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Warp Speeds

Warp drives are the primary propulsion system used by most faster-than-light interstellar spacecraft in the Star Trek universe. Federation starships enter into warp speed using warp engines, which employ controlled annihilation of matter and antimatter, regulated by dilithium crystals, to generate the tremendous power required to warp space and travel faster-than-light speeds, also referred to as warp speeds. In 2063, Zefram Cochrane invented the warp drive and made Earth's first contact with an alien race, the Vulcans. The tumultaneous event ushered in a new age of peace and prosperity for mankind (Star Trek First Contact).

The units of measure for warp speeds are called "warp factor". Warp factor 1 is c, the speed of light. Higher warp factors are computed geometrically under one of two different formulae, with one set of formula for the TOS era, and another set for the TNG-DS9-VOY era (for simplicity, I shall refer to this as the TNG era). The reason for there being two different formulae is this; The TOS series occasionally had starships and other objects travelling at warp 10 or faster. However, during the preproduction of TNG, Gene Roddenberry was worried that having a starship move too fast would make the galaxy too small a place to be interesting. Indeed, the producers realised that beyond a certain speed, a starship would be able to cross the entire galaxy within a matter of just a few months. As a result, Roddenberry revamped the warp-speed scale to put warp 10 at the absolute top of the scale, a speed that was supposedly unattainable because doing so required infinite power.

The Phoenix, Earth's first warp-capable vessel.

TOS Warp Speeds The TOS never actually established the actual speeds for warp factors in any episode or movie, although the warp factor cubed formula has come to be generally accepted. The cubed formula was also mentioned in the book The Making of Star Trek, which laid down certain technical details that TOS was meant to follow. Therefore, warp 2 = 8 c (2^3 = 8), warp 3 = 27 c (3^3 = 27), and so on. Below is a table of TOS warp factors and their corresponding actual speeds.

USS Enterprise NCC-1701

The TOS Constitution-class USS Enterprise had a cruising speed of warp 6, and could reach warp 8 only with significant danger to the ship itself. The Enterprise nevertheless reached warp 11 in 2267 when modified by the probe Nomad to increase engine efficiency by 57% ("The Changeling" [TOS}). The Kelvans were also successful in modifying the ship's engines to reach warp 11 ("By Any Other Name" [TOS}). Enterprise reached warp 14.1 in 2268 when the engines were sabotaged by Losira ("That Which Survives" [TOS]).

TNG Warp Speeds The producers of TNG, in order to accomodate with Roddenberry's recalibrated warp scale, came up with a new asymptotic warp curve in which, the exponent of the warp factor increases gradually, then sharply as you approach warp 10. At warp 10, the exponent (and the speed) would be infinite, so you could never reach this value. The warp curve does not follow any particular mathematical equation, although many fans have came up with various formulae that closely reproduce the curve. The limit of an unattainable warp 10 is referred to as Eugene's Limit in the Star Trek: The Next Generation Technical Manual, aptly named after Roddenberry's first name.

USS Enterprise-D at warp speed.

Warp speed graph

A close-up of the warp 9-10 region

It is generally assumed that the new warp factor scale had been adopted by Starfleet by the 24th century, sometime between TOS and TNG. It is also assumed that all the speeds shown in TOS were actually less than the "new" warp 10, even if they were mentioned as warp 11 or warp 14.1. Warp 10 is said to be unattainable and meaningless, and that a starship travelling at warp 10 would theoretically occupy all points in the universe simultaneously ("Threshold" [VOY]). Interestingly, in "All Good Things..." (TNG), both USS Pasteur and USS Enterprise-D in an alternate future travelled at warp 13. This may yet mean another recalibration of the warp curve, unless that future was only a fabrication made by Q. It has been suggested by some fans that speeds of warp 10 and above may actually represent speeds of increasing decimal places above warp 9 (such as warp 9.99 or 9.999), and that these speeds, although technically below the instantaneous speed of (the previous) warp 10, have been relabeled to integer numbers of 10 and above, so that it is much easier to say out these speeds. (Imagine a captain giving an order, "Take us to warp 9.99999999!", when it might obviously be much easier to say, "Take us to warp 15!") It is possible that warp factors of more than 10 may allude to some kind of implementation of the transwarp drive, to be further discussed below. Here is a table of the TNG warp factors, as given in The Star Trek Encyclopedia.

