From: jsbell@acs.ucalgary.ca (Joshua Bell)
Date: 2 Dec 93 17:44:17 GMT
Newsgroups: rec.arts.startrek.tech
Subject: Mini-FAQ: Warp and Subspace

Warning! Spoilers for some 6th and 7th season TNG episodes follow.



		      Warp and Subspace  Mini-FAQ
		       (updated December 2, 1993)
                                                                 
At least, answers to common questions as theorized by me, and
based on canonical (see note at the end of this FAQ) and
quasi-canonical information.

I *strongly* suggest reading Jason Hinson's "Relativity and FTL"
FAQ.  I'll try to avoid dealing with real science in this FAQ,
and focus on that portrayed in Star Trek (in all its
incarnations).

......................................................................

Glossary:

FTL	- Faster Than Light (usually communication or travel)
STL	- Slower Than Light
M/AMR   - Matter/Antimatter Reactor (also called Warp Core)
IPS     - Impulse Power System
c	- Speed of Light ( ~= 3 * 10^8 m/s )
......................................................................

Part I: Gettin' Nowhere Fast

"Warp speed is <insert formula here>!"

Many things have shown up in that spot. Here's the lowdown on
figuring out how fast Warp travel is.

v = velocity		c = speed of light in vacuum
W = Warp factor		^ = "to the power of"

TOS:	v = (W ^ 3) * c				"TOS scale"
TAS:	v = (W ^ 3) * c
TFS:	v = (W ^ 3) * c 			[I, II, III, V, VI]
	v = (W^(10/3)+(10-W)^(-11/3)) * c	[IV]
TNG:	v = (W^(10/3)+(10-W)^(-11/3)) * c	"TNG scale"
DS9:	v = (W^(10/3)+(10-W)^(-11/3)) * c

Note that the "TNG scale" formula is only approximate. The "real"
equation is a complex array of variables derived from the very
structure of spacetime itself, on the subspace level.  (Actually,
its on Michael Okuda's Macintosh computer in an Excel
spreadsheet, but close enough).

Here's an ASCII version of a graph from the TNG Tech 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
     =|   ::/ |  :  |     |     |     |     |     |     |     |       :=
     -|:_:-'  |::   |     |     |     |     |     |     |     |       :-
   0 -| ,-----|-----|-----|-----|-----|-----|-----|-----|-----|-----. :- 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

The above formula was calculated by someone out there, based on
the graph. It holds most accurately for 1 < W < 9.3. Below Warp 1
it is inaccurate, and above Warp 9.3 its only speculation, but
follows the curve as started in the Tech Manual.

If anyone knows who did the calculations to get the formula,
please let me know!

....

"Whats a cochrane?"

The Tech Manual has this definition: "The cochrane is the unit
used to measure subspace field stress. Cochranes are also used to
measure field distortion by other spatial manipulation devices...
Fields below Warp 1 are measured in millicochranes."

Basically, its a new unit of measurement. The Tech Manual gives
the chart of integral Warp values:

	Warp Factor 1 = 	   1 cochrane
	Warp Factor 2 = 	  10 cochranes
	Warp Factor 3 = 	  39 cochranes
	Warp Factor 4 = 	 102 cochranes
	Warp Factor 5 = 	 214 cochranes
	Warp Factor 6 = 	 392 cochranes
	Warp Factor 7 = 	 656 cochranes
	Warp Factor 8 = 	1024 cochranes
	Warp Factor 9 = 	1516 cochranes

These values correspond to the velocity of a ship in multiples of
c, but are only approximate.

....

"What does cochrane stand for?"

The units are named after the scientist credited with the
development of the Warp drive, Zefram Cochrane, known as Zefram
Cochrane of Alpha Centauri. With a drive capable of Warp 1, his
team from earth relocated to colonies on Alpha Centauri
(established with sublight ships).

In TOS "Metamorphosis", we learn that Cochrane, at age 87, left
Alpha Centauri and was presumed dead. It turns out he was kept
alive by an energy entity, and met by Kirk, Spock, and McCoy,
although no official record of this encounter is made.

