Warp factor

File:AR Enterprise viewscreen.jpg

In the alternate reality, the main viewscreen of USS Enterprise depicted the sublight and faster-than-light speed of the ship in warp factors at a three decimal place accuracy.

A warp field dynamics monitor displayed the warp factors of the Warp 5 engine and their relative faster-than-light speed equivalents

"They say gossip travels faster than warp speed"

– The Doctor, 2375 ("Someone to Watch Over Me")

Warp factor was the primary means of measuring speeds attained using warp drive. An alternative term time-warp factor was also used. (TOS: "The Cage") The term was often shortened to warp when followed by its value, so that saying "warp six" is the same as saying "warp factor six." Faster-than-light travel began after warp one, whereas lower fractional values were sometimes used to measure sublight speeds. (Star Trek: The Motion Picture; Star Trek; ENT: "First Flight" display graphic) Spacecraft ordinarily traveled at a higher integer warp factor.

By the 24th century, infinite velocity was designated as warp factor ten. It was considered to be unattainable by conventional means. (VOY: "Threshold") Because of this, extremely high warp factors were indicated with fractional values between nine and ten, such as warp 9.975. (TNG: "Encounter at Farpoint"; VOY: "Caretaker")

According to Geoffrey Mandel's reference book Star Trek Maps, the alternative term "time-warp" used in TOS: "The Cage" [1] is so called due to the time dilation effects that occur during warp travel.

Subspace communication speeds have also been given high warp factors in several reference materials.

Warp factor vs. average speed

The following is a list of warp factor values that have been given a relativistic speed equivalent on screen. Average speeds are typically calculated from given values for travel time and distance. Some figures were depicted in charts and others given as statements in dialogue. See: Variations in relative speed for more information.

Warp factor	Average speed (*c)	Distance traveled	Travel time	Reference
.5	0.304 - 0.496	~3.95 - 6.45 AU (Earth-Jupiter)	1.8 hours	Star Trek: The Motion Picture
1	1	depicted in warp factor chart		ENT: "First Flight"
2	8	depicted in warp factor chart		ENT: "First Flight"
3	27	depicted in warp factor chart		ENT: "First Flight"
3	39	0.102 light years	23 hours	TNG: "The Most Toys"
3	487	4 light years	3 days	ENT: "Damage"
4.4	100	30,000,000 km	1 second	ENT: "Broken Bow"
4.5	79.7 - 87.2	~57.5 - 62.92AU (Earth-Neptune and back)	6 minutes	ENT: "Broken Bow"
5	200	50 light years (Earth-An area inside the Delphic Expanse)	~3 months	ENT: "The Expanse", "The Xindi"
6+	0.02	10,000 kilometer intervals as a Klingon D7 approached	~2 seconds per interval	TOS: "Elaan of Troyius"
8.4	765,000	~990 light years	11.337 hours	TOS: "That Which Survives"
9	834	approximately 300 billion kilometers (0.032 light years)	~20 minutes	TNG: "Bloodlines"
9.9	21,473	about 4 billion miles (0.0007 light years)	1 second	VOY: "The 37's"
9.975	1,554 - 1,721	132 light years	1 month	VOY: "Relativity", "Friendship One"
9.975	2,922	40 light years	5 days	VOY: "Relativity", "Scorpion, Part II"
10	∞	∞	0	VOY: "Threshold"
n/a	8,300	2.5 million light years (to Andromeda Galaxy)	300 years	TOS: "By Any Other Name"

Warp ten and above

Multiwarp speeds

An Orion scout ship at warp 10

In the 23rd century, warp factors of 10 and higher were known as generally unsafe velocities. (TOS: "Journey to Babel") They were called multiwarp speeds. (TOS: "The Changeling")

