Warp drive (Star Trek)

In the fictional universe of Star Trek, the warp drive is a form of faster-than-light (FTL) propulsion. Hyperdrive and jump drive are alternative methods of FTL travel commonly used in fiction. However, these work on the principle of moving from one dimension at point "A" to another, then back to your own at point "B", while the warp drive does not do this.

The concept of using spatial warping as a means of propulsion has been the subject of theoretical treatment by some physicists (such as Miguel Alcubierre, see Alcubierre drive), although no concrete technological approach has ever been proposed, nor is there any known way of inducing the effect described by Alcubierre.

Fictional Warp history

On Earth it was invented by Zefram Cochrane, with the first warp flight taking place in 2063 as depicted in First Contact. According to the latest Star Trek series, Enterprise, many other civilizations had warp drive before humans, notably the Vulcans, who had more advanced warp drive technology than humans even in the 22nd century. In the Star Trek pilot episode "The Cage", warp was mentioned with the term "time warp". The episode revealed that the "time barrier" had recently been broken, but since this was given as news to a group of shipwrecked interstellar travelers, it could not refer to the breaking of the light barrier.

The rate of warp travel is usually given only in warp factors. Warp factors are not simply a fancy unit of speed that is related to regular units of speed through a fancy formula. Warp factors must measure something for which our SI system does not have a unit ; what we do know is that according to the official manuals integer warp factors are related through a complex warp formula to warp field strengths in cochranes (named after Zefram Cochrane) that represent local minima of power usage. For example, a warp field of 10 cochranes in TNG-era engines corresponds to warp factor 2. Finally, only under average conditions does a certain cochrane-value correspond to a multiple of c. All of this is essential to understanding the purported "errors" in onscreen travel times.

Achieving warp factor 1 is equivalent to breaking the light barrier, while at higher factors the average speed increases according to a specific warp formula. Several episodes of the original series placed the Enterprise in peril by having it travel at high warp factors, once as high as warp 14.1 ("That Which Survives"). However, the actual speed of any given warp factor is rarely explicitly stated on screen, indicating that it is not of much use to our characters. Travel times for specific interstellar distances are not quite consistent , indicating that different average speeds can correspond to the same warp factor.

The creators of The Next Generation decided that warp 10 should be the maximum. The warp factors above warp 10 in the Original Series, such as the one above, were "actually" less than warp 10 on the new scale. According to The Star Trek Encyclopedia, warp 6 is equal to 392c and about warp 7.3 on the old scale and warp 9.2 to about 1649c and warp 11.8 on the old scale. The scale reaches an asymptote at warp 10 which represents infinite speed in accordance with the speed limit imposed by the producers. The Voyager episode "Threshold" agreed with this, in that the characters said attaining the velocity of warp 10 was impossible — but then they achieved it anyway, with the side effect that they hyper-evolved (reversibly) into anthropomorphic newts. Many dismiss this episode by wondering how the shuttle could have travelled at infinite speed; the producers did as well as the episode was removed from canon. It is unclear whether the warp 13 achieved in the possible future shown in "All Good Things..." represents a new recalibration of the warp curve or some form of transwarp, though as this future was a creation of Q it might not occur in the "real" Star Trek timeline.

A ship travelling at warp or impulse speeds will not experience any form of time dilation, indicated by the numerous cases where impulse speeds were stated as being far above the limitation of 1/4c mentioned in the technical books, nor will they require huge quantities of fuel to achieve such speeds. Impulse drive is only partly conventional propulsion, the other part being based on the same technologies used in warp drive.

Transwarp drive

The term "transwarp" has been used a number of times, referring to an advanced form of warp drive most commonly used by the Borg, but also the subject of an unsuccessful Starfleet development project in The Search for Spock. Just as the generation of a warp field around a starship is required to enter warp speed without using infinite amounts of energy, thereby breaking the light barrier (a theoretically impossible event in our universe), so is a transwarp field required to reach very high FTL speeds (making a ship capable of crossing galactic distances in a very short time).

