The Warp Drive and Other Hyperlight Technologies in Star Trek, Part I
written by Tim Farley
originally published in Stardate 7, December 1980

During the history of Star Trek fandom, many fans have wondered about the speed of the Enterprise during its journeys. This matter was never cleared up in the show, and all we do know for sure is that the warp speeds are indeed faster than light, since in "The Lights of Zetar," when the lights are said to be traveling at warp speed, Kirk says, "Impossible...no natural phenomenon can travel faster than light."

As in the area of dating, Gene Roddenberry did not wish to tie the show down to exact figures. Just as the stardate system leaves it largely up to the viewer as to the time of the occurrences in the episodes, the warp factor system leaves it up to the viewer as to the exact speed of the Enterprise. This was wise indeed, as it freed the writers and consultants of the show from tedious calculations of distances and speeds in their quest to make to show scientifically accurate.

However, just as he was forced to tie himself down in dating (saying the show occurred 300 years in the future), Roddenberry felt compelled to offer some explication on the ship’s speed. He invented a system whereby the ship’s speed is equal to the stated warp factor cubed, multiplied times the speed of light, and he included this system in the show’s Writer’s Guide. Although this theory on warp speed was never expressly stated in any of the aired episodes, it has made its way into fandom and is now almost universally accepted as "the way it is." It’s presence in the Writer’s Guide has apparently led to the widespread belief that it is "true" and to its inclusion in the Star Trek Encyclopedia. Let us examine the circumstance s of the Enterprise’s journey and see if this "warp factor cubed" theory actually fits the facts.

In "Where No Man Has Gone Before," the Enterprise visits the edge of the galaxy, some 16,000 (plus or minus a few thousand lightyears) from Sol. To travel there in one year (quite an enormous time in the only five year mission of the ship) would require an average speed of 16,000 times the speed of light. If we reduce the required average time to a still long but now reasonable six months, the required average speed goes up to 32,000 times speed of light. These two speeds are warp factors 25.2 and 31.7 respectively, in the "warp factor cubed" theory. This is far beyond the emergency speed of the Enterprise, warp 8. Obviously, the "warp factor cubed" theory is inadequate to explain the speed of the Enterprise in this case.

Some will argue that the galaxy is only 1000 lightyears "thick," and that the Enterprise actually went up or down to the top or bottom of the disk-shaped section of the galaxy. Even if that were true, which is questionable considering they’ve clearly delineate the "edge" of the galaxy, not the "top" or the "bottom," to go five hundred lightyears in six months would require a speed of Warp Factor 10, which is was unattainable at that time in the series timeframe. Clearly, "warp factor cubed" can’t explain this episode, even if you argue the destination.

In "The Squire of Gothos," the distance to Earth from Gothos is stated as 900 light-years. Yet to travel that distance at a continuous speed of warp 6 would require a travel time of 4.2 years. That doesn’t leave a lot of time for the other episodes, does it?

In "Arena," the ship is displaced by the Metrons a distance of 500 parsecs, or roughly 1,900 light-years. To travel this distance at a continuous speed of warp 6 would take 7.5 years (under the "warp factor cubed" theory), yet Captain Kirk casually says, "Take us back to where we’re supposed to be...warp factor one." A 7.5 year journey would have been almost insurmountable setback for the mission, but Kirk never bats an eye, and uses a low warp speed (at least for starters, any way) to travel that enormous distance.

In "Bread and Circusses," Chekov states that planet 892-IV is 1/16 of a parsec away and that "we’ll be there in seconds." That distance is roughly 6.4 million light-seconds. To travel it in one minute (let alone "seconds") would require a speed of warp 47.4 under the "warp factor cubed" theory, which again fails.

In "Obsession," the creature leaves the ship and heads for Tycho IV, a planet "over a thousand lightyears" from their position. "Round trip time" (so they could deliver supplies to the U.S.S. Yorktown) is stated as 1.7 days. To travel 2,000 lightyears (round trip) in 1.7 days would take a continuous speed of Warp 75.4 under the "warp factor cubed" theory.

In "By Any Other Name," the Enterprise is set on a course toward the Andromeda galaxy, some 2.2 million lightyears distance. At Warp 11, their travel time is estimated at 300 years. But to travel that distance in that time would require a speed of Warp 19.4 under the "warp factor cubed" theory, which is again inadequate.

In "That Which Survives," the Enterprise is beamed exactly 990.7 lightyears by the Kalandan computer. Scotty coaxes his engines to Warp 8.4, and Spock calculates an ETA of 11.337 hours. But to travel that distance in that time would require a speed of Warp 91.5 under the "warp factor cubed" theory.

In "The Magicks of Megas-tu" and in Star Trek V: The Final Frontier, the Enterprise visits the center of the galaxy which is roughly twice as distant from us as the edge is. To travel there in one year or six months would require speeds of Warp 31.7 or Warp 40.0. To travel there in one week’s time would require a speed of Warp 118.9!

In Star Trek: The Motion Picture, the V’ger cloud is three days away from Earth when it destroys three Klingon ships. Its speed was indicated at Warp 7 or 8 in press releases and in the film (how else could they rendezvous with it?). Using "warp factor cubed," that would put Klingon territory within 4.2 lightyears of Earth, closer than the nearest star, Alpha Centauri. When they say "the Klingon menace," they really mean it! Also in the movie, Scotty says that he can have Spock back on Vulcan in four days. No doubt he meant the shortest possible time—a direct trip at maximum cruising speed—means, using the "Warp Factor cubed" theory, that Vulcan is between 3.29 and 4.22 lightyears from Earth. If they did not go directly, it would have to be even closer. I guess the Federation had to physically move it closer to Earth to protect it from the Klingon menace!

During the entire live action series, the ship visited or mentioned some 30 real stars—ones that are identifiable today. Of these, many are very close to Earth, but a number are hundreds of lightyears from Earth. Rigel, one of the more distant stars, is about 800 lightyears from Earth. Many of the "invented" planets visited have been said to be "hundreds of lightyears from Earth," as in "Miri" and "Return to Tomorrow." Many more must be at least that distant, by the laws of probability and stellar distribution. These stars, real and unreal, are undoubtedly distributed equally around Earth in all directions. The real stars certainly are.

In the course of the five year mission, then, the ship must have traveled literally thousands of lightyears. A round trip from Earth to Rigel alone would account for 1,600 lightyears. Of course, very few trips were from Earth to the star in question, but the distances covered would be just as great or greater. All of the specific journeys cited above add up to several thousand lightyears, and they represent only a small fraction of the ship’s total journey. But even if the ship cruised continuously at Warp 6 (which is obviously NOT the case), the "warp factor cubed" theory would allow the ship to travel only 1,080 lightyears over the entire five-year mission. Thus, over the entire mission, the trend of speed discrepancies is continuous.

Thus, we see that the "warp factor cubed" theory is entirely inadequate to account for the speed of the Enterprise during the course of the series, in general and in many specific instances. This indicates that even the Great Bird of the Galaxy was not perfect (sorry, Gene). However, his cautiousness in technical matters has saved us from this dilemma. By using the vague term "warp factor" instead of actual speed quotes, he did not tie the ship down to a specific speed, as I pointed out before. Thus we are now free to develop a new mathematical relationship to tie the warp factors to actual speeds which adequately account for the Enterprise’s journeys during the series.

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