• Warp factor 10. In 2267, the USS Enterprise engaged an Orion scout ship capable of warp 10, if not higher speeds, since crew safety was of no concern to them, prompting Spock to remark that it was "interesting." The ship was too fast for the Enterprise to hit it with phasers or photon torpedoes. (TOS: "Journey to Babel") In 2268, Bele, upon commandeering the engine and directional controls of the Enterprise, propelled the starship faster than warp 10 towards Cheron. (TOS: "Let That Be Your Last Battlefield")

• Warp factor 11. In 2267, the Nomad probe improved efficiency in the antimatter input valve and energy release controls on the Enterprise, allowing the ship to achieve at least warp 11. When this happened, Montgomery Scott was in disbelief. Captain James T. Kirk ordered Nomad to reverse the modifications though, as the structure of the Enterprise was not designed to handle the stress of that much power output. (TOS: "The Changeling") In 2268, the Kelvans who commandeered the ship made similar modification. At that time the ship could maintain warp 11 without danger. (TOS: "By Any Other Name")

According to the Star Trek Spaceflight Chronology (page 180) and Mr. Scott's Guide to the Enterprise (page 14), after the refit of the Constitution-class USS Enterprise in Star Trek: The Motion Picture, the maximum speed of the ship was warp factor 12.

• Warp factor 14. In 2268, the Enterprise achieved a speed of warp 14.1 when the engine of the ship was sabotaged to overload by a Kalandan planetary defense system. At that velocity the ship came within moments of destroying itself. (TOS: "That Which Survives")

• Warp factor 15. In 2267, the Nomad probe was armed with a weapon system capable of firing energy bolts that traveled at the speed of warp 15. (TOS: "The Changeling")

Karla Five's vessel capable of warp 36

In the comic book A Warp in Space set in the late-2260s, Starfleet tested the prototype Warp 15 engine on several test ships. Zefram Cochrane also devised modifications to the USS Enterprise that allowed the ship to achieve the speed, though the ship was almost torn apart at that velocity.

• Warp factor 22. In 2270, the Enterprise was accelerated to speeds in the excess of warp 22, while being linked to Karla Five's vessel with a tractor beam. (TAS: "The Counter-Clock Incident")

• Warp factor 36. In 2270, the Enterprise encountered Karla Five's vessel, that was about to enter the Beta Niobe nova. At maximum speed, the ship was traveling at approximately warp 36. (TAS: "The Counter-Clock Incident")

Infinite velocity

USS Enterprise-D accelerated to incredible warp speeds by the Traveler

Shuttlecraft Cochrane accelerating to warp 10

In 24th century warp theory, warp factor 10 had been redesignated to correspond with infinite velocity. A vessel traveling at warp 10 occupied all points in the universe simultaneously. Warp 10 was also known as the transwarp threshold. (VOY: "Threshold") Warp 10 had also become a slang term referring to anything extremely fast. Kathryn Janeway made the observation in 2376 that rumors traveled fast on the USS Voyager. Chakotay agreed with Janeway, quipping at "warp 10." (VOY: "The Voyager Conspiracy")

The slang term was also used in the script for DS9: "Sons and Daughters", where Alexander Rozhenko's adrenaline was described as "pumping at warp 10." [2]

According to Star Trek: Starship Spotter, the redesignation of warp 10 as infinite speed occurred in 2312. The warp factor specifications prior to 2312 were rated by Starfleet using the Original Cochrane Unit warp scale, abbreviated as the OCU. Warp factors after 2312 use the Modified Cochrane Unit warp scale, abbreviated as the MCU.

• Warp factor 10-. In 2364, the Traveler used the energy of his thoughts to move the USS Enterprise-D through space at a speed that registered on instruments as exceeding warp factor 10 and going off the warp scale. (TNG: "Where No One Has Gone Before")

According to Star Trek: The Next Generation Technical Manual (page 55), the ship didn't actually achieve warp 10 or go beyond it, but it did travel at the extreme speed of about Warp 9.9999999996. This would be confirmed in "Threshold" where Tom Paris becomes the first Human to travel at warp 10.

