6.1 Concept of Warp Factors
A warp factor is a unitless figure that describes the speed of a starship or of a signal traveling faster than light. There is a non-linear dependence between the warp factor and the speed. In every known variant of the warp scale the speed rises more than proportionally with the warp factor.
Bearing in mind that the speed of light c is already as much as , it is obvious that with units like meters per second or kilometers per hour as they are used for the speeds of today’s planes or spaceships we would end up with unreasonably large figures when describing FTL travel. Generally, it may have been possible to switch to something like light years per day or similar manageable time and distance units. The reason why Starfleet introduced the apparently abstract and strangely non-linear warp factor must lie in the physical background or the technical implementation of the propulsion system. In other words, the function of speed vs. warp factor most likely reflects how strong a warp field must be to achieve a certain speed.
The sawtooth curve of the power expenditure (the so-called peak transitional thresholds) as shown for the TNG scale in Fig. 6.1 and discussed in 3.3 Subspace Fields and Warp Fields is further evidence that something significant happens at integer warp factors, justifying that the scale is based on these prominent points.
Gene Roddenberry may have originally conceived warp factors for the sake of the dramatic impression of Kirk’s commands. “Mr. Sulu, ahead Warp factor two.” is more precise than “half speed ahead”, and it sounds much more to the point than “increase to three light years per day.” Moreover, with warp factors obscuring the real speed of the ship calculation errors between speeds, times and distances mentioned on screen were less likely to occur. It was as late as in TNG that a correlation between the three figures was made on screen by Data.
There is no common symbol or abbreviation for warp factors, although “WF” or “Wf” are sometimes used in more or less non-canon textbooks. In spoken language they are referred to as “Warp X” (always written with a capital “W”) or, now rather antiquated, “Warp Factor X” during the time of TOS. In the known warp scales “Warp 1” equals the speed of light. Warp factors below Warp 1 are occasionally mentioned only in the scope of the 24th century scale, consequentially these refer to sublight speeds. Warp factors may be real numbers, although it seems that starships most often travel at speeds corresponding to integer warp factors.
6.2 TOS Scale (22nd/23rd Century)
During the era of The Original Series (TOS) a warp scale was in use where the curve of speed v vs. warp factor was described with:
So the warp factor was the cubic root of the ship’s achieved speed ratio , with c being the speed of light. Warp 1 equals exactly the speed of light. The continuous curve suggests that smaller warp factors and fractional values were well possible in this measurement system. Warp factors below 1, however, were not mentioned once before the time of TNG, and fractions occurred only occasionally.
Warp factors higher than 10 are possible in the TOS warp scale. We know of just two occasions where the Enterprise was said to have achieved such high speeds. The first one is in TOS: “That Which Survives” where a modification to the engines by Losira accelerates the Enterprise to Warp 14.1. This is also one of very few examples of fractional warp factors. On another occasion in TOS: “By Any Other Name” the Enterprise was tampered with by the Kelvans who were going to reach the Andromeda Galaxy, 2.3 million light years away, in three centuries. This gives us an indirect speed reference of Warp 19.7. Yet, a speed figure was not mentioned.
The TOS scale is often referred to as “Cochrane scale”, but this is conjecture and, like the underlying formula, was never mentioned in the series.
Strictly speaking, the warp scale used in the TOS era is completely conjectural. There is no reference that would allow us to relate a warp factor stated on screen to a distance and a time. The now widely accepted scale, however, must have been established behind the scenes in a kind of writer’s guide. David Whitfield, who had access to essential documents of Roddenberry’s staff mentions the scale in his book The Making of Star Trek as soon as 1968. In his reproduction of the warp scale Warp denotes the speed of light, Warp 3 is 24c, Warp 6 is 216c and Warp 8 is 512c. Actually, Warp 3 should be 27c, but with the other values following exactly the third-power law of Eq. 6.1 we have a confirmation that the scale was really being used at least as a guideline.
6.3 TNG Scale (24th Century)
Not yet available.
6.4 Possible Future Scale
Not yet available.
See also: Warp factor @ Memory Alpha