Subject: REC.ARTS.STARTREK.TECH FAQ: Warp Velocities
From: [email-masked] (Joshua Sean Bell)
Newsgroups: rec.arts.startrek.tech

Warp Velocities FAQ
                                       
   Last modified: Friday, 25 April 2003 02:03 AM -0700
   Maintained by: Joshua Bell, [email-masked]
   Archive site (WWW): http://www.calormen.net/Star_Trek/
   FTP site (text versions): ftp://ftp.cc.umanitoba.ca/startrek/minifaqs/
     _________________________________________________________________
   
   Copyright (c) 1994-2003, Joshua Bell. Not in the public domain.
   Permission to distribute this document, unedited and including this
   copyright notice is granted, provided no fees are charged for access
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   Star Trek (R), Star Trek: The Next Generation (R), Star Trek: Deep Space
   Nine (R) and Star Trek: Voyager (R) are trademarks of Paramount Pictures
   registered in the United States Patent and Trademark Office.
     _________________________________________________________________
   
   This FAQ does not discuss subspace or the mechanics of warp travel.
   See the Warp and Subspace FAQ for discussions of the how warp drive
   works, and what subspace actually is.
     _________________________________________________________________
   
Contents:

    1. TOS-era: The Original Series
    2. TNG-era: The Next Generation, Deep Space Nine, and Voyager
    3. AGT-era: "All Good Things..." (TNG final episode)
    4. VOY-era: Transwarp Frogs In Spaaaaaaace!
    5. Speed Limits
    6. Q & A
    7. Contributors
    8. Glossary
    9. References
     _________________________________________________________________
   
   In all of the formulas in this FAQ, the following hold:
   
   v   velocity
   c   speed of light in vacuum
   W   Warp factor
   ~   approximate
   ^   exponential operator ("to the power of")
   log log base 10
   ln  log base e
     _________________________________________________________________
   
   "Who the heck is Mike?"
   
   Mike is Michael Okuda, a member of the Star Trek television production
   crew as a scenic artist and technical advisor. He designs the computer
   displays and alien writing seen in TNG, DS9 and VOY. He is also
   co-author of the TNG Technical Manual, which mentions that the the TNG
   Warp formula exists in a Excel spreadsheet on his Macintosh. Thus,
   when it comes to warp calculations, Mike is god. At the very least, a
   patron deity. He is also co-author of the Encyclopedia and Chronology.
   
   "So who's Rick?"
   
   Rick is Rick Sternbach, the "other" author of the TNG Technical
   Manual, and the main writer of the DS9 Technical Manual. He is also a
   member of the Star Trek television production crew, designing most of
   the ships and props seen in TNG and VOY.
     _________________________________________________________________
   
1. TOS-era: The Original Series

   The original series warp equation is generally accepted to be:
       v = (W ^ 3) * c

   But this has never appeared in any episode. However, it has such wide
   acceptance that it has pretty much stuck. It's even in the
   Encyclopedia.
   
   Boris S. writes:
   
     The equation is almost certainly the work of TOS producers. Stephen
     Whitfield extensively researched the show in the period of 1967-68
     and published the information in his book The Making of Star Trek
     (1968). He states that Warp 1 is the speed of light, Warp 3, 24
     times the speed of light, Warp 6, 216c and Warp 8, 512c. With the
     exception of the value for Warp 3 (which should be 27c), the W^3*c
     formula holds. Whitfield almost certainly obtained the numbers from
     the TOS writer's guide which contained a small technical manual.
     
   This chart compares TOS-era Warp speeds with the speed of light:
   
   Warp Factor Velocity
   1           1        Speed of Light
   2           8
   3           27
   4           64
   5           125
   6           216      Maximum stable speed of NCC-1701
   7           343
   8           512      Emergency speed of NCC-1701
   9           729
   10          1000
   11          1331
   12          1728
   13          2197
   14.1        2803     "That Which Survives" [TOS]
   
   It is also generally accepted that the TOS scale was also used for the
   first few movies. Since speeds are rarely quoted in the movies,
   however, that's only speculation.
   
   Joe Chiasson, describing Star Trek Maps, a map and manual combination
   by Bantam Books from 1980, offers:
   
     The booklet contains quite a lot of written information on the
     development of warp drive systems and how warp travel is affected
     by matter density in a given area of space. The above formula was
     written as v = Wf^3 * c. This was further modified to include the
     Greek letter chi (X), which was a variable denoting the local
     density of matter, which changed depending on where you happened to
     be. So the proper formula for TOS level warp drive is
        v = c * Wf^3 * X

     where Wf was the warp factor, and c was the speed of light.
     Included was a table of corrected warp speed for a given average
     value of X.
     
   Wf Wf^3 X * Wf^3 Time per parsec
   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 1000 1,292,723.8    00 01 19
   
   This correction factor does make a lot of sense, given that v = W ^ 3
   by itself is almost ludicrously slow given the speeds quoted by TOS.
   Joe also suggests that by the time of TNG warp fields have been
   refined to the point that the chi factor is dropped from the formula.
   I think that the numbers are a little too high, however, when compared
   to TNG speeds.
   