• Warp factor 10. Although considered a theoretical impossibility at the time, Tom Paris of the USS Voyager reached the warp 10 threshold in 2372, using shuttlecraft Cochrane which was equipped with a transwarp drive and an extraordinarily rare form of dilithium discovered earlier that year. After it was discovered that such travel induced hyper-evolution, this technology was discontinued after the initial test. (VOY: "Threshold")

• Warp factor 10+. It was possible to travel backwards in time by surpassing warp 10. In 2365, Captain Jean-Luc Picard and Commander William Riker speculated on what phenomenon could have thrown the El-Baz back through time. While Riker knew the shuttlepod didn't have warp drive, he still suggested the theory that it could have somehow accelerated beyond warp 10. Picard suggested this could have been achieved by a warp-powered slingshot using the gravitational pull of a star. (TNG: "Time Squared")

Alternate timelines

An alternative future USS Enterprise-D refitted for warp 13

In an alternative future, around the turning point of the 24th to 25th century, warp factor values beyond warp 10 were again used to describe extremely fast speeds. (TNG: "All Good Things...")

• Warp factor 13. The Enterprise-D traveled at warp 13 in the incident concerning the anti-time eruption in the Devron system. (TNG: "All Good Things...")

In the October 1995 issue of OMNI, science advisor Andre Bormanis stated the idea of warp factors beyond 10 in the alternative future was in a recalibration of the warp scale, as ships had gotten faster. Maybe warp 15 was set to be the transwarp threshold instead, according to Bormanis, and warp 13 in that scale would have been the equivalent of warp 9.95 of the previous scale.

According to Star Trek Encyclopedia, (3rd ed. p. 555) warp 13 from "All Good Things..." may also allude to some type of implementation of the Federation transwarp drive technology from VOY: "Threshold".

Appendices

Related topics

• Bessel function
• Cochrane
• Cochrane equation
• Maximum warp
• Time warp
  • Slingshot effect
• Warp equation
• Warp barrier
  • Time barrier
  • Transwarp threshold
  • Warp 2 barrier
• Warp theory

Background information

Variations in relative speed

Although formulas to calculate a relative speed from a warp factor have existed in the writer's guides, these were rarely used for reference in the episodes and films. To explain the apparent discontinuities of relative speed equivalents for warp factor speeds, reference sources have given several explanations:

• Star Trek: The Next Generation Technical Manual (pg. 55) states the actual speed values of a warp factor are dependent upon interstellar conditions, for example gas density, electric and magnetic fields in different regions of the galaxy, and fluctuations of the subspace domain. Also quantum drag forces and motive power oscillation cause energy penalties to a ship using warp drive.

• Star Trek Maps (pg. 6) introduced a similar concept as the Cochrane's factor, that influences the actual speed by multiplying it. It can be as high as a multiplication of 1500 to the relative speed within the curvature of space caused by the interstellar dust and gas of a galaxy, and as little as 1 in the empty intergalactic void. In the vicinity of massive objects it is so high that disproportionately high speeds are created when approaching them, and they tend to result in the slingshot effect. Between the galaxies there is only the empty void, so the speed follows only the basic cubic formula. (see below) Within the interstellar medium of Federation space the average value for the Cochrane's factor has been calculated to be 1292.7238. This value explains for example the ball park of the fast relative speed equivalent for warp factor 8.4 from TOS: "That Which Survives": 8.4³ x 1292.7238 = 766202.57 times the speed of light.

The slowing down effect of moving away from a source of gravity to the relative speed has been well established in canon. For example in Star Trek, the Enterprise is at maximum warp but is not moving in space at all, due to the gravity of a black hole behind it. Similarly, in Star Trek IV: The Voyage Home, the HMS Bounty engages warp speed while in the atmosphere of Earth, and it takes over two minutes in the film for the ship to achieve and break out of Earth's orbit. In TOS: "Elaan of Troyius", a D7-class starship moving away from a star system at a speed better than warp 6 is moving slower than the speed of light. In some areas of space with unstable or disrupted subspace, it is impossible to use warp drive at all, as was established in such episodes as VOY: "Bride of Chaotica!" and "The Omega Directive".

