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Update
For the duplicate flag: I am not asking why Voyager would take 75 years to return home, but rather, assuming that is true, I question the accuracy of Tom's statement (below).


In Voyager season 2 episode 1 The 37s, Tom tells Amelia Earhart that warp 9.9 is approximately 4 billion miles per second. The back of the envelope math shows, based on that, they could travel 70000 lightyears in 3.25 years at warp 9.9.

While I understand that it's not feasible to travel at high warp for an indefinite amount of time, Voyager is rated to top out at Warp 9.975 which is even faster than 9.9, so I don't understand the 75 year estimate (approximately 1000 lightyear/year) to get back to earth. Also it was odd that Tom used mph versus kph, but I assume its because he knew Earhart's generation used imperial units instead of metric.

The speed of light 299792458 metres/s, 1609 metres to a mile is ~186171 miles/s so 70000 lightyears is 186171 miles × 60 seconds × 60 minutes × 24 hours × 365 days × 70000 = 410976205920000000 miles. Now divide by 4000000000 yields 102744000 seconds, and 102744000/60/60/24/365 is around 3.258 years at warp 9.9.

So was Tom's number just pulled out from thin air?

  • 5
    According to Wolfram|Alpha, warp 9.9 is about 3000 c, which is slower than the quoted speed by nearly an order of magnitude. So I would say that Tom doesn't know what he's talking about, but Wolfram|Alpha's "extrapolated from the hand-drawn curve" makes me a bit nervous about the canonicity of its data. – Kevin Dec 10 '17 at 22:18
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    It may not be that the estimate is wrong, so much that it doesn't address the point, its no use being able to travel 70,000 light years in 3.25 years if your dilithium reserves are used up in three months, and your nacelle pylons shear after a year and a half (to imagine arbitary constraints). 75 years is the 'get back safely at best possible sustained speed' estimate, max possible speed isn't the same thing. – Simon Bucher-Jones Dec 10 '17 at 22:26
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    Could also be that he simply didn't know his imperial conversions. they would have been historical trivia at this point after all. – ApproachingDarknessFish Dec 10 '17 at 22:40
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    @ApproachingDarknessFish I doubt that since he is an antique earth car expert and would have to be familiar with imperial units if he studied American cars, and especially familiar with the conversion if he studied both american and European cars – chiliNUT Dec 10 '17 at 22:55
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    This isn't a duplicate as it doesn't answer whether Tom's number of 3.258 ears was pulled out of thin air. – Edlothiad Dec 11 '17 at 11:10
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More or less he made it up. There's a couple of things to back this up

  1. Star Trek does everything in the metric system. Of course, that would confuse Earhart, because a good portion of the world converted long after 1937 (the UK didn't formally start until 1965 and the US has not switched). So Tom is probably picking a number and then slapping a MPH onto it, since he doesn't consult anything to try and make a realistic conversion from metric to imperial. The fact that it's such a large and neatly round number also leads one to conclude it's off-the-cuff.
  2. The transcript leaves the impression he's trying to impress the lady. Take note of the context

    (Amelia is admiring the helm.)
    AMELIA: How fast?
    PARIS: Warp nine point nine. In your terms, that's about four billion miles a second.
    AMELIA: Think I could take her out for a spin?
    PARIS: Well, er

    This bolsters point #1. "In your terms" points to an off-the-cuff number. I mean, you're trying to explain warp drive to a person whose fastest form of transportation was about 200MPH (or 0.05 miles per second).

If we take Memory Alpha's numbers about warp 9.975 (which canon kinda plays fast and loose with anyways), 1721c converts to about 320M miles per second, and 2922c is about 522M miles per second

I think he's trying to say his warp drive brings all the ladies to his sector, and it's better than yours.

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    He could teach you, but it would violate the Prime Directive. – F1Krazy Dec 11 '17 at 9:27
  • @F1Krazy p sure the prime directive doesn't apply to humans – Steve Cox Dec 11 '17 at 15:21
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    @SteveCox pretty sure it does since we don't have warp technology yet. – BlackThorn Dec 11 '17 at 16:28
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    @F1Krazy And he'd have to charge. Wait. – corsiKa Dec 11 '17 at 16:34
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    @TBear good point. forgot about the temporal prime directive – Steve Cox Dec 11 '17 at 16:35
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There is also an episode of Voyager where Janeway asks Tom to pull back at least half a lightyear away at maximum warp (I believe it was the asteroid they were looking into the S01E09: Eminations). He pulls back to a stated 0.6 lightyears and it takes about ten seconds.

I think that someone just didn't do their math.

