Distances and Speeds in TOS

[Unicron]

It's one aspect I like as well, having the universe feel appropriately "large" for storytelling. In the Battletech RPG universe, they've been reasonably consistent about capital ships having technological limits (most ships can only jump a maximum of roughly 30 light years, and can only make two sequential jumps before recharging if they have a lithium fusion battery) because moving large vessels consumes a huge amount of energy. It takes time for a ship to recharge its batteries via solar sail, and it's not uncommon for many worlds in the Deep Periphery to be highly isolated and have very limited contact (if any) with the major powers. Some areas have simply never been reliably explored, because if something goes wrong on the voyage the crew could be in serious trouble.

Some Periphery worlds also got cut off from any major resources after the Star League fell apart, which was problematic for those planets functioning as experimental laboratories. Some of the sourcebooks offer some interesting player options dealing with such worlds, and even doing unique groups to add a bit of extra spice if they want.

 

[publiusr]

Here is an idea: one chart—saucer based reactor. Scotty goes ape-shit going past warp six on that one. Used when engineering hull is on downtime.

Second chart—main reactor in the secondary hull.

Third chart—both reactors together.

Warp factors now variables dependent of status reports. Floating point variables so as to not give ships capability away in communiques.

 

[Falconer]

This was on of the things I enjoyed back in the day of playing the FASA Trek RPG. We had these big maps with the distances laid out, and we knew how fast the ships were. There was never any 'crossing the Federation in two days' kind of stuff. When a ship left spacedock at Earth, it could take weeks or months to reach its destination. We didn't roleplay all of that time, but we kept track of it in-campaign. A couple of crews actually completed 5-year missions where much of it was transit-time, with plenty of adventures in between. Good stuff.

Yes, I like that too. That’s why, with apologies to some fellow posters, I personally like to consider Warp Factors to be absolute, measurable velocity benchmarks rather than any kind of squishy or situational explanation that allows them to be variables (eg., energy output). How else, for example, can the Enterprise crew marvel at the Warp 10 attained by the Orions?

But to your point about transit time contributing to the feel of a voyage in vast space, I love that, too. But with regard to the particularities of FASA, it must be admitted that TOS doesn’t seem to countenance Rigel being 14 months away from Earth at Warp 6. Enterprise just went back and forth too frequently within its five years. (And FASA even places Rigel much nearer to Earth than it should be.) Furthermore, when playing FASA you have scenarios like “Where Has All the Glory Gone?” in which there is an emergency 1.25 light years away, and your ship must travel at Warp 9 in order to reach it in 15 hours. I’m sorry, but it doesn’t seem like Star Trek.

 

[Jedi Marso]

FASA even places Rigel much nearer to Earth than it should be.) Furthermore, when playing FASA you have scenarios like “Where Has All the Glory Gone?” in which there is an emergency 1.25 light years away, and your ship must travel at Warp 9 in order to reach it in 15 hours. I’m sorry, but it doesn’t seem like Star Trek.

We never had any real quibble with where FASA put the Orions on the map- we just played it like it was presented. We also accepted the idea that some stars with 'real' names weren't the actual real stars, but other stars with the same name. None of the game writers were astronomers (that I know of) and neither were we.

For anomalies like you mention in "Where Has All the Glory Gone," the GM would jettison or retrofit whatever was necessary to make speeds and times work out the way they were supposed to. We never played at the speed of plot, even if it meant altering some of the facets of a module. That was just how we rolled!

 

[Falconer]

Sure, I agree with you, and in my own games Rigel is only half as far as it should be, and I adjusted the distance in WHAtGG to 22.5 ly to fit my campaign (and a totally different WF scale that I devised which is practical for hex crawling) and still maintain that aspect of calculating speed and time, which I love. It’s a satisfactory experience because it’s tangible and relatable, and scientific realism and adherence to screen canon are not super important there.

Here in this particular thread, however, I want to try to get as close to TOS as possible. So again, here is my stab:

Now, some comments for everyone’s consideration.

The three versions are essentially the same from about WF4 and upward. I devised v. 1 for those in the thread who like WF1=c and see no reason to change it. And, indeed, it works just fine. Nobody is going to be cruising at that speed, but for starting up the engines and leaving a system, anything goes. One reason to prefer to set WF1 > c, though, is that that allows impulse speeds > c, which is helpful for situations when your dilithium is shot.

I kind of like WF1 = 1 ly/day (v. 3) due to my gaming background (see above). My maps have 1 ly hexes, you see, so if you want all speeds to be meaningful, then you set the lowest speed to one hex/day. Possible problem: WF2 is basically indistinguishable from WF1. In other words, it’s weird that going from dead stop to WF1 would be this massive increase in speed, but then going to WF2 would be nothing.