Transwarp Drive The transwarp drive was first introduced in Star Trek III: The Search for Spock, with the USS Excelsior being the testbed vehicle for Starfleet's Transwarp Development Project. The movie did not state exactly how does transwarp speeds operate, and many fans, in particular some RPG companies, have came up with their own ideas on what is transwarp velocity. Some people think that transwarp speeds are simply the warp factor to the fourth or even fifth power, ie. x^4 or x^5, with x being the warp factor. Another RPG company regards the use of transwarp as beaming the warp field in front of the starship via transporter!

USS Excelsior, "the great experiment"

Another attempt to explain transwarp velocities is presented in the book Mr. Scott's Guide to the Enterprise. The author suggested that transwarp velocities involves a starship entering into a parallel dimension where time moved at a slower rate than in normal space. While in the parallel dimension, the starship would travel at its normal warp speed towards its destination. Upon arrival, the starship would re-enter into normal space, only to find that a shorter time had passed in normal space than onboard the starship. The nett result is a shorter travel time taken by the starship with respect to normal space. For example: A starship engages its transwarp drive, enters into the parallel dimension and travels for three weeks towards a star system. Upon arrival, the starship re-enters into normal space, and finds that only four days had passed in normal space. In other words, a route that should have taken three weeks to travel had actually been reduced to only four days, this is no doubt a significant improvement in propulsion systems! Presumably, the starship's chronometers would have to be reset accordingly, perhaps even during the passage of travel. Of course, the above explanation, and even the entire book, has been disavowed by more recent publications. Nevertheless, the book makes an interesting good read, giving an idea of what had been preceived before canonical information are created. As there was no mention of any Starfleet vessel using the transwarp drive during the entire run of TNG, it was assumed that the Transwarp Development Project was deemed unsuccessful by Starfleet Command. One can presume that Scotty's sabotage of Excelsior's engines in ST3 might have been so crippling that it played a role in the eventual failure of the transwarp project. USS Excelsior was refitted with a standard warp drive, and it became the prototype for numerous other Excelsior-class starships that were later built.

In 2372, USS Voyager, while lost in the Delta Quadrant, discovered a new form of dilithium which was more stable at a much higher warp frequency than the crystals normally used in Federation starships. The crew believed that the new dilithium may allow a starship to exceed the warp 10 threshold and attain transwarp speeds. Testing the new dilithium on the Shuttlecraft Cochrane, Lt. Thomas Paris piloted the Cochrane and became the first Human to exceed warp 10 and fly a spacecraft at transwarp speeds.

Shuttlecraft Cochrane

Postmission data analysis confirmed that the Cochrane did attain an infinite velocity, occupying every point in the universe, but no means was found for a transwarp vehicle to return to normal space at any particular predetermined point ("Threshold" [VOY]). Transwarp velocity was also shown to have extremely dangerous effects on living beings, causing dramatic mutations. Lt. Paris and Capt. Janeway subsequently suffered from these mutations when they crossed the transwarp threshold, but they were later cured of the effects. Although the episode "Threshold" (VOY) finally established the operation of transwap velocities, many fans have decried the episode for numerous reasons. The new warp scale had already stated that warp 10 requires infinite power to achieve, and many fans seriously doubt that the Shuttlecraft Cochrane could actually had achieved infinite power to cross the transwarp threshold, even with a new form of dilithium. Also, the thought that travelling at transwarp could cause dangerous mutations on living beings is simply too ridiculous to many fans, almost unacceptable. Personally, I think the episode was still credible, even barely! For crying out loud, these fans also decry each and every other episodes too! From "Threshold" (VOY), I can assume that transwarp velocities involves a starship first occupying every point in the universe (!), and then returning to normal space at its desired destination. Higher transwarp factors would mean having a more efficient way of determining the point of your desired destination, ie. travelling at warp 13 would allow you to arrive at your destination much faster than say, at warp 12. This would also mean that at warp 10, although it allows you to achieve infinite velocity and occupy all points in the universe, you would only exit at the point where you started at.

