Star Trek Technology

Article 16306 of rec.arts.startrek:
Path: deimos.cis.ksu.edu!unmvax!tut.cis.ohio-state.edu!ucbvax!hplabs!hpl-opus!hpccc!okamoto
From: okamoto@hpccc.HP.COM (Jeff Okamoto)
Newsgroups: rec.arts.startrek
Subject: Star Trek Technology (troff)
Message-ID: <5090069@hpccc.HP.COM>
Date: 17 Jul 89 22:39:42 GMT
Organization: Area 88
Lines: 1503

A short while ago,an article on Star Trek Technology was posted.
I took the article and have hacked on it to work in troff.  You'll
need tbl, eqn, and the -ms macros.

 \      oo The New Number Who,
  \____|\mm Jeff Okamoto
  //_//\ \_\ HP Corporate Computing Center
 /K-9/  \/_/ okamoto%hpccc@hplabs.hp.com
/___/_____\ ..!hplabs!hpccc!okamoto
----------- (415) 857-6236

#! /bin/sh
# This is a shell archive.  Remove anything before this line, then unpack
# it by saving it into a file and typing "sh file".  To overwrite existing
# files, type "sh file -c".  You can also feed tncli as standard input via
# unshar, or by typing "sh <file", e.g..  If tncli archive is complete, you
# will see the following message at the end:
# "End of shell archive."
# Contents:  warp.troff
# Wrapped by okamoto@hpccc on Mon Jul 17 15:36:31 1989
PATH=/bin:/usr/bin:/usr/ucb ; export PATH
if test -f 'warp.troff' -a "${1}" != "-c" ; then
  echo shar: Will not clobber existing file \"'warp.troff'\"
else
echo shar: Extracting \"'warp.troff'\" \(60652 characters\)
sed "s/^X//" >'warp.troff' <<'END_OF_FILE'
X.fp 1 G
X.fp 2 GI
X.fp 3 GB
X.ls 1
X.nr PO 0.75i
X.nr LL 6.5i
X.ds CH
X.ds CF - % -
X.LP
X.EQ
Xdelim $$
X.EN
X.TL
XSTAR TREK\(rg TECHNOLOGY
X.FS
XStar Trek is a registered trademark of Paramount Pictures Corporation
X.FE
X.AU
XLeon Myerson
X.AI
X06/23/88
X.sp
X.ce
XCOPYRIGHT \(co 1988 by Leon Myerson
X.LP
XPermission to download and reprint this essay for free distribution
Xwithin the ranks of Star Trek fandom is hereby granted
Xprovided the author's name and this copyright notice are retained.
XThis essay may be periodically superseded by revised versions
Xuploaded to Data Library 2 of CompuServe's Science Fiction Forum.
X.SH
XDISCLAIMER
X.PP
XNone of the ideas expressed in this essay are ``official''.
XAll concepts put forth are solely my own opinions and speculations,
Xand as such, might be completely contradicted by ``official''
XStar Trek material issued in the future.
XI have drawn as much as possible upon the filmed
XStar Trek episodes and features,
Xand refer to such ``references'' as the Franz Joseph blueprints
Xand Technical Manual, and to the ``Spaceflight Chronology'' book,
Xwhen I have found it useful to do so.
XAt other times, I made it up.
XThis material and any companion essays I may upload,
Xare for the sole purpose of having fan-fun
Xwith the Star Trek universe.
XI have no connection whatsoever with ST:TNG or with Paramount,
XI just like to speculate regarding futuristic science.
X.sp 3
X.PP
XWarp numbers do not directly refer to speed, but to power.
XWarp 1 is the power level required to enter the warp continuum,
Xand is known as Threshold power.
XWarp 2 is twice that power level, etc.
XFractional warp is simply less than Threshold power while the ship,
Xthough traveling via warp field effect,
Xis still ``in'' the Einstein space-time continuum at sub-light speed.
XThe unit of power between whole warp factors for a given vessel
Xis one ``Impulse'', as in the ST:TNG episode ``Conspiracy''
Xwhen Geordi answers Riker's command to increase from Warp 5 to Warp 6
Xby acknowledging the addition of yet another full impulse
Xto the power already coursing through the warp nacelles.
X.PP
XThe formula relating the Warp number W to velocity in terms of C is not
Xthe hopelessly inadequate $V = W sup 3$.
XIn Trek Classic's very first episode the Enterprise was seen
Xat the edge of our galaxy.
XEven assuming this to be the near edge reached
Xby going perpendicular to the galactic plane,
Xit is still at least 1500 light years from Earth.
XAt a cruising speed of Warp 6 = 216 C,
Xthe ship would have spent at least 7 years getting out there,
Xthen 7 more back.
X.PP
XNor would that formula fit the size
Xof the United Federation of Planets' Treaty Exploration Zone
Xmapped in the ``StarFleet Technical Manual''.
XThis zone was pictured as being approximately 12,000 light years
Xin radius, with both the Klingon and Romulan empires
Xlocated at the rim some 60 degrees apart.
XClearly, Enterprise did not require an excess of 50 years
Xto reach the neutral zone.
X.PP
XIn the ST:TNG episode ``Conspiracy'', Picard and Riker
Xconfront the parasite mother creature in the guise
Xof Lt.\0Cmdr. Remmick as he/it sends a beacon
Xto the parasite beings' homeworld via StarFleet's own CommNet.
XThe 3-D map of that network on the wall behind him
Xfits almost perfectly the Treaty Exploration Zone
Xof the Trek Classic Era.
X.sp
X.PP
XInstead of $V = W sup 3$,
Xvelocity is defined by the sum of an infinite series
Xknown as the 3rd-order Cochrane function,
Xwhich is applicable to Tertiary warp effect fields
Xsuch as are utilized by major Federation vessels from the
X\f2Tritium\fP class onward.
XThe first term of this series is the familiar $W sup 3$,
Xthe second term is the integral of the first term, $W sup 4 over 4$,
Xthe third is the integral of the second, $W sup 5 over 20$,
Xand so on, ad infinitum.
XEach term is the integral of the preceding term.
XThus the common mistake so often made is to quote only the first term
Xof the series as if it were the entire function.
X.PP
XThe behavior of this series is such
Xthat the terms rise in value at first,
Xthen become increasingly smaller so as to converge
Xon a definite value.
XThis may be calculated by the equivalent formula:
X.EQ
XV =  6 ( e sup W - ( {W sup 2} over 2 + W + 1) )
X.EN
Xwhere V = velocity, W = Warp factor,
Xand e = base for natural logarithms (2.71828...).
X.sp
X.PP
XWhen calculated in this manner,
Xthis function gives the following values:
X.TS
Xbox, center, tab(~);
Xc c
Xn n.
XGenerated Power~Uncorrected Warp Speed (c)
X_
X1~1.31
X2~14.33
X3~69.51
X4~249.59
X5~779.48
X6~2270.57
X7~6384.80
X8~17639.75
X9~48315.50
X10~131792.79
X11~358809.85
X12~976018.75
X13~2653889.35
X14~7214947.68
X15~19613332.78
X.TE
X.PP
XFor starship designers, these numbers seemed too good to be true,
Xand indeed they were.
XFrom the earliest days of starship operations,
Xwarp engines had always registered a small power loss
Xas they were fed more than Warp 1 power.
XDefined as the difference between Generated Power and Delivered Power,
Xthis drain was ascribed to the faintly conceived notion of
X``continuum drag''.
XIt was Delivered Power that determined actual velocity
Xaccording to the 3rd-order Cochrane function.
XAs the phenomena was still too poorly understood
Xfor mathematical description,
Xprogressive increases in power generation capability
Xhad to be matched empirically with increases
Xin Delivered Power via actual flight testing,
Xand the term Warp Factor continued to refer to Generated Power.
X.PP
XThe Dilithium breakthrough made it possible to generate unprecedented
Xmultiples of threshold power,
Xand led to the Federation's investment
Xin the \f2Constitution\fP class vessels.