Federation experiments

The USS Excelsior (NX-2000), under the command of Captain Stiles was a Federation testbed for transwarp technology. Though not explained on-screen in The Search For Spock, it is assumed that transwarp is a faster version of the conventional warp drive. Excelsior's first operational test failed due to sabotage by Scotty, thus preventing Excelsior from pursuing the Enterprise. By the events of The Undiscovered Country, the Excelsior (under command of Captain Sulu) had been fitted with standard warp drive, so it is assumed that even after repairing Scotty's tampering, the transwarp tests were unsuccessful.

In 2374, the crew of the USS Defiant was sent on a mission to study a rare subspace compression phenomenon in Federation space. It was hoped that further study of the anomaly would lead to the creation of working transwarp drives. Unfortunately the mission was interrupted by a Jem'Hadar attack but the ship was successfully retaken by Lt. Commander Jadzia Dax, Chief Miles O'Brien, Dr. Julian Bashir and Lt. Commander Worf.

The Borg and other aliens

The Borg (in the Star Trek: The Next Generation two-part episode "Descent" and in the Star Trek: Voyager final episode "Endgame") have discovered anomalies called "transwarp conduits" — regions in subspace that facilitate transwarp travel at up to 20 times faster than conventional warp drives. Borg transwarp conduits are activated by an encoded tachyon pulse. When a Borg vessel enters a transwarp conduit, it is subject to extreme gravimetric shear. To compensate, the Borg project a structural integrity field ahead of the vessel. Artificial conduits are linked together with transwarp hubs. Six hubs were known to exist, but in the Voyager episode "Endgame" one was destroyed, possibly along with the entire borg collective due to the neurolytic pathogen which Admiral Janeway infected herself with. This has yet to be clarified, but since the Borg are all connected, it may be that every Borg in existence was destroyed.

Borg transwarp technology is similar to the Quantum Slipstream Technology used by Arturis' people (Species 116).

Warp velocities

In the Original Series, according to the Star Trek episode writer's guide, warp factors were supposedly converted to multiples of light speed with the cubic function

s(w) = w^3c

. With that being said, that means the table for the Original Series warp speed is as follows:

Warp Factor	x c	Velocity (all figures approximate)
Warp 1	1 c	3.0x10⁵ km/s
Warp 1.5	3.375 c	1.0x10⁶ km/s
Warp 2	8 c	2.4x10⁶ km/s
Warp 3	27 c	8.0x10⁶ km/s
Warp 4	64 c	1.9x10⁷ km/s
Warp 5	125 c	3.7x10⁷ km/s
Warp 6	216 c	6.5x10⁷ km/s
Warp 7	343 c	1.0x10⁸ km/s
Warp 8	512 c	1.5x10⁸ km/s
Warp 9	729 c	2.2x10⁸ km/s
Warp 9.25	~791 c	2.4x10⁸ km/s
Warp 9.5	~857 c	2.6x10⁸ km/s
Warp 9.75	~926 c	2.8x10⁸ km/s
Warp 10	1,000 c	3.0x10⁸ km/s
Warp 11	1,331 c	4.0x10⁸ km/s
Warp 14.6	~3,112 c	9.3x10⁸ km/s
Warp 15	3,375 c	1.0x10⁹ km/s

However, this cannot possibly be the whole story, as it would make the Enterprise far too slow for the voyages depicted in the television series. These speeds do not even correlate with solid facts and figures in some of the episodes, for example in "That Which Survives" (1969) the Enterprise travels at warp 8.4 for 11.33 hours and traverses 990.7 light years (as indicated in Spock's dialogue), which makes the speed more than 600,000 times the speed of light, which is two orders of magnitude larger than even warp 15. There is also the fact that the Enterprise could quite easily travel to and from the edge of the galaxy at will ("Is There in Truth No Beauty" and "By Any Other Name" (1968)), a journey which should take years at the typical warp 8, if warp 8 is merely a cube of the warp factor.

