Warp Velocities FAQ
Last modified: Mon Jun 08 1998 13:49:19 PDT
Maintained by: Joshua Bell, joshb@microsoft.com
Archive site (WWW): http://www.aa.net/~skeksis/Star_Trek/
FTP site (text versions): ftp://ftp.cc.umanitoba.ca/startrek/minifaqs/
_________________________________________________________________
Copyright (c) 1998, Joshua Sean 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
beyond charges for downloading or connection time from a commercial
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Star Trek (R), Star Trek: The Next Generation (R) and Star Trek: Deep
Space Nine (R) are trademarks of Paramount Pictures registered in the
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trademark of Paramount Pictures.
_________________________________________________________________
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 another member of the Star Trek television production
crew.
_________________________________________________________________
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 Skrbic writes:
In The Making of Star Trek (1968), it is stated that Warp 1 is
speed of light, Warp 3 is 27c, Warp 6 is 216c and Warp 8 is 512c.
Since this book is based on the Writer's Guide, the numbers
probably come from there.
This chart compares TOS-era Warp speeds with the speed of light:
Warp Factor Velocity Comment
1 1 Speed of Light
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000
11 1331
12 1728
13 2197
14.1 2803.221 "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. Inclued
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.)
_________________________________________________________________
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:
Warp speed/power graph
| :| .- 10^10
| : | :=
| + : | :-
| ::: ' :- 10^9
10^4 -| + : | :=
=| + : : | :-
=| + : ::::: ,/ :- 10^8
-| + : : :: __*-' :=
1000 -| : : :::: __*--' | ???:-
=| + : :: __*--' | | :- 10^7
=| : :: __*--': | | | :=
-| + : __*--': |::: | | | :-
100 -| : _*--': |:: | | | | :- 10^6
=| : _-':| : | | | | | :=
=| + _*' : |:: | | | | | :-
-| : _-':| : | | | | | | :- 10^5
10 -| *' :| : | | | | | | :=
=| + ,'| : |:: | | | | | | :-
=| : ,' :| : | | | | | | | :- 10^4
-| :/ :| : | | | | | | | :=
1 -| :* : |:: | | | | | | | :-
=| :/| : | | | | | | | | :- 10^3
=| ::/ | : | | | | | | | | :=
-|:_:-' |:: | | | | | | | | :-
-| ,-----|-----|-----|-----|-----|-----|-----|-----|-----|-----. :- 10^2
------' | 1| 2| 3| 4| 5| 6| 7| 8| 9| | `::::::::
| Warp Factor |
`--- Velocity in Power usage in ---'
multiples of c Megajoules/cochrane
__.---' Velocity * Integral Warp Values
::::::: Power + Power Thresholds
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
6 392 TM
7 656 TM
8 1024 TM
9 1516 TM
9.2 1649 Encyc
9.6 1909 Encyc
9.9 3053 Encyc Enterprise-D maximum speed.
9.975 ? Episode Voyager "cruise velocity" ("Caretaker" [V
OY])
9.99 7912 Encyc
9.9997 ~198696 TM (derived) Subspace radio speed
9.9999 199516 Encyc Maximum boosted subspace radio speed
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 ammends 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.aa.net/~skeksis/Star_Trek/FAQs/warp_formulae.html, but that
page will probably never look too pretty.
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 travelled 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 Skrbic:
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 datapoints, 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 Skrbic:
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.
* "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 Skrbic 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 Skrbic:
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").
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 muckup. (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
accessable 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 Skrbic found
the following explanation:
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.
Star Trek Science Adviser Andre Bormanis, 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. And then Paris (killed by
the trip) turns into a frog, mates with Janeway, and alters the future
of humanity.
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
"Whats 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
barier 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 Traveller's tweaking of the warp
drive and the Enterprise's speedometer don't get along well.
....
"This new Warp 5 speed limit - whats 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] ?"
It's safe to say that the USS Pasteur and USS Enterprise, cruising at
Warp 13, were able to ignore the Warp 5 limitation enforced by
Starfleet. There are a couple of 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 happy Star Trek Universe,
however.
The second is that changes to warp technology allow warp travel
without the nasty side effects. The Pasteur had very different nacelle
designs, the Enterprise had "fins" on the nacelle pylons which would
affect the shape of the warp fields, and it even had a third nacelle
which might be used to eliminate the nasty effects of warp drive.