   As a side note, wf(n) = n * c appears in James Blish's TOS script
   adaptations, which have been widely read, so you may see that formula
   cropping up from time to time as well. Those speeds would be
   ridiculously slow, so that formula isn't really worth considering.
   (Thanks to Taki Kogoma for pointing that out.)
   
   John "Eljay" Love-Jensen points out that in "By Any Other Name" [TOS]
   the Kelvans were using there technology to propel the Enterprise "to
   Andromeda, 300 years of travel". Andromeda is 2.3 million light-years
   away. For 300 years of travel, that translates into Warp 19.7! They
   probably intended to accelerate to that speed once they made it
   outside the galaxy, and the Enterprise didn't end up going that fast
   during the episode, but it means they thought it was possible for the
   ship to make it.
     _________________________________________________________________
   
2. TNG-era: The Next Generation, Deep Space Nine, Voyager

   By the time of Star Trek: The Next Generation, the warp scale has
   changed. Warp 1-9 are roughly the same, but Warp 10 is infinite speed.
   Going Warp 10 or faster is hogwash on the TNG scale. It isn't a speed
   barrier that can be or needs to be broken, but an energy barrier.
   
   At least, that's what the Tech Manual says. Many fans disagree, saying
   that this has been contradicted on air, most clearly by the episode
   "Where No One Has Gone Before" [TNG] where someone says "We are
   passing Warp 10." See the Warp and Subspace FAQ for more discussion of
   this.
   
  Graph
  
   Here's the graph of warp vs. speed and warp vs. power consumption from
   the Technical Manual:

  Chart
  
   This chart was compiled with data from episodes, the Encyclopedia, and
   the TNG Technical Manual:
   
   Warp Factor Velocity Source  Comment
   1           1        TM      Speed of Light
   2           10       TM
   3           39       TM
   4           102      TM
   5           214      TM      Federation speed limit (2370)*
   6           392      TM
   7           656      TM
   8           1024     TM
   9           1516     TM      Defiant maximum speed**
   9.2         1649     Encyc
   9.6         1909     Encyc
   9.9         3053     Encyc   NCC-1701-D maximum speed
   9.975       ?        Episode Voyager "cruise velocity"***
   9.99        7912     Encyc
   9.9997      ~198696  TM      (derived) Subspace radio speed
   9.9999      199516   Encyc   Maximum boosted subspace radio speed
   
     * * "Force of Nature" [TNG]
     * ** "The Sound of Her Voice" [DS9]
     * *** "Caretaker" [VOY]
       
  Sources
  
   The Tech Manual (on page 111) says that a subspace radio signal
   travels at Warp 9.9997, and takes 45 minutes to reach 17 light years,
   which works out to 198696c.
   
   As an interesting anomaly, Pete Carr also points out the following
   tidbit from the Tech Manual:
       ______________________________________________________________
     
     ... the TM goes on to say that TNG Warp 9.7 is about 14.1 on the
     TOS scale. So [TNG Warp] 9.7 ~= 14.1^3 [c] and 14.1^3 [c] = 2803
     [c]. I went and graphed the new value with our current values.
     Unfortunately the new value doesn't fit into the exponential curve
     ... it should be lower.
       ______________________________________________________________
     
   I suspect Mike made a rounding error; TOS Warp 14.1 is much closer to
   TNG Warp 9.8 by all of the accurate formulas that have been found or
   sheer reckoning off the graph.
   
  Formulae
  
   Unlike TOS (where we have a formula but no scale), for TNG we have a
   scale but no formula! The reason for this is that the graph was drawn
   by Mike Okuda rather than calculated, as is related in the following:
   
   On June 22, 1995, Jeff Reinecke forwarded the following letter from
   Michael Okuda to rec.arts.startrek.tech:
       ______________________________________________________________
     
     Date: Fri, Jan 27, 1995 02:09 AM EST
     From: MOkuda
     Subj: Re: Star Trek Warp
     To: Yar of Spit
     
     The warp factors we've used in ST:TNG were computed in an arbitrary
     way to fit some specific characteristics we needed.
     
     First, the speed for any given warp factor had to be greater than
     it was in the original Star Trek series. This was primarily to
     satisfy fan expectations.
     
     Second, the new warp speeds couldn't be TOO much faster, or it
     would be possible for the ship to cross the galaxy in a fairly
     brief time. (In a way, maintaining this restriction made Voyager's
     story situation possible. If we hadn't done this, Voyager could
     have gotten home too quickly.)
     
     We used an exponent of (I think) 3.33 or 3.33333... for warp
     factors less than 9.
     
     Between 9 and 10, I gradually increased the exponent so that it
     approached infinity as the warp factor approached 10. Lacking
     knowledge of calculus, I just drew what looked to me to be a
     credible curve on graph paper, then pulled the points from there. I
     think I re-created the curve fairly accurately in the Star Trek:
     The Next Generation Technical Manual.
     
