Warp factor

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Warp factor (symbolic abbreviation wf), alternatively known as time warp factor, is a unit of speed. (TOS: "The Cage"; Star Trek II: The Wrath of Khan) Another common abbreviation is "warp". The value is given after the unit. For example "warp factor 5" or the abbreviation "warp 5". The increase in warp factor speed values corresponds to a non-linear increase in actual velocity.

The most common usage is to describe the speed of a spacecraft traveling at a faster than light (FTL) speed, using a warp drive. Sublight speeds can also be measured in warp factor values, such as "warp .5". (Star Trek: The Motion Picture)

Subspace communication signal speeds have also been given warp factor speed values in several reference materials.

[edit] Warp factors vs. speed

Warp factor	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
3	487	4 light years	3 days	ENT: "Damage"
3	39	0.102 light years	23 hours	TNG: "The Most Toys"
4.5	79.7 - 87.2	~57.5 - 62.92AU (Earth-Neptune and back)	6 minutes	ENT: "Broken Bow"
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"
10	∞	∞	0	VOY: "Threshold"
n/a	8,300	2.5 million light years (to Andromeda Galaxy)	300 years	TOS: "By Any Other Name"
n/a	2,737,421 - 2,908,510	~16 - 17 light years (Earth-Vulcan)	3 minutes	ENT: "Daedalus"; Star Trek

"Speed" values are typically calculated from given values for travel time and distance.

[edit] Warp 10...

In 24th century warp theory, a warp factor of 10 corresponds to an infinite velocity. Theoretically, a vessel traveling at warp 10 would occupy all points in the universe simultaneously. Warp 10 was the transwarp threshold, representing infinite velocity. (VOY: "Threshold")

In theory, it was possible to travel backwards in time by surpassing warp 10. (TNG: "Time Squared")

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 an extraordinarily rare form of dilithium discovered earlier that year. After it was discovered that such travel induces hyper-evolution, this technology was discontinued after the initial test. (VOY: "Threshold")

Kathryn Janeway made the observation in 2376 that rumors travel fast on board Voyager. Chakotay agreed with Janeway, quipping at "warp 10." (VOY: "The Voyager Conspiracy")

In the script for "Sons and Daughters", Alexander Rozhenko's adrenaline was described as "pumping at warp ten."

[edit] ...and beyond

However, in the 23rd century, warp factors of 10 and higher, seemed to denote extraordinarily fast, but not infinite, speeds. In 2267, for example, Nomad fired energy bolts that traveled at warp 15, as well as made the USS Enterprise (by improving efficiency in the antimatter input valve and energy release controls) go at least warp 11. When this happened, Montgomery Scott was in disbelief and stated that it would be impossible. (TOS: "The Changeling") Later that year, the 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." (TOS: "Journey to Babel")

In 2268, the Enterprise achieved a speed of warp 14.1 after being sabotaged by a Kalandan planetary defense system, though at that velocity the ship came within moments of destroying itself. (TOS: "That Which Survives") Bele, upon commandeering the Enterprise, propelled the ship faster than warp 10. (TOS: "Let That Be Your Last Battlefield")

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. The Enterprise was accelerated to speeds in the excess of warp 22, while being linked to the ship with a tractor beam. (TAS: "The Counter-Clock Incident")

In 2364, the USS Enterprise-D, after modification to its warp drives by the Traveler, exceeded warp factor 10 and went off the warp scale. (TNG: "Where No One Has Gone Before")

In an alternative future, around the turning point of the 24th to 25th century, warp factor values as high as warp 13 were routinely achieved by Federation starships. The Enterprise-D traveled at warp 13 in the incident concerning the temporal anomaly in the Devron system. (TNG: "All Good Things...")

Rather than "faster than infinite", these alternative future warp factors seemed to also point to extraordinarily fast speeds.

