Author Topic: TLF Time Scale: A mathematic approach. ;) [Seriously Nerdy]  (Read 1059 times)

Offline Drak

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Because I'm a Nerd, (and v1.019 is bugging me, so I'm not playing much), I figured I'd see how x4k's proposed time scale works out...

On time scale: A mathematic approach. ;)

Ok, I make a couple of assumptions in this that may or may not be true (and discuss what happens should they be adjusted at the bottom of the note):

The first (and most important) of which is that the TLF system is simialr in scale to the Sol system we live in (this may easily not be the case, especially if their primary star is substantially different from ours, which the presence of 8 habitable planets can easily imply unless extreme terraforming is assumed - which also would not be lore inappropriate).

And second, that the player ship is capable of near light velocities (as it seems to be substantially faster than NPC ships, and as the fastest thing in the system this seems to be the case) and near-instantaneous accelleration. But NOT actual FTL travel, which is generally upheald by the lore (FTL is never mentioned, and the computer makes mention of the Hydral lifespan as he/she points his/her ship out of system, which would only matter if travelling at subluminal speeds).

Based on these assumptions, we can use the speed of light, and observable phenomena in the game to figure out the length of a "day" in the game (and thus a month, and a year).

Using Neptune's orbit (the farthest planet out in our system capable of hosting reasonable populations with terraforming technology) to figure out the diameter of the Sol system (and assuming TLF is similar), we get an aproximate radius of 4.5 Billion Km (according to http://en.wikipedia.org/wiki/Solar_System [^]). This gives us a diameter of 9 billion Km. Now, based on earlier experiments by myself, it seems possible for the player ship to make aprox 44 one-way trips between the farthest points in the TLF system per Solar Month, or 2.2 TLF Daiameters per Solar Day. A quick google search ("speed of light km/day") gives us a C of aprox 26billion Km/Earth Day. So, at the speed of light, our player ship could make (26/9=) just shy of 2.9 SolDiameters/Earth Day. This would actually make a TLF Solar Day shorter than an Earth Day (2.2/2.9=0.76 Earth Days per TLF Solar Day). And a TLF year shorter than an Earth Year (400*.76=303 Earth Days per TLF Solar Year). :)

How this could change:
Player Speed. If FTL is allowed, then the relation between distance and time no longer necessarily even exists and anything's possible, but generally this will decrease the TLF year further (in relation to earth years). ;) Slowing the player ship on the other hand, decreases the "2.9 Solar Diameters/Earth Day" estimate and therefore increases the number of Earth Days per Solar Year. Using x4k's statement (in ticket 0015084) that TLF Years are aprox 15-20x an earth year, we can figure out how slow the player ship would have to go to make this work: Based on 15-20 Earth Yr/Solar Yr, our ship has to slow to 0.12-0.16 SolDiamaters/EarthDay, or 0.04-0.05C or a very reasonable 12,000-16,000 Km/s (12,000 Km/s is aprox 1,000*Earth's escape velocity - in other words, several several times faster than our fastest rockets. :) So there you have it, if the TLF system is similar in size to our own, our player ship travels at 1/25th the speed of light, and the NPC ships travel MUCH slower (but probably still fast enough to make escape velocity of the worlds ;).

Size of the TLF System. If the TLF system is larger than the Sol system (which is likely), then our 2.9 Diameters/Earth Day again decreases. If the player ship is travelling at nearly light speed, then (using the same math above) the system would have to be 25 times larger (or the furthest orbitting habital planet would have to be 12.5 times further from the TLF sun than Neptune is from ours, this seems unlikely to produce a habital planet without a very large/bright sun. For reference Pluto's maximum distance from our sun takes it about 1.6 times as far away as Neptune and it is barren and can't hold a stable orbit). Of course, if the TLF System is Smaller, then the TLF year gets even shorter, which x4k has indicated isn't desired, so to make it work, our player ship has to go much slower than above...

Offline lifehole

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Re: TLF Time Scale: A mathematic approach. ;) [Seriously Nerdy]
« Reply #1 on: May 16, 2014, 06:34:14 pm »
Haha, tempted to post this to r/theydidthemath, heh. It's always fun to get fan-made rough approximation of speed, distance, size etc of various things in fictional gameworlds.

It could be a way of pacing things, adding traveltime. Certainly not a bad idea.

Offline Misery

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Re: TLF Time Scale: A mathematic approach. ;) [Seriously Nerdy]
« Reply #2 on: May 17, 2014, 12:43:40 am »
Ow.  Math.  The numbers.  They hurt.

I prefer to distill it down to something more simple: "This stuff here, and this other stuff here, it works like THIS.  It's caused by this thing over here.  Because yes."

And there ya go, everything figured out well enough for me.

Offline Drak

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Re: TLF Time Scale: A mathematic approach. ;) [Seriously Nerdy]
« Reply #3 on: May 17, 2014, 02:50:15 am »
Yes, this is meant mostly as a farce, not to be taken too seriosly. Still, it's interesting to see how it plays out in real world terms.  ;)

Also, any combination of speed and size that follows the following relation is ok.

Average Flight Speed (in % of C) / Ratio of TLF system diameter compared to Sol System Diameter = 0.04 (for 20 years) to 0.05 (for 15 years)

So 0.04C, same size, gives 0.04/1=0.04 which gives 20x year length,
or 0.08C, twice as big, also gives 0.08/2=0.04 which gives 20x year length
« Last Edit: May 17, 2014, 03:27:04 am by Drak »

Offline Misery

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Re: TLF Time Scale: A mathematic approach. ;) [Seriously Nerdy]
« Reply #4 on: May 17, 2014, 04:22:37 am »
I..... see.

Imagine me smiling and nodding in a sagely fashion as if I understood any of that.   :P

Offline Drak

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Re: TLF Time Scale: A mathematic approach. ;) [Seriously Nerdy]
« Reply #5 on: May 18, 2014, 07:21:53 am »
::Kindly pats Misrery on the head:: It'll come in time.. no need to rush...  ;)