XAble to safely generate and sustain Warp 8 power,
Xthese ships found the drag/drain worsening rapidly at the higher levels.
X.PP
XIt was the USS \f2Enterprise\fP, under Christopher Pike,
Xthat first challenged the ``Warp Barrier''.
XAfter three month's total overhaul at the Terran Orbital Shipyards
Xpersonally supervised at every stage by Montgomery Scott,
Xthe ship went on speed runs pushing her anti-matter reactors
Xas high as Warp 13 for a few seconds at a time.
XThe resulting measurements at last permitted Scott
Xto define the continuum drag equation:
X.EQ
XCDF = G - { { tan A } over { (G - S) + sqrt { tan sup 2 A + {(G - S) } sup 2 - 1}}} + 10
X.EN
Xand thus
X.EQ
XD = G - CDF
X.EN
X.LP
Xwhere D = Delivered Power;
XG = Generated Power;
XCDF = Continuum Drag Factor;
XA = 5.1050881 radians;
Xand S = 9.8658770244 (Scott's constant).
X.PP
XThe corrected table of Warp speeds is therefore:
X.TS
Xbox, center, tab(~);
Xc c c
Xc c c
Xn n n.
XGenerated Power~Delivered Power~Warp Speed (c)
XOld Warp~New Warp
X_
X1~1.00000~1.31
X2~1.98354~13.91
X3~2.96260~65.98
X4~3.93509~230.94
X5~4.89755~696.42
X6~5.84370~1926.80
X7~6.76140~4999.38
X8~7.62571~12075.26
X9~8.38615~26048.20
X10~8.96633~46707.91
X11~9.33067~67348.90
X12~9.53548~82717.85
X13~9.65322~93087.64
X14~9.72615~100151.85
X15~9.77477~105155.01
X.TE
X.PP
XA graph of Scott's equation plotting Generated Power as $X$
Xagainst Delivered Power as $Y$,
Xshows that at threshold power
X(Scott's equation and the 3rd-order Cochrane's function
Xare not applicable below this point) $X = Y = 1$,
Xand the graph line proceeds at an almost 45 degree angle
Xassuming equal scales\**.
X.FS
XThis graph is available as WARP10.RLE in DL2 for those with IBM PCs
Xor compatibles.
X.FE
X.PP
XBut as Generated Power exceeds 8 times threshold level,
XDelivered Power deviates ever more significantly
Xand the graph curves sharply to the right.
XThe curve is half of a hyperbola, rotated by angle $A$,
Xwith the significant asymptote line
Xrepresented by the equation $Y = 10$,
Xso that while the Generated Power may go arbitrarily high,
Xthe Delivered Power will only approach ever more closely
Xbut never equal 10.
XThe speed value for Warp 10 from the uncorrected chart,
X131792.39 times the speed of light,
Xis the theoretical limit of the Tertiary warp effect,
Xand can only be approached, never equaled or exceeded.
XThis is also the velocity
Xof such warp continuum energy transmission phenomena
Xas sub-space radio and the standard phaser effect\**.
X.FS
XThe complete hyperbola is graphed in WARP_X.RLE, also in DL2.
X.FE
X.PP
XBy the time of ST:TNG, it had become standard practice to quote Warp
Xfactors in terms of Delivered, rather than Generated, power.
XThis explains the apparent discrepancy between the eras.
XOverall Generated Power capabilities are still crucial
Xto military vessels,
Xas even a few dozen extra C's may mean the difference
Xbetween success and failure when outrunning or pursuing an opponent.
XHere then is the standard warp factor scale used in the
X24th century:
X.TS
Xbox, center, tab(~);
Xc c c
Xc c c
Xn n n.
XDelivered Power~Generated Power~Tertiary Warp
XNew Warp~Old Warp~Velocity x C
X_
X1~1.0000000000~1.31
X2~2.0167653720~14.33
X3~3.0383208502~69.51
X4~4.0670614879~249.59
X5~5.1072983806~779.48
X6~6.1676537197~2270.57
X7~7.2682459514~6384.80
X7.5~7.8487197368~10628.50
X8~8.4694304149~17639.75
X8.2~8.7364919027~21588.78
X8.4~9.0203187626~26414.32
X8.6~9.3280961537~32310.48
X8.8~9.6717993420~39514.34
X9~10.0729838055~48315.50
X9.1~10.3071067812~53422.73
X9.2~10.5747605008~59067.65
X9.3~10.8903152831~65306.85
X9.4~11.2777216596~72202.80
X9.5~11.7800905867~79824.61
X9.6~12.4836439773~88248.61
X9.7~13.5895662949~97559.17
X9.8~15.7014109302~107849.55
X9.9~21.8369448362~119222.79
X10~INFINITE~131792.79
X.TE
X.PP
XTo calculate the Generated Power corresponding
Xto a given Delivered Power level, use the formula:
X.EQ
XG = S - {{ {(D - 10)} sup 2 ( {( tan A)} sup 2 - 1) - {( tan A)} sup 2} over { 2 (D - 10) tan A }}
X.EN
X.PP
XAn interesting aspect of the 3rd-order Cochrane function
Xis that Warp 1 is not C but 1.31\0x\0C.
XTaking the reciprocal of this number, 0.763,
Xgives what is known as threshold velocity.
XUnder fractional warp power,
Xa starship ``accelerates'' as the power is steadily increased.
XAt Warp .99999 etc., the ship is traveling at 0.763\0x\0C.
XTransition occurs, an explosive event accompanied by
Xthe hauntingly beautiful phenomena known as the Chromatic Detonation,
Xthe optical analog of a sonic boom.
XIn the next micro-instant, the ship is on ``the other side'',
Xtraveling through the warp continuum at 1.31\0x\0C.
XThe ship is never observed at speeds $0.763 < V < 1.31$ under normal
Xconditions.
X.PP
XIt should be noted however,
Xthat the boundary layer of the warp field effect
Xcreates an envelope of 4 dimensional Einsteinian space-time
Xwithin which the ship travels.
XTherefore, all the familiar physical laws
Xof the ``ordinary'' continuum still apply within the envelope.
XFrom the outside, it appears as though a space-time anomaly
Xwere manifested sequentially along a linear path.
XFleeting, multiple images of the vessel in the center of the anomaly
Xare created at widely spaced intervals which grow more distant at
Xhigher warp factors.
XLight coming from within the envelope gathers at the boundary layer
Xuntil it reaches optical crossover threshold,
Xat which point it ``pulses'' through,
Xthus re-entering normal space-time to project the image of the ship.
XThis effect was nicely filmed for the climactic scene
Xin ST:TSFS\**
X.FS
XShould this perhaps be ST:TWOK?
X.FE
Xwhen we see the \f2Enterprise\fP fleeing the detonation
Xof the Genesis Device.
X.PP
XExternal light enters the envelope via complex optical interaction
Xwith the warp field boundary layer.
XThe micro-instant lost for photons in front of the ship's path
Xto cross the boundary layer causes them to appear to originate
Xfrom directions shifted away from the line of motion in favor of
Xapparent origins perpendicular to the direction of travel.
XWhile an optical blind spot exists directly behind the ship
Xalong the direction of motion,
Xdue to the superluminal velocity involved,
Xthe tear-drop shape of the overall warp field
Xminimizes the area so blanked out to a vanishingly small region.
X.PP
XThe overall effect is curiously symmetrical to that observed
Xby vessels approaching light speed in normal space-time.
XSuch a vessel would see its 3-dimensional field of view
Xcollapsed into twin circles of light in front of and behind the ship,
Xwith a band of darkness around its mid-section.
XA vessel in the warp field traveling at superluminal velocities
Xexperiences a tunnel-like effect in which the dark region
Xconsists of circles in front of and behind the vessel,
Xand its view of the universe is projected onto a cylindrical tube
Xwhich the ship appears to travel through.
X.PP
XOf course, the ship's computers correct for this effect
Xto present an intuitively ``normal'' view upon the bridge
Xand other viewscreens.
