Time, Distance, and Speed Problems in Star Trek

Well, it's not TOS canon, but it is "The Cage" canon, and as far as I know, there's no reason to declare "The Cage" noncanonical.

The TOS version of the adventure does create travel time problems: Spock claims that "it" is six days away at maximum warp, yet the only travel in the adventure, from SB 11 to Talos, doesn't appear to drag on for the better part of a week.

Did the adversaries jam the throttle at more than maximum warp? This wouldn't be a rare occurrence for poor Kirk. Perhaps the ship did warp 10 for a day, which is labeled suicidal in the manuals, while Spock was thinking on doing warp 8 for six days?

Or did Spock initially plan on stealing a warpshuttle rather than the Enterprise? Why would he change that plan? (Heck, I would - anybody with a decent starship could otherwise catch me during those six days!)

Of course, DSC "If Memory Serves" now gives us hard figures, and a plot where the heroes' not particularly fast starship covers the same distance (now explicated as just 2 ly) in hours. Perhaps SB 11 warped out to a greater distance after those events?

Timo Saloniemi

 

Back in Season One after this episode, the fastest the Enterprise was clocked at was only Warp 8 in Arena, and we heard how dangerous that was, so, I think an extended safe "maximum" was Warp 6, tops. (In mid-Season Two, Norman takes her to Warp 7 for four days.) If you use the stupid cubed formula, Warp 6 for 6 days works out to about 3.5 lys. Seems kinda close, i.e. the next solar system. If Warp 6 is much faster, it could be over 40+ lys. YMMV .

After nabbing the Enterprise, it looks like we skip ahead about five plus days into the journey as the court martial convenes. I guess Kirk was trying to regain control of the ship, etc. during this period, and Spock was confined to his quarters as he prepares for his court martial.

Stardates given (if you determine them to be present tense and not the dates of recordings looking back in his mission report) by Kirk start just before the court martial with only 0.7 Stardates pass in his logs, so, either the first part of the trial took about 6 hours including the recess, or Kirk is working on his mission report after the fact. Total, the whole event should take 6 days or about 17 Stardates. Again, YMMV .

 

Good questions all around. You'd think the Vulcans would appreciate the fine distinction between "we are being attacked" vs "something bad is happening" and why accurately relaying information is critical for timely and effective responses.

 

I thought Nero blocked all communications, so, the Vulcan distress signal was a Nero fake to draw the Federation Fleet into a trap. Once the battle took place, zero communications were transmitted by the fleet, so, Nero had to be able to block them. Kirk only figured it out (Nero's ship attacking the fleet and Vulcan) while the Enterprise was in transit to Vulcan. Otherwise, they would have flown into the trap too.

 

Indeed, it seems Nero only started attacking the planet with his drill after the cadet fleet left Earth. That is, his beam makes Amanda rush out and gasp in awe in a scene that comes after the fleet has been alerted and has departed. Did she gasp in awe repeatedly for hours upon hours? "Ooooh, that beam is STILL on!"

There was no seismic trouble. There was just Nero jamming everything, faking a distress call, and then fighting Vulcan to submission (either with those fancy missiles of his, or then with red matter), then starting drilling. (And incidentally causing some tremors, but those weren't what prompted the "call for help").

Timo Saloniemi

 

That actually does make sense. Guess he wanted to tangle with the Federation fleet when they were in an unprepared posture. It worked. For a crazy person he had some good tactical thinking.

Also, always wanted to know what the hell was happening in the "Laurentian system". And how large/how many ships/what kind were there, anyways? This is before Starfleet heavily militarized, and I just have so many background/world-building questions about the situation in the Fed...

 

It's obvious that as early as the .73 ly per hour from an early treatment, that it was always intended to be alot faster than the cubed scale. Certainly in many episodes there are wildly divergent numbers. There is no completely satisfying way to reconcile them all. Nor is it clear why you need any scale at all. They could say "set course for Vulcan. Speed: 5,000c" instead of giving whatever number equals 5000c on some scale. The cubed system would be fine if that were a warp jump. Warp 8 meaning an instantaneous jump of 512 light years. But too slow if it means 512c. It would be better to establish far higher speeds, but say they cannot be maintained for long.