Which brings us to the “compromise” (v. 2), which basically has no downsides, but not sure it’s got anything in particular to recommend it.

 

[blssdwlf]

How else, for example, can the Enterprise crew marvel at the Warp 10 attained by the Orions?

You could go Warp 10 right next to a star and appear to be moving like molasses in TOS so it isn't an indicator of speed relative to fixed objects, IMHO. We do know a few episodes earlier in "The Changeling" that Warp 10 requires alot of energy and the Enterprise isn't structured for it. So seeing the Orions blow by them at Warp 10 would imply that their ship had a huge power output and a structure to take it (which Spock says at the end of "Journey to Babel".

But I do understand the desire to standardize the numbers from a board game perspective.

 

[Falconer]

Two more thoughts for everyone’s consideration.

First, the fact that you can travel quickly along a straight line doesn’t make space small. A sphere with a 950 ly radius has an area of 1.13×10^7 cubic light years. So there’s that.

Second, given that WF 7 and 8 are considered dangerous, having them be WAY faster than WF 6 gives you the best of both worlds. Since you normally must travel at WF 6, you retrain that sense of journey as you traverse space. But if you really need to go somewhere fast you can pull out the emergency speeds—with the appropriate risks and complications. Thus the Yorktown wants to stay in its sector and make its delivery and keep its schedule, whereas the Enterprise is able to zip across known space.

 

[Falconer]

Here is one more iteration of my “TOS” scale, with the goal of simplifying the formula as much as possible (4.08693 * 4.243113 ^ WF). In the process, we discover what WF1 really “wants” to be.

 

[DEWLine]

Delta Scorpii will definitely fall within that diameter.

 

[Falconer]

Let’s take these speeds for a test drive, shall we?

In The Menagerie, travel from Star Base 11 to Talos is “only six days away at maximum warp.” From everything we have seen, the maximum speed sustainable for six days is WF6. The distance should therefore be between 325 and 390 ly.

Now, we have no way of knowing for sure where SB 11 and Talos lie, but I like the Star Trek Maps placement for SB 11 and the FASA placement for Talos—they pass the “smell test.” Talos should be near Rigel, since that’s where the Enterprise is returning from in The Cage. And SB 11 seems to be the home base for the Enterprise’s quadrant of exploration and patrol.

So here we go. Talos is 1.2 pc west and 34.8 pc south of SB 11, so a linear distance of 34.8 pc, or 113.5 ly. But our UFP is 3.24 times the size of the FASA UFP, thus the distance is now 368 ly.

 

[Falconer]

Going a bit deeper. In The Final Reflection, a journey from Klinzhai to Earth “will exceed a year, at Warp 4 speed.” Now, to traverse the radius of the Federation (950 ly) is a 262-day journey at WF4. Add in the distance to Klinzhai, about 56 pc according to the map in The Klingons, 2nd Edition, which we will then scale up to 593 ly, a 164-day journey at WF 4, giving us a total travel time of 14 months. NEEDLESS TO SAY there is a lot of guesstimation going on here, but basically I can’t help but be pleased that everything seems to be falling in the right ballpark.

 

[Falconer]

In The Voyage Home, as the HMS Bounty is en route from Vulcan, Sulu states, “Estimating Planet Earth, 1.6 hours present speed.” Vulcan supposedly orbits the real star 40 Eridani, which is about 16.5 ly away from us. Fandom differs on whether this ship’s cruising speed is WF 6.5 or WF 7, so let’s calculate 16.5 light years at each speed:

WF 6.5 - 2.9 hours
WF 7 - 1.4 hours

6.5 works better, since we can assume the ship has been underway for some time before Sulu makes this calculation. Or they are some speed in-between (“present speed” might well indicate this). Either way… once again we are damned close.

 

[Mytran]

In The Voyage Home, as the HMS Bounty is en route from Vulcan, Sulu states, “Estimating Planet Earth, 1.6 hours present speed.” Vulcan supposedly orbits the real star 40 Eridani, which is about 16.5 ly away from us. Fandom differs on whether this ship’s cruising speed is WF 6.5 or WF 7, so let’s calculate 16.5 light years at each speed:

WF 6.5 - 2.9 hours
WF 7 - 1.4 hours

6.5 works better, since we can assume the ship has been underway for some time before Sulu makes this calculation. Or they are some speed in-between (“present speed” might well indicate this). Either way… once again we are damned close.