XWindows facing port or starboard reveal a relatively normal view
Xwithout sophisticated correction,
Xothers have internal holographic layers which serve
Xas the functional equivalents of corrective lenses
Xto keep the view at least intelligible, if not exactly accurate.
X.PP
XSometimes a foreign body,
Xsuch as small pieces of asteroidal rock or chunks of cometary ice
Xare pulled into the forming continuum envelope
Xas a starship achieves transition.
XUsually this is a harmless occurrence,
Xunless the ``dragger'' is massive enough to damage the hull
Xif it should collide with the vessel.
XIf so, the ship will usually power down below threshold
Xto release the object,
Xotherwise it can remain within the influence of the warp field effect
Xand go along for the ride to the starship's scheduled destination.
XAn unusually extreme instance of this effect occurs in ST:TMP
Xwhen the old \f2Enterprise\fP,
Xbucking wildly from her imbalanced engines,
Xpulled a whole asteroid into the warp envelope formed around herself,
Xand was forced to pulverize it with a photon torpedo.
X.PP
XOld space junk from various inhabited systems
Xoften gets distributed about the galaxy in this fashion,
Xcenturies in orbit about their star of origin
Xaffording plenty of time for a chance encounter
Xwith a transitioning starship.
XSome of places identifiable objects ultimately turn up
Xcan be downright humorous.
XItems too small to possibly damage a vessel
Xthrough its deflector shield are usually ignored,
Xespecially when they have no possible salvage value.
X.PP
XAn example would be the cryonics satellite found just prior to the
XNCC-1701-D's recent visit to the Neutral Zone
Xwhich originally WAS orbiting Sol,
Xminding its own business for centuries.
XPeople in the future tend to leave space junk that old alone,
Xthe objects most popular as tourist sights
Xactually being protected with ``landmark'' status.
XA sleeper ship such as Khan's would certainly have been detected,
Xbut the cryonauts registered NO life signs at all,
Xso no one ever knew what was in this craft.
XEventually, a starship pulled it into its envelope
Xand carried it thousands of light years
Xout to the vicinity of the starbase \f2Enterprise\fP
Xwas visiting for Captain Picard's conference
Xwith StarFleet authorities regarding the apparent loss
Xof stations near the Neutral Zone.
X.PP
XThis is also now considered the most probable explanation
Xfor the early 1990's \f2Voyager 6\fP probe having reached a black hole
Xcapable of sending it to the ``machine'' planet,
Xas various research ships have made many voyages
Xdirectly from the Sol system to known black holes
Xsince warp drive was first employed.
XIts return to the Sol system as ``V'ger'' prompted some talk
Xoff a system wide clean up of old hardware, but nothing ever came of it.
X.sp
X.PP
XThe relativistic time dilation experienced at Tertiary threshold
Xvelocity is such that time passes at 64.6% per cent, or roughly 2/3's,
Xthe ``normal'' rate of objects ``at rest''.
XThis time dilation factor goes along with the ship
Xas the warp effect envelope separates from normal
Xspace/time in crossing over the threshold,
Xand remains stable thereafter,
Xso that all the time spent under way at superluminal
Xvelocities is discounted by 1/3 for those on the vessel
Xvs. those staying behind.
XThe effect is rather convenient for starship crews,
Xas it effectively cuts by 1/3 the travel time between stop-overs,
Xand since all Tertiary warp vessels experience it,
Xthere is no disadvantage in reaction time against opponents.
X.PP
XThere are social aspects to the cumulative effect
Xof a lifetime career devoted to star travel,
Xin that one's age starts falling behind that of friends,
Xfamily, and above all spouse's left behind.
XIn the 2nd, 3rd, and 4th feature films,
Xwe see James Kirk wearing four bars and three dots on his sleeve,
Xindicating 23 years service in StarFleet.
XYet his birthday depression in ST:TWOK
Xand the presence of the fully grown David Marcus all
Xpoint towards a 50th birthday.
XAssuming Kirk graduated the Academy at the normal age of 22,
Xadding 23 years leaves a 5 year gap.
XThe gap is simply the cumulative effect of the time
Xhe's spent cruising at warp speed.
XFor married personnel, this ``age gapping''
Xbecomes a serious problem over a lifetime,
Xand was a major factor in StarFleet's decision to allow families
Xto go along on its latest vessels of the ST:TNG era.
X.PP
XA very important aspect of this effect
Xderives from the behavior of the threshold cross-over phenomena
Xin the presence of intense gravitational fields,
Xsuch as would be found near stellar bodies.
XThe intense warping of space/time already imposed
Xupon the region of the continuum nearest the star
Xcauses it to become more tolerant of extreme profile skewing
Xthan normal space.
XAs a nearby ship accelerates, the threshold velocity is reached,
Xbut cross-over does not occur,
Xone has to increase the degree of skew with still more power.
XThis means going nearer to lightspeed while still in the normal
Xcontinuum, thus the time dilation factor increases.
XSince the time dilation at cross-over remains in effect
Xthroughout the period spent in the warp continuum's sub-space,
Xit is possible to retard one's own rate of time passage
Xto an arbitrarily high degree to assist
Xin making extremely long voyages.
X.PP
XSome of the early Federation exploration ships,
Xsuch as the famous USS \f2Horizon\fP,
Xused this sort of maneuver on occasion,
Xbut more often avoided it due to the detrimental effect
Xupon shipboard reaction time it causes.
XMerchant vessels sometimes tried it,
Xbut the extreme danger of maneuvering so close to a star
Xled first to uninsurability and finally to outright
Xregulatory prohibitions against the practice.
XShips full of colonists almost always housed them in sleeper chambers,
Xan old and proven technology dating as far back
Xas the late 20th century, leaving only the crew awake.
X.PP
XOne of the greatest scientific discoveries
Xmade by the original NCC-1701 \f2Enterprise\fP
Xwas that if a ship went EXTREMELY close to an object
Xof stellar mass while in the normal continuum,
Xthen poured on maximum power to force its way to threshold
Xbefore putting significant distance between itself
Xand the gravity field of the celestial body in question,
Xthen the effective threshold velocity could actually be
Xslightly above lightspeed,
Xand the associated time dilation
Xnot only extremely large but NEGATIVE.
XThis is the essence of time travel under what has become
Xknown as the ``breakaway maneuver''.
X.PP
XThe class of phenomena known as ``time travel''
Xare extremely complex and remain poorly understood.
XMost recorded incidents have involved multiple effects which,
Xin the absence of a fully developed theory of time,
Xare often difficult to untangle for separate description and analysis.
XThe \f2Enterprise\fP's unintentional journey to the Terra
Xof the late 1960's began with an accidental encounter
Xwith an uncharted black hole.
XThe unusual properties of this particular hole
Xhad attracted their attention,
Xresulting in the \f2Enterprise\fP making a low warp speed sensor pass.
XThe anomalous readings prevented them from realizing the
Xnature of this object until it was too late.
XThe hole's intense distortion of the continuum
Xpulled the \f2Enterprise\fP out of warp,
Xwhere the ship was in imminent danger
Xof being sucked into the hole itself.
X.PP
XOn Kirk's orders, Sulu applied full emergency power
Xin a desperate attempt to fight their way back to threshold
Xso as to to re-enter the warp continuum,
Xbut even as the mighty starship trembled under the effort,
Xthe threshold power level was moving higher and higher as they
Xneared the event horizon.
XWith seconds left before the end, Mr.\0Scott
Xin engineering surmised the nature of their situation.
XKnowing the ship could never make
Xthe rising tertiary warp threshold in time,
Xhe engaged the emergency circuit breakers
Xto take the tertiary booster coils offline,
Xand diverted 100% of the reactor output
Xinto what was now a lower threshold secondary warp field system.
XThe collapse of the tertiary field into a secondary one ``collided''
Xwith the rapidly growing overall power level,
Xkicking the ship into the warp continuum with such explosive force
Xthat she briefly left sub-space itself on a kind of ``ballistic arc''
XOVER rather than through the warp-space she would normally traverse.