Many examples of more subtle variations exist. For example, in "By Any Other Name", the Kelvans modified the USS Enterprise to accelerate to a speed of warp 11 in order to safely cross the galactic barrier. If this was also meant to represent the velocity of travel to the Andromeda Galaxy, a travel time of 300 years would indicate a far greater speed than can be derived from the basic cubic scale from the writer's guide. Warp 8.4 was stated to be much faster in "That Which Survives" than warp 9.9 in "The 37's". In TNG: "Allegiance", warp 7 was stated to be about 55 times faster than warp factor 2, again confirming that fluctuations in the relative speeds exist that are not covered by the basic formula.

Star Trek: The Original Series

In his initial draft proposal, Star Trek is..., Gene Roddenberry established the maximum velocity of the starship as ".73 of one light year per hour". This would translate to a top speed of approximately 6,400 c (equivalent to TOS warp 18.57, or somewhere between TNG warp 9.9 and 9.99).

The original warp scale was described in the writer's guide, The Star Trek Guide, (third revision, pg. 8) as a set of warp factors and multiples of lightspeed that can be obtained by raising a warp factor to the third power. [3]. This information appeared in widespread print in The Making of Star Trek (1968, pg. 191). The book also states a shift in relative time occurs while traveling at warp, an hour might equal to three hours experienced outside the ship. (pg. 198) In 1975, the warp scale given a more technical gloss in Franz Joseph's Star Fleet Technical Manual, now extended to include warp factors below 1. In 1977 Roddenberry again adopted the scale for the abortive Star Trek: Phase II series, but abandoned it for The Next Generation series. It was not until the the 2003 episode "First Flight" of Star Trek: Enterprise, that the warp factor scale made an official on screen debut. Warp factors from 1 to 5 were depicted with their corresponding relative speed values on a large computer graphic.

The scale used by Starfleet in the 22nd and 23rd century is based on a geometric progression, where the speed of a vessel (measured in multiples of c, the speed of light) is equal to the cube of the given warp factor. The warp factor was calculated as follows:

$wf=\sqrt[3]{\frac{v}{c}}$

with

• v being the speed of the signal or starship
• c being the speed of light (3.0 × 10⁸ m/s) and
• wf being the resulting warp factor

Or, to calculate speed (v) in terms of c, the formula would be:

$v=wf^{3}c$

At warp 1, a starship would reach c; at warp 6, it would reach 216 c. This is a much slower speed than initially proposed by Roddenberry.

Using this scale:

Warp factor	Calculated speed (*c)	Distance traveled in 24 hours (*light years)	Travel time from Earth to Alpha Centauri
0.5	0.125	0.0003	34.64 years
1	1	0.003	4.33 years
2	8	0.022	197.69 days
3	27	0.074	58.57 days
4	64	0.175	24.71 days
5	125	0.342	12.65 days
6	216	0.591	7.32 days
7	343	0.939	4.61 days
8	512	1.402	3.09 days
9	729	1.996	52.07 hours
10	1000	2.738	37.96 hours
11	1331	3.644	28.52 hours

Star Trek: The Next Generation

According to the Star Trek: The Next Generation Technical Manual, the warp factor scale used by Starfleet in the 24th century was based on a recalibration of the scale used in the Original Series. Rather than a simple geometric progression based on relative speed, warp factors were established to be based upon the amount of power required to transition from one warp plateau to another. For example, the power to initially get to warp factor 1 was much more than the power required to maintain it; likewise warp 2, 3, 4, and so on. Those transitional power points rather than observed speed were then assigned the integer warp factors. These transitional points were established to apply to the original warp scale as well in the canonical warp chart presented in "First Flight".

According to a Star Trek: The Magazine article by André Bormanis, this scale change occurred in 2312. A term was added to the above equation that caused the speed to rise slightly at lower warp factor, but to become infinite at warp 10. The ratio v/c at a given warp factor is equal to the corresponding cochrane value that describes the subspace distortion.