[edit] Appendices

[edit] Related topics

Warp Theory

[edit] Background

Although formulas to calculate speeds from warp factors existed in the writer's guides, these were not always used consistently. As an example, in "By Any Other Name" the Kelvans modified the USS Enterprise to maintain a speed of warp 11 in order to return to their home in the Andromeda Galaxy. They estimated that the journey would take less than 300 years, indicating a far greater speed than the scale would indicate.

As evidenced in the chart above, actual speeds represented by a warp factor have not always been kept consistent throughout every Star Trek incarnation. Warp 8.4 would appear to be much faster than warp 9.9 or even warp 11. In fact, given the cited speed of warp 8.4, the Voyager crew (having some 70,000 light years to travel) should have made it home in approximately 33 days, not 75 years. And at Warp 9.9, at the above cited speed, Voyager should have been able to reach home in a little over 3 years.

Star Trek: The Next Generation Technical Manual 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 causes energy penalties to a ship using warp drive. (pg.55)

Star Trek Maps introduced a similar concept as the Cochrane factor, that influences the actual speed by multiplying it. It can be as high as a multiplication of 1500 times within dense interstellar dust and gas , and as little as 1 in the intergalactic void. In the vicinity of massive objects it is so high that disproportionately high speeds are created, and they tend to result in the slingshot effect. Between the galaxies there is no density of matter or curvature of space so the speed follows only the basic cubic formula. (see below) Within the interstellar medium of Federation space the average value for the Cochrane factor has been calculated to be 1292.7238. (pg.6)

In the shooting script of Star Trek: The Motion Picture, USS Enterprise was slated to be traveling past Saturn as Kirk is making his log entry, stating 2.7 hours have passed since their launch from Earth. A distance of 8 AUs traveled in that time would have made warp .5 equal to approximately a speed of 0.411 c.

[edit] Star Trek: The Original Series

During TOS, the warp factor scale wasn't clearly defined. 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 18.56, and approximately warp 9.98 on the TNG scale).

The warp scale now commonly known as "TOS scale" first appeared in widespread print in 1968 in The Making of Star Trek (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.

According to these publications, the scale used by Starfleet in the 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:

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:

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

[edit] 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 23rd century. Rather than a simple geometric progression based on relative speed, the scale was based upon the amount of power required to transition from one warp plateau to another. For example, the power to initially get to the recalibrated warp factor one was much more than the power required to maintain it; likewise warp two, three, four, and so on. Those transitional power points rather than observed speed were then assigned the integer warp factors.

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:

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:

In this case, warp 1 is equivalent to c (as it was in the 23rd century scale); warp 6 is approximately 392 c.

Above warp 9 the exponent was increased above "10/3" exponentially, approaching infinity as the warp factor approaches 10.

This scale was used from TNG onwards.

[edit] Star Trek: Enterprise

Although it has not been directly confirmed, the Enterprise NX-01 may use the "TOS scale". In ENT: "Broken Bow", Archer specifically stated that the ship was traveling at 30,000,000 kilometers per second, which translates to approximately 100 times the speed of light, or approximately warp 4.6 on the 23rd century scale.

Archer also states in "Broken Bow" that the ship travels to "Neptune and back in six minutes." Although the engine is designed for travel at speeds of up to warp 5, this particular statement translates to a speed of warp 4.5.

In ENT: "Regeneration", Trip states that warp 4.8 (~110 times the speed of light in the TOS scale) is "double" the speed of warp 3.9 (~59 times the speed of light), which is a close enough margin of error, considering it was an offhand comment made without navigational implications.

However, in ENT: "Fortunate Son", it is claimed that warp 1.8 is "ten times slower than warp 3". This doesn't work out in either of the formulas above - warp 3 would be about five times faster in both cases.

These occurrences suggest that 23rd century scale has warp factor speeds faster than their 22nd century counterparts.

[edit] External links

Warp factor at Memory Beta, the wiki for licensed Star Trek works
Warp Speed Anomalies at DITL