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    Math is hard. Let's study creative writing!!! – RonJohn Dec 11 '17 at 3:55
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    In the episode credits: Math Consultant: J.K. Rowling – Irishpanda Dec 11 '17 at 14:50
  • That is about 400 billion miles/second. So that simply implies that warp 9.975 is at least that fast, and Tom was driving a bit aggressive. ;) – Yakk Dec 11 '17 at 18:58
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    That neglects acceleration. Warp may not be a step function. – fectin Dec 11 '17 at 19:25
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    @Irishpanda Hahahaha, +1 for your comment! :D That’s like +3 in J.K. Rowling math! :P – Bellatrix Dec 13 '17 at 2:14
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We have little official/canonical data on how fast Warp drive is on an actual warp scale.

What we do know however is that most of the time in TNG, Warp 9.6 was a temporarily sustained maximum velocity for the Enterprise-D in early Season 1 of TNG. It's sustainable warp velocity was at the time Warp 9.2... past 9.3 (at least according to the pilot episode, the ship is past the red line and will likely be able to sustain that/any further increases in velocity for a limited period of time).

We also know that Data said in 'Where no one has gone before' that it would take the Ent-D over 300 years to traverse 2.7 million lightyears at maximum warp... indicating a speed of about 9000 times LS. Now, what that maximum speed is, we don't know for certain, however, if Paris' statement that 9.9 = 4 billion miles per second... then Ent-D maximum speed would have been LOWER than Warp 9.9 (probably around Warp 9.6 given that for most of TNG the Galaxy class topped out at that speed).

Bear in mind that most Federation (and other ships) in the 24th century were not really seen traveling or being able to sustain Warp 9.9.

Yes, Voyager was stated it's top cruising speed is 9.975, but in the episode 'Threshold', the ship neared 'maximum warp velocity' upon achieving Warp 9.9 and the computer said 'structural collapse imminent'. This means to me that the writers were either wrong... or, Voyager's top cruising speed is technically Warp 9.975, but due to the pull to the DQ (which was violent), the ship suffered catastrophic damage to it's hull and engines (which we witnessed in the pilot episode, and the Warp core had a microfracture too which was later repaired), effectively reducing it's maximum sustainable cruise velocity from 9.975 to below 9.9 (or in line with what we saw in TNG).

Ergo, from canonical point of view, Paris' statement seems more accurate because no ship was usually seen to have been traveling at 9.9 (it was usually well below that).

Besides, the closer you get to 9.9, speeds start increasing by quite a bit, and past 9.9, every incremental increase would result in exponential increase.

So, I'd say that the Enterprise-D Warp 9.6 = 9000 times LS (which it would be able to sustain say indefinitely/or for as much fuel the ship has later in the show as the engines were improved/modified but not during Season 1).

Voyager's cruising speed of 9.975 would bring the ship back to the Federation in just under 7 days using exponential increase with every increment past 9.9, ... but, because the ship suffered massive damage in transition to the DQ, it was effectively stuck with using much lower speeds and had to conserve energy due to variety of problems as they happened - plus, Voyager was seen cruising at Warp 6 for the most part - seems like a really low speed when its official specs put its top cruising speed at 9.975 - and 'top cruising speed' means that your engines can run this speed continuously with minimal maintenance, or for as how much energy you have to run the engines - higher warp speeds than that would forcibly shut down the drive much faster).

Also, of note would be that the USS Prometheus (from Voyager's 4th season) was seen using Warp 9.9 in a sustainable capacity.

So, its more likely that the writers might have meant that Voyager's top cruising speed was Warp 9.75.

Anyway... it seems more likely (at least from a canonical point of view) that Paris statement has merit because most ships of that era were never seen or said to be using Warp 9.9. 9.5 and 9.6 yes in emergencies, but anything more and you risk structural collapse (at least until just prior to and during/after the Dominion War - because Warp 9.9 would seem plausible by that point with SF's desire to improve their warp engines).

Also, in their decoded message from SF, it was said by Admiral Hayes that 2 deep space vessels were redirected to Voyager and that they should meet up with them in 5 to 6 years... indicating these ships might have had better Warp drives (capable of achieving and sustaining say 9000 times LS) than the rest of the fleet as they'd be needed for deep-space exploration.

  • This doesn't really address the question asked. Interesting, but not especially relevant. – Valorum Apr 2 '18 at 6:58
  • It's not a mess of conflicting figures (because the figures need to be reconciled with on-screen canon data somehow). The USS Prometheus was stated by its own EMH that it was designed to go faster than anything in the fleet, and it was seen travelling at Warp 9.9 heading straight for Romulan space.. So, on-screen canonical data is conflicting with itself. On one hand majority of it never shows ships traveling at 9.9, and on the other a starship, 4 years after Voyager's launch is seen doing that. As far as probability goes, 9.975 could have been a writers mistake – Deks Apr 2 '18 at 16:54
  • Or, Voyager's ability to achieve speeds at 9.975 was taken away with the violent transition to the Delta Quadrand which heavily damaged the ship (which is also what happened). – Deks Apr 2 '18 at 16:55

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