     Hope this helps.
     
     -Mike
       ______________________________________________________________
     
   So it looks like there isn't a grand formula to end all formulas after
   all!
   
   On May 29th, 1996, Dominic Berry wrote:
       ______________________________________________________________
     
     Since Mike calculated the speeds for the various warp factors up to
     9 simply using the exponent 10/3, it is more sensible to use a
     piecewise function for the speeds that gives an exponent of 10/3
     for W<9 and gives higher exponents for higher warp factors. My
     suggestion is
                                                   n
                ( 10/3  +  u(W-9) * A * (-ln(10-W))  )
          v = W

     where u is the step function, i.e. u(x)=0 for x<0 and u(x)=1 for
     x>0. Note that the term multiplying the step function is zero at
     W=9, so the step function introduces no discontinuity in the
     formula. If the value of n used is greater than 1, then both the
     function and its derivative are continuous at W=9. (In order to
     have continuous higher order derivatives a function like c(w) could
     be used.)
     
     [Martin Shields amends that with:
     
     There is a better alternative to the step function as follows:
       / 0 ; x <= 0
       |
u(x) = <
       |
       \ e ^ ( -1 / (bx^2)) ; x > 0

     Where b is a constant whose value remains to be determined. This
     function is "infinitely smooth" (that is, no matter how many times
     you differentiate it, the value of the differential is 0 at x=0).
     As b approaches infinity, the function approaches the pure step
     function.
     
     ]
     
     I take A and n as
                      A = 0.03684678
                      n = 1.791275

     I then get the correct warp factors for W<9, and for the warp
     factors above 9 I get
                    Warp | Actual   Formula   Modified*
                  -------------------------------------
                  9.2000 |   1649      1641      1640
                  9.6000 |   1909      2019      2017
                  9.9000 |   3053      3035      3029
                  9.9900 |   7912      7939      7912
                  9.9997 | 198696     79352     79240
                  9.9999 | 199516    199415    199516

     [* Martin Shields offers A = 0.036528749373 and n = 1.79522947028
     which are slightly better for some values.]
     
     My formula agrees with the values for warp factors of 9.2, 9.9,
     9.99 and 9.9999 to within 0.6%, though it is about 6% out at 9.6
     and it is way out at 9.9997. If you calculate the exponents for the
     data points at 9.9997 and 9.9999, however, you get 5.29826 and
     5.30000, suggesting that the exponent 5.3 was used to calculate the
     speed at both of these warp factors. Since the exponent should be
     increasing with the warp factor, one of these data points should be
     ignored. Ignoring the data point for W=9.9997, my formula is
     perfect for W<9, and is slightly better than that of Tahk for W>9.
     
     Now the exponent corresponding to the speed given for W=9.2 was
     about 3.33810. If we linearly extrapolate this to W=9.6 then the
     exponent should be about 3.34763. The exponent corresponding to the
     speed for W=9.6 is 3.34002, which is slightly less! This means that
     a formula for the exponent that gives values similar to the given
     values for warp factors of 9, 9.2 and 9.6 must have a derivative
     that decreases. (This means that the function for the exponent
     would have to curve downwards between 9.2 and 9.6.) Since this is
     not a desirable property if we want an exponent that gradually
     increases, I also left out the data point for W=9.6 in fitting the
     curve.
     
     I mentioned before that the speeds for W=9.9997 and W=9.9999 seemed
     to have both been calculated using an exponent of 5.3. If you
     calculate the exponents corresponding to the other warp factors
     above 9, you get:
                     Warp  | Exponent
                    -----------------
                    9.2000 |  3.33810
                    9.6000 |  3.34002
                    9.9000 |  3.50000
                    9.9900 |  3.89998

     The speeds for warp factors of 9.6, 9.9 and 9.99 were obviously
     calculated using exponents of 3.34, 3.5 and 3.9 respectively, and
     the speed for a warp factor of 9.2 was probably calculated using an
     exponent of 3.338. Therefore it is not reasonable to ascribe any
     greater accuracy to the warp factors given than is implied by the
     number of significant digits in the exponents used to calculate
     them. By this criterion my formula gives speeds well within the
     uncertainty for warp factors of 9.9, 9.99 and 9.9999, although it
     gives an exponent of about 3.336 for W=9.2, which is a little low.
     Since the points were originally taken off a hand drawn curve, this
     is still reasonable accuracy.
       ______________________________________________________________
     
   I used to have a bunch of formulae in here from various posters who
   made some pretty good attempts at finding the Holy Grail of an
   accurate formula. However, due to length considerations I'm only going
   to keep the current best. Older formulae (basically an excised chunk
   of this FAQ) can be found at
   http://www.calormen.net/Star_Trek/FAQs/warp_formulae.html, but that
   page will probably never look too pretty.
   
