safety considerations considering the large civilian
(family)
populations?
7. The TOS table seems inadequate considering the many systems the old
starship
"Enterprise" has visited. Cochrane's Factor is a "fix" for this problem,
first
postulated by Geoffrey Mandel back in the 1970s. Essentially it assumes that
a variable taking into account space density known as Cochrane's Factor acts
as a linear shortcut for warp driven ships. Going back to the detailed nav-
igational info in the episode "That Which Survives" the value of 1292.7238
was
factored out: the "average" value of Cochrane's Factor in UFP space. This is
multiplied by the warp factor cubed to give the "real" velocity of the ship,
or more realistically the ship's true E.T.A. This holds true since warp
drive
functions by "grasping" at the space-time matrix and more mass in space
(which
is not present in subspace, where space isn't curved) the shorter the travel
time between points. So while the "Enterprise" can travel from the
vicinity of
Earth to the galactic rim and back--several times ("Where No Man Has Gone
Before" "By Any Other Name" "Is There In Truth No Beauty?" etc.)--it will not
take years even at her maximum speed of warp 8 (512c) as it would in "flat"
space where a perfect vacuum exists (as in the void between galaxies) and
CF is
the value of 1.00. In such cases, the "corrected" equation of V=XxWf^3
(where
or Chi, is Cochrane's Factor) reverts to the classic V=Wf^3. When one
consider
the TAS episode "The Magicks of Megas Tu" and the 5th movie "The Final
Frontier
where the "Enterprise" voyages to the galactic core and back again in minimal
time, this formula can't be ignored (even if these two examples are the worst
of their mediums!). Star Trek Maps states that Cochrane's Factor was
discovered
in 2053 and here is a table of "corrected" warp speeds. One wonders if CF
applies to the TNG warp equation and/or others...
Wf Wf^3 XWf^3 Time per Parsec
Warp with C.F. hrs.min.sec.
---------------------------------------
1 1 1,292.7238 22 05 29
2 8 10,341.7904 02 45 41
3 27 34,903.5426 00 49 05
4 64 82,734.3232 00 20 43
5 125 161,590.4750 00 10 36
6 216 279,228.3407 00 06 08
7 343 443,404.2634 00 03 52
8 512 661,874.5856 00 02 35
9 729 942,395.6502 00 01 49
10 1,000 1,292,723.8 00 01 19