Conversely, Scott in TMP tells Spock that he can have him back on Vulcan in 4 days (from Earth), a speed equivalent to WF11 on the cubed scale (which is probably what the writers had in mind) and something our favourite engineer considers worth boasting about!

It's possible that Scott isn't boasting but apologising though, especially if Enterprise's systems were damaged during the V'ger incident. In that case, a limping speed of Warp 4 (on your scale) would also make sense.

Of course, speeds in general suddenly got a lot faster in ST3 and ST4, with journeys which previously took days now being covered in mere hours.

 

[blssdwlf]

Conversely, Scott in TMP tells Spock that he can have him back on Vulcan in 4 days (from Earth), a speed equivalent to WF11 on the cubed scale (which is probably what the writers had in mind) and something our favourite engineer considers worth boasting about!

It's possible that Scott isn't boasting but apologising though, especially if Enterprise's systems were damaged during the V'ger incident. In that case, a limping speed of Warp 4 (on your scale) would also make sense.

Of course, speeds in general suddenly got a lot faster in ST3 and ST4, with journeys which previously took days now being covered in mere hours.

I had taken it as, "A proper shakedown will take four days and we'll have you back on Vulcan after that." Afterall, Spock made the trip from Vulcan to Earth in probably less than a day in the same movie in a warp sled.

 

[Falconer]

Yeah, interesting question. Enterprise multiple times in TMP attains a maximum speed of WF7. V’Ger must also travel at WF7 or less, since Enterprise is able to keep pace with it. Let’s analyze the time passage, a bit.

7412.0*
V'ger <3 days away
Enterprise to launch in 12 hours

0400 hours
V'ger 53.4 hours away

7412.6
1.8 hours from launch
Enterprise passes Jupiter
Enterprise calculated to travel for 20.1 hours at WF7 to reach V'Ger
Wormhole incident; presumably negligible headway made.
V'Ger is <2 days from Earth
Spock rendezvous

7413.4
Spock has helped repair Warp engines for 3 hours.
Enterprise to WF7.
V'Ger 1 day from Earth.
Intercept
20 hours from Earth
... 6 hours from Earth

7414.1
4 hours from Earth

* - The first stardate given in the movie, 7410.2, appears to be a mistake since, in the whole rest of the movie, time appears to pass at a rate of 1 SD = 24 hours (agreeing with the TOS Writer's Guide). Therefore I have corrected it to 7412.0, which is 0.7 days (16 hours) before the actual eventual launch time of 7412.7. The 0400 briefing would then take place at 7412.2, which is 52 hours before V’Ger indeed arrives at Earth on 7414.3. I’ve done a lot of rounding, here, but things line up enough that it seems the writers were generally paying attention (other than the one goof).

Now, Spock’s shuttle arrives at the Enterprise in or near the Solar system on 7413.2. There’s no telling exactly how long before that he left Vulcan, but IMO it was obviously 2 days before at the very max, and probably more like 1.

 

[Mytran]

I had taken it as, "A proper shakedown will take four days and we'll have you back on Vulcan after that."

I'd never looked at the dialogue from that perspective before, but it definitely could work!

KIRK: Mister Scott! Shall we give the Enterprise a proper shakedown?
SCOTT: I would say it's time for that, sir, aye. We can have you back on Vulcan in for days, Mister Spock.
SPOCK: Unnecessary, Mister Scott. My task on Vulcan is completed.​

Afterall, Spock made the trip from Vulcan to Earth in probably less than a day in the same movie in a warp sled.

Now, Spock’s shuttle arrives at the Enterprise in or near the Solar system on 7413.2. There’s no telling exactly how long before that he left Vulcan, but IMO it was obviously 2 days before at the very max, and probably more like 1.

Only if the Vulcan scene occurs in chronological order with the others

 

[blssdwlf]

Yeah, interesting question. Enterprise multiple times in TMP attains a maximum speed of WF7. V’Ger must also travel at WF7 or less, since Enterprise is able to keep pace with it. Let’s analyze the time passage, a bit.

7412.0*
V'ger <3 days away
Enterprise to launch in 12 hours

0400 hours
V'ger 53.4 hours away

7412.6
1.8 hours from launch
Enterprise passes Jupiter
Enterprise calculated to travel for 20.1 hours at WF7 to reach V'Ger
Wormhole incident; presumably negligible headway made.
V'Ger is <2 days from Earth
Spock rendezvous

7413.4
Spock has helped repair Warp engines for 3 hours.
Enterprise to WF7.
V'Ger 1 day from Earth.
Intercept
20 hours from Earth
... 6 hours from Earth

7414.1
4 hours from Earth

* - The first stardate given in the movie, 7410.2, appears to be a mistake since, in the whole rest of the movie, time appears to pass at a rate of 1 SD = 24 hours (agreeing with the TOS Writer's Guide). Therefore I have corrected it to 7412.0, which is 0.7 days (16 hours) before the actual eventual launch time of 7412.7. The 0400 briefing would then take place at 7412.2, which is 52 hours before V’Ger indeed arrives at Earth on 7414.3. I’ve done a lot of rounding, here, but things line up enough that it seems the writers were generally paying attention (other than the one goof).

