Time, Distance, and Speed Problems in Star Trek

[Boris Skrbic]

That one irritated me so much when I noticed it. All there needed to be was some kind of time break to let you know they'd traveled for a while, but instead you have the impression that ftl is practically instantaneous instead.

Why? In “That Which Survives”, the travel time for 990.7 light-years at Warp 8.4 is given as 11.337 hours. If Vulcan is 16 light-years away, that’s just an eleven-minute trip (Pike asked for maximum warp).

These deviations from the norm are fully etched in canon, so you can’t use the norm to criticize a future iteration that also chooses to deviate. Sometimes warp speeds are higher: how else could one travel to the edge or the center of the galaxy if a story demands it?

 

[Ronald Held]

Cochrane factor is higher in certain areas of the Galaxy.

 

[XCV330]

Stars are moving at various velocities away from or close to each other depending upon their relation to one another in space and time. These perceived velocity differences can be quite extreme (For instance the most distant galaxies from us on the other side of the universe are moving away from us at such a great speed the velocity between us is superluminal, and thus we cannot be affected by their gravity, nor will we ever receive light from them).

Obviously they don't take such things into account in star trek, but it is easier to think of travel in star trek not like steamships going at constant rates of speed across largely endless expanses of sea, but a three dimensional white water rapids expedition. There are all sorts of collisions to avoid, gravity wells to navigate around, subspace pheonomina that apparently can't always be predicted or scanned well ahead of time, and the ability to be pulled out of "Warp."

Warp speed itself may be consistent but how that consistency applies within the real universe may be significant variable. Navigating a faster than light ship must be difficult stuff.

 

[Timo]

That one irritated me so much when I noticed it. All there needed to be was some kind of time break to let you know they'd traveled for a while, but instead you have the impression that ftl is practically instantaneous instead. Oh well, needs more lens flare.

Hmh? We get several things that absolutely require the passage of time.

Kirk has to wake up. McCoy has to get a change of clothes. Everybody has to get used to doing their jobs, despite specifically not really being up to speed. The most probable duration for the trip before Kirk finally reaches the bridge is several hours (a couple, for Kirk to sleep off his medication, is the preferable lower limit).

We can stretch that if we want to, but why should we, when Vulcan has always been a neighbor and emergency warp has always been fast? The absolute upper limit is the fact that Chekov over the PA refers to "2200 hours" for a key event that took place before the departure, therefore no more than 24 hours from the current time or he'd have to give a date in addition.

What may appear out of place is Pike asking Chekov to do this mission briefing just before the ship reaches Vulcan. But it would be equally odd for him to do that right after the ship leaves Earth: even Pike doesn't have all the facts yet at that time. The plot doesn't require us to think that the hop from Earth to Vulcan takes mere minutes, then. The editing just removes some slack there.

Ditto at the end of Discovery season 1. They warp from earth with Sarek waiting on the bridge to arrive at Vulcan. Although the distress call from the Enterprise comes in and they never make it, it doesn't change the fact Sarek was either going to stand in the same spot for days or they were minutes from Vulcan a la ST 2009.

Or then Sarek is there to watch as the ship departs the Sol system. Nothing precludes the action from taking place right next to Earth.

Except nobody ever explains why Pike would wish to intercept the Discovery in the first place. Does his starship just randomly stall there, against all odds? I mean, yeah, he could and would stall next to some starship or another if close to the UFP core worlds - the odds are just against him doing so next to a) his science officer's adopted sister and b) the one ship that can complete his assumed mission. So, does he specifically intercept the hero ship because he needs the spore drive? But he indicates no familiarity with it when they do make use of it. Did one or the other of the Red Angels guide him there? But we never see Burnham Jr do it, and in any case there is no Red Event mentioned other than the Hiawatha one that the Enterprise in vain tried to reach before getting winged.

It's not a speeds and travel times issue, then, but a general plot one where, as usual, Trek cuts corners and the audience is at liberty to invent excuses.

Timo Saloniemi

 

[lazarus+]

Sorry to the two people that answered me but there is something hincky about that. "Star Trek 11" and "Earth to NuVulcan"

Shouldn't it be either Star Trek IX for that or Qo'nos to Earth. I missed that when I quoted it but that is what I meant.

When in Star Trek 11 did anyone go from Earth to Vulcan, because I don't remember that at all.

edit:

the confusion is mine, I am so used to thinking of the new Star Trek series as being referred to by name and I always think of the first new one as "Star Trek 2009" and confused myself.