The 24th century scale was created at the start of Star Trek: The Next Generation. Gene Roddenberry stated that he wanted to avoid the ever-increasing warp factors used in the original series to force added tension to the story, and so imposed the limit of warp 10 as infinite speed.

For warp factors up to 9, the revised formula became:

$wf=\sqrt[{\frac{10}{3}}]{\frac{v}{c}}$

with

• v being the speed of the signal or starship
• c being the speed of light (3.0 × 10⁸ m/s) and
• wf being the resulting warp factor

Or, to calculate speed in terms of c (up to warp 9), the formula would be:

$speed=wf^{\frac{10}{3}}c$

In this case, warp 1 is equivalent to c (as it was in the 23rd century scale), but above warp 9 the speed increases exponentially, approaching infinity as the warp factor approaches 10.

Using this scale:

Warp factor	Calculated speed (*c)	Distance traveled in 24 hours (*light years)	Travel time from Earth to Alpha Centauri
0.5	0.099	0.0003	43.64 years
1	1	0.003	4.33 years
2	10.079	0.028	156.91 days
3	38.941	0.107	40.61 days
4	101.594	0.278	15.57 days
5	213.747	0.585	7.4 days
6	392.498	1.075	4.03 days
7	656.135	1.796	2.41 days
8	1024	2.804	37.07 hours
9	1516.381	4.152	25.03 hours
10	∞	∞	0

Star Trek: Deep Space Nine

According to DS9: "Emissary" and "Battle Lines", the Bajoran Wormhole connected the Bajoran system to a region in the Gamma Quadrant 70,000 light years away. In "Battle Lines", Sisko stated that it would take Starfleet's fastest ship over 67 years to cross the distance, suggesting the fastest ship in 2369 could travel at approximately 1044 times the speed of light on a flight of that duration. The figure was further explained in the series bible, that it is more specifically a 60 year journey at warp 9, [4] suggesting warp 9 would be about 1167 times the speed of light.

In "The Sound of Her Voice", the USS Defiant, traveling at warp 9, is three days away from a planet. Increasing speed to warp 9.5 took almost a full day away from the travel time. This indicates that warp 9.5 is almost 50% faster than warp 9.

Star Trek: Voyager

In Star Trek: Voyager Technical Manual (pp. 12 & 13) several other speed equivalents are established: Warp 9.6 is 1,909 times the speed of light. Warp 9.99 is 7,912 times the speed of light. Which in turn is nearly three times the speed of warp 9.9. Subspace communication signals travel at warp 9.9999, a hundred times faster than warp 9.6, 199,516 times the speed of light.

In the pilot episode of the series, VOY: "Caretaker", it is established that "at maximum speeds" it would take 75 years for Voyager to reach Earth, that was at that time approximated to be 70,000 light years away. This would mean that the maximum speeds of the Voyager were around approximately 933 times the speed of light. According to the Star Trek: Voyager Technical Manual, this calculation was meant to be based on an unrealistic non-stop direct journey at the speed of warp 9.6 (p. 14) or at warp 9.99 (p. 36). A realistic estimate, according to the manual, was that the journey would last somewhere between 200 and 400 years when taking into account the required engine cooling time needed on such an extended journey.

According to Star Trek: Voyager Technical Manual (pp. 4 & 27), a sector (about 20 light years) took 4 days to cross at warp 9.6, 5 days at warp 9 and about 19 days at warp 6. According to VOY: "The Voyager Conspiracy" however, the ship could cross only 30 sectors in 3 years. So it actually took Voyager over a month, or approximately 36.5 days to cross a sector in the series.

In the episode VOY: "Flashback", Captain Kathryn Janeway stated that the current Starfleet starships in 2373 were twice as fast to what the USS Enterprise-A and the USS Excelsior were in the 2290s. According to Star Trek: Voyager Technical Manual, (p. 13) the maximum rated speed of the ship was warp 9.975 or 3,053 times the speed of light. According to the Star Trek Spaceflight Chronology (p. 180) and Mr. Scott's Guide to the Enterprise (p. 14), the maximum speed of ships like the Enterprise-A was warp 12 in the old scale, or 1,728 times the speed of light.

