Warp Drive - Warp Velocities

Warp Velocities

Warp drive velocity in Star Trek is generally expressed in "warp factor" units, which—according to the Star Trek Technical Manuals—correspond to the magnitude of the warp field. Achieving warp factor 1 is equivalent to breaking the light barrier, while the actual velocity corresponding to higher factors is determined using an ambiguous formula. Several episodes of the original series placed the Enterprise in peril by having it travel at high warp factors; at one point in "That Which Survives" the Enterprise traveled at a warp factor of 14.1. In the Star Trek: The Next Generation episode "The Most Toys" the crew of Enterprise-D discovers that the android Data may have been stolen while on board another ship, Jovis. At this point the Jovis, which has a maximum warp factor of 3 has had a 23 hour head start which the Enterprise-D figures puts her anywhere within a 0.102 light year radius of her last known position. However, the velocity of any given warp factor is rarely the subject of explicit expression, and travel times for specific interstellar distances are not consistent through the various series.

According to the Star Trek episode writer's guide for The Original Series, warp factors are converted to multiples of c with the cubic function v = w3c, where w is the warp factor, v is the velocity, and c is the speed of light. Accordingly, "warp 1" is equivalent to the speed of light, "warp 2" is 8 times the speed of light, "warp 3" is 27 times the speed of light, etc.

For Star Trek: The Next Generation and the subsequent series, Star Trek artist Michael Okuda devised a formula based on the original one but with important differences. For warp factors 1 through 9, v = w10/3c. In the half-open interval from warp 9 to warp 10, the exponent of w increases toward infinity. Thus, in the Okuda scale, warp velocities approach warp 10 asymptotically. There is no exact formula for this interval because the quoted velocities are based on a hand-drawn curve; what can be said is that at velocities greater than warp 9, the form of the warp function changes because of an increase in the exponent of the warp factor w. Due to the resultant increase in the derivative, even minor changes in the warp factor eventually correspond to a greater than exponential change in velocity. In the episode "Threshold", Tom Paris breaks the warp 10 threshold.

Exact velocities were only given in the Voyager episode "The 37's" where Tom Paris describes Voyager's velocity at warp factor 9.9 (under the new warp table formula) as being about 4 billion miles per second, which would be about 21,500 times the speed of light (although Voyager cannot maintain this velocity for very long). Voyager was about 70,000 light-years away from home. Simple calculation reveals that it would take "just" about 3.3 years to travel such distance.