Now, Spock’s shuttle arrives at the Enterprise in or near the Solar system on 7413.2. There’s no telling exactly how long before that he left Vulcan, but IMO it was obviously 2 days before at the very max, and probably more like 1.

Yeah, I was just watching the V'ger time. Spock rendezvous at <2 days from Earth. He would've left when V'Ger was <3 days from Earth. So that leaves about a day of travel time or less since Spock would've had to do the ritual and pack and such.

 

[Falconer]

Only if the Vulcan scene occurs in chronological order with the others

Hard to say, but I suppose we are meant to assume the Vulcans “felt” the Klingon Battle scene somehow.

 

[Falconer]

For V’ger to travel from the Klingon Border to Earth — 950 light years as I’ve estimated it — at Warp 7 — 277 ly/day according to my scale — take just over 3 days. Uncanny.

Enterprise was assigned this mission based on being “the only Starship in interception range” (not THAT ridiculous given that only a few years before there were established to be only 12 Starships per se), but perhaps more to the point, assuming it was the first Starfleet ship upgraded from WF 6 engines to WF 7, any other ship that might have been able to intercept V’ger would have been left in its dust.

Perhaps poor logic, but we’ve seen that even though the TOS-era Enterprise was capable of up to WF 8.4 in emergencies, Starfleet tended to make orders based on safe speeds (WF6 or less), and other captains generally adhered to that.

And of course Kirk had his own reasons for wanting the Enterprise to launch.

And of course we have to forget everything we know about the Entente!

* * *

Spock’s shuttle possible travel times:

WF 4.5 - 53 hours
WF 5.0 - 26 hours
WF 5.5 - 12 hours
WF 6.0 - 6 hours

I don’t know how fast shuttles are supposed to be able to go. The one chasing the Enterprise in The Menagerie obviously couldn’t catch them, but that would be true with even a small differential.

 

[Falconer]

I am attempting to analyze “Amok Time.” We’ve been talking about Vulcan, and the episode is rich with course and speed changes. Here are the quotes:

On our present course (?) you can divert to Vulcan with a loss of but 2.8 light days (???).
We’re headed for Altair VI.
Alter course to Vulcan. Increase speed to Warp 4.
Stardate 3372.7. On course, on schedule, bound for Altair VI via Vulcan.
Inauguration ceremonies, Altair VI, have been advanced 7 solar days.
We’ll have to head directly there at Warp 6, sir. Insufficient time to stop off at Vulcan.
Head directly for Altair VI.
How late will we arrive for the ceremonies if we increase speed to maximum and divert to Vulcan…?
We’re on course for Vulcan.
Now we’re headed back to Altair.
If you don’t get him to Vulcan within a week, 8 days at the outside, he’ll die.
Lay in a course for Vulcan. Tell Engineering I want Warp 8 or better.
We’ll be there in just a few days.

If we assume Vulcan is at its conventional position orbiting 40 Eridani, then it is quite close to Altair, only 29.2 ly distant according to Star Trek Maps. Just for fun, here is a map I made based on Star Trek Maps, zoomed in on this region (hex = 2 ly):



Before I get too deep into analyzing this episode, I have to say I think it will be impossible based on any of the WF scales we’ve explored. The problem is that all the travel times are given in terms of days, yet the warp speeds range from <4 to >8. Here I’ve guesstimated the ETAs:

WF 3.5 - to Altair - 11 days
WF 3.5 - to Vulcan then Altair - 13.8 days
WF 4 - to Vulcan then Altair - 11 days
WF 6 - to Altair - 4 days
WF 8 - to Vulcan - 3 days

Even if I’m off a bit somewhere, it doesn’t matter, there is no WF scale that we’ve looked at in which there is such a negligible difference in transit time between WF 4 and WF 8.

EVEN IF Vulcan and Altair are on completely opposite sides of the Federation (and I’d say the episode clearly suggests this is not the case), and EVEN IF the Enterprise lost some days zig-zagging, I don’t think I can come up with a rationalization of this episode.

But if someone wants me to try, I can try!