I was thinking entirely of the travel between Qo'nos and Earth in Into Darkness.

My B.

edit again: I'm still like, which numbers are Nemesis, Insurrection..? Have to count out the TNG movies. Man the whole thing gets confusing when your franchise stopped counting up...

 

[F. King Daniel]

For whatever it's worth, I think a 24 hour round trip to Kronos and back (Into Darkness, as per Scotty's "One bloody day!") at warp 8-9ish is consistent with a 4 day journey at warp 5 in "Broken Bow"

But really, the powers that be don't much care and perhaps neither should we.

 

[lazarus+]

For whatever it's worth, I think a 24 hour round trip to Kronos and back (Into Darkness, as per Scotty's "One bloody day!") at warp 8-9ish is consistent with a 4 day journey at warp 5 in "Broken Bow"

But really, the powers that be don't much care and perhaps neither should we.

Certainly that number seems consistent enough (without checking what the actual warp factors would say about it).

I just find the idea of those locations being that close to each other to be fairly ridiculous from a world building perspective. Just too close...

 

[Timo]

Well, Klingons are old acquaintances of the heroes, while every set of heroes keeps encountering new folks, too. Why not have your best fiends close? Proximity breeds hatred etc.

...The weirdest warp travel thing about the numovies is the return flight in STID, from Klingon space to the far side of the Moon.

1) It takes only as long as it takes for Carol Marcus to reach the bridge. Did she forget that turbolifts exist, run all the way, and take sixty-eight wrong turns?
2) It gets cut short by the guns of the Vengeance, yet hits the parking lot of Earth spot on.
3) It treats a warp chase as an entirely unheard-of thing.

Also odd is that the villains are masters of "transwarp beaming", yet the heroes have no fear of getting boarded at warp... Or make no attempt to reach Earth by beaming.

Timo Saloniemi

 

[Henoch]

Also odd is that the villains are masters of "transwarp beaming", yet the heroes have no fear of getting boarded at warp... Or make no attempt to reach Earth by beaming.

"Transwarp beaming" could have completely been avoided with the use of high-speed shuttles:
1. For example, after ejecting Kirk from the Enterprise, the damaged Enterprise may have "moderately" left the star system while Kirk eventually finds old Spock and Scott. Instead of "transwarp beaming", Scott could have been working on a pet project of a "souped-up, stealthy" shuttle (use the ship that was used to do the "transwarp beaming"; why have the ship at all if you aren't going to use it?) which can overtake the Enterprise, then when in normal beaming range, beam onto the ship.
2. Ditto for Khan's "transwarp beaming" to Kronos. Instead of beaming directly to Kronos, Khan could have beamed into a "souped-up, stealthy" shuttle in orbit (stolen from the Vengeance which makes sense being that the Vengeance is souped-up and stealthy itself), then raced to Kronos. Next, have Scott use his technical brilliance to detect the warp trail to Kronos. Same events without the stupid "transwarp beaming".

 

[Ronald Held]

I am certain the relative velocities of current and destination star are taken into account,but they are small compared to the speed of light.

 

[F. King Daniel]

stupid "transwarp beaming".

I never understood the hate for it. TOS gave us loads of aliens with long-distance transportation. TNG gave us "subspace beaming" which may be the same thing and DS9 gave transporters with 10 light year range (and the ability to pluck people from that range) to the Dominion.

So why is it bad that Starfleet circa 2387 figure it out and then Spock introduces it to the past?

 

[Timo]

...We even got to see the backlash in the very next movie, much as with Genesis in the original movies. And the backlash ought to be pretty much the same in the "original" 2380s (if that really is when Scotty figures it out, rather than in, say, the 2280s).

So, will we get long range transporters in the hands of the privileged and the shady in PIC, too...?

Timo Saloniemi

 

[NCC-73515]

1) It takes only as long as it takes for Carol Marcus to reach the bridge. Did she forget that turbolifts exist, run all the way, and take sixty-eight wrong turns?

She asked and waited for permission whenever she entered a new room.

 

[F. King Daniel]

Carol clearly came up via turbolift somewhere behind the bridge and ran the rest of the way.

 

[MAGolding]

As we all know, the writers guides for TOS and The Making of Star Trek gave a semi canonical warp formula for starship speeds a t various warp factors.

The speed of a starship would equal the speed of light multiplied by the TOS era warp factor cubed.

Warp factor one,equals the speed of light.