This discrepancy between the behavior of warp speeds in the show and the simple formula of the warp factor cubed was picked up by fans in the 1970's and 80's who published books like Star Trek Maps (all published material is considered non-canon, even if it is by Paramount-approved Pocket Books) where the idea of an additional factor, referred to as the Chi factor or the Cochrane factor, was used in the warp calculations. The idea was that since warp drive pulls in space, you get higher speeds in areas where there is high density of mass, and lower speeds in areas of low density. If we take a warp factor and cube it, we take that product and multiply it by the number 1292.7238 (the Chi or Cochrane factor), to get the actual speed that the ship travels at (this is the number that was factored out of the factoids from "That Which Survives" (1969)). The Cochrane factor represents an "average" density of space in the UFP. Other areas of space will have different values for it. This is one way to explain the relationship between stated warp factors and actual calculable speeds as given in the dialogue in the episodes. Although it is not actually canon, it at least explains how the ships behaved as they did, without having to find higher exponents to factor the warp base numbers by, as Star Trek artist Michael Okuda did later for TNG (which nobody on the show ended up paying attention to anyway).

For the later series, Okuda devised a formula based on the older one but with important differences. For warp 1–9, if w is the warp factor, s is the speed in km per second, and c is the speed of light, then $s(w) = w^{10 \over 3}c$ . In the half-open interval from warp 9 to warp 10, the exponent of w increases toward infinity. Thus, in the Okuda scale, warp speeds approach warp 10 asymptotically. There is no exact formula for this interval because the quoted speeds are based on a hand-drawn curve.

Here is a table with new-style warp factors and their approximate values in kilometers per second and multiples of c:

Warp Factor	x c	Velocity
Warp 1	1 c	3.0x10⁵ km/s
Warp 2	10.079 c	3.0x10⁶ km/s
Warp 3	38.941 c	1.2x10⁷ km/s
Warp 4	101.59 c	3.0x10⁷ km/s
Warp 5	213.75 c	6.4x10⁷ km/s
Warp 6	392.50 c	1.2x10⁸ km/s
Warp 7	656.13 c	2.0x10⁸ km/s
Warp 8	1,024 c	3.1x10⁸ km/s
Warp 9	1,516.4 c	4.5x10⁸ km/s
Warp 9.2	1,649 c	4.9x10⁸ km/s
Warp 9.6	1,909 c	5.7x10⁸ km/s
Warp 9.9	3,053 c	9.2x10⁸ km/s
Warp 9.9753	6,000 c	1.8x10⁹ km/s
Warp 9.99	7,912 c	2.3x10⁹ km/s
Warp 9.9999	199,516 c	6.0x10¹⁰ km/s

Here is a table of the times it would take to cover a number of distances. Since warp 1 is c, the distances for warp 1 (in years) is the light year distance. Earth's solar system is approximately 1.2x10¹⁰ km wide, measured as the diameter of the Oort Cloud.

Warp	x c	Across Sol System (12 billion km)	To Alpha Centauri (4.2 light-years)	Across Sector (20 light-years)	Across Federation (10,000 light-years)	Across Galaxy (100,000 light-years)	To Andromeda Galaxy (2,000,000 light-years)
Warp 1	1 c	11 hours	4.2 years	20 years	10,000 years	100,000 years	2,000,000 years
Warp 2	10.079 c	1 hour	6 months	1 year	100 years	10,000 years	200,000 years
Warp 3	38.941 c	17 minutes	6 weeks	6 months	25 years	2,564 years	51,000 years
Warp 4	101.59 c	6.5 minutes	18 days	2 months	10 years	990 years	19,800 years
Warp 5	213.75 c	3 minutes	8.4 days	34 days	4.6 years	467 years	9,345 years
Warp 6	392.50 c	1.7 minutes	4.6 days	18.6 days	2.5 years	255 years	5,102 years
Warp 7	656.13 c	1 minute	2.8 days	11.3 days	1.52 years	152 years	3,048 years
Warp 8	1,024 c	38 seconds	1.7 days	7.1 days	1 year	100 years	1,953 years
Warp 9	1,516.4 c	26 seconds	1.2 days	4.8 days	8 months	66 years	1,319 years
Warp 9.2	1,649 c	24 seconds	1.1 days	4.4 days	7 months	61 years	1,217 years
Warp 9.6	1,909 c	20.7 seconds	23 hours	3.8 days	6 months	53 years	1,051 years
Warp 9.9	3,053 c	13 seconds	14 hours	2.4 days	3.8 months	33.3 years	660 years
Warp 9.9753	6,000 c	6.6 seconds	7.1 hours	1.2 days	1.9 months	16.9 years	335 years
Warp 9.99	7,912 c	5 seconds	5.4 hours	22 hours	1.4 months	12.8 years	254 years
Warp 9.9999	199,516 c	.2 seconds	12.8 minutes	52 minutes	18 days	6 months	10 years