X.PP
XIt would take Spock many weeks of theoretical study and analysis
Xbefore he would devise a tentative explanation
Xfor their seemingly miraculous appearance within the Terran atmosphere.
XUltimately, his explanation for their movement through space
Xas well as time rested upon two major points.
X.PP
XFirst, time travel does not permit violation
Xof the conservation of mass law.
XOne cannot simply send 200,000 metric tons of starship
Xback in time to coexist with an ``earlier'' copy
Xof the same 200,000 tons of matter without in some way compensating
Xfor the effect such functional duplication of mass will have
Xon the overall gravitational process of the cosmos.
X.PP
XSecond, in this particular incident the mode of compensation
Xtook the form of an exchange or displacement of the 20th century matter
Xthat would one day be the \f2Enterprise\fP and her crew,
Xthis material swapping out of the normal plane of existence
Xto reside in the hyper-continuum the ship had traversed
Xto reach its destination.
XTherefore, in a manner related to the phenomena
Xof ``symmetry breaking'',
Xthe cosmos ``selected'' as the ship's re-entry point
Xa location determined by the whereabouts at that time
Xof the raw materials which would one day be the \f2Enterprise\fP
Xand her crew.
X.PP
XAs most of this material would be found on Terra in the 1960's,
Xthat is where the ship materialized.
XFortunately, not quite all of the material
Xconstituting the \f2Enterprise\fP was of Terrestrial origin,
Xor the ship would appeared at the center of the Earth
Xinstead of 5 miles above its surface.
XThat it wasn't 5 miles below the surface instead
Xwas simply good luck as to the total net effect
Xof the mass-origin location factors.
XWhen the \f2Enterprise\fP returned to its proper place in time,
Xthe older version of her material constituents
Xresumed their proper place in the continuum as well.
X.PP
XLater studies of the ``breakaway maneuver''
Xand its associated parameters revealed that had this early incident
Xnot involved such extreme conditions,
Xthe time traveling starship would have remained ``linked''
Xto the net gravitational influence of the star
Xused as the initiator mass.
XThis would have caused the celestial body itself
Xto assume the role of adjusting its own impact
Xon the expansion of the universe to compensate
Xfor sending a vessel back in time,
Xand would permit such voyages through time
Xwhile retaining the ability to target spatial destinations as well.
XThis type of controlled temporal translation
Xwas successfully demonstrated by the \f2Enterprise\fP via Sol
Xduring the mission Kirk's log describes as ``Assignment: Earth'',
Xand was later employed from a captured Klingon cruiser
Xto solve the ``Whalesinger'' crisis.
X.PP
XGiven the operational parameters of starship reactor systems,
Xthe time it takes to build up power
Xapplied to generating the warp field effect
Xnormally requires an initiator mass the size of a star or greater
Xto perform the breakaway maneuver.
XA planetary mass is just too small under most circumstances
Xas the vessel will have already moved too far
Xfrom the center of its gravitational field
Xbefore attaining threshold power where the time dilation effects
Xare manifested.
XThis does not mean it isn't possible to use a planetary mass
Xas the initiator,
Xonly that the ship in question would have to bring up its power output
Xin an incredibly rapid surge to do so.
XThe only known means of doing this is the all but suicidal technique
Xof deliberate implosion to ``cold-start''
Xcompletely shut down power systems.
XOnly one ship, NCC-1701, is known to have ever survived this procedure.
XHistorians remained baffled as to why the crew dubbed the gambit
Xan ``Irishman's Chance''.
X.PP
XWere you to travel back in time
Xwithout triggering some form of gravitational impact compensation
Xfor your mass,
Xthe continuum would soon destroy you via an effect
Xstrikingly similar to the manner
Xin which a living creature's immune system destroys that
Xwhich does not belong.
XThe unfortunate time traveler would experience progressive
Xdisintegration as the particles of his/her body
Xare randomly pushed back to their own correct time.
X.PP
XAn advanced form of such compensation
Xwas an integral part of the Atavachron,
Xwhich functioned by actually forcing open ``portals'' between times.
XAs Kirk, Spock, and McCoy went through the portal
Xbut bypassed the compensation stage,
Xthey were in grave danger and had but little time to return.
XZarabeth could not return with them
Xunless they could have learned to use the machine
Xto compensate for her entry into their era,
Xbut alas there was no time for that
Xbefore the star in that system went nova.
X.sp
X.PP
XJust as the 3rd-order Cochrane function is known as Tertiary Warp,
Xthe 1st and 2nd orders represent Primary, and Secondary Warp.
XPrimary Warp is the function consisting of the sum
Xof the infinite series beginning with $X$ plus $X sup 2 over 2$
Xplus $X sup 3 over 6$ etc.
XAs with the 3rd-order series,
Xit may be calculated with the equivalent formula $e sup W - 1$.
XThis was the first type of warp field effect propulsion system
Xdeveloped, and it is still in use on later vessels
Xas the Impulse Drive sub-system.
X.PP
XWhen Secondary Warp drive systems were developed,
Xgoverned by the 2nd-order Cochrane function
Xconsisting of the sum of the infinite series
Xbeginning with $X sup 2 + {X sup 3} over 3 + {X sup 4} over 12$ etc.,
Xequivalent formula: $2 (e sup W - (W + 1))$,
Xit was learned that they,
Xand all higher order warp fields,
Xwere dangerously unstable at low fractions of threshold power.
XThis forced the retention of some form of Primary warp drive,
Xthough it need not handle enough power to go superluminal.
X.PP
XAll warp field effects are created via the use
Xof superconducting Cochrane coils,
Xwhich are wound according to the complex topological patterns
Xdefined by Impulsor Calculus,
Xthe branch of mathematics developed by Zephram Cochrane
Xto express the new kinematics and mechanics
Xresulting from his successful unification of gravity
Xwith the electro-strong-weak force of quantum physics.
XAs this essay is intended for a 20th century audience,
Xethical constraints place severe limits on the range of comments
Xthat can be made on this subject,
Xbut the inference should be obvious that
Xif theoretical physics has mastered the unification
Xof the primal forces of nature,
Xit becomes possible to use a force easily generated and controlled,
Xsuch as electromagnetism,
Xto manipulate phenomena normally governed by another force,
Xsuch as gravity.
X.PP
XCochrane's mechanics superseded Einstein's,
Xas his in its time supplanted Newton's.
XEach is ``true'' or at least acceptably valid, within its range,
Xand may be thought of as a special case approximation of its successor,
Xwhich is itself regarded as a superset of its predecessor.
XThe following clues to Cochrane's accomplishment,
Xparaphrased from the preface to his own textbook,
Xare deemed safe for 20th century humans.
X.PP
XThe first is that while current attempts to build
Xever larger particle accelerators will lead to the unification
Xof the strong nuclear force with the electro-weak force,
Xthis approach will not be successful with gravity.
XThe reason is that while accelerators of sufficient power
Xapproximate the fantastic extremes of temperature and pressure
Xfound during the era immediately following the Big Bang,
Xit was not these aspects of the early universe
Xbut rather the extreme curvature of space-time then in force
Xwhich wedded gravity to the other forces.
XAs space-time expanded, or flattened,
Xgravity was the first force to de-couple from the others.
X.PP
XThe second clue is that while Newton's mechanics
Xwere based upon the Euclidean model of geometry,
Xand Einstein's was grounded in 19th century alternatives
Xsuch as that of Riemann, Cochrane found the mathematical tools
Xhe needed to join the probability functions of quantum physics
Xto the structures defined by distortions of space-time
Xin the ``strange attractors'' of Fractal Geometry's framework
Xfor the study of ``chaos''.
X.PP
XThe warp effect itself derives from Cochrane's advanced concepts
Xof gravitation under which the interaction between the mass
Xof a physical body and the surrounding space/time matrix
Xdefines a complex mathematical field known as a continuum profile.
XOn a purely theoretical level,
XCochrane was able to establish a new understanding
Xof the term velocity by demonstrating an intriguing difference
Xin the continuum profiles of moving objects versus
Xthose stationary relative to the observer.
