Where did Warp 3 in the original series is 27 times the speed of light come from? In the book The Making of Star Trek page 191 it states that Warp Factor 3 is 24 times the speed of light. Which one is correct?
Modern source material would say nominally TOS warp factor is cubed, so 3 × 3 × 3 is 27. (TNG has the 3 and 1/3 power.) However, it also said the actual speed is subject to local conditions in space and subspace. So 24 can be correct in practice.
I know there are TOS writers guides and Gene Roddenberry comments that will imply the writers thought the ship was much, much faster in the 1960s, but that's not really the question. For example in "The Cage," Pike said he was from the other side of the galaxy.
EDIT: Regarding sources of the cubed formula. See http://hem.bredband.net/locutus/faq_wa12.html "Taki Kogoma writes: I'm reasonably confident that this first appeared in the old Star Fleet Technical Manual by Franz Joseph and was quickly adopted by fandom. (Note that in some of James Blish's episode transcriptions, he had WF n = n*c.)
Joe Chiasson, describing Star Trek Maps, a map and manual combination by Bantam Books from 1980, offers:
The booklet contains quite a lot of written information on the development of warp drive systems and how warp travel is affected by matter density in a given area of space. The above formula was written as v = Wf^3 * c. "
I just checked my copies of The Making of Star Trek Stephen E. Whitfield and Gene Rodenberry.
My copy of the sixth printing, October, 1970, at PART II: AN OFFICIAL BIOGRAPHY OF A SHIP AND ITS CREW, Chapter 2. The USS Enterprise, says on page 191:
Warp Factor One is the speed of light. Warp Factor Three is 24 times the speed of light. Maximuml safe cruising speed of the Enterprise is Warp Factor Six, or 216 times the speed of light. At Warp Factor Eight (512 times the speed of light) the ship's structue begins to show considerable strain, due to theinabilityof the ship's field mechanisms to compensate. Warp facto Six is therefore excceeded only in instances of extreme emergency.
I then checked my copy of the third printing, dated January, 1969. And it has the same words on page 191 including:
Warp Factor Three is 24 times the speed of light.
So possibly The Making of Star Trek always said that warp factor three was 24 times the speed of light.
there may be other discussions of the speed of TOS warp factors elsewhere in the book.
As I remember, the writer's guides for TOS said that the (TOS) warp factors were the speed of light multiplied by the warp factor cubed, so that:
warp one was the speed of light
warp two was 8 times the speed of light
warp three was 27 times the speed of light
warp four was 64 times the speed of light
warp five was 125 times the speed of light
warp six was 212 times the speed of light
warp seven was 343 times the speed of light
warp eight was 512 times the speed of light
And that could be extended to higher warp factors mentioned in several episodes including:
warp nine 729 times the speed of light
warp ten 1,000 times the speed of light
warp eleven 1,331 times the speed of light
warp fifteen 3,375 times the speed of light
and warp thirty seven 50,653 times the speed of light, and so on.
And if anyone has access to various editions of the Star Trek writer's guide they can check to see if my memory is correct about what it says about warp factors.
One thing that is certain is that many writers failed to do the math, and the star Trek staff often failed to check and correct, and so examples of distances, speeds, and voyage times which agree with the TOS warp speeds are the exception rather than the rule.
Addition 10-19-2020 NKCampbell commented just three minutes after I posted with a link to this pdf of the third revision of the Star Trek Writers Guide dated April 17, 1967.
On page eight it says:
Hyper-light speeds or space warp speeds (the latter is the terminology we prefer) are measured in WARP FACTORS. Warp factor one is the speed of light -- 186,000 miles per second (or somewhat over six hundred million miles per hour.) Note: warp factors two, three and four and so on are based upon a geometrical formula of light velocity. Warp factor two is actually eight times the speed of light; warp factor three is twenty-four times the speed of light; warp factor four is sixty-four times the speed of light, and so on. Maximum safe speed is warp six. At warp eight the vessel begins to show considerable strain. We have established in preceding episodes that warp seven or eight are used only in emergencies, in hot pursuit and so on, and can be highly dangerous.
The speeds stated all agree with the cube of the warp factor except for warp factor three being 24 times the speed of light instead of 27, and the formula is not stated. Thus I think more research is needed.