Rumors of Cochrane being native to Alpha Centauri were once
spread by Klingon sympathizers who wanted to knock Earth down a
peg, but fortunately this disinformation campaign seems to have
ended.

....

"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.

....

"But in TOS "Is There in Truth no Beauty?" and TOS "That Which
Survives", the old Enterprise went over Warp 14!"

Yes, but thats on the old scale. By the new scale, that
translates to about Warp 9.7, which the Enterprise-D can do for
brief periods (its emergency speed is Warp 9.6). The original
Enterprise was being shaken apart.

....

"So why'd the Warp scale change between TOS and TNG?"

Gene Roddenberry himself put Warp 10 at inifinite speed,
according to the TNG Tech Manual. To keep the scale fluid, Okuda
and Sternbach made it asymtotal, while starting off similar to
the TOS scale.

The best explanation for why it changed internally (from the
characters' point of view), is that the original 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.

....

"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.

....

"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 (asymtotal) 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.

......................................................................

II. A Wrench in the Works


"Warp works by <insert idea here>!"

Some favorites include:

- Making space into waves, and skipping between the crests.
- Bringing points in space closer together. (Ala "A Wrinkle in
 Time")
- Changing the speed of light around the ship.*
- Having the ship's mass is reduced to 0, and it can go as fast
 as it wants.
- Leaving our universe, and going through a hyperspace.
- Going into subspace, and taking a bubble of real space with you.
- Compressing space around the ship to make the distance shorter.

None of these, however, match the evidence seen on screen and in
the Tech Manual.

Further, without any additional effects, each of these can lead
to a violation of causality, meaning every time you go into Warp
you time travel, from a certain frame of reference. This is 
addressed in great detail in Jason Hinson's "Relativity and FTL"
FAQ.

Ships in Warp stay in normal space. They interact with things in
normal space, hence the navigational deflector. Things in Warp
require a subspace field to enter and stay in Warp, and it takes
an enormous amount of power to generate this.

* The point has been made that by constructing a space with a
hyperbolic(?) geometry between the source and destination of
two points, you can get away with FTL travel without the nasty
effects pointed out by Jason's FAQ. However, this doesn't
appear as similar in effect to what we see on Star Trek as
Jason's proposal.

I've mangled the above horribly as I'm working from memory. If
anyone out there with more clue than I in the realm of GR can
take a crack at a short summary, I'd be very greatful.

....

"Well, so how *does* Warp work?"

The Tech Manual is rather verbose about it. A subspace field is
established around the ship by the Warp nacelles. The field is
composed of nested layers, each pushing against the one beyond
it. This drives the ship forward, at a super-luminal velocity.

The nacelles are powered by a tuned plasma stream from the Warp
core Matter/Antimatter Reactor (M/AMR). Injectors feed the plasma
into Warp field coil segments at specific times, causing pulses
to run the length of the nacelle, front to back. This peristaltic
flow causes the push of the nested Warp fields, and moves the
ship forward.

The Warp field wraps around the ship in a two-lobed bubble, with
the locus at Main Engineering (by design). The shape of the ship
determines the efficiency of the field, and this explains why the
Enterprise has such a sleek design.

Meanwhile, the subspace field reduces the inertial mass of the
ship, aiding in maneuvering. In fact, a small subspace field is
kept around the ship at Impulse speeds, so the Impulse drives
have less mass to push around.

....

"But, but... thats just what it does! How does it work!!!"

Alas, there is no canonical answer. The "Relativity and FTL" FAQ
offers a possibility, that the subspace field forces the ship to
take on the reference frame of subspace itself, which is a
special reference frame, circumventing the limits of General
Relativity.

Unfortunately, this *still* isn't an explanation of how it works.
The Tech Manual offers that each of the nested fields couple and
decouple from each other at velocities near (but less than) c. It
could be that the interaction of these fields, combined with the
special frame subspace provides, causes the ship as a whole to
travel at FTL speeds.

If two nested fields have their outer edges "locked" into the 
special frame, while the inner edges travel at c relative to
one another, this might cause the FTL effect, as an artifact of 
the special frame trick. This has the added support of being
almost exactly what the Tech Manual describes, but it doesn't
mention the special frame.