   Martin Shields has a warp speed calculator up on his web site:
   http://www-personal.usyd.edu.au/~mshields/TV/ along with discussion of
   the formula used.
   
  Evidence
  
   Do any of these values actually match up with what we've seen on the
   show? There are often claims that these speeds are much to slow to
   allow the kind of adventuring that the Star Trek series portrays. But
   amazingly enough, when they do quote numbers and we can time things
   without cuts (wherein we may miss hours of ship-time), the numbers do
   match up:
     * "The Most Toys" [TNG]:
       Ges Seger offers:
       
     The numbers I remember were about how far a ship doing warp 3 for
     23 hours would travel, and the answer they came up with was 0.102
     light-years. I worked the math just now and got 0.1022 light-years.
     * "Bloodlines" [TNG]:
       Riker calculated in his head the time required for the Enterprise
       to travel 300 billion kilometers at Warp 9, and gets 20 minutes:
       Warp 9 = (300e12 m) / (20 min * 60s/min) ~= 2.5e11 m/s
       From the chart: Warp 9 = 1516c ~= 4.548e11 m/s
       Discrepancy? Riker did the calculations in his head in about 5
       seconds given arbitrary numbers. He's within a factor of two, so I
       won't complain. Bok's ship was "holding position", so it was a
       simple flight path.
     * "Emergence" [TNG]:
       The Enterprise jumped to Warp 7.3, and traveled 30 billion
       kilometers in a couple of minutes.
       All of the formulas we have for warp speeds predict Warp 7.3 to be
       approximately 746c. Using c = 3e8 m/s, we get v = 2.24e11 m/s. 30
       billion km = 3e13m. So t = 134s, or just over two minutes.
     * "Allegiance" [TNG]
       c/o Boris S.:
       
     Wesley gives the ETA of the Enterprise to Lonka Pulsar as 34
     minutes at Warp 7. When Picard orders Warp 2 instead, he comments
     that at that speed it would take 31 hours to get there. Using the
     first two data points, 34 minutes at Warp 7, I calculated a
     distance of 4.012e14 m. At Warp 2, it would take the Enterprise 37
     hours to travel that distance. This clearly shows that the TNG
     production staff used the established warp scale when they
     calculated the travel time, and the 6-hour discrepancy can be
     explained by the use of a less accurate value for the speed of
     light.
     * "Clues" [TNG]
       c/o Boris S.:
       
     the Enterprise is transported 0.54 parsecs by the Paxans. Riker
     says something like "nearly a day's travel in 30 seconds" (I cannot
     give you the exact quote since I am watching TNG on German TV). At
     Warp 6 (Enterprise cruising speed), the Enterprise would need 1.6
     days to travel that distance. Given that Riker calculated the
     travel time without a computer in a couple of seconds, you can
     allow for the deviation. On the other hand, if you calculate the
     travel time at Warp 7, you get 23.5 hours, which fits the quote.
     * "Caretaker" [VOY]
       The basic numbers involved in Voyager's journey home support the
       TNG formula. Voyager is transported 70,000 LY from home, and
       expects to take 70 years to make the journey. This speed of 1000c
       corresponds closely to Warp 8, a high but conceivable average
       speed for a long journey for an Intrepid-class ship.
     * "The 37s" [VOY]
       Paris states that Warp 9.9 is equal to 4 billion miles per second.
       Unfortunately, that turns out to be over 20,000c, which doesn't
       fit in at all. Bummer. But then, Paris is an idiot.
     * "Maneuvers" [VOY]
       Kim states the ships speed as 2 billion km/s, which is 2*10^12
       m/s, which is roughly 6667c. This is in the same ballpark as what
       Warp 9.975 (Voyager's top cruise speed), it turns out.
       Boris S. speculates that if Okuda picked an exponent of 3.83 (a
       nice roundish number off the graph) for Warp 9.975, you get 6696c.
       Pretty close to the value above.
     * "Threshold" [VOY]
       Commentary aboard the ship confirms that Warp 10 is indeed
       infinite speed.
     * "Dreadnought" [VOY]
       c/o Boris S.:
       
     B'Elanna gives the distance to Rakosan system as more than 10
     light-years. A day or so later Chakotay states that the vessel has
     resumed its journey at Warp 9 and will reach Rakosan V in 51 hours,
     which works out to a distance of 8.8 light-years.
       
  Counter Evidence
  
   There have been several times where the warp velocities proposed don't
   match what we see on-screen. The most blatant example of this kind is
   a call by the captain to head somewhere at Warp 1, or some other
   ridiculously slow speed. This happened several times in TOS, but does
   crop up from time to time. Here are some examples:
     * "Where Silence Has Lease" [TNG]:
       Roger M. Wilcox offers:
       
     The Enterprise-D gets sucked into a black nebulous void. Before
     Nagilum announces his/her/its presence to our intrepid crew, they
     find an opening in the void "1.3 parsecs away". (1.3 parsecs would
     be 4.243 light-years.) Picard orders the crew to head for the
     opening at Warp 2.
       
