Past Blog Tie-in:
• Musings: 3D Rectangular Coordinates
So, my purpose here is simply to emphasize that the galaxy (let alone the universe) comprises a very large volume, most of which is empty space, depending on where you're looking at it: "The true stellar density near the Sun is estimated as 0.004 stars per cubic light year." 
In the previous blog, I discussed how to map points in three-dimensional space, and how to calculate the distance between two points.
That's useful information for a worldbuilder—especially for science fiction—but it also highlights a singular problem with the sheer magnitude of distances involved in interstellar travel.
For example, the bright star Deneb (α Cygni) is 2600 light years from the Sun. That's not a long way, considering that the Andromeda Galaxy is 2.5 million light years away, and the edge of the visible universe is 13.8 billion light years away.
Still, if we think about what the term light year means, we start to intuit the problem. It is the distance light—the fastest-traveling thing in the entire universe—travels in an Earth-year. So, it takes light—again, the fastest thing in the universe--two thousand and six hundred years to reach us from Deneb.
The first to become widely known was almost certainly Star Trek's "warp drive".
In the Star Trek universe of the Original Series (ST:TOS), the speed at which starships could travel was measured in "warp factors", such that Warp Factor 1 was the exact speed of light. Each succeeding Warp Factor was a multiple of the speed of light (c), calculated by the warp factor raised to the power of 3 and multiplying by c:
v = the speed of travel in multiples of the speed of light;
w = the warp factor number;
c = 1 (times the speed of light)
Thus, Warp Factor 2 is 8 times the speed of light:
Well ... not really. Not compared to the distances between stars.
Alpha Centauri is 4.37 light years from the Sun; thus, it takes light 4.37 years to reach the Sun from Alpha Centauri. At Warp Factor 8 (ST:TOS), Constitution-class cruisers would take just slightly over 3 days to make the journey.
Star Trek: The Next Generation
In The Next Generation series (ST:TNG), warp factors were re-defined to use an exponent of ¹⁰/₃, so the equation became:
Again, that seems pretty fast, doesn't it?
But let's look again at Deneb, 2600 light years from the Sun. Even at Warp Factor 8, the ST:TOS Enterprise would still need 5.08 years to reach Deneb, assuming it didn't blow itself up at some point from pushing the 'wee bairns' too hard for too long. The ST:TNG Enterprise (a Galaxy-class ship) would take just over 2.5 years.
And yet, the Star Trek wiki site, Memory Alpha, clearly states, "By 2373, the Federation's territory was spread across 8,000 light years...." 
Thus, a single ST:TOS ship traveling at maximum warp would need 15.63 years to traverse the entire Federation; a ST:TNG ship at their Warp 8 would require 7.81 years.
Star Trek: Voyager
Star Trek: Voyager (ST:VOY) used the same warp formula as The Next Generation. The USS Voyager was an Intrepid-class ship, and it was stated several times that its top speed was Warp 9.975, which is—to-all-intents-and-purposes—2136c, so a cross-Federation jaunt would take 3.744 years.
Clearly, United Federation warp drive is not that fast at all when compared to true stellar distances.
For discussions of the other kinds of starship drives used or mentioned in the various series of the Star Trek universe, please visit Memory Alpha.
Other Kinds of Drive Systems
The Orville frequently uses the term "quantum drive" to describe their FTL drive; Star Wars talks about "hyperdrives"; The FreeSpace series of games uses "subspace drive"....
Not all franchises go so far as to give actual formulas for calculating warp drive speeds; a recent notable exception is The Orville's Captain Ed Mercer's statement in Episode 5, "Pria", "We have a ... quantum drive system capable of speeds exceeding ten light-years per hour".
Below is a comparison of 34 ships from various universes (with light, itself, as a comparison), showing travel-times for a 1000 light year distance:
Note: The top speed values used here were gathered from several sources around the internet, and I'm certain there will be disagreements about them, depending on whom you ask. I've only included them for illustration purposes, not to reflect any kind of "canon".
V = the number of times the speed of light listed in the table above.
The Alcubierre Metric
While it is highly speculative whether such a drive would work—or even be safe for living travelers to use—even assuming technologies are developed at some point that would allow it to be built in the first place, it appears that such a propulsion system would top out at about 10 times the speed of light.
While this is certainly faster than the propulsion systems we currently have, it is only 20% better than Warp Factor 2 in the ST:TOS universe, or right at Warp Factor 2 in ST:TNG. In other words, it is paltry compared to interstellar distances.
