Distances and Speeds in TOS

[Falconer]

Last year I had a thread over at TrekBBS in which I came to some conclusions about the size and scope of the Federation, and developed a practical Warp Factor scale.

www.trekbbs.com/threads/distances-and-speeds-in-tos.311096/

It dovetailed with some of my work over here but developed in a certain way over there. Anyway, since it encapsulates my current thinking on some very important matters, I figured I would link to it here. I was hoping to rewrite it in more concise form, but I think it’s basically the most interesting (hopefully to some) to see how it originally unfolded. Enjoy!

[Jack Photon]

I read a few pages in and it got deeper than I was ready for at the moment. lolz. Lots of great comparative data has been gathered there! Thanks for posting it here.

For my purposes the other year, I simply doubled the FASA map scale, making 10pc now 20pc. That helped fix FASA maps a little for my jack photon revision as I dint' want to perpetuate the original bad scale to future generations. It's now a little better, at least.

As to:
That Which Survives... I did the math the other week on that and while Spock admonishes Lt Rhada for not being precise, it is in fact Spock who is off by a factor of 100! If that 990.7 light years moves two decimal places to 9.907 ly, then the travel time lines up with the show's ETA at stated speed. (Or was it factor 10 @ 99.07 ly?)

Arena. It's great that maybe in a thousand years or so mankind will be ready to meet the Metrons, because 500 parsecs at warp 1 is going to take that long to get back to where they are. I mean were. I mean...

Gamesters is one episode where ETA did meet distance/speed if you apply a small dollop of fudge and assume that between editorial cuts the speed changed some and that the thralls were there for more than a few days, perhaps a week of training when 1701 finally arrives.

I mostly find writers were simply pulling big numbers seemingly to sound impressive than anything else. 990.7 is a lot further than 99.07 or 9.907, thus sounding more intimidating. Humans, especially TV audiences, like big sounding numbers that sound big and intimidating -adds to a superficial sense of drama.

In many cases, taking what was said and moving the decimal works. Sulu's 500 parsecs at 50 parsecs suddenly becomes 'reasonable' and still justifies "clear across the galaxy' in 'local terms'; similar to "driving clear across town" as opposed to "down the street" or "around the corner" though that corner or destination 'down the street' in fact be many miles away, for example. There's "around the corner" in small-town USA and then there's "around the corner" in big city USA. Two very, very different perceptions and definitions for the same phrase.

Once local gravitic and spatial density is accounted for ala' the Cochrane factor (or as that is interpreted in my Helm/Nav rules to alter speed), the travel times are mostly patched up. At least patched well enough for any given GM to move forward with in their own game.

No formula will ever fully match. The only solution is a time machine back to '65, get hired by the show as a script consultant who specifically does the travel math, time warp back here to the present day and enjoy the fruits of your labor and admiration of the four or so people in the world who care enough to look into it as deeply as the few of us here have. lolz.

Awesome work on your part, Falconer!

[Jack Photon]

Speaking to exaggerations of distances, Gamesters provides two.

1.
SPOCK: Plot a follow course, Ensign Haines.
HAINES: (now in Chekov's seat) Aye, sir.
MCCOY: You're going to leave here without them and run off on some wild goose chase halfway across the galaxy just because you found a discrepancy in a hydrogen cloud?
SPOCK: Doctor, I am chasing the Captain, Lieutenant Uhura, and Ensign Chekov, not some wild aquatic fowl. This is the only lead we've had.
HAINES: Course plotted and laid in, Mister Spock. Three ten mark two four one.
SPOCK: Initiate. Warp factor two.


2.
SPOCK: Projecting back along the path of ionisation, the nearest system is M two four alpha.
SCOTT: That must be two dozen light years away.
SPOCK: Eleven point six three zero.


And to follow up on the previous post.

SPOCK: Mister Scott, can we manage anything faster than warp six?
...
SPOCK: Agreed. Mister Scott, could you manage warp seven?
SCOTT: I would be more than content to do so, sir, and maybe a wee bit more.
SPOCK: Ensign, warp seven.

Thank you www.chakoteya.net !!!

At least for Gamesters, we have initial warp 2, an apparent jump to warp 6 for presumably much of the journey and then a last burst at warp 7 or a wee bit more. The nature of the warp formula and unknown time precludes stating "an average speed of...", however as mentioned in the previous post, with the assumption of a few days/week of time, a dollop of fudge, a squirt of whip cream, a nice cherry on top to distract and it's not bad. 10 ly at w6 = 17days or 10days at w7.

The result is that Kirk and crew were stuck for up to about two weeks given the standard cubed warp formula. If one takes gravimetric/spatial density into account, the 2 week window becomes an upper limit and they could have been there as short as 8-12 days. Less than one week travel is unrealistic given the fictional constraints. More than two weeks becomes unrealistic for the action portrayed by the PCs on ship and planet.