XAll objects having mass distort the space/time continuum around them,
Xbut when an object is in motion relative to the observer,
Xthe pattern of the this distortion, known as the continuum profile,
Xbecomes skewed along the direction of travel.
X.PP
XSpace/time is not infinitely malleable,
Xit takes a minute but finite interval for gravitational distortions
Xto be fully manifested upon newly encountered regions.
XBecause of this propagation-time factor,
Xthe region of space/time in front of a moving object
Xat a given instant is not as distorted as it would be
Xhad the object in question been exerting its gravitational influence
Xon it for an arbitrarily long period,
Xand the region behind the traveling body shows excess distortion
Xbecause of the time it takes to flatten back to its undisturbed state.
XThe concept of relative motion remains in force,
Xfor the skewing of the continuum profiles of all objects
Xin the universe is measured from the vantage point
Xof the observer's own comparably skewed line of travel.
XIn measuring the velocity relative to himself,
Xthe observer is actually noting the degree of continuum profile skewing
Xrelative to his own,
Xand an inertial frame of reference becomes one
Xwith a constant degree of skew.
X.PP
XIn astrophysics, this effect is largely muted by the ability of
Xspace/time to ``remember'' repeated transits,
Xso that all cyclic motions, such as the orbits of planets,
Xliterally ``groove'' their paths into the very fabric of the continuum,
Xdiminishing the skewing effect to almost vanishing levels.
XAlso, such circular motions involve the interaction
Xof mutually influencing bodies,
Xso that each experiences far more change in
Xthe direction of its skewing factor than in its absolute magnitude.
X.PP
XBut for non-cyclic motions,
Xsuch as that of spacecraft executing huge linear translations
Xthrough the continuum,
Xthe effect is sufficiently pronounced to impact observations
Xmade from onboard instruments.
XGenerations after Cochrane,
Xthe ability of the space/time continuum
Xto store such information-laden ``memories'' would be used
Xby Dr.\0Carol Marcus to establish the theoretical basis
Xfor the long suspected existence of morphogenetic fields,
Xand would lead her to attempt the exploitation of this phenomena
Xvia the ``Genesis'' technology.
X.PP
XIn creating his unified field theory,
XCochrane opened the door to full-scale interaction/exchange
Xbetween the primal forces of nature.
XUsing the analytic tools of his carefully derived Impulsor Calculus,
Xhe has able to map out complex yet stable forms
Xof interwoven electro-magnetic fields
Xwhich would cross ``the line'' by manifesting part of their effect
Xin the form of gravitational phenomena.
XHe was then able to follow the conceptual trail back
Xto the actual design and construction of field generating coils
Xthat could transform his theories into useful technology.
XIn his first great practical success,
Xhe proved that if his coil systems were used
Xto reconfigure the continuum profile of a ``stationary'' object
Xso that it acquired the relative ``skew'' of a moving one,
Xit moved accordingly.
X.PP
XThis led first to the development of the long wished-for
X``jetless'' space drive, ultimately called ``Impulse drive'',
Xin which designers no longer needed to bother about reaction mass
Xcarried onboard only to serve as kinetic exhaust.
XLater studies revealed that the application of sufficient power
Xto the skewing field would produce a degree of skew effect
Xso highly pronounced as to be insupportable
Xby the familiar Einsteinian continuum.
XAttaining this ``threshold'' level would so stress
Xthe ordinary continuum that a vessel and its surrounding field envelope
Xwould literally be ejected into a higher order continuum
Xin which the speed of light was no longer relevant as a limiting factor.
XCochrane himself visualized our familiar continuum as ``floating''
Xabove the larger realm,
Xand so described the transition process as ``dropping into sub-space''
Xrather than apply an upward linguistic bias
Xand the overused ``hyperspace''.
X.PP
XA gentle, private, and in some respects almost old-fashioned man,
XCochrane lived far enough into his twilight years
Xto see his work send humanity to the stars,
Xbefore he mysteriously vanished.
XSome say that the warp-driven space yacht presented to him
Xby the greatful governments of several worlds
Xdisappeared at the same time,
Xfueling speculation that he headed into unknown space
Xon some final adventure.
XWhile historians argue over his ultimate fate,
Xnone dispute the enormity of his contributions,
Xwithout which the very founding of the Federation
Xcould never have occurred.
X.sp
X.PP
XJust as the 20th century's mastery of undreamed of natural forces
Xsuch as electricity produces technological wonders
Xinconceivable to 17th century minds,
Xso did Cochrane's breakthrough set the stage
Xfor a vast family of related discoveries and devices
Xthat seem almost magical to residents of our time.
XIn the decades following the construction
Xof the first ``impulsor drives'',
Xfurther experimentation and theoretical studies
Xled to totally different, often unexpected,
Xapplications of the basic Cochrane coil system.
XThe coil itself would become as basic a concept
Xto an entire branch of technology as the ``circuit'' is
Xto the field of electrical engineering.
X.PP
XPhysicist Alicia Chalmbers interwove two coils,
Xone wound clockwise, the other anti-clockwise,
Xand sent twin currents through them in opposite directions.
XThe ``Chalmbers'' coil did not move,
Xas its external effect upon the continuum was balanced
Xbetween opposite and equal influences,
Xbut within the dual-coil itself a profound disruption
Xof space/time took place.
XWave like patterns of variation in the ``topological gradient''
Xor distortability of space/time, went out equally in all directions.
XA second Chalmbers coil, though unenergized,
Xreacted to the distortion pattern
Xby converting part of its energy content back into electricity.
X.PP
XOf course, modulations in the current flow
Xto the first Chalmbers coil were echoed analog fashion
Xin the current output of the second ``receiving'' coil,
Xgiving birth to sub-space radio.
XThe effect propagates at the theoretical limit of the warp effect,
XWarp 10, the actual speed depending on whether the Chalmbers coils
Xare of the Primary, Secondary, or Tertiary variety.
XAll StarFleet, and virtually all modern civilian vessels,
Xuse Tertiary Chalmbers systems,
Xallowing communications at 131792.79 x C.
XPassive listening for natural occurrences of this phenomena,
Xand the active use of a form of sub-space radio in ``radar'' mode,
Xconstitute much of the sensor technology of Starships.
X.PP
XAnother variation of the basic Cochrane device
Xbends the coil away from its ``barber-pole'' configuration,
Xto double back on itself full circle,
Xin effect coiling the coil in a single loop.
XThe result is an artificial gravity field projected perpendicular
Xto the plane of the loop,
Xin either pull or push mode depending on the orientation
Xof the windings and/or the direction of current flow.
XWithin its housing,
Xthe loop coil is physically anchored or it would simply spin
Xin a warp driven circle rather than impart its effect
Xto the gravity field.
XSuch units are always paired so that the torque from each
Xcancels the other rather than be imparted to the vessel
Xvia the structural elements holding them in place.
X.PP
XOther variants of the Cochrane coil take the form
Xof conical shaped pairs of coils nested within each other
Xfacing in opposite directions.
XThe conical shape causes the warp field's skewing effect
Xto be projected away from the coil system rather than centered upon it.
XBy using the two coils in tandem,
Xone can induce any desired combination of push or pull force
Xup to the system's operational limits on a distant object,
Xmoving it arbitrarily close to the starship's hull and holding it there.
XKnown as a tractor beam, this piece of equipment is indispensable
Xfor modern spacecraft operations;
Xwithout it sleek warp-driven starships would be reduced to reliance
Xupon primitive manipulator arms
Xsuch as the one found on the 1980's space shuttle.
XWhen holding a derelict vessel via tractor beam,
Xit is possible to apply the the repulsive force
Xagainst selected portions of the outer hull,
Xconcentrating the attractive force through the vehicles' center,
Xso as to not only retrieve and stabilize it,
Xbut provide artificial gravity
Xas well for the comfort of boarding parties.
