Quote:
Originally Posted by scc
this speed factor is important because this cubed is how much faster vessel that used it is faster then it would be in real space
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How much space is your game going to cover? That is, how much of our galaxy? How long should it take to get from one "close" planet to another -- and how far apart are those habitable planets? Any particular famous spots that you want to include in the area reachable by ships? Those decisions affect how fast your hyperdrive needs to be. A formula comes second; you pick that (if you want one at all) to suit your game's story.
Star Trek: TOS used the cubic formula. It sounded good. But if you do the math, it means that the Enterprise doing warp 6 (warp 8 was emergencies only) would only being doing 216c, which in turn means on that 5-year mission, it could travel a total of about 1000 light years, if it did nothing but travel (as opposed to hanging around in orbit having adventures). If Kirk went only one place (instead of around 70) and came back, that one place would be at most 500 ly away. In other words, a pretty small region of the galaxy. And even that's assuming a real-space speed of 1.0 c. Your setting has a top speed, presumably some relatively small fraction of that value, so that much smaller of a region to play in.
So before picking a formula that calculates hyper-speed from real-space-speed, decide how much you want to reach. Galaxy-spanning empires? Small cozy corners where you can concentrate on details of a few planets? It's first and foremost a narrative question. Formulae and technobabble come second -- as you say, we're already breaking the laws of physics just to have the game at all, so there's no point in getting hung up on trying to cling to any particular rule just because it feels mathematical.
(ST:TNG changed to the scale to warp 10 being infinitely fast, warp numbers asymptotically approaching 10 based on a hand-drawn sketch of a curve with no formula, just something that seemed like it would kind of work without being too terribly different from previous shows on the low end. Worked fine as far as the show was concerned. Made no noticeable difference in practice IMO, because Trek was never really concerned with exactly how far apart two different planets were in the first place. Travel time is a plot point -- can Starfleet intervene, or are the PCs out there on their own? Can you actually ship medicine to a planet before the plague runs its course anyway? Are the invading bad guys going to reach Earth before you can build another fleet to stop them after they wiped the first one? That's travel time versus build speed... so you also care about whether it's guys in EVA suits with space welders, or nanofacs 3D printing more ships as fast as the guide/power lasers can scan.)