Warp factor two, the maximum speed of a freighter according to "A Private Little War", equals 8 times the speed of light.

Warp factor three equals 27 times the speed of light.

Warp factor four equals 64 times the speed of light

Warp factor five equals 125 times the speed of light

Warp factor six, the maximum safe speed of the Enterprise, equals 216 times the speed of light

Warp factor seven equals 343 times the speed of light

Warp factor eight, the maximum emergency speed of the Enterprise, equals 512 times the speed of light

Warp factor nine equals 729 times the speed of light.

And so on.

In some episodes starships seemed to travel no faster than the warp formula indicated.

In "Who Mourns for Adonais?" On the planet Pollux IV Kirk says:

KIRK: On you, Lieutenant! Reject him, and we have a chance to save ourselves. Accept him, and you condemn all of us to slavery, nothing less than slavery. We might never get help this far out. Or perhaps the thought of spending an eternity bending knee and tending sheep appeals to you.

So Kirk think that Pollux would be a long way for a rescue mission to come looking for them. Pollux is only about 33.8 light years from Earth. At warp factor one it would take 33.8 years for a ship from Earth to reach Pollux, at warp factor two it would take about 4.225 years for a ship from Earth to reach Pollux, at warp factor three it would take about 1.25 years, at warp factor five it would take about 0.52 years, at warp factor five it would take about 0.27 years (98.76 days) at warp factor six it would take about 0.156 years (56.9 days), at warp factor seven it would take about 0.098 years (35.99 days) and at warp factor eight it would take about 0.066 years (24.106 days).

So the way Kirk emphasizes how far they are from help, it doesn't seem like Kirk expects any hypothetical rescue ships to come, if at all, much faster than the TOS warp formula indicates.

In "This Side of Paradise"" Kirk & a landing party beam down to Omicron Ceti III:

KIRK: Another dream that failed. There's nothing sadder. It took these people a year to make the trip from Earth. They came all that way and died.
ELIAS: Hardly that, sir. Welcome to Omicron Ceti Three. I'm Elias Sandoval.

If "a year" equals 0.5 to 2.0 Earth years, and if Omicron Ceti is Mira or Omicron Ceti, which was believed to be about 220 light years from Earth, but is nwo believed to be about 299 light years from Earth, it is simple to calculate the average speed of the voyage. The average speed of the voyage should have been between 110 times the speed of light and 598 times the speed of light.

If the transport ship was limited to warp factor two, the maximum speed of a freighter, it would have traveled 13.75 to 74.75 times as fast as it should have. If the transport ship traveled as fast as warp factor six, the maximum safe speed of the Enterprise, it would have traveled 0.509 to 2.768 times as fast as it should have.

So the transport ship could have traveled many times as fast as the official TOS warp formula if it traveled a low warp, but if it traveled at a high warp factor like warp 6 it didn't have to exceed the official TOS warp formula.

So there are some TOS episodes where spaceships seem to travel at about the official TOS warp formula speeds, and others where spaceships don't have to travel any faster than a few tens of times the official TOS warp formula.

Bu there are other TOS episodes where spaceships travel at speeds of thousands of times the official TOS warp formula.

In "Arena" Kirk finds that aliens have destroyed the outpost on Cestus III. Before beaming back to the Enterprise Kirk orders:

KIRK: I want a search party of thirty medical personnel beamed down immediately to search for survivors. Notify the transporter room. Lock onto us. We're beaming up.

Then the Enterprise begins to pursue the alien ship:

SULU [OC]: Sulu here, sir.
KIRK: Is the alien still making warp five?
SULU [OC]: Affirmative, sir.
KIRK: Initiate warp six.
SULU [OC]: Affirmative, sir.

An unspecified time later:

KIRK: Mister DePaul.
DEPAUL: Yes, sir.
KIRK: Position.
DEPAUL: Twenty two point three parsecs beyond latest chart limit, sir.
KIRK: All scanners lock into computer banks. I want a complete record of this. Mister Spock, what do we have on this general area?
SPOCK: Virtually nothing, Captain. No records of any explorations. There are rumours of certain strange signals on subspace channels. However, none has ever been recorded.
KIRK: Anything on intelligent life forms?
SPOCK: Nothing specific, Captain. Unscientific rumours only. More like space legends.
KIRK: Mister Sulu, status, alien vessel.
SULU: They must be aware we're after them, sir. They've gone to warp six also.
KIRK: Warp factor seven.