   It may be best to just pretend that these didn't happen, or
   rationalize them on a case by case basis (going Warp 1 until outside
   of the solar system, then switching to a higher speed "off camera").
   
   ...
   
   A bigger problem which crops up on rec.arts.startrek.tech is the size
   of the Federation. Sizes of up to 10,000 LY across have been quoted as
   diameters, and this corresponds to the occasional graphic displayed on
   screen showing the Federation's size and position within the galaxy.
   Other evidence points to a somewhat smaller size, but such questions
   as the distance from Earth to Bajor appear to present a paradox: some
   routes between Federation locations which are known to be far apart
   are traveled much more quickly than the TNG formula appears to allow.
   
   The leading speculation on the newsgroup is a concept called "Warp
   Highways". Distinct from wormholes, these "highways" represent either
   natural (pre-existing) or artificial (thanks to heavy traffic)
   pathways where warp travel is much faster than the TNG formula, which
   represents a baseline.
   
   The highways do not require additional technology beyond warp drive.
   Highways are not easily detectable in unknown space. This means that
   an exploration ship, such as the Enterprise, or a ship in unknown
   territory, such as Voyager, will travel between two arbitrary points
   at the nominal velocities presented in the TNG formula. A well-known
   region of space - such as the route from Bajor to Earth - would
   probably contain several well-known warp highways and allow less
   powerful ships to make the route in weeks rather than years, and
   top-of-the-line Starfleet ships to make the trip in mere days. Contact
   with local civilizations would allow Voyager to take shortcuts through
   the Delta Quadrant - which they frequently seem to.
   
   Perhaps the Hekaras Corridor in "Force of Nature" [TNG] is one such
   route, explaining the frequent travel in that area. The whole notion
   of starship travel affecting local subspace properties in a permanent
   way supports the notion that at least some warp highways are created
   by frequent warp travel - that is, as a route is used it becomes more
   efficient. Other speculation includes the notion that gaseous
   anomalies are indicators of the presence of warp travel. Why else
   would Excelsior - one of Starfleet's latest ships - be engaged in
   charting such anomalies in Star Trek IV?
   
   This is strongly reminiscent of the X (chi) factor first presented in
   Star Trek Maps, where the warp equation varies with local spatial
   conditions.
   
   (Other speculation or comments?)
   
  Why did it change?
  
     * In terms of a real-world "Star Trek is just a TV show" reason,
       Gene Roddenberry himself put Warp 10 at infinite speed, according
       to the TNG Tech Manual. To keep the scale fluid, Mike and Rick
       made it asymptotic at Warp 10, while starting off similar to the
       TOS scale.
     * From the characters' perspective, the best explanation is that the
       TOS scale was established before warp was fully understood.
       Looking at the graph, you can see that the energy costs for
       cruising at integral Warp values are much lower than for
       non-integral Warp factors. The first explorers to travel past Warp
       1 must have realized this. Since for Warp values in the 1-3 range
       follow the v = (W ^ 3) * c formula, it makes sense that a scale
       based on the formula would come into use.
       When ships started cruising at Warp values larger than 5, the
       difference between what v = (W ^ 3) * c predicted to be the most
       energy efficient speeds and what actually were must have become
       noticeable. It may have taken a long time for a new, accurate
       scale based on new observations came into use. (Look at the USA
       and SI, for an example of a large sociopolitical body taking a
       long time to adopt a more useful, universally used scale.)
       Sulu's readings of Warp velocity in Star Trek IV seem to hint that
       the Klingons had moved to an accurate scale by the 2280s, but the
       Federation didn't catch up until much later, even though it must
       have been painfully obvious that the old scale was next to
       useless. Fortunately, some time before TNG, the new accurate scale
       was adopted by Starfleet.
     _________________________________________________________________
   
3. AGT-era: "All Good Things..." (TNG final episode)

   Quoted in the final episode of Star Trek: The Next Generation, in a
   possible or imaginary future, is the speed Warp 13. Both Admiral Riker
   and Captain Beverly Picard call for this speed, and at another point
   in the episode, Admiral Riker calls for "maximum warp", which is
   either Warp 13 or greater.
   
   While we haven't a clue how fast this is, they're presumably faster
   than Warp 9 on the TNG scale, and necessarily slower than Warp 10 on
   the TNG scale (since TNG Warp 10 is infinite speed). A few
   possibilities present themselves:
     * Just another technical muck-up. (But that won't stop this intrepid
       FAQ maintainer!)
     * Warp 10-13+ are shorthand for Warp 9.x. One possibility is that
       9.90 is called Warp 10, 9.91 is called Warp 11, etc.
     * New warp technologies provide at least 13 power usage minima
       between c and infinite speed, instead of the 9 possible with old
       warp technologies.
     * Further research revealed that there were more than 9 minima
       accessible with traditional drives, and that they simply required
       more power to attain than had been previously attempted, but less
       power to maintain than 9.x values.
     * The Federation switched back to the TOS scale.
       
