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star trek - How did Tom Paris come up with this warp to miles-per-second estimate in The 37s?


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?



Answer



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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