During that unspecified length of time the Enterprise has traveled from Cestus III to the limit of their charts and then 22.3 parsecs beyond that limit. 22.3 parsecs equals 72.73287 light years, or 26,565.68 light days, or 637,576.32 light hours. So if the Enterprise traveled at least 22.3 parsecs in what seems to be a short time, perhaps between 1 hour and one day, the speed of the Enterprise would be at least between 26,565.68 and 637,576.32 times the speed of light, and thus at least between 122.98925 and 2,951.7422 times the speed of warp factor six according to the official TOS warp formula.

Later, the Metrons transport the Enterprise far from Metron space:

SULU: Captain.
KIRK: Mister Sulu.
SULU: It's impossible, but there's Sirius over there when it should be here. And Canopus. And Arcanis. We're. All of a sudden, we're clear across the galaxy, five hundred parsecs from where we are I mean, were. I mean
KIRK: Don't try and figure it out, Mister Sulu. Just plot a course for us back to Cestus Three.
SULU: Aye, aye, sir.

So now Kirk wants to return to Cestus III, which should be five hundred Parsecs (plus or minus a few tens of light years) from where they are now. Kirk knows that the medical personnel on Cestus III can survive for only a short time on their own.

So a few minutes later:

KIRK: I don't. Not anymore. And maybe in a thousand years or so, we'll be able to prove it. Never mind, Mister Spock. It doesn't make much sense to me either. Take us back to where we're supposed to be, Mister Sulu. Warp factor one.
SULU: Warp factor one.

So if the medical personnel and any survivors they find can survive for perhaps a day, or a week, or a month, Kirk expects to return to Cestus III before that time is up.

Five hundred parsecs is 1,630.78 light years, or about 19,569.36 light months, or 85,091.77 light weeks, or 595,642.39 light days. This indicates that the speed of the Enterprise at warp one would be 19,569.36 times the speed of light and the official TOS formula if the voyage will take one month, 85,091.77 times the speed of light and the official TOS formula if the voyage will take one week, and 595,642.39 times the speed of light and the official TOS formula if the voyage will take one day.

And there are other, similar examples.

One fan theory to explain such problems has been "Cochrane factors". Different regions of space will have different "Cochrane factors". A starship traveling at warp with a region of space will have a speed that is the official TOS warp speed for its warp factor multiplied by the "Cochrane factor" of that region of space. For example, In a region of space where the "Cochrane factor" is 2.187 a starship will travel at its warp speed multiplied by 2.187, and in a region of space where the "Cochrane factor" is 1,457 the starship will travel at its warp speed mulitpilied by 1,457, and so on.

But there are other theories to explain those problems.

In "By Any Other Name":

KIRK: What do you want?
ROJAN: Your ship, Captain Kirk. It will serve us well in the long voyage that is to come.
KIRK: Voyage? Where?
ROJAN: To your neighbouring galaxy, which you call Andromeda.
KIRK: Andromeda? Why?
ROJAN: It is our home.

And:

KIRK: What's the point of capturing my ship? Even at maximum warp, the Enterprise couldn't get to Andromeda galaxy for thousands of years.
ROJAN: Captain, we will modify its engines, in order to produce velocities far beyond the reach of your science. The journey between galaxies will take less than three hundred of your years.
Spock Fascinating. Intergalactic travel requiring only three hundred years. That is a leap far beyond anything man has yet accomplished.

The Andromeda Galaxy is about 2,540,000 light years from Earth.

If Kirk meant that the Enterprise couldn't reach Andromeda Galaxy in one thousand years, maximum warp must be less than 2,540 times the speed of light.

If Kirk meant that the Enterprise couldn't reach Andromeda Galaxy in two thousand years, maximum warp must be less than 1,270 times the speed of light.

If Kirk meant that the Enterprise couldn't reach Andromeda Galaxy in three thousand years, maximum warp must be less than 846.666 times the speed of light.

If Kirk meant that the Enterprise couldn't reach Andromeda Galaxy in four thousand years, maximum warp must be less than 635 times the speed of light.

If Kirk meant that the Enterprise couldn't reach Andromeda Galaxy in five thousand years, maximum warp must be less than 508 times the speed of light, and that is less than the Enterprise's official maximum emergency speed of Warp factor 8, 512 times the speed of light.

And so on. At warp factor 6, the Enterprise's official maximum safe cruising speed of 216 times the speed of light, it would take 11,759.259 years to reach the Andromeda Galaxy from Earth.