Star Trek: Enterprise

Officially and according to the large warp chart featured in "First Flight", the warp drive of the Enterprise NX-01 uses the TOS-scale. Speeds mentioned in ENT: "Broken Bow" of traveling at 30,000,000 kilometers per second, and going to "Neptune and back in six minutes." fit well into the ballpark of cubic warp factors between 4 and 5. In ENT: "Regeneration", Trip states that warp 4.8 (approximately 111 times the speed of light in the TOS-scale) is double the speed of warp 3.9 (approximately 59), which is also a close enough margin of error considering it is an offhand comment made without navigational implications.

A location was given to Archer on where to go look for the Xindi inside the Delphic Expanse in the episode ENT: "The Expanse". The location was stated to be a three month trip away from Earth at warp 5. In the next episode, ENT: "The Xindi", when Enterprise had arrived to look for the Xindi in that region, it was said they were 50 light years away from Earth. This indicates warp 5 would equal to a speed of approximately 200 times the speed of light. This would fall closer to the TNG-scale figure for warp 5 instead of the TOS-scale figure of 125 times the speed of light estimated in the canonical chart.

There are however instances in "Broken Bow" that do not appear to be compatible with any of the basic scales. Zefram Cochrane notes in his recorded speech that the warp five engine would allow a ship to travel a hundred times faster than what they could in 2119. Warp 2 was later on established to be the maximum warp ships in the early-22nd century had achieved in ENT: "Horizon" and "First Flight". Warp 5 however is only 16 or 21 times faster than warp 2 in the scales. The journey from Earth to Qo'noS in four days is another instance. In either scale Enterprise wouldn't even reach the closest star to Earth in four days.

In ENT: "Fortunate Son", it is stated that a warp three engine would allow a ship to travel ten times faster than warp factor 1.8. This doesn't work out in either of the basic formulas, unless we interpret the statement to indicate that a warp three engine would allow a speed of warp factor 3.9 in the TOS-scale or 3.6 in the TNG-scale. Warp factor 3 would be only around five times faster in either scale.

Alternate reality

The alternate USS Enterprise at warp in Star Trek

In the alternate reality, seen in Star Trek, the USS Enterprise traveled from Earth to Vulcan at maximum warp. According to ENT: "Daedalus" Vulcan is located slightly over sixteen light years away from Earth. According to background sources maximum warp of the ship was warp factor 8. [5] Directly after the ship had accelerated to and attained maximum warp, Captain Christopher Pike ordered Pavel Chekov to give an announcement of the mission to the crew. At the end of the broadcast, Chekov stated that the ship would arrive within three minutes.

However, there was an unknown amount of time the ship spent accelerating to maximum velocity, so there is no accurate way to ascertain the total voyage time of the Enterprise from Earth to Vulcan, beyond the obvious implication that it was not an especially lengthy trip. By comparison to the prime reality, in Star Trek IV: The Voyage Home, when the crew was returning to Earth from Vulcan on board the HMS Bounty, Sulu reported they would arrive in 1.6 hours.

In Star Trek Into Darkness, the Enterprise and the three times faster USS Vengeance were capable of traveling from the Sol system, through the Neutral zone to the edge of Klingon space and back in less than a day. Co-writer Roberto Orci acknowledged Scotty's line about his time away from the Enterprise should have been something like "one week" rather than "one day". [6] As a comparison, in Star Trek VI: The Undiscovered Country, the internal clock of the USS Enterprise-A read 08:27 as the ship left Earth Spacedock and 16:12 when it arrived to the edge of Klingon space to meet up with Kronos One. A trip of a little under 8 hours.

External links

• Template:NCwiki
• Warp Speed Anomalies at DITL