The later series were better at keeping to these speeds than the original; however, they were still far from perfect. Later episodes of The Next Generation (such as "Descent" (1993)) contradicted these speeds and Deep Space Nine depicted Federation Starfleet strategic operations (fleet movements) which would have been impossible under the Okuda scale. Voyager, though its premise was generally based on the Okuda scale, had several notable instances, such as in the episode "Parallax" or "The '37s" (1995), where the stated warp velocities varied wildly from the Okuda standard.

In general, the farther away a Star Trek show is in production date from the publish date of the Star Trek Technical Manual, the more likely a ship would be to travel at the "speed of plot". For example, in the Enterprise pilot episode they give a time and speed to Neptune that accords with the original series' formula, but then they estimate a trip to the Klingon Homeworld at warp 5 as a four-day journey, placing it just one light-year away from Earth—far closer than the nearest stellar system, Alpha Centauri. This plot hole has later been wrapped up by various sources that suggest that there is a spatial rift that allowed the Enterprise to arrive at the Klingon homeworld in such a short length of time, and that it was the Vulcans who provided Enterprise with the whereabouts of this shortcut. It should be noted, however that such a high speed for warp 5 is consistent with the extremely high speed given for warp 8.4 in "That Which Survives," which has the speed at over 600,000 times lightspeed (therefore warp 5 would be 161,500 times lightspeed). In those terms, four days travel at warp 5 places the Klingon homeworld at 1,772 light years (or 536 parsecs) away from Earth.

This is why any theory matching a warp factor to a specific speed is inconsistent with the show. Imagine driving on a highway under ideal weather conditions: it is quite possible to order a speed of 100 km/h and expect the order to be executed. Try leaving the highway and driving on diverse terrain, and maintaining a specific speed is no longer meaningful. All one cares about is keeping the engine intact, which in Star Trek terms is equivalent to maintaining a safe warp factor and estimating travel times based on the properties of the area of space. Newer engines may allow a greater cochrane output per warp factor and have no minimum beyond warp nine. Finally, many kinds of engines could be built over the years with different limitations and different cochrane-levels per warp factor.

Warp theory and technology

For a more in-depth discussion of warp propulsion systems, refer to the The Next Generation Technical Manual by Rick Sternbach and Michael Okuda. Chapter 5, "Warp Propulsion Systems", discusses the following topics:

Warp field theory and application, including warp measurement, velocities, and limits.
Matter-antimatter reaction assembly, including reactant injectors, magnetic constriction segments, reaction chamber, the role of dilithium, and power transfer conduits.
Warp field nacelles, including plasma injection system, warp field coils, and warp propulsive effect.
Antimatter storage and transfer, warp propulsion system fuel supply, Bussard ramjet fuel replenishment, and onboard antimatter generation
Engineering operations and safety, emergency shutdown procedures, and catastrophic emergency procedures

However, it should be noted that the shows often contradicted both the TNG and DS9 technical manuals.