If you want a scale, and you move up to the 4th power, things get a little better. The .73 ly per hour figure (6,384.8 x C) would then be warp 8.94, which is a more reasonable figure for a near max speed, despite some TOS episodes that go far beyond that.

1= 1
2= 16
3= 81
4= 256
5= 625
6= 1,296
7= 2,401
8= 4,096
8.94 = 6,384.8 (.73 ly per hour)
9= 6,561
10= 10,000

On balance though even the 4th scale would be slow compared to what they often want the ships to be able to do. The 6th or 7th scale finally gets you nearer to it, but then is far too fast for other episodes on the low end.

 

Another variable is needed in any equation that is, well...variable. Hence, with the right variable, any speed can to achieved.

 

The biggest outliers are in That Which Survives, Obsession (going 1000 lys in the episode back to the Cloud's home planet) and Arena (getting back 500 parsecs or 1630 lys to the starting planet in a reasonable time). In two cases, the Enterprise was "transported". Others on this site have proposed that the ship flies back along the transporter energy trail resulting in a most favorable variable value. For Obsession, who knows? Perhaps, the Cloud monster itself stretched space with its own passage, and the Enterprise followed it in its wake gaining a favorable speed variable.

 

You are what we call a glass is half full kind of person!

 

^ We already have the Cochrane factor for that, assumed to be variable with region, to explain why certain routes are much slower or faster than others.

However, I think they also should have made it variable with time, to account for discrepancies between instances, series, and eras (for example why the Earth-Q'nos trip seems a lot quicker in the 22nd than in the 24th century, and so on).

 

Well, whatever he was, he wasn't a soldier. But he had a couple of tools that he could use: the drill/jammer, 24th century computers (and possibly also computer weapons, these coming as preinstalled applications on every Romulan ship like Explorer with Windows), and then those relatively feeble and easily intercepted missiles. He would make use of that.

Since Nero wasn't a soldier, he probably wouldn't have that much tactical experience and repertoire. Rather, he'd do the same thing over and over again. Strike with excessive force, kidnap a kingpin, torture him for information, use that information as a weapon. Sending Starfleet into Laurentius with a false "Klingons are getting slaughtered here, you're next!" message, then sending the remaining second-rate force to Vulcan unprepared with a false "We are having an earthquake, please bring blankets!" message, is what buys Nero his precious windows of opportunity. After all, he can't hope to win in a fair fight, what with not being a soldier, not having a warship or weapons of war, and generally being outnumbered about six zillion to one.

Is this before Starfleet was militarized? Or back when Starfleet still was militarized, even though Pike (no doubt parroting his mentor Marcus) thought it was growing weak and wussy? I could well see a high level of preparedness, which goes up in smoke in the following decade and prompts Kirk to make all those "violence is a thing of the past, I am no longer a soldier" speeches. And DSC has the heroes establish that Starfleet in the aftermath of Burnham's War has some 7,000 ships left, most of those apparently not with NCC registries; the fleet in the other timeline might be bigger.

It's also possible that the 1,000 ly bit from "Obsession" is poetic license, like Kirk's "we're a thousand lightyears away from the law so let's start gobbling up this illegal booze" in TUC, and actually stands for some 22.7 ly...

Story logic wouldn't much support the cloud monster covering such a vast distance if it just wants to find a new home or breeding or hunting grounds. Not even if it has very exacting specs (say, "I want a papier-mache rock exactly like this in my new home, just like in the old one!").

Timo Saloniemi

 

• KIRK: And what if it is the same creature that attacked eleven years ago from a planet over a thousand light years from here?

It's over a thousand light years and not an exaggeration. Kirk was to get to the planet and back to meet the Yorktown in 48 hours, or about 2000+ lys. in 48 hours (Sulu said they could do it in 1.7 days or 41 hours). That's fast: over 400,000c with Sulu's estimate. The trip would be at less than Warp 8 since Kirk chased the Cloud at Warp 8 and they pooped out and had to reduce speed to Warp 6 during the chase. Good thing the ship's reliability at high Warps speeds got better in Season 3, so that it could go Warp 8.4 for ~11 hours and cover 1000 lys which gives a speed of over 700,000c.
@blssdwlf did a great analysis of warp speeds.