X.PP
XIn man's first experience with interstellar combat,
Xthe technological level of the participants
Xhad the vessels of both sides drop into sub-light speeds
Xto maneuver against each other in a tight volume
Xof laser crossfired space.
XThese primitive battles were analogous to the way in which late 20th
Xcentury fighter planes would reach a combat zone via supersonic travel,
Xthen go subsonic for the actual dogfight.
XThe advantages of a weapon that could unleash its effect at warp speed
Xwere so obvious that an all out technology race to build such a device
Xbegan even before the first Romulan War was over.
X.PP
XUltra high velocity missiles carrying powerful matter/anti-matter
Xwarheads were already in use.
XAs the M/A annihilation produces a shower of photons
Xin the extremely high energy gamma ray portion of the spectrum,
Xthese missiles were dubbed photon mines.
XThough their highly developed fusion thrusters
Xcould accelerate them at hundreds of G's,
Xthey were still so slow compared to even the sublight capabilities
Xof impulse driven starships that one had to use them
Xin the manner of depth charges, simply deploying them in
Xthe expected path of the enemy ship and hoping for the best.
XAttempts to replace the fusion thruster
Xwith a warp engine enjoyed some success
Xagainst vehicles moving at sublight speeds,
Xbut against vessels traveling at warp speeds
Xwhat was needed was a weapon
Xthat could travel substantially faster than any ship.
X.PP
XThe answer was ultimately inspired by the ancient submarine torpedo,
Xwhich used steam power pumped into the torpedo by the submarine rather
Xgenerated onboard the weapon itself.
XThe modern analog of the torpedo tube emerged
Xas an inside out warp engine coil which generated its field
Xwithin its own interior and imparted an enormous skewing effect
Xon any object placed inside.
XThe specially designed warhead pod would zip out of the tube at
Xextremely high warp speeds, having an unprecendented degree of skew,
Xbut free of the mass of any onboard warp field generating equipment.
XThough the warhead pod is designed to retain its imparted skew
Xas long as possible, it does begin to decay
Ximmediately after leaving the tube.
XAs this takes at least several minutes,
Xthe effective range is quite adequate for the tactical role
Xthese weapons play.
XNote that these devices have almost no steering,
Xonly a slight course correction capability,
Xand so must be carefully aimed.
XThe parallel to ancient submarine weapons was so close
Xthat the term ``photon torpedo'' became permanently attached
Xto these deadly implements of celestial combat,
Xwhich in the ST:TNG era are capable of as much as 10 to 15 minutes
Xtravel at speeds approaching warp 9.9.
X.sp
X.PP
XEarly experiments with Dilithium crystals
Xfound that two such crystals, a mirror, a semi-reflector,
Xand a light source made a marvelously efficient laser,
Xas Spock once demonstrated in escaping from Gestapo headquarters
Xon the planet Ekos.
XWhen Science Officer Bruno Wilhelm placed a dilithium laser
Xsetup inside a Chalmbers coil,
Xthe crystals synchronized so as to overlap the coinciding lightwaves
Xexactly out of ``phase'' making the light energy
Xeffectively vanish from our continuum,
Xonly to re-emerge as a uni-directional highly intense disruption
Xof the space/time continuum now known as the ``phaser effect''.
XSuch synchronization of the crystals
Xrequired a super-luminal transfer of coordinating influences,
Xand so was only possible in the context
Xof a coil-induced sub-space environment.
XWithin the coil, one can reasonably construe the laser as being
X``in'' sub-space.
X.PP
XWhen fully powered,
Xthe phaser effect travels at the Warp 10 limit
Xfor the type of Chalmbers coil used,
Xbe it Primary, Secondary, or Tertiary.
XNaturally, StarFleet vessels are armed only with Tertiary phasers,
Xanything less would produce a ``beam'' literally too slow
Xto catch a Tertiary warp starship with Dilithium focused
Xanti-matter reactors.
X.PP
XHowever, hand phasers don't have access to quite enough power
Xto energize the coil component to its equivalent threshold power level.
XThe result is that the phaser beam produced
Xtravels at a speed dependent upon the power level applied to the coil.
XWhereas a beam emitted from a coil at threshold power
Xwould always move at Warp 10,
Xwith additional coil power just boosting the intensity
Xor striking power of the beam,
Xat just below threshold power the beam's speed
Xis the reciprocal of Warp 10.
XThis is a mere $7.58766 x 10 sup -6$\0x\0C,
Xor approximately 7300 feet per second from a Tertiary coil,
Xtherefore hand phasers use Primary coils
Xso that the phaser effect propagatation velocity
Xis proportional to the reciprocal of the Primary warp
Xfield's Warp 10 limit of 22025.47\0x\0C.
XThe reciprocal value is therefore approximately 8.45 miles per second.
XAt still less coil power, the speed diminishes in direct proportion
Xto the fraction of threshold power applied to the coil.
XOperational maximums for ST:TNG hand phasers take their coils to
Xabout 1/3 of threshold velocity,
Xso that the weapons full power effect moves
Xat roughly 2.82 miles per second.
X.PP
XOne can vary the proportion of coil vs. initiating light energy levels
Xonly so far without overloading the hand phaser,
Xcausing burnout or even detonation.
XThus to moderate the phaser effect down to stun levels,
Xthe beam in some models of hand phaser may travel as slowly
Xas 200 or 300 feet per second.
XWe've seen this effect quite clearly when Kirk once fired his phaser
Xset for stun at the metabolically accelerated Deela of Scalos,
Xwho simply stepped out of the way.
XHand phaser on stun is definitely a close quarters
Xonly weapon, where speed is not significant.
X.PP
XUnlike sub-space ``radio'',
Xwhich simply attenuates under an inverse square law,
Xphaser beams have a much shorter range
Xdue their propensity to ``decay'' by losing their energy
Xto the creation of visible spectrum photons
Xall along their path of travel.
XThis is what the observer sees, not the phaser beam itself.
XThe actual phaser effect is one of micro-range random space/time
Xfluctuations in the topological gradient of the space encountered,
Ximparting warp impulses to the atoms encountered.
XThe effect tends to spread and propagate through solid matter,
Xso that material objects are likely to distribute the effect
Xthroughout their particularly shaped volumes.
X.PP
XAt high power, the effect is so severe
Xthat all molecular bonds are snapped,
Xand all of the particles are ``impulsed'' in random directions.
XWhat had been a solid object
Xbecomes an expanding cloud of particles
Xmoving fast enough to penetrate other solid matter
Xto an enormous extent.
XA body so ``disintegrated'' on a ship
Xwould pass right through the hull like a burst of gamma rays,
Xbut because the particles are traveling
Xvia impulse rather than momentum,
Xtheir behavior apes that of neutrinos in that they do almost no
Xdamage to the matter they pass through.
X.PP
XLower power simply stretches the molecular bonds without breaking them,
Xtheir rebounding motions translating into simple heat.
XIn this manner, a hand phaser may be used to heat rocks for warmth,
Xcook food, or even act as a very precise cutting torch.
XAt the lowest useful power, the jolting of
Xmolecules is too slight to really impact inanimate matter,
Xbut does tend to produce neurological shock
Xas large numbers of synapses have their firing
Xthreshold randomly raised or lowered.
XThe vast number of additional versus inhibited synaptic firings
Xcauses a biological equivalent of ``systems crash''
Xleading to unconsciousness,
Xas the nervous system becomes hopelessly confused
Xand overloaded by spurious signals.
XAs no actual tissue damage is sustained,
Xthe nervous system ``reboots'' itself eventually.
XSomewhat higher power can do permanent,
Xeven lethal damage to the nervous system however,
Xand can cause a seizure-like muscular convulsion.
XThis minimally lethal effect is not unlike electric shock.
X.sp
X.PP
XTo residents of the 20th century,
Xthe transporter is perhaps a more incredible application
Xof Cochrane's Unified Field Theory than superluminal travel,
Xsince the later affords no real Terrestrial gauge
Xfor appreciating the effect,
Xwhereas the wonder of instantaneously materializing elsewhere
Xhas been part and parcel of Earth's mythology/magic belief systems
Xfor millenia.
