Commodore Decker

Uhh, "evacuating Earth" shouldn't be something we should rationalize away for not happening. It just shouldn't be within the realm of possible, in this scifi universe or most of the others. So this is just a fun exercise in rationalizing the first bit.

And then you get to the point of theoretical intercept, and the target whizzes by at superwarp, and that's it.

To intercept a moving target, you generally need to be quite a bit faster than that target - or then perform some sort of a split-second action at the point of intercept. Missiles are good at the latter, blowing up and hoping that the target does as well (although no missile manages this much without being faster than its target, too). But this was not Kirk's mission, and apparently it wouldn't have been the Klingons', either, even if they're folks with more aggressive goals and more open minds about suicide missions or weapons of mass destruction. Blowing up V'Ger in one pass wasn't an option, as the Klingons so nicely told Starfleet.

In order to achieve something meaningful, Kirk would need to match velocities, at least sufficiently to slip into that big field of V'Ger's where ships apparently can tag along without applying their own warp engines. Would a head-on collision allow for that? A question of academic worth only, since this is not what Kirk attempted. So he just plain couldn't have believed in V'Ger being particularly fast.

Hey, we're all assholes here; it's not a competition. But please don't get personal, as there's no real point.

But Goldilocks is not something you directly spoke of, so I don't quite get where you're coming from here. Yes, I think you are wrong about quite a many things regarding this piece of fiction, both fictional and factual. But so what? Let's keep it specific, as it's more fun that way.

Timo Saloniemi

 

Why not? Not the whole population but a percentage? Why do you get to presume things and no one on another side gets to?

I think he believed V'Ger at the time of departure was going warp 7 - as the movie says.

Never got personal. Not once.

 

I was bored over lunch, so here's some math:

The galaxy is approximately 1000 light years in thickness.
If we take the technical manual as being correct that the Federation is 10,000 Light years in diameter
we have approximately 314,000 cubic light years for Starfleet to cover.
If we accept that there are 7000 active ships in that volume, we get a figure of around 22 ships
per 1000 cubic light years.
If the Enterprise can cruise 1000 light years in 12 hours (Per That Which Survives & Obsession), that puts approximately 22 ships within 12 hours travel at any given time for a rescue or intercept or rendezvous.

To me, that doesn't jibe with what we saw in TOS.

Now, if I recall correctly, the Technical Manual puts Earth dead center of the Federation disk.
So for V'ger to travel from Klingon Territory to Earth it would have to pass through the territory of approximately 220 ships without getting anyone able to intercept boggles the imagination.

I really think the lesson is this:
Star Trek doesn't lend itself to mathematical analysis.

Scott Kellogg

 

@Scott Kellogg Actually, your math is wrong. The volume of a cylinder is V = pi * height * radius ^ 2
So the volume of your 10,000 ly wide, 1000 ly thick Federation would round to 78,539,816,370 cubic light years.
So a fleet of 7000 would put one ship per every 11,219,974 cubic ly. That's a box that is about 224 ly x 224 ly x 224 ly.

Spoiler: Showing my work

r = 5000, h= 1000
V = pi * 1000 * 5000 ^ 2
V = pi * 1000 * 25,000,000
V= pi * 25,000,000,000
V= 78,539,816,339.744830961566084581988
v / 7000 = 11,219,973.762820690137366583511713
cube root of 11,219,973.762820690137366583511713 = 223.87071197542978417369073042603

 

Oops, sorry, it's supposed to be 10K lightyears in Radius, not wide. My mistake.
1K*10K^2*pi= 314K^3 light years volume.

 

1K*10K^2*pi = 314,159,265,359 (rounded to whole numbers)

Edit to add: The Franz Joseph Tech Manual says that the Federation is 7 parsecs in radius and the treaty-negotiated exploration zone is 4750 parsecs in radius. That's 22.82 ly and 15,485 ly respectively.

 

Yes.
I figured K lightyears would be a useful unit in this case, because we know it takes approximately 12 hours for the TOS-Enterprise to cover that distance.

Scott

 

If those 7000 starships are evenly distributed throughout the volume, then they would each be at least 224 ly apart (5000 ly radius) or 355 ly apart (10,000 ly radius.) It's unlikely that they are evenly distributed though.

 

I bow to your figures. I'm afraid it's been... probably a decade since I looked through the Franz Joseph manual. I was just going by the 10K lightyear figure people mentioned in this thread.

I was estimating a rough area of operations of approximately 1K lightyear. If we use the 15.5K Lightyear radius, the 7000 ship fleet drops to approximately 9 ships per 1K Lightyear cube.

 

[/Begin Thread Tangent/Derailment]
I've owned a Franz-Joseph TOS Tech Manual since 1975 - and even when I saw it I always thought (WF^3)*c was TOO SLOW!