Since this makes for boring drama, its unlikely we'll ever
"really know" how Warp works in Star Trek.

....

"So what stops the ship from accelerating and getting faster and
faster?"

Warp travel is non-Newtonian. Without a constant influx of
energy, the subspace field will decay, and the ship will drop out
of Warp. In other words, you *must* continue to provide energy to
maintain your Warp velocity. 

Anything which travels at FTL speeds must use a Warp field (or
some other technology) to keep moving at those speeds. 

....

"What about "continuum drag" ?"

This was an idea proposed in the forgotten past to explain the
above problem. To me, however, it seem that there is no need for
such a force, since we are not dealing with Newtonian
action/reaction drives, or force/acceleration systems.

....

"So how'd the Saucer travel at Warp speeds (in "Encounter at
Farpoint") ?" 

The Tech Manual states that the subspace field generators coupled
to the Impulse drive can be used to maintain a decaying subspace
field for brief periods of time. The decay is inevitable, but it
can be drawn out, to allow the saucer section to get out of
danger.

|By field-saturating the nacelles (according to TNG "Force of
|Nature"), after a 6 second burst of maximum warp the Enterprise
|can "coast" at warp for 2 minutes 8 seconds before dropping out
|of warp. This is a form of "warp without warp drive", although
|the effect does not last very long.

This is similar to how photon torpedos can be used at warp
speeds. They have small "warp sustainer" engines that allow them
to cruise at their launch velocity (if launched while in Warp)
for brief periods.

....

|"This new Warp 5 speed limit - whats up with that?"
|
|In TNG "Force of Nature" it is discovered that the Hekaras
|Corridor, a region of space where warp travel is hindered except
|for a narrow path, that 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. While the problem
|was/is being researched, the Federation imposed a Warp 5 speed
|limit on *all* warp travel. Overkill? Probably. Typical
|bureaucratic overcompensation? Yep.

....

|"What are Tetrions and Verterons?"
|
|These are also mentioned in TNG "Force of Nature". A verteron
|mine is used to disable the Flemming, a Ferengi ship, and the
|Enterprise. It somehow manages to break all devices which use
|subspace. Simplest explanation - it inhibits interactions with
|subspace, causing a massive overloads and feedback which damages
|the equipment. 
|
|Tetrions appear to be the mediating particles of subspace
|interactions with normal space. I believe we've even heard them
|referred to in other episodes, although I can't confirm that.

......................................................................

III. Can We Talk?


"Whats subspace?"

Sigh, another toughie. Well, we know you can send messages
through it (subspace radio). A field reduces the inertial mass of
an object placed in it. It exists everywhere in normal space, and
is a feature of spacetime itself.

We do know what subspace is not, however. Subspace is *not* a
hyperspace or other alternate reality. The Enterprise does not
"enter" subspace. We have much evidence present on the show
that subspace is just an aspect of normal space which doesn't
usually present itself, and hasn't been yet identified by 20th
century science. However, many normal things do affect subspace,
and leave residual effects, hence the many times where an object
not moving FTL can be tracked via subspace anomalies.

I've got some theories about it, but they aren't supported by the
show, so I won't include them here. (They aren't contradicted
either, but I'm trying to keep this kinda pure). 

....

"How fast is subspace radio?"

Under ideal conditions, Warp 9.9997. (TNG TM, page 99) This is
"sixty times faster than the fastest starship, either existing or
predicted" - assuming traditional Warp technology.

....

"Why is it instantaneous in the movies?"

No ad breaks.

....

"How come in TNG "Schisms", Riker et. al. could "enter"
subspace?"

We know so little about it, its hard to say. There's always room
for whatever writers may want to add.

......................................................................

IV. Nitty Gritty


"FASA says the Enterprise-D uses UltraWarp, so nyeah!"

According to the TNG Tech Manual and Star Trek Chronology, the
Enterprise-D uses the same old Warp technology seen in TOS...
just a much more advanced version.

....

"What's TransWarp?"

According to the Star Trek Chronology, the Excelsior was
commissioned as NX-2000 in 2284 as a test bed for the new
TransWarp technology. By 2287, the TransWarp Development Project
was deemed unsuccessful by Starfleet Command, and experiments
were halted.