"This puts Alpha Centauri, home of the nearest detected extrasolar planet, at 156 days [~5.12 months] travel time. So, for practical purposes, a 10c drive isn't an interstellar one. At 40c apparent velocity, the Alpha Centauri system becomes reasonably practical. This means that, unless apparent speeds higher than [Harold] White's 10c examples are practical, the Warp Drive is going to still be an in-system drive. A 0.01c drive puts Mars a mere few hours away. At furthest distance, Mars is about 18 light minutes [distant]; 1800 minutes travel time is 30 hours - not even 2 days." 
And, it appears that the equations also show that travelers using an Alcubierre drive system would not experience time-dilation effects: "[B]oth inside the warp bubble and outside the warp bubble [the following equation holds true:] ds² = -dt². In other words, proper time inside the ship equals proper time outside the warp bubble." 
Space-Folding and Other Methods
Others have opted for different methods.
Perhaps one of the better-known is Frank Herbert's space-folding in the Dune universe; Spacing Guild navigators, using mental abilities enhanced by the substance melange (commonly called "spice), cause two distantly separated points in the universe to momentarily come into contact (or very close proximity), and the ship moves from the origin to the destination, without traveling through the intervening space. When space is "unfolded", the ship now resides at the destination location.
Jump drives accomplish much the same thing by mechanical/technical means, and are the drive technology referenced in Battlestar Galactica (both incarnations). A jump drive was also a central plot device in the (sadly short-lived) Dark Matter series.
Space-folding and jump drives may be specified either to require some finite amount of effective time, or to function instantaneously. Alternatively, travel from point-to-point may be instantaneous, but the drive may need "recharge" time between jumps.
Travel by wormhole, the method employed by the stargates and supergates of the STARGÅTE franchise, and central to the milieu of Star Trek: Deep Space Nine, accomplishes something similar, in that wormholes are hypothesized to be conduits through a substrate of normal space that connect two distant points. The limitation of wormholes (at least naturally occurring ones), is that their endpoints are fixed, whereas with jump drives and space folding, the origin and destination points can be arbitrarily chosen.
With jump drives and space-folding, instead of determine a maximum velocity in terms of multiples of he speed of light, one would specify a maximum distance traversable in a single jump, and then calculate the total number of jumps needed to span a given distance.
As an example, let's say the Serelm Union uses a jump drive system with the following parameters:
- Jumps can be between 1 and 100 light years in span
- The more distance a jump covers, the more energy it takes to accomplish
- The farther the jump, the longer the drive takes to re-charge, such that it works out to basically 1 minute of recharge per 1 lightyear of travel.
Distance to travel: 4835 light years
Maximum Jump Span: 100 light years
Recharge time per jump: 100 minutes (1 hour, 40 minutes, or 1.667 hours)
Let's say the captain of the Tonqua is responding to a disaster and doesn't want to make any long stops on the way, so the she chooses to make 48 jumps of 100 light years and 1 final jump of 35.
Jumps of 100 light years each require 100 minutes of recharge for the drive. The last jump of 35 light years will require 35 minutes of recharging, but since the Tonqua will be at the destination after that jump, those minutes don't need to be figured into the travel time. So, 48 jumps at 100 minutes between jumps amounts to 4800 minutes total, which is:
If we divide the 4800 light years traveled in those 48 jumps by the total number of days of travel:
This is about 1/17 as fast as the Millennium Falcon from Star Wars; about ¾ as fast as the GunStar from The Last Starfighter; 1.44 times faster than the Moya from Farscape; exactly 6 times faster than the Orville; 548.45 times faster than the Pillar of Autumn from Halo, and exactly 2435 times faster than Warp Factor 6 in Star Trek: The Original Series.
As it turns out, using the above parameters for the Serelm jump drive, one can calculate that the Tonqua travels at 1 light year per minute, regardless of the number of jumps taken.
- Create a space-warping drive technology, specify its maximum travel velocity, and then build an empire, federation, etc., that is small enough to be traversed by a ship traveling at that maximum velocity;
- Create your milieux, determine the distance between the two most distant points within a given empire, federation, etc., and then devise a space-warping technology with a sufficiently rapid top speed to make travel between those points in a reasonable and manageable amount of time;
- Build your empire, federation, etc., however you want, as far-flung as you desire, and then invoke the Omega Argument and declare that your civilization has developed a space-folding or point-jumping technology that enables them to traverse (and control) such a mind-bogglingly large volume of the universe.