   The last one is demonstrably incorrect (see below). Among the others,
   there's no way to tell which is correct. Sharp-eyed Boris S. found the
   following explanation by Andre Bormanis, Star Trek's science advisor:
   
     I raised that question in a TECH note. Basically, the idea there
     was that they recalibrated the warp scale. I don't think that ended
     up in the final draft teleplay, but the idea there was that if
     you've got ships that can routinely travel at speeds in excess of
     Warp 9, then maybe it makes sense to recalibrate your speed scale
     so that Warp 10 is no longer infinite velocity. Maybe Warp 15 will
     be the ultimate speed limit, and Warp 13 in that scale will be the
     equivalent of warp 9.95 or something like that.
     
                                                     OMNI, October 1995.
     
  Evidence
  
   Tom Bagwell writes:
   
     I timed the interval in AGT between when Data reported the second
     Klingon ship to be disengaging and when Riker's helmsman reported
     it to be a "half a light year away" at about 22 seconds, so I
     calculated the speed assuming 20 seconds to reach 1/2 a light year
     and assuming 30 seconds to reach 1/2 a light year.
     
     At 30 seconds, the velocity would be approximately 525,960c which
     equates to roughly Warp 9.97244 on the TNG scale and approx. Warp
     81 on the TOS scale.
     
     At 20 seconds, the velocity would be approximately 788,940c which
     equates to roughly Warp 9.97535 on the TNG scale and approx. Warp
     92.4 on the TOS scale.
     
   Martin Shields updates that with:
   
     Assuming 30 seconds to travel 1/2 a light year, v = 525,960c which
     he estimates is Warp 9.97244 on the TNG scale. However, the Tech
     Manual and Encyclopedia tell us that Warp 9.9999 (a higher warp
     factor) is set at 199,516c (less than half the speed calculated).
     This figure comes from the M = -11/3 equation. My equation gives
     the TNG warp factor of 9.999974 (approx.) which better fits the
     known data.
     
   If a damaged AGT-era Klingon ship can limp home at TOS Warp 81, while
   a Federation ship trying to be sneaky can only manage TOS Warp 13, the
   Klingons have nothing to worry about. I consider this adequate
   evidence that the TOS scale was not returned to use in the AGT future.
     _________________________________________________________________
   
4. VOY-era: Transwarp Frogs In Spaaaaaace!

   As you may have guessed, the .tech community was less than impressed
   with "Threshold" [VOY] in which Voyager - a ship running low on
   supplies, with half its crew dead, stranded away from repair or
   research facilities, on the other side of the Galaxy from the
   Federation - manages to upgrade one of its never-ending supply of
   shuttles to make a Transwarp flight, something that has defied the
   best minds in the Federation for a century. Things go
   higglety-pigglety after that, and many people (including some of the
   production crew) just pretend it didn't happen.
   
   Forgiving that, however, the episode's technobabble isn't too bad. The
   Voyager crew mention how Warp 10 = Infinite Speed = being everywhere
   at once. An interesting tidbit is that once Transwarp drive is active,
   the shuttle's speed registers at Warp 10.
     _________________________________________________________________
   
5. Speed limits

   "What's this about a Warp 10 barrier?"
   
   In the TNG scale, Warp 10 is infinite speed. As you approach a
   position on the graph corresponding to Warp 10, your power
   requirements increase astronomically compared to your increase in
   speed. But you can keep speeding up forever, unlike the light barrier,
   which keeps you from getting to the speed of light.
   
   In other words, keep piling on the 9s. Warp 9.99 is a lot faster than
   Warp 9.9, while Warp 3.99 is only marginally faster than Warp 3.9. The
   barrier is only one of energy, not velocity.
   
   Once again, in case you missed it, TNG Warp 10 is not a speed barrier;
   it cannot be broken like the sound barrier. Any warp factor greater
   than 10 must be on a different scale than the TNG scale (either TOS or
   AGT or something else), since a speed faster than infinite speed is
   nonsensical.
   
   ....
   
   "But in "Is There in Truth no Beauty?" [TOS] and "That Which Survives"
   [TOS], the old Enterprise went over Warp 14!"
   
   Yes, but that's on the old scale. By the new scale, that translates to
   about Warp 9.7 (TM), which the Enterprise-D can do for brief periods.
   The original Enterprise was being shaken apart. Voyager can cruise at
   that speed without blinking.
   
   ....
   
   "But in "Where No One Has Gone Before" [TNG] they went past Warp 10!"
   
   Chalk this one up to instrument failure. While Geordi did say they'd
   passed Warp 10, later in the episode they were booting along at some
   outrageously huge speed, while the instruments only read Warp 1.5. So
   there's canonical evidence that the Traveler's tweaking of the warp
   drive and the Enterprise's speedometer don't get along well.
   
   Daryle Walker points out that the real-world explanation for this is
   probably that the Warp 10 rule hadn't been established yet - this was
   an early first-season episode.
   
   ....
   