Before all the 'official' things trying to explain/codify various aspects of Trek tech - I always assumed WF = LY travelled per hour of "real time".
^^^
That was the only way one could rationalize Kirk often ordering low warp speeds when leaving planets at the end of or during episodes). Most times he'd order Warp 1 or Warp 2 and occasionally a blistering Warp 3. <--- But that was the only way to even rationalize being able to get to another star system in a few hours/days.

I have to assume the writers felt something similar because in TOS S2 "Friday's Child"; when the 1701 is out looking for a Frieghter (it was a faked distress call done by Klingons of course) - Sulu makes the comment:

Sulu: "At best a freighter might manage Warp 2..."

to which Mr. Scott replies:

Scotty: "I'm WELL AWARE of a freighter's maximum speed..."

My point being: baring all the stuff that's come out AFTER TOS - during the series run, in the 23rd century world of that era, "Warp 2" would have to be a VERY FAST FTL speed; hence my old (outdated/debunked by ancillary 'official' Tech Manuals) fan idea that

WF = LY per hour

was the only thing that made such interstellar travel even remotely possible as depicted in TOS. (WF^3)*c is just way too slow.

[/End Thread Tangent/Derailment]

 

I'm in full agreement.
If the measurement was in terms of the speed of light and it took between 1 to 4 years to get from here to Alpha Centauri , the stars would never streak by on the viewscreen.

Scott

 

So according the formula that warp factors equal the number of light years (LY) travelled per hour:

Warp factor 1 is 1 ly per hour, 24 ly per days, 168 ly per week, 8,766 ly per year, 87,660 ly per decade, and 876,60 ly per century.

Warp factor 2 is 2 ly per hour, 48 ly per day, 336 ly per week, 17,532 ly per year, 175,320 ly per decades, and 1,753,200 ly per century.

Warp factor 3 is 3 ly per hour, 72 ly per day, 504 ly per week, 26,298 ly per year, 262,980 ly per decade, and 2,929,800 ly per century.

And so on.

Warp factor 6, the fastest safe speed, is 6 ly per hour, 144 ly per day, 1,008 ly per week, 52,596 ly per year, 525,960 ly per decade, and 5,259,600 ly per century.

Warp factor 6, the fastest emergency speed safe for only a short period of time, is 8 ly per hour, 192 ly per day, ly per week, 70,128 ly per year, 701,280 ly per decade, and 7,012,800ly per century.

In Obssesson":

So a round trip of over 2,000 light years would take 1.7 days, at a speed of over 49.09196 light years per hour. But the Enterprise would be travelling at warp factor 8, not warp factor 50.

In "That Which survives":

Later the Enterprise heads back to the planet:

Later:

Travelling 990.7 light years, or about 8,684,476.2 light hours, in 11.337 hours requires a speed of about 766,029.4787 times the speed of light, many times warp factor 8.4, according to you, whch would be only 73,634.4 times the speed of light.

So in some episodes the warp factor formula you suggest would be much too slow for the distances and times in voyages.

Bu the warp factor formula you suggest would also be too fast for some episodes.

In "This Side of Paradise", set on Omicron Ceti III, Kirk says:

Even at warp factor 1 according to your proposed scale, a ship could travel 8,766 light years in one year. And of course every good science fiction fan should know that Mira, or Omicron Ceti, is only a small fraction of that distance from Earth.

In "By Any Other Name":

And:

The distance to the Andromeda Galaxy is estimated to be approximatley 2,540,000 light years. If it takes about 250 to 300 years to travel that distance, the speeds will be approximately 8,466.66666 to 10,160 times the speed of light. And your suggested warp factor 1 is about 8,766 times the speed of light, within that speed range.

And Kirk said the Enterprise couldn't make the journey in thousands of years, even at maximum warp. If that is interpreted as meaning the trip will take 2,000 to 10,000 years, whcih may not be correct, kirk would imagine the speed of the Enterprise to be on the order of 254 to 1,270 times the speed of light, which is slower than your proposed warp factor scale.

Thus it is seen that your proposed warp factor scale is to slow for some episodes and too fast for others.

 

The fits with it being a Borg world in The Return.

 

Speaking of Warp Factors...
I don't recall very clearly, but in "The Paradise Syndrome" doesn't Spock take the Enterprise to intercept an Asteroid at Warp 9 speeds causing the engines to be damaged? But, if the asteroid is already in the star system, it can't be more than a few AU away. It then takes a good deal of time for the Enterprise to travel back to the planet without warp. Enough for Kirk to start a new life, get married and get his new wife pregnant.

The bottom line is: Star Trek's engines take as much time as the writers need them to,
which leads us back to what I said earlier:

I know we all want it to, but...
Star Trek doesn't lend itself to Mathematical Analysis.

 

OTOH, that's one of the easier things to just plain treksplain away.

We can see with our own eyes that warp speeds close to stars are extremely slow - to wit, ST4:TVH and the slow passage of the Klingon ship around our Sun at extreme warp. Which is no wonder, because apparently looping around Sol results in time travel - to wit, "Tomorrow is Yesterday"! Surely your speedometer will go wonky there. (At least your chronometer does, as seen.)