The Slingshot Effect

A side effect of Warp travel which has been shown throughout Star Trek is the "Slingshot effect." First discovered by accident in "Tomorrow Is Yesterday" (1967), one of the first episodes of the original Star Trek series, it is a method of using a Warp drive to travel through time. While the actual procedure is intentionally obscure, it involved travelling at high warp speed towards a star (established in The Voyage Home (1986) to be somewhere over Warp 9.8), on a precisely calculated "slingshot" path, and if successful it can allow for travel to the future or past. The same technique was used later in the episode " Earth (TOS episode)" (1968) intentionally for historic research (where it is given the technical name "light speed breakaway factor"), and again in Star Trek IV (where it was called "time warp"). The technique was mentioned as a viable method of time travel in the Star Trek: The Next Generation episode "Time Squared" (1989).

Warp and the environment

In the Season 7 Next Generation episode "Force of Nature" (1993), it was revealed that warp drive travel can be detrimental to subspace, and in some areas it can cause subspace fissures along heavily travelled routes. Travel faster than warp 5 was banned in the aforementioned episode, but there is argument among fans as to whether the ban exists only in the affected areas of space, or in all areas. If it is a universal limit, it is widely ignored and rarely even mentioned in later episodes and series. In the TNG episode "Eye of the Beholder" (1994), advance permission was required from starfleet command for the Enterprise to travel above warp 5 (in this case on a mission of mercy). A technological solution was found, involving the warp engines on the USS Voyager. This has been confirmed by the www.startrek.comlibrary, explaining that Voyager was designed to go faster than warp 5 without causing subspace damage such as fissuring of space. The Sovereign Class Enterprise-E also featured advanced Warp Drive engines that allow travel at very high warp velocities without damaging the fabric of space.

Is a nonfictional warp drive possible?

As many Star Trek fans know, many of the futuristic technologies featured on Star Trek have actually been created (such as the hypospray) or are currently being researched (e.g., the VISOR). In 1996, NASA established the Breakthrough Propulsion Physics Program, which sponsored some speculative work on warp drives. This program was discontinued in 2002.

While thought experiments on the wilder shores of theoretical physics continue, no scheme that may allow "warp speed" travel has yet been devised that has been accepted by mainstream science. Some physicists have proposed a model of FTL travel, formulated in the context of Lorentzian manifolds, which are used in general relativity to construct spacetime models. However, contrary to a common misunderstanding, these models are in no sense solutions to the Einstein field equation, and they give absolutely no hint of how to actually make a warp bubble. These models do however show that while it is indeed impossible to go faster than the speed of light, in principle it might be possible to circumvent the problem by suitably "warping" spacetime itself. The best known such, known as the Alcubierre drive, has the amusing feature that its terminology is in accord with Trek jargon: "warp factors" measure the warping of space (or rather spacetime), not actual speed.

Recently, the Heim theory has been considered as a possible theoretical basis of creating a hyperdrive - see the links under header: Magazine articles on the Burkhard Heim's biography wikipedia web page.

External links

NASA's Marshall Space Flight Center's Space Transportation website
Special Relativity Simulator What would things look like at near-warp speeds?
Warp Drive, When? A NASA feasibility article
Alcubierre Warp Drive at the Encyclopedia of Astrobiology, Astronomy, and Spaceflight

Here is a small selection of speculative articles from the physics literature:

The warp drive: hyper-fast travel within general relativity, by Miguel Alcubierre
Null geodesics in the Alcubierre warp drive spacetime: the view from the bridge by Chad Clark, William A. Hiscock, and Shane L. Larson
The unphysical nature of "Warp Drive", by Michael J. Pfenning and L. H. Ford
A Superluminal Subway: The Krasnikov Tube, by Allen E. Everett and Thomas A. Roman
Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes by Michael John Pfenning and L. H. Ford
A "warp drive" with more reasonable total energy requirements, by Chris Van Den Broeck
Warp Drive With Zero Expansion by Jose Notario,
Fundamental Limitations on warp drive spacetimes by Francisco S. N. Lobo and Matt Visser
Problems with Warp Drive Examined

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