If "less than three hundred years" means between 250 and 300 years, the Kelvin modified Enterprise would travel at 8,466.6666 to 10,160 times the speed of light or about warp factor 20.4 to 21.6.

Spock says:

Intergalactic travel requiring only three hundred years. That is a leap far beyond anything man has yet accomplished.

If Spock means that no man made ships have ever traveled fast enough to reach the Andromeda Galaxy in only 300 years, and thus at about 8,466.666 times the speed of light, that would strongly imply that the Enterprise never reached speeds of 8,466.666 or more times the speed of light in any previous episode.

So that would strongly imply that starships do not attain speeds of 8,466.6666 times the speed of light, or higher, by taking advantage of the "Cochrane factors" in some regions of space to multiply their warp speeds.

And that would limply that every time the Enterprise appear to reach speeds that were thousands of times the speed of light, it actually did not. Instead the Enterprsie reached its destinations in travel times equivalent to travelling thousands of times as fast as light, without actually reaching speeds thousands of times that of light, using something totally different from"Cochrane factors".

 

[valkyrie013]

Enterprise wad usually good at speed/ distance inn the series, but always speed of plot..
But basic to me was..
Warp 5 ish was 1 light year a day
And voyager warp 9 was 3 ly a day.

So quonos 1 day away is 3 light years? Closer than alpha centauri? Nope.
Tmp said 4 days to vulcsn at warp 7

 

[F. King Daniel]

Tmp said 4 days to vulcsn at warp 7

That gets quoted a lot, but they'd have zero need to be travelling at maximum warp in TMP, as they would be on their rescue mission to Vulcan in ST'09

 

[valkyrie013]

well, Various episodes, mainly Enterprise says its 16 lightyears to Vulcan. 2 weeks in Enterprise, and Tmp's 4 day quote is going 4 light years a day.. which is faster than warp 9 in voyager at 3 light years a day. ST 09 ( and Kelvinverse speeds and times) speeds and times are all jacked up.
Now the Klingon home world being 4 days away in enterprise means at max 5 light years? Thats WAY to close!

 

[Timo]

Sixteen lightyears to Vulcan matches fifteen to Rigel in "Broken Bow"; it's a fairly short hop in ENT terms. That it would take two weeks (it doesn't!) is inconsistent with all ENT datapoints save for the "Broken Bow" dialogue that follows the cubic formula. And there we can always use the excuse that warp within star systems is slower for the given factor than warp outside systems (because we can see that this much is true in adventures like "Tomorrow is Yesterday" and ST4:TVH).

Why would it take four days for our heroes to cover the sixteen lightyears in TMP, then? Well, Scotty wanted to give the ship and her new engines a proper shakedown. Perhaps the engineer finally gets his wish, and the ship will crawl to Vulcan at speeds that assuredly won't blow her up now that there is no longer a hurry. That is, "We can get you to Vulcan in four days" is a lament.

Since the cubic formula really never applies, we learn nothing about how far away the Klingons are. Except, of course, that they are four days away. Which is fine and well: it's much farther out than Vulcan, which can be reached in fewer than four days in all normal circumstances including ENT, yet OTOH it need not really be out in the sticks since distance is no protection against these marauders anyway. What matters in that respect, too, is that Vulcan lies closer - and thus has dibs to Earth's neighborhood.

Timo Saloniemi

 

[Mytran]

Roddenberry once provided around the first or second pilots that maximum speed of the Enterprise was 0.73 ly/hr, be that either warp 6 or 8. This equates to 6400 c. If we assume GR meant that max. speed at warp 8, then the cubed formula becomes: speed = 12.5 x 8^3. I like to think that this is deep space or interstellar normal factor between star systems away from their gravity and solar wind effects.

Interestingly enough, the 0.73ly/hr was one of the few FTL formulas that was actually adhered to in the show! Well, once anyway

• In The Cage the captain laments about the current state of his life with Dr Boyce
• A few minutes later the Enterprise sets off for Talos, which is 18 light years away
• 18 ly at 0.73 ly/hr would take 24.66 hours
• A short while after arriving Pike is captured and not long after that he tells Vina:

PIKE: It's funny. It's about twenty four hours ago I was telling the ship's doctor how much I wanted something else not very different from what we have here. An escape from reality.

The term "24 hours" is often used as a synonym for a calendar day. So even if Pike spent several hours as a prisoner before making that statement the 0.73ly/hr formula still holds.

Of course, Pike's line was edited out of The Menagerie so does it actually count as part of the series canon?