   "This new Warp 5 speed limit - what's up with that?"
   
   In "Force of Nature" [TNG] it is discovered that in the Hekaras
   Corridor, a region of space where warp travel is hindered except for a
   narrow path the intense use of warp drives in an already sensitive
   area can (over time) cause subspace rifts to form, where subspace
   manifests itself in real space on a macroscopic scale. This is not a
   good thing.
   
   "Does this take effect everywhere?"
   
   Yes. In "The Pegasus" [TNG] an Admiral Pressman gives Picard
   permission to travel faster than Warp 5 for the duration of the
   mission. Ditto in "Eye of the Beholder" [TNG], when Picard is given
   permission to exceed the speed limit to delivery needed medical
   supplies. The Encyclopedia concurs as well, naming Warp 5 as the new
   cruising speed for starships. Overkill? Probably. Typical bureaucratic
   overcompensation? Yep.
   
   ....
   
   "So what about in "All Good Things..." [TNG] and post-TNG shows?"
   
   It's safe to say that the U.S.S. Pasteur and U.S.S. Enterprise,
   cruising at Warp 13, were able to ignore the Warp 5 limitation
   enforced by Starfleet. While the limitation was mentioned in a few
   later TNG episodes, it was ignored in DS9 and VOY episodes set only a
   few years later. There are a few possible explanations. The first is
   that Starfleet simply repealed the ruling, and is allowing ships to
   muck up subspace. That isn't what we'd expect in the eco-friendly Star
   Trek Universe, however.
   
   Another is that changes to warp technology allow warp travel without
   the nasty side effects. Rumors abound that Voyager's folding nacelles
   and/or warp core design mitigate the effect, although Rick Sternbach
   (the designer of Voyager) isn't so sure. The most probable explanation
   is that internal technological changes allow warp drive without
   damaging subspace.
   
   Franz Joseph's "Field Restoration" nacelle end-cap, anyone? (Star
   Fleet Technical Manual)
     _________________________________________________________________
   
6. Q & A

   "What causes fractional warp speeds?"
   
   As you can see from the above chart, travelling at integral Warp
   factors is much more energy efficient. But there are times when a
   fractional value must be used - for example, staying a certain
   distance from another ship, or keeping pace with some phenomenon.
   Also, beyond Warp 9, only fractional speeds are possible. (Modulo "All
   Good Things..." [TNG], of course.)
   
   ....
   
   "Why not use impulse drive within the warp field to create a higher
   velocity?"
   
   There's no reason to think that a Newtonian drive (Impulse) would
   augment a non-Newtonian drive (warp). Also, consider that the maximum
   velocity attainable with a Newtonian drive is c. At Warp 2, which is
   ~= 10c, this gives you a whole 11c at maximum (overloading, fuel
   wasting) impulse. Warp 2.1 is about 12c anyway, so overloading the
   impulse drive doesn't get you much.
   
   "What about "The Corbomite Maneuver" [TOS] or The Voyage Home?"
   
   Kirk and Sulu use a combination of warp drive and Impulse to break
   free of the First Federation pilot craft. The combination of a tractor
   beam, impulse drive, and warp drive would be very strange, and many
   explanations come to mind, such as the warp field causing the tractor
   effect to "slip" away, while the impulse provides propulsion, or the
   impulse fighting the tractor beam inertially while the warp drive
   provides propulsion, etc.
   
   In The Voyage Home, for the trip back to the future, thrusters are
   used by Spock to get the last burst of speed just before entering time
   warp. Also, during both trips, the ship is brought out of time warp by
   braking thrusters. The H.M.S. Bounty is visibly moving slower than the
   speed of light toward the sun and certainly slower than the Warp 8
   quoted by Sulu, so the time warp slingshot (in an intense gravity
   well) may be one case where Impulse drives are useful to augment warp
   drives.
   
   ....
   
   "Whoah! Hold on! They must be moving faster - look at the stars that
   shoot past while they're in warp!"
   
   Joseph Haller offers:
   
     The most extreme ship induced speed discussed ... is W(ST:TNG) =
     9.97535, or 788,940c.
     
     This would give a characteristic angular speed for nearby stars of
     1578 arc-seconds per second or 1 degree every 2.3 seconds. This is
     indeed verified in the simulations. Travel at high warp speeds, on
     the ST:TNG warp scale, does not match very well the appearance of
     the bridge view screen on a typical episode. Indeed, most visible
     stars are not nearby but are further away with correspondingly
     lower angular speeds. I offer no solutions to this discrepancy
     other than the dramatic necessity that stars go whooshing by at
     high warp speed.
     
   Or should we give up so easily?
   
   There's a lot of support on rec.arts.startrek.tech for the notion that
   those things aren't really stars. For one, as the Enterprise drops out
   of warp (with the camera tagging along for the ride) some of the
   "stars" do some pretty strange things, such as suddenly angling off in
   various directions, disappearing, etc.
   