X.PP
XBuilding on the ability of the ``looped coil''
Xto project gravitational fields,
Xexperimenters eventually learned to handle gravity waves
Xin ways that parallel optical technology's capabilities
Xwith light waves.
XUltimately, command of these techniques was sufficient
Xto produce a gravitational wave ``hologram''
Xin which the system literally captured the continuum profile
Xof an object down to the minutest detail of atomic constituents
Xand molecular bondings in the intersection between
Xits stationary ``reference beam'' and the rotating ``scanning beam''.
XSophisticated split beam techniques permitted the
X``projection'' of a second ``continuum profile image'',
Xwhich, depending on the operational limits of the equipment,
Xcould be located at an arbitrarily large distance and direction
Xfrom the source.
XThese experiments were originally conceived in pursuit
Xof improved medical technology following the progression of X-rays,
Xultrasound, nuclear magnetic resonance,
Xand positron emission tomography,
Xwith the result enabling Dr. Crusher to obtain a clear view
Xof the parasite creature embedded in Admiral Quinn during the
X``Conspiracy'' period.
X.PP
XThe transporter breakthrough grew out of experiments
Xattempting to manipulate matter via alterations of the continuum profile
Xassociated with an object.
XIf a continuum profile projection were maintained long enough,
Xit began to fill itself in with atoms picked up from the environment.
XEventually, it would recreate the original,
Xthough in the meantime,
Xif sufficient power was used to intensify the projection,
Xthis profile construct could behave like the original,
Xeven appearing to be solid matter,
Xas long it remained within range of the projection radius.
XAt the same time,
Xit was shown that changes in the profile of the original
Xwere reflected in the original object as well in the projection,
Xestablishing the real-time linkage between the two.
XEarly attempts at matter manipulation were usually destructive,
Xnot until the early 24th century would the raw computer power
Xbe available for such things as the holodeck,
Xwhere the projection could be based on computer simulations
Xrather than real life / real time models,
Xbut in these pioneering efforts,
Xthe ability to project a profile back on its own source object,
Xwhile maintaining an independent second projection elsewhere,
Xwas developed.
X.PP
XDr. Janet Hester of the Deneva Research Station
Xfirst conceived the idea that if one reversed
Xthe ``topological polarity'' of the image
Xprojected back upon the source,
Xin effect FLATTENING the impression it made in space/time,
Xwhile simultaneously boosting the gravitational intensity,
Xand thus the DEPTH of the spatially projected image,
Xone could create a situation in which the probability
Xof finding any given constituent of the source object
Xat the original location could be reduced to zero,
Xeven as the probability of finding it at the projection's location
Xwent up to unity.
XEvery component of an object, its atoms,
Xthe chemical bonds between them, even the ongoing molecular processes,
Xwould cascade back and forth
Xbetween the twin loci of probable locations,
Xfinally coming to rest at the one brought to unity.
XOf all the marvels that have sprung from Zephram Cochrane's insights,
Xnone more clearly demonstrate his success
Xat unifying gravitational space/time continuum phenomena
Xwith quantum mechanical probability functions.
X.PP
XIt would take another four decades of dedicated experiment and study
Xbefore Science Officer Winston of the USS \f2Moscow\fP
Xbecame the first human to transport across to the USS \f2Tehran\fP.
XStill more work was required
Xbefore the ability of the transporter to project a ``virtual''
Xyet functional copy of the active components of the scanning
Xand projection processes to envelope
Xthe retrieval site would eliminate the need
Xfor physical hardware at both ends of the transport linkage,
Xand then to learn to bend the projection around the
Xsurfaces of planets using the natural gravitational field
Xso that transport could be free of line-of-sight restraints.
XThe depth of dense planetary matter the transporter can penetrate
Xis still limited, but the often life-saving speed and convenience
Xof transport in general has proved well worth the time,
Xcost, and often sacrifice it took to perfect.
X.sp
X.PP
XThe Secondary Warp field effect was originally achieved
Xby winding a second-stage ``booster'' coil
Xaround a specially designed Primary coil.
XThe early versions of this system
Xwould energize the Primary coil first
Xto navigate at low percentages of threshold power.
XOnce clear of stellar and planetary gravitational fields,
Xthey would engage the booster coil reconfiguring their warp field
Xinto the 2nd order type.
XWhen this was accomplished,
Xpower would be steadily increased
Xuntil the threshold level was attained
Xand transition to the warp continuum occurred.
XThe Primary and the booster together constitute the Secondary coil.
XShould the booster fail under operational stress,
Xa fairly common occurrence in the early days,
Xthe Primary alone could be used
Xand could operate above its threshold level
Xto take the ship to superluminal velocities.
X.PP
XWhile later vessels retained the above system layout,
Xexperience proved it far more efficient
Xto energize the whole Secondary coil system as a single circuit,
Xand to navigate at very low power and speeds with an independent
Xminiature Primary system.
XThis became known as the Impulse Drive.
XAs it was intended only for low speed operations,
Xthis system would not normally be capable of handling the power load
Xit would require to bring the vessel past the threshold point.
XHowever, engineers took advantage of this dual propulsion system
Xto split the vessel itself,
Xletting each major sub-division of the hull house one of the systems.
XIt became customary to place the major living quarters in the hull
Xwith the smaller Impulse Drive,
Xboth to better shield the crew from the higher radiation levels
Xthe more powerful Secondary system created,
Xand also with the idea of better accomodating the entire crew
Xshould ``coil burnout'' force the abandonment of the other hull.
X.PP
XThe terminology of vessel design adopted the convention
Xof referring to the hull housing the Secondary coil system
Xas the Secondary Hull,
Xand the other housing the Primary coil only Impulse Drive
Xas the Primary Hull.
XTertiary drive systems simply wound yet another type of booster coil
Xaround the Primary and Secondary stages nested inside it,
Xbut as there were still only two drive systems
Xand two main hull sections,
Xthe one with the large engine system
Xcontinued to be called the Secondary Hull.
X.PP
XIn the event of separation, the Primary Hull's Impulse Drive,
Xfreed of the weight of the entire Secondary Hull
Xand the even more massive main drive engine nacelles,
Xis usually large enough for superluminal propulsion.
XThis has been shown quite clearly in ST:TNG
Xduring the initial encounter with Q,
Xwhen the Primary Hull found its way to Farpoint
Xafter the entire ship spent some 10 minutes
Xpushing itself to its operational limits while going in
Xexactly the opposite direction.
XIt is equally well implied by Geordi's instructions to Engineer Logan
Xto take the Primary Hull to a Starbase
Xif unable to re-establish contact with him
Xafter performing the saucer separation manuever
Xin the ``Arsenal of Freedom'' incident.
X.PP
XThe first three orders of warp field phenomena
Xcorrespond to the first three ``generations''
Xof warp drive technology in the ``Spaceflight Chronology''.
XLogically, a ``Fourth generation'' designation
Xshould have waited for the development of Quaternary warp,
Xthe sum of $X sup 4 + X sup 5 over 5 + X sup 6 over 30$ etc.,
Xequivalent formula
X$24 ({e sup W} - (W sup 3 over 6 + W sup 2 over 12 + W + 1))$,
Xbut the impact of Dilithium on power generation,
Xand thus overall performance,
Xwas so great that the ``Fourth generation'' label
Xtook hold for the \f2Constitution\fP class.
XAll orders of warp field phenomena
Xremain subject to the Warp 10 limit on Delivered Power,
Xbut higher order warps produce greater velocity for the same
XDelivered Power than lower orders.
X(See Appendix for tables of Primary, Secondary,
Xand Quaternary Warp Factor Equivalent Velocities).
X.PP
XThe term ``Fifth generation'' is usually applied
Xto the abortive attempt to harness ``Trans-Warp'',
Xa misbegotten application of the Interphase phenomena
Xfirst observed by the \f2Enterprise\fP NCC-1701
Xduring the ``Tholian Web'' incident.