So, transwarp velocities appear to have extremely dangerous effects on living beings. The Borg, however, seem to have solved these problems as they were already using transwarp conduits in 2369 ("Descent" [TNG]). The Enterprise-D also travelled through the Borg transwarp conduits in order to pursue a Borg ship, and the crew did not suffer from any ill effects either. The Borg maintained a network of transwarp corridors and there were six Borg transwarp hubs, one of which was destroyed by USS Voyager in 2377, when Voyager used one of the transwarp corridors to return to the Alpha Quadrant ("Endgame" [VOY]). Interestingly, Mr. Scott's Guide to the Enterprise states that the parallel dimension was discovered by the USS Enterprise during the encounter with the Tholians in "The Tholian Web" (TOS), it was the dimension the USS Defiant phased into and became missing. The Defiant's crew were said to have gone insane when their prolonged presence in the 'doorway between normal space and the parallel dimension' caused 'an imbalance in the chemical composition of neural and muscular tissue', ultimately resulting in their deaths. This sounds similar to the plot of "Threshold" (VOY), and makes one think if B&B got their story from this non-canon source.

Borg vessel

ENT Warp Speeds ENT has yet to state the actual speeds of the warp factors used in the series, but logically speaking, ENT would have to be following the TOS warp scale, since ENT supposedly comes before TOS. Enterprise NX-01 is said to have a warp 5 engine, which would allow the starship to travel much further than any other previous Earth vessels. As ENT would later establish, in the 80 years after Cochrane's Phoenix broke the warp barrier in 2063, Earth only had vessels which travelled less than warp 2. These included colony ships, cargo vessels, and presumably exploration vessels and space probes, though the latter two have yet to be explicitly mentioned. The SS Valiant was said to have been launched in 2065 on a deep space exploration mission, at least by the authors of Star Trek Chronology anyway ("Where No Man Has Gone Before" [TOS]). The probe Friendship 1 was launched from Earth in 2067 with a message of peace to other worlds, contact with the probe was lost in 2247, and it was later recovered in the Delta Quadrant by USS Voyager in 2377 ("Friendship One" [VOY]).

Enterprise NX-01

It is unknown whether the Valiant would have been a suitable deep space exploration vessel if it could travel only under warp 2, or whether the Valiant could actually had exceed warp 2 if it was constructed with help from the Vulcans. Knowing well that Humanity was anxious to explore space, I believe that Earth would probably had gone ahead with exploring space with a vessel even if it could only travel at less than warp 2. As for the probe Friendship 1, it is possible that the probe, being of relatively small size and not constrained with having to carry a heavy load or any passengers, could have been originally designed to travel faster than warp 2. Even if not so, the probe probably could have travelled all the way to the Delta Quadrant on its own engines (at less than warp 2), since the approximate location of the probe was determined by Starfleet and relayed to Voyager. It is also possible that the probe could have encountered with some unknown force which might have swept it into the Delta Quadrant (just as the Voyager 6 probe fell into a black hole and emerged on the other side of the galaxy, as mentioned in ST:TMP), though it is not known whether Starfleet could have projected an approximate course of the probe if this had actually happened.

In any case, the warp 2 barrier was only broken in 2143 by the NX-Alpha, which was however destroyed in the test flight. Another prototype, the NX-Beta, subsequently achieved warp 2.5. The following year (2144), the NX-Delta broke the warp 3 barrier ("First Flight" [ENT]). Construction on the Enterprise NX-01 began in 2149, and the starship was launched in 2151 ("Broken Bow" [ENT]).

NX-Alpha

NX-Beta, of the same design as NX-Alpha.

Personally, I think that TPTB are referring to the TNG warp factors in ENT, since they probably think that most people would only remember  TNG, and that TOS no longer exists (or if it had ever existed, it was almost 35 years ago, and nobody remembers!). If this is true, one possible explanation for this is that, when the USS Enterprise-E travelled back in time to 2063 in Star Trek First Contact, both Zefram Cochrane and Lily Sloane were exposed to the future technologies presented by the Enterprise-E, including the "new" TNG warp scale. They might have incorporated the new technologies into their later designs, therefore accounting for the use of the TNG warp scale, and the more advanced-looking equipment seen in ENT than those in TOS, in particular design of the NX-01. Somehow, TNG warp 5 (214 c) makes more sense to travel at than TOS warp 5 (125 c), the latter of which is not official anyway. Until an episode or a canon article is published on the subject of ENT warp factors, I will not make any judgment on exactly how fast warp speeds are in ENT.

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