The third possibility is that these new integral speeds above Warp 9
just don't hurt subspace the same way that other speeds do.
Personally, I go for the second option.
....
"And how about Star Trek: Voyager?"
The ship is quoted in "Caretaker" [VOY] as having a "maximum
sustainable cruise velocity of Warp 9.975". That seems to be in
violation of the new speed limit.
Jon Mitchell tells me that he remembers some dialog in "Caretaker"
that Voyager can exceed the Warp 5 "speed limit" because of its
folding nacelle design. This is something indicated by many
behind-the-scenes sources - that Voyager's nacelles are "green"
(environmentally benign). If anyone can rustle up anything official on
this, please submit it!
Another point - that can't be a speed at which Voyager can cruise for
a long period of time, despite the quote; at that speed, Voyager could
cross 70,000 light years in a little under 10 years, making their
journey much shorter.
_________________________________________________________________
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 intertially 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 arcseconds 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 wooshing 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!) blueish 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 viewscreen are explicitly identified as meteoroids.
_________________________________________________________________
7. Contributors:
Roger M. Wilcox, rogermw@ix.netcom.com
Jon Mitchell, jonmitchell@usa.net
Jonah Rapp, j.rapp@usa.net
Boris Skrbic, ibctel@ibctel.anet.cz
Dominic Berry, berry@physics.uq.oz.au
Alex Tahk, 71324.2003@compuserve.com
Jeff Reinecke, reinecke@sonic.net
Martin Shields, mshields@extro.ucc.su.oz.au
Joe Chiasson, 01FORTEC@ac.dal.ca
Jason Hinson, hinson@bohr.physics.purdue.edu
Greg Berigan, gberigan@cse.unl.edu
A.J. Madison, ajm@walrus.sw.stratus.com
Axis, nakazawa@tango.seas.upenn.edu
Sharon Collicutt, 864677@academic.stu.StThomasU.ca
Ges Seger, segerge@sd2.sews.wpafb.af.mil
Michael M. Welch, mwelch@netcom.com
Tom Bagwell
Joseph Haller, haller@as.arizona.edu
Chris Franklin, clf6873@acs.tamu.edu
Pete Carr, pcarr@interlog.com
Taki Kogoma, quirk@swcp.com
_________________________________________________________________
8. Glossary:
c
Speed of Light ( ~= 3 * 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 full details on the volumes mentioned
above and below.
More recently presented information is considered to supercede old
information, unless the weight of the evidence supports the original
data.
Greatest faith is placed on aired live-action material (canon) and
documents produced by or quoting the production crews for Star Trek
(quasi-canon), most notably the technical advisors to TNG, DS9 and
VOY: Michael Okuda and Rick Sternbach.
Other materials are not considered reliable sources of information,
and anything gleaned from these is of questionable relevance.
Canonical material:
* Star Trek: Voyager [VOY]
* Star Trek: Deep Space Nine [DS9]
* Star Trek: The Next Generation [TNG]
* Star Trek feature films [TFS]
* Classic Star Trek [TOS]
Quasi-canonical material:
* The Star Trek Encyclopedia: A Reference Guide to the Future
(Encyc)
* Star Trek Chronology: The History of the Future (Chron)
* Star Trek: The Next Generation Technical Manual (TM)
Questionable (but useful) materials:
* The Star Trek: The Next Generation Companion
- contains some behind-the-scenes notes of interest
* Other episode guides (Compendium, Concordance, etc)
- useful, esp. for spellings and details
* The Making of Star Trek
- contains Roddenberry-approved TOS ship systems info
* Episode scripts
- spellings and fiddly details, except where they say [TECH]
* Trading and playing cards (esp. Skybox)
- technical stuff often prepared by production staff
Material that is ignored (other than where it reproduces material from
the above, e.g. photographs, descriptions, etc.):
* Star Trek: The Animated Series [TAS]
* Mr. Scott's Guide to the Enterprise
* Worlds of the Federation (WoF)
* Star Fleet Technical Manual (SFTM)
* Starlog's Star Trek: The Next Generation Technical Journal (TJ)
* Other "reference" guides
* Novels, incl. novelizations of films and episodes
* Blueprints, drawings, photographs, models, etc.
_________________________________________________________________
Joshua Sean Bell <joshb@microsoft.com>