XThe abandonment of this dangerous system
Xwas made doubly disappointing
Xby the continued failure of Federation science
Xto perfect a workable Quaternary warp drive.
XThe seemingly insurmountable difficulties encountered
Xin the early attempts at Quaternary drive design
Xwere the prime reason for the costly ``Trans-Warp'' interlude.
X.PP
XHowever, in the intervening decades advanced theoretical studies
Xhave led to vastly simpler, more reliable Tertiary drives
Xwhich can be pushed, and above all held,
Xfar closer to the Warp 10 limit of Delivered Power than the
Xoriginal design multi-stage units.
XThese single stage ``integrated'' units
Xwere first used in ship's of the NCC-1701-C's \f2Ambassador\fP class,
Xand marked the arrival of warp technology's ``Sixth generation''.
XA highly refined and advanced version of this type of drive
Xserves as the main propulsion for \f2Galaxy\fP class starships
Xsuch as \f2Enterprise\fP NCC-1701-D.
XGone are the inefficiencies of the nested, three coil approach,
Xadvances in Impulsor Calculus theory
Xand supercomputer simulation techniques having found
Xa single coil equivalent.
X.PP
XAs the early efforts at Quaternary warp
Xfloundered on the complexities of a four level multi-stage approach,
Xthe success of the single stage ``integrated'' approach
Xfor Tertiary warp has scientists of ST:TNG's era once
Xmore confident of eventual success,
Xand aggressively paced research programs
Xare again under way in the race for the Quaternary drive.
XIt should be noted that the extra heavy warp nacelle mountings
Xand overall structural strength rating of the \f2Galaxy\fP class design
Xshould easily permit retrofitting of Quaternary Warp engines
Xwhen they become available.
X.PP
XMontgomery Scott correctly predicted
Xthe crippling deficiencies of the Trans-Warp system,
Xbut was unable to dissuade StarFleet from investing in it.
XRightly convinced that Quaternary warp would have to await improvements
Xin warp theory permitting ``integrated'' designs,
Xhe attempted to convince StarFleet to allow him
Xto challenge the Warp 10 Barrier itself.
XAlas, Scott was never able to secure StarFleet backing for his proposal,
Xand only a handful of ST:TNG era technical persons
Xwho've studied his original notes even know what he had in mind.
X.PP
XRealizing that the ``SuperWarp'' scheme
Xwas far too radical for his era,
XScott dedicated his leisure time engineering studies
Xto the design of the ship he felt StarFleet should build
Xin place of more ``Excelsior'' class vessels.
XYet this project also offered too many radical advances,
Xas Scott was allowing for upgrades to integrated Tertiary
Xor even Quaternary main drives in his huge dreamship.
XBut while the \f2Galaxy\fP class would ultimately be larger
Xand incorporate advances beyond his wildest imaginings,
Xeven a cursory glance at Scott's old plans and drawings
Xreveals the striking similarities that mark the true lineage
Xof these greatest of all StarShips.
XNCC-1701-D's operational status is the way Scott would most have wanted
XStarFleet Engineering to acknowledge its continuing debt
Xto its greatest practitioner.
X.PP
XAs for the mechanics of SuperWarp,
Xthe mathematically inclined are invited to contemplate the significance
Xof the other half of the hyperbola
Xrelating Generated to Delivered power,
Xwhich most Federation scientists dismiss as a mere geometric curiousity.
XOf course, scientists once thought that C itself
Xrepresented an impassable barrier, yet as Spock would say,
X``There are always possibilities.''
X.PP
XWithout giving too much away, I can offer the following clue,
Xthat the \f2Constitution\fP class USS \f2Enterprise\fP NCC-1701
Xunder James Kirk, once broke through the Warp Barrier by accident,
Xthe result of her Captain's famous propensity
Xfor taking desperate gambles in otherwise hopeless situations.
XStudents of warp physics correctly identifying the occasion
Xare eligible to win a scholarship to StarFleet academy,
Xwhich, alas, may not be used until the 23rd century.
X.LP
XLeon Myerson; 72157,3432; 6/23/88
X.bp
X.ce
XAPPENDIX 1 - PRIMARY WARP
X.TS
Xbox, center, tab(~);
Xc c c
Xn n n.
XGenerated Power~Delivered Power~Primary Warp x C
X_
X1~1.00000~1.72
X2~1.98354~6.27
X3~2.96260~18.35
X4~3.93509~50.17
X5~4.89755~132.96
X6~5.84370~344.05
X7~6.76140~862.85
X8~7.62571~2049.24
X9~8.38615~4384.92
X10~8.96633~7833.82
X.TE
X.LP
XTheoretical Limit = 22025.47 x C
X.br
XThreshold Velocity = 0.5814 x C
X.br
XTime Dilation at threshold = 0.813205
X.bp
X.ce
XAPPENDIX 2 - SECONDARY WARP
X.TS
Xbox, center, tab(~);
Xc c c
Xn n n.
XGenerated Power~Delivered Power~Secondary Warp x C
X_
X1~1.00000~1.44
X2~1.98354~8.57
X3~2.96260~30.77
X4~3.93509~92.46
X5~4.89755~256.13
X6~5.84370~676.42
X7~6.76140~1712.18
X8~7.62571~4083.24
X9~8.38615~8753.06
X10~8.96633~15649.70
X.TE
X.LP
XTheoretical Limit = 44030.93 x C
X.br
XThreshold Velocity = 0.6944 x C
X.br
XTime Dilation at threshold = 0.717939
X.bp
X.ce
XAPPENDIX 3 - QUATERNARY WARP
X.TS
Xbox, center, tab(~);
Xc c c
Xn n n.
XDelivered Power~Generated Power~Quaternary Warp
X_
X1~1.0000000000~1.24
X2~2.0167653720~25.34
X3~3.0383208502~170.05
X4~4.0670614879~742.36
X5~5.1072983806~2617.92
X6~6.1676537197~8218.29
X7~7.2682459514~24167.20
X7.5~7.8487197368~40826.52
X8~8.4694304149~68510.99
X8.2~8.7364919027~84149.66
X8.4~9.0203187626~103286.47
X8.6~9.3280961537~126697.69
X8.8~9.6717993420~155331.49
X9~10.0729838055~190346.01
X9.1~10.3071067812~210676.62
X9.2~10.5747605008~233155.87
X9.3~10.8903152831~258009.95
X9.4~11.2777216596~285488.88
X9.5~11.7800905867~315868.94
X9.6~12.4836439773~349455.49
X9.7~13.5895662949~386586.00
X9.8~15.7014109302~427633.43
X9.9~21.8369448362~473009.97
X10~INFINITE~523171.18
X.TE
X.LP
XTheoretical Limit = 523171.18 x C
X.br
XThreshold Velocity = 0.8065 x C
X.br
XTime Dilation at threshold = 0.590200
X.bp
X.PP
XFor comparison, here is a chart of Quaternary Warp Factor equivalent
Xvelocities keyed on the older ``Generated Power'' scale.
X.TS
Xbox, center, tab(~);
Xc c c
Xn n n.
XGenerated Power~Delivered Power~Quaternary Warp x C
X_
X1~1.00000~1.24
X2~1.98354~24.41
X3~2.96260~159.92
X4~3.93509~680.00
X5~4.89755~2315.80
X6~5.84370~6908.99
X7~6.76140~18761.08
X8~7.62571~46527.25
X9~8.38615~101833.70
X10~8.96633~183948.24
X11~9.33067~266146.24
X12~9.53548~327403.32
X13~9.65322~368752.42
X14~9.72615~396927.10
X15~9.77477~416884.29
X16~9.80915~431599.84
X17~9.83463~442835.76
X18~9.85421~451667.92
X19~9.86971~458779.77
X20~9.88225~464622.34
X21~9.89262~469503.75
X22~9.94445~494688.02
X.TE
END_OF_FILE
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    echo shar: \"'warp.troff'\" unpacked with wrong size!
fi
# end of 'warp.troff'
fi
echo shar: End of shell archive.
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