Past Blog Tie-in:

• Musings: 3D Rectangular Coordinates

The universe is a very big place. We quite often don't have a real mental grasp of just how big.

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." [1]

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

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." [1]

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.## "Warp" Drives

Drives which accomplish faster-than-light (FTL) have been posited in a wide variety of science fiction novels, movies, television shows, etc.

The first to become widely known was almost certainly Star Trek's "warp drive".

The first to become widely known was almost certainly Star Trek's "warp drive".

**Star Trek: The Original Series**

****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*:

Where:

Thus, Warp Factor 2 is 8 times the speed of light:

*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:

The the maximum safe cruising speed Constitution-class starships in

*ST:TOS*could travel—and then only for short periods of time—was Warp 8, which gives a speed of:... 512 times the speed of light. Wow, that's fast!

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 (

In

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:... which puts Alpha Centauri just over 1.5 days from the Sun at

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

And yet, the

Thus, a single

Clearly, United Federation warp drive is not that fast at all when compared to true stellar distances.

*ST:TNG*Warp Factor 8.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...." [2]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

Other franchises have, in fact, made use of far speedier craft.

Not all franchises go so far as to give actual formulas for calculating warp drive speeds; a recent notable exception is

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:

*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'mcertainthere 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".

If—for whatever reason—you wish to convert the above to

*Star Trek*warp factors, use the following:Where:

*V*= the number of times the speed of light listed in the table above.My purpose here isn't to suggest "the best" warp drives (or hyper drives or jump drives, etc.), or to promote a particular way of calculating velocities or travel times. I'm just pointing out that, if a Worldbuilder is going to want their civilization to span large portions of a galactic volume, then extremely fast travel speeds (or wormhole travel or "space folding", etc.) is going to have to be assumed.

## The Alcubierre Metric

Since Miguel Alcubierre floated the idea of a warp drive as a legitimate scientific possibility in 1994, I'd be remiss if I didn't mention it here. Alcubierre hypothesized a system whereby the space behind a ship is "built-up" into a wave, while the space in front of the ship is "dug-out" into a trough, creating a sort of wave upon which the ship would "surf" through normal space. Because Einstein's physics does not put any speed limit on how fast

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

"This puts Alpha Centauri, home of the nearest detected extrasolar planet, at 156 days [~5.12 months] travel time. So, for practical purposes, a 10

And, it appears that the equations also show that travelers using an Alcubierre drive system would

*space itself*can "move", the wave could be made to propagate at many times the speed of light, while the ship being pushed along by it would not technically move at all relative to "normal" space.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 10

*c*drive isn't an interstellar one. At 40*c*apparent velocity, the Alpha Centauri system becomes reasonably practical. This means that, unless apparent speeds higher than [Harold] White's 10*c*examples are practical, the Warp Drive is going to still be an in-system drive. A 0.01*c*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." [3]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." [4]## Space-Folding and Other Methods

The concepts of warp drives, hyperdrives, subspace drives, quantum drives, etc., all share in common the basic notion of actual travel through space or some subset or analog of space. Even the Alcubierre metric assumes forward "motion" within a bubble of "normal" space.

Others have opted for different methods.

Perhaps one of the better-known is Frank Herbert's space-folding in the

Jump drives accomplish much the same thing by mechanical/technical means, and are the drive technology referenced in

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

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:

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)

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.

*Tonqua*to travel 4835 light years between the Serelm homeworld and their most distant outpost on Rylburu?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)

The captain could choose to make 48 jumps of 100 light years each and a final jump of 35 light years, or an initial jump of 35 light years, followed by 48 jumps of 100 light years each, or, indeed, any number of jumps of any distance, such as 40 jumps of 60 light years, 30 jumps of 50 light years, 20 jumps of 40 light years, 10 jumps of 10 light years, and five jumps of seven light years. How the trip is divided up would depend on a number of factors, possibly including the need to make stops along the way to refuel, to pick-up/deliver passengers/cargo, etc.

Let's say the captain of the

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

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:Assuming Serelm has a 24-hour day, that's

... or three days, eight hours.

If we divide the 4800 light years traveled in those 48 jumps by the total number of days of travel:

If we divide the 4800 light years traveled in those 48 jumps by the total number of days of travel:

... we see that the

*Tonqua*travels 1440 light years per day. Multiplying by the number of days in a year:... shows that the

This is about 1/17 as fast as the

*Tonqua*travels 525,960 light years per year. Since light travels 1 light year per year, that means the*Tonqua*travels 525,960 times the speed of light.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.

## Conclusion

All this being said, the Worldbuilder will be confronted with a decision in designing interstellar polities:

Either:

Either:

- 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.