The Warp Drive and Other Hyperlight Technologies in Star Trek, Part III
written by Tim Farley
originally published in Stardate 10, May 1981

In Part I of this series, the idea that the speed of a warp-driven craft is not the warp-factor-cubed-times-C was proposed. In Part II, it was proposed that the velocity produced by the engines at a given warp factor varies due to the nature of the space around the ship. In this article, we will examine some possible replacements for the warp factor cubed formula, keeping in mind the idea of variable velocities in subspace.

When careful examination of the known facts about the Enterprise’s journeys indicates that the warp factor cubed formula is inadequate, some fans have turned toward the idea of alternate formulae. In order to create such formulae, we need to examine some of the more specific data available from the show.

In several episodes, very specific information was included in the "throwaway dialogue" which allows us to calculate the speed of the ship in these instances. In Star Trek: The Motion Picture, the dramatic achievement of warp one indicates that this speed is indeed equal to C. From "Bread and Circuses," we can calculate that a speed of around Warp 2 to 5 is equal to 110,000 C or higher. From "Obsession," Warp 6 equals 430,000 C. From "That Which Survives," Warp 8.4 equals 770,000 C. And, finally, from "By Any Other Name," Warp 11 equals 7,000 C. It is obvious that the data from the last episode does not fit the pattern. This is because it is related to an extragalactic journey, during the course of which the warp drive operates at a much lower efficiency.

Thus, we have three exact pieces of information and one rather vague relationship with which to tie down an exact formula. This is not nearly enough data to work with. In fact, many different relationships could be devised such that these pieces of data fall close to the predicted values. Obviously, none of these would be of much use since they are merely approximations.

But there’s more. As was pointed out in the last article, a given warp factor may produce different speeds at different points in the galaxy, depending on the nature of the space the ship is in. Thus any "exact" formula we could derive, had we enough data to do so, would only be an approximation subject to the position of the ship.

Thus there doesn’t seem to be much hope for a formula to replace the "warp factor cubed" formula as a hard-and-fast velocity rule. However, we can look at the form such a replacement rule might take.

Geoffrey Mandel has proposed an alternate speed rule which uses the form

V = k W ³

in which V is the speed in multiples of C, k is a constant relating to the space the ship is in ("Cochrane’s Index") and W is the warp factor. The figure for k varies with position producing the variable velocities my research has indicated. The only problem with this rule is that it makes warp one equal to k times light speed, which is obviously not the case.

Many mathematically elegant formulae can be proposed, and made to roughly fit our data. Here are some of them:

1) V = k W ³ - k +1

2) V = k (W -1)³+1

3) V = k e ^W

4) V = W ^k

5) V = k ln (W)

6) V = k ^W

Each of these uses some form of exponent, some using e (which is a useful transcendental number, similar to pi), and some using the natural logarithm function (In, which is related to e). Each of these can be made to fit the available data.

And in each case, a varying value for k will allow for variable velocities in subspace.

Which of these is most useful? Really, there is no way to tell without more data from the show. And it’s just as well, isn’t it? After all, the more vague the relationship between warp factor and velocity, the less chance there is for an inconsistency to crop up in a future Star Trek! 

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