TNG Tech Manual, p 14: "While the attempt to surpass the primary
warp field efficiency barrier with the TransWarp Development
Project in the early 2280s proved unsuccessful, ..."

It seems as though the designers were trying to get around the
energy limits traditional Warp entailed, after passing Warp 9.

A few sources offer speculation on what TransWarp might be.
Unfortunately, when we finally saw TransWarp in action, they were
blown out of the water.

TNG "Descent" portrays the Borg using TransWarp Conduits. They
are still an artifact of subspace, but appear to be artificial.
Transfer through the conduits is 200 times faster than the
fastest Warp available to Federation science (Warp 9.7 or 9.8),
covering lightyears in a matter of seconds rather than hours.

It *may* be that a TransWarp drive attempts to tunnel through
subspace, bypassing the limitations of Warp entirely. If this is
the case, then it is no wonder Starfleet was forced to give up -
the energy requirements are beyond what the Borg have. Instead,
they use semi-stable conduits, accessed via a tachyon interaction
with a subspace distortion.

....

"Why do ships always meet the same way up?"

I know it's been proposed as a joke, but the idea that Warp
travel requires a universal "up" isn't as silly as you might
think. What defines the subspace reference frame? If it really
*is* universal, that violates Relativity, doesn't it? So what if
it's just a *galactic* effect, and the reference frame is relative
to, say, the center of the galaxy, and the background subspace
field is polarized in the galactic plane?

This gets you a number of interesting effects. The first is that
it might be more efficient for ships to align their Warp drives
with the plane of the galaxy, so flying "up" and "down" in the
galactic plane (which is relatively thin, about 1/10th to 1/40th
the diameter of the galaxy) would take more energy, but is
necessary at times. This also explains the banking into turns
and such.

If you have galactic-up and galactic-down to chose from, why
always the same way up? Probably a matter of protocol. Only 
loser races don't adhere to the standard. You'll also note that
many small ships are vertically symmetrical, perhaps as their
designers aren't quite up to snuff when it comes to designing
warp drives.

The second is that the subspace field of the galaxy would do
really weird things at the edge and at the center. Remember the
Great Barrier of TOS fame ("Where No Man Has Gone Before" and "By
Any Other Name") does nasty things to the Enterprise, and the one
near the center of the galaxy (if you believe in Star Trek V) was
pretty scary too.

Kirk made a number of references in "By Any Other Name" about
Warp drive not working outside the galaxy, or something to that
effect. While the Kelvans of Andromeda had got that licked, this
does give the theory a little bit of support.

Another note: the subspace shockwave seen in Star Trek VI was 
both planar and aligned with the direction of the Excelsior's
|vertical axis, and shockwaves within the subspace rift of TNG
|"Force of Nature" were also aligned coplanar to the ship.

......................................................................

Contributors:
	Jason Hinson		<hinson@bohr.physics.purdue.edu> 
		(In spirit, anyway.)

......................................................................

----------------------------------------------------------------------
* My personal scale of "canon" for the purposes of *Treknology*:
	Canonical:	ST:TNG episodes
			ST:DS9 episodes
	Quasi-Canon:	ST:TNG Technical Manual
			ST Chronology: The History of the Future
			ST:TFS I-VI (+ any future films)
			ST:TOS episodes
	Semi-Canon:	ST:TNG Companion
			The Making of Star Trek
			Any *drawings* based on the episodes/
			films (eg, Starlog Tech Journal, 
			Mr. Scott's Guide, etc)
	Non-Canon:	Everything else, including:
				ST:TAS
				Books (incl. novelizations)
				Games (FASA, et. al.)
				Collectibles (toys, cards)
				Old Tech Manuals
				Rec.arts.startrek.tech posts
----------------------------------------------------------------------
Comments, questions, answers, mints, et. al. appreciated.

Joshua
--
|        "Has it been a bad year, or what?"    - Meriadoc Brandybuck,        |
|           upon returning to the Shire after the War of the Ring.           |
| jsbell@acs.ucalgary.ca  Academic Computing Services, University of Calgary |