 

My problem with the "Cochrane Factor" is that in practice it seems indistinguishable from "Speed of Plot Factor". If the warp trip is suddenly a 1,000 times faster or 100 times slower well, there must have been some weird variation in the local density of HandWavium. Which sounds like there is no system at all. It's just whatever they say it is week to week.

 

Bingo! You hit it on the nail. Correct analysis. Done. Let's go home.

 

Oops! I didn't get to finish this earlier. Here goes.

After the second attack on Argus X:

So, at Argus X, Kirk says that Tycho IV is in "another part of the galaxy". That is vague but doesn't indicate the two planets are close.

(By the way, there is a science fiction anthology titled Another Part of the Galaxy http://www.isfdb.org/cgi-bin/pl.cgi?2808)

When Kirk and Spock question Kirk in his quarters about his reasons for hunting the dikironium cloud creature:

So Kirk says that Tycho IV is over a thousand light years from Argus X.

While chasing the creature, Nurse Chapel visits Ensign Garrovik in his quarters:

So Chapel is clearly exaggerating since "half way across the galaxy" should be about fifty times as far as Kirk said. Unless she meant that the chase was going half way through the thickness of the galactic disc instead of half way across the diameter of the galactic disc.

I suppose that Kirk could have been exaggerating when he said the distance between Argus X and Tycho IV was over a thousand light years, but that would mean that Chapel was exaggerating even more than fifty times when she said the chase was "half way across the galaxy".

Later Kirk decides to chase the creature to the Tycho system:

So Kirk's plan is apparently to travel over one thousand light years to Tycho IV, take a few minutes to destroy the creature, travel over one thousand light years back to the vicinity of Argus X, and then resume the voyage to rendezvous with the Yorktown.

1.7 days is 40.08 hours. 40.08 hours subtracted from 48 hours leaves about 7.2 hours to reach the rendezvous with the Yorktown - minus time spent destroying the creature.

Soon after the first attack on Argus X:

So apparently the travel time to reach the rendezvous with the Yorktown will be about hte same as it would have been if the Enterprise had left two days earlier at the beginning of the episode.

 

And here I thought you were a positive thinker! Not sure that means "going home". It does mean that there is no completely satisfying answer to every example. The preponderance of examples show speeds higher than the cubed formula. As early as the treatment for the show, a speed 12x faster than cubed Warp 8 was posited. So I think it is easier to just say that the warp speeds were always alot faster than that. But due to writer/showrunner/producer laziness some examples are hard to make fit no matter what you do.

 

I didn't mean to be negative. I just meant to hammer the point that there is no formula for the fuzzy warp speed scale, especially one that will be considered canon or will make sense. Speed of plot is unfortunately the formula exhibited during the series.

I have fooled around with various warp speed formulas and "Cochrane variables" involving adjustments for things like space matter and subspace environments. It's a fun exercise. As an engineer, I would greatly prefer order and a nice neat formula; but the early Star Trek writers had other, or rather, no plans. All I know is that the simple cubed warp formula is just too slow to ever explore the galaxy plus no writers really used it anyway. 12x is a good compromise; I've used 10x to 50x for "normal" interstellar flight but variables of 1000 have to be in play for very special situations using the Cochrane factor formula v=xWF^3. The Cochrane factor x can be less variable if put inside the cubed part of the formula: v=(xWF)^3, so variable values of 1 to 11 range are used instead. This makes sense since things that may affect warp travel are themselves three dimensional environments such as matter, gravity, energy, etc. I can buy a forth order equation since we also have the other dimensional effects of subspace. YMMV .

 

I pick a scale that seems to fit most of the examples, and would give otherwise reasonable travel times given the scale of the Federation. Call it high, middle and low scales. In Picards time it is spread out over 8,000 ly. Even at 8,000 x C would take an entire year to make the trip. That seems certainly wrong. On the 5th scale, Warp 8 would be 32,768c. That would mean doing it in 3 months, which seems more reasonable. Maybe they used the 4th scale (low) in TOS and 5th scale (middle) in TNG if you want to say the scale changed? Or 5th in TOS and 6th (high) in TNG? That works even better. Anything too far outside of that, I just retcon in my head canon.