If the big bad asteroid approached from the direction of the local star (and supposedly it did, since its shadow was said to precede its arrival), Spock might have to fly close to that star to reach the asteroid when it was still on the other side. And since McCoy insisted that they waste time looking for the missing Kirk, Spock now had to take that shortcut that turned warp 9 into fairly low sublight...

But the adventure touches upon our topical Commodore Decker in a way. Sure, the hero ship was basically immobilized. But what about the other starships? Where were they? Could they not be summoned to help, in the two months this adventure takes? Admittedly, Kirk himself sometimes came to the aid of his colleagues in no less than six months... A pretty solid theme in all Trek, but especially TOS, is that starships generally can't make it to places in time. And this is another thing where mathematical analysis breaks down: we can't argue that Starfleet would be sized to meet the task trusted upon it, because it fails to meet the task! And we really can't tell by how much...

Timo Saloniemi

 

Continuing the theme of my post number 152 above:

https://www.trekbbs.com/threads/commodore-decker.307680/page-8

The first scene in the first Star Trek pilot "The Cage" show the Enterprise receiving a (real or fake) distress signal from the SS Columbia at Talos IV:

Pike later decides to diver to Talos IV to look for survivors, at high speed:

Later, in an illusionary picnic, PIke tells Vina:

So apparently the Enterprise traveled about 17.5 to19.5 light years, or about 153,405 to 170,937 light hours, in about 22 to 26 hours, at a speed of about 5,900.1923 to 7,769.8636 times the speed of light.

The line about 24 hours since Pike talked to Boyce in PIke's cabin was cut from the version of "The Cage" in "The Menagerie", But "The Menagerie" retains the line which PIke says in the illusion of the fight on Rigel VII:

Assuming that two weeks equals 10 to 18 days, and that 0 to 18 days pass between the fight on Ribel VIII and receiving the distress call, the voyage to TAlos IV after receiving the distress signal could last from 0 to 18 days. Make that 0.5 to 18 days.

Since the journey was 17.5 to 19.5 light years, or about 6,391.875 to 7,122.375 light days, the speed of the Enterpirise at "time warp factor seven" would be about 355.1041 to 14,244.75 times the speed of light.

The Enterprise was heading from Rigel VII to the Vega colony when it received the signal from Talos IV. It is usually assumed that Rigel VII is a planet orbiting the star Rigel, or Beta Orionis, which is probably at least 800 light years from Earth, and that the Vega colony is on a planet orbiting the star Vega, or Alpha Lyrae, about 25 light years from Earth.

Thus the straight line distance from Rigel to Vega should be at least 800 light years. Assumng that it would take less than one year for the Enterprise to travel 800 light years from Rigel VII to the Vega colony, the Enterprise should have an average speed of at least 800 times the speed of light.

At a speed of 14,244.75 time the speed of light, the Enterprise could travel 142,447.5 to 256,405.5 light days or 390 to 702 light years, in 10 to 18 days, and up to 14,244.75 light years in up to one year.

In both "The Cage", and "Menagerie Part 2", PIke tells his Talosian captors:

Pike is probably lying to his unknown alien captors, but if Pike is not lying to the Talosians Talos IV must be beyond the central point of the Milky Way Galaxy as seen from Earth. Since the central point of the Milky Way Galaxy, at the supergiant black hole at Sagittarus A West, is believed to be about 27,000 light years from Earth, a journey from Earth or from the comparativley nearby Rigel, to the other end of fhe galaxy" should be at least 27,000 light years long.

So at a minimum the Enterprise traveled at least 27,000 light years or 9,861,750 light days in a straight line from Rigel to Talos which would be right beyond the supergiant black hole (even though that would be a dangerous and unlikely region to find planets with life). in two weeks or about 10 to 18 days. Thus the speed of the Enterprise would have to be at least 547,875 to 986,175 times the speed of light.

At speeds of 547,875 to 986,175 times light speed, the side trip to Talos IV would take 0.0000177 to 0.0000355 days, or 1.52928 to 3.075154 seconds

Of course a planet "on the other end of the galaxy" could be tens of thousands of light years beyond the central point of the galaxy, which would make the speed of the Enterprise on the voyage to Talos IV much faster.

Thus I believe that Pike was probably lying to the Talosians when he said he came from "the oher end of the galaxy" from Talos IV.

But there is no proof that the Enteprise was travelling in a stright line from Rigel to the Vega Colony. It could have been taking a more roundabout route and thus have had a much greater average speed than 800 times the speed of light.

And that is the evidence about the speed of the Enterprise in "The Cage" and "The Menagerie", the earliest evidence about that speed.

 

Why deny the (highly variable) Cochrane Factor to adjust the speed formula?

 

Q: How fast is warp 6?
A: Yes

 

Heck, since warp propulsion is obviously affected by gravity, you could attribute the factor to the distribution of dark matter in the Milky Way.

 

What Cochrane Factor?