Warp factor

From Memory Alpha, the free Star Trek reference

Warp factor (commonly abbreviated to warp) is the primary means of specifying warp speed. The increase in warp factor values corresponds to a non-linear increase in actual velocity. The most common usage is to describe the speed of a spacecraft traveling faster than light, using a warp drive. Although usually specified in fractions of impulse, sublight speeds can also be measured in warp factors (e.g. warp .5). (Star Trek: The Motion Picture)

Contents 1 Warp factors vs. speed 2 Warp 10... 3 ...and beyond 4 Appendices 4.1 Related topics 4.2 Background 4.2.1 Star Trek: The Original Series 4.2.2 Star Trek: The Next Generation 4.2.3 Star Trek: Enterprise 4.3 Alternate reality 4.4 External links

[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"
4.4	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"
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 [1]	8,300	2.5 million light years (to Andromeda Galaxy)	300 years	TOS: "By Any Other Name"

[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")

[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...")

[edit] Appendices

[edit] Related topics

• Warp Theory

[edit] Background

Warp factors are rarely abbreviated wf, popularized originally by Franz Joseph's publications and shown in Star Trek II: The Wrath of Khan. TOS: "The Cage" featured time warp factor, which was was rapidly superseded by warp factor and warp. 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 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 the scale would allow.

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.

To explain the apparent discontinuity of the canonical warp factor speeds, background sources have given several explanations. 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 cause 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" was described in the series bible and 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.

Using this warp factor formula, a trip from Earth to Alpha Centauri (4.33 light years) would take:

Warp factor	Calculated speed (*c)	Travel time
.5	0.125	34.64 years
1	1	4.33 years
2	8	197.69 days
3	27	58.57 days
4	64	24.71 days
5	125	12.65 days
6	216	7.32 days
7	343	4.61 days
8	512	3.09 days
9	729	52.07 hours
10	1000	37.96 hours
11	1331	28.52 hours

[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.

Using this warp factor formula, a trip from Earth to Alpha Centauri (4.33 light years) would take:

Warp factor	Calculated speed (*c)	Travel time
.5	0.099	43.64 years
1	1	4.33 years
2	10.08	156.91 days
3	38.94	40.61 days
4	101.59	15.57 days
5	213.75	7.4 days
6	392.5	4.03 days
7	656.14	2.41 days
8	1024	37.07 hours
9	1516.38	25.03 hours
10	∞	0

[edit] Star Trek: Enterprise

Although it has not been directly confirmed, the Enterprise NX-01 may use 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 warp factors between 4 and 5. A journey from Earth to Qo'noS in four days is however not compatible with the scale.

In ENT: "Regeneration", Trip states that warp 4.8 (approximately 111 times the speed of light in the TOS scale and 186 times the speed of light in the TNG scale) is double the speed of warp 3.9 (approximately 59 or 93 times the speed of light respectively), which is a close enough margin of error for either scale, considering it was an offhand comment made without navigational implications.

However, in ENT: "Fortunate Son", it is stated that warp 1.8 is "ten times slower than warp 3". This doesn't work out in either of the formulas above - warp 1.8 would be only 5.4 or 5.5 times slower.

[edit] Alternate reality

In the alternate reality, seen in Star Trek, USS Enterprise traveled to Vulcan at maximum warp. According to background sources [1] this corresponds to warp factor 8. Directly after the ship had achieved 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 3 minutes. According to ENT: "Daedalus" Vulcan is located slightly over 16 light years away from Earth.

[edit] External links

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