   Also, in Star Trek: First Contact, the Phoenix barely breaks Warp 1
   and stays relatively close to Earth, but we still see the streaks.
   Definitely not stars.
   
   The predominant theory is that what we're seeing are free particles in
   space interacting with the expanding boundaries of the warp field. As
   they cross the warp field, they are repeatedly accelerated to FTL
   velocities and then slowed to STL speeds, and start spewing out
   something like Cerenkov radiation, a (real!) bluish light emitted when
   particles moving faster than the local speed of light (in a dense
   medium) are forced to slow down. If not exactly Cerenkov radiation,
   then something similar.
   
   Jon Mitchell tells me that in the TNG video game for the Sega Genesis
   console platform states the streaks are part of the visual
   manifestation of Einsteinian space in subspace. So people other than
   us .techers have noticed this problem too.
   
   As a side note, in "The Cage" [TOS], the moving particles seen through
   the forward view-screen are explicitly identified as meteoroids.
     _________________________________________________________________
   
7. Contributors:

   John "Eljay" Love-Jensen Daryle Walker
   Roger M. Wilcox          Jon Mitchell
   Jonah Rapp               Boris S.
   Dominic Berry            Alex Tahk
   Jeff Reinecke            Martin Shields
   Joe Chiasson             Jason Hinson
   Greg Berigan             A.J. Madison
   Axis                     Sharon Collicutt
   Ges Seger                Michael M. Welch
   Tom Bagwell              Joseph Haller
   Chris Franklin           Pete Carr
   Taki Kogoma
     _________________________________________________________________
   
8. Glossary:

   c
          Speed of Light ( ~= 3 x 10^8 m/s )
          
   FTL
          Faster Than Light (usually communication or travel)
          
   warp
          One method of FTL travel used in Star Trek, in which nested
          subspace fields create a propulsive effect.
          
   Warp
          "Unit" for warp factor, as opposed to the technology.
     _________________________________________________________________
   
9. References:

   See the Reading List FAQ for more details on the reference volumes
   mentioned above and below.
   
   The question of "what is canon" has been argued for years in the Star
   Trek newsgroup hierarchy. In the realm of technical discussions, this
   can be refined to the question of "what evidence is factual, and what
   is apocryphal". These FAQs follow the currently dominant notion that
   "canon" is aired live-action material and nothing more, with the
   caveat that materials produced off-camera by the production crew are
   often (but not always) reliable predictors of the direction future
   canonical material will follow, and are therefore granted a special
   "quasi-canonical" status. Any other material falls into the realm of
   speculation - it may be perfectly well grounded speculation useful for
   building up technical arguments, or wild flights of fancy that have no
   rational basis.
   
   In addition, more recently presented information is considered to
   supercede old information, unless the weight of the evidence supports
   the original data. While this may seem highly biased and may be eyed
   with some skepticism as a form of Orwellian "newthink", it is a more
   useful predictor of what those directly responsible for the creation
   of the series are likely to include as canonical material in the
   future.
   
   For example, the excellent and groundbreaking Star Fleet Technical
   Manual, by Franz Joseph created in the 1970's was a very well thought
   out look at the technical world of Starfleet just slightly beyond what
   was seen in the original series. Unfortunately, and perhaps for purely
   arbitrary reasons, the future development of "canon" Star Trek
   diverged from this speculation. This in no way implies that there was
   anything wrong with that volume or any others, merely that due to
   later "evidence", it can no longer be regarded as an authoritative
   overview of Trek technology. On the other hand, the author performed a
   lot of research to create it, and therefore its speculation should not
   be dismissed out of hand.
   
   That said, we are dealing with a universe in the process of being
   created by scores of (usually) non-technical people, aiming to provide
   weekly entertainment for a mass audience. There are many
   inconsistencies even amid the canonical material, and often times the
   wildest speculation on the newsgroup makes more sense than what we see
   in the episodes.
   
   Canonical material:
     * Star Trek: Voyager [VOY]
     * Star Trek: Deep Space Nine [DS9]
     * Star Trek: The Next Generation [TNG]
     * Star Trek feature films
     * Classic Star Trek [TOS]
       
   Quasi-canonical material:
     * The Star Trek Encyclopedia: A Reference Guide to the Future
     * Star Trek Chronology: The History of the Future
     * Star Trek: The Next Generation Technical Manual
     * Star Trek: Deep Space Nine Technical Manual
     * The Making of Star Trek
     * Other "behind the scenes" information from the production crew,
       including:
          + Newsgroup postings
          + Convention presentations
          + Interviews
          + Email conversations
       
   Highly regarded, but non-canonical material:
     * Star Trek: The Animated Series [TAS]
     * Mr. Scott's Guide to the Enterprise
     * Star Fleet Technical Manual
     * Starlog's Star Trek: The Next Generation Technical Journal
     * Other "reference" guides
     * Novels, incl. novelizations of films and episodes
     * Blueprints, drawings, photographs, models, etc.
     _________________________________________________________________
   
   Joshua Bell, [email-masked]