Warp Speed calculations using Fibonacci numbers
- Thread starter Sgt_G
- Start date
OK, I'm gonna be "that guy!"
KIRK: Impulse power, Mister Sulu. Ahead, warp point five. ...Departure angle on viewer
http://www.chakoteya.net/movies/movie1.html.
http://www.chakoteya.net/movies/movie1.html.
It's the corresponding factor for a sublight velocity under rocket power, but it's still a fractional warp factor.
Since a Fibonacci spiral (image) approximates a golden spiral, there is the potential for a retcon of the meaning of the TOS engineering patch...
IIRC, it was a 4 day trip back to Vulcan but in context it was after a "proper shakedown". Spock in a warp sled shuttle went from Vulcan to Earth in approx 12 hours in the same movie. If we assume 16 LY then that's 11,680c.
If we assume the Klingon border is 1,000 LY away from Earth (based on "The Undiscovered Country") then V'ger's 3 Day flight to Earth is 121,000c.
All those speeds are well within the speeds demonstrated by the Enterprise in the original series episodes.
OK, I'm gonna be "that guy!"
KIRK: Impulse power, Mister Sulu. Ahead, warp point five. ...Departure angle on viewer
http://www.chakoteya.net/movies/movie1.html.
It's the corresponding factor for a sublight velocity under rocket power, but it's still a fractional warp factor.
Yep, that's under impulse. Sulu also counts off Warp point eight, warp point nine, etc as they accelerate through to Warp 7.
Interestingly, when Kirk uses impulse drive in "Elaan of Troyius" he makes a distinction to use "Sublight Factor .037". So I'd imagine that he could have said "Impulse Drive, Warp Factor 0.037" and it would have meant something different.
Good reference, but why can't they just be two different ways of referring to the same thing?
It's possible they could mean the same thing.
I just think it's interesting that there are two speed units or factors, "Sublight" and "Warp".
"Sublight Factor" could refer to "space normal speed" or speeds that do not vary
While "Warp Factor" has variable speeds depending on local space conditions.
Or in other words, "Sublight Factor .037" is really .037c no matter where you are while "Warp Factor .037" could range from .0001c to .1c depending on how close you are to a gravity source or other space phenomena.
All IMHO and specific to only TOS
No, not per source documents of the day. The ship's top speed was closer to one-thousand time light speed, not ten-thousand nor a hundred-thousand.
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The actual on screen episodes would beg to differ
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@Mytran is correct, the actual on screen episodes are quite different than the source documents of the day (which I assume are the Writer's Guide and/or Tech Manual?).
TOS' Warp speeds can be broken down into three speed categories that appear to be tied to the "local space terrain" in the episodes:
- Interplanetary - Near large masses / within a star system = High Warp < 5.0c
- Interstellar - Between star systems = High Warp > 100,000.0c
- Intergalactic - Between galaxies = High Warp < 9,000.0c
1. "Breads and Circuses" - Enterprise travels 1/16th parsec in 30 seconds = ~214,000c
2. "Obsession" - Enterprise round trip from where they are to Tychos ("over a thousand light years" away) to rendezvous Yorktown in 1.7 days = lower range 236,000c for 1,100LY round trip to upper range 450,000c for 2,100LY round trip
3. "That Which Survives" - Enterprise at Warp 8.4 traveling 990.7LY to rescue Kirk's party with ETA of 11.337 hours = 765,000c
@Sgt_G - Food for thought: when the Enterprise is thrown 990 LY away and has to race back to save Kirk in "That Which Survives" is a top speed of 1,000c even workable in the context of the episode?
All of which is why I wanted to come up with some other math to calculate the high-warp speeds.
Over in the game Star Fleet Battles, they have it locked-in that up to Warp 3, they use the W-cubed formula. This doesn't work for the strategic level game Federation & Empire. They came up with a chart (see link below) as some sort of hand-wave to "fix" the problem. They never explained how/why it works, and the scale slides from mid-ranges Warp 4-7 to a different scale at the high end Warp 8+. For years, I've struggled with coming up with something "better", if only to use in fiction stories. I've even considered dropping the Warp Factor usage and simply described speed in light-years per hour, with 60-80 being very near the top end. Of course, being that specific can lead to plot/story problems, which is probably why Roddenberry invented the Warp system to begin with.
http://www.starfleetgames.com/documents/Warp_Speed_in_SFU.pdf
Over in the game Star Fleet Battles, they have it locked-in that up to Warp 3, they use the W-cubed formula. This doesn't work for the strategic level game Federation & Empire. They came up with a chart (see link below) as some sort of hand-wave to "fix" the problem. They never explained how/why it works, and the scale slides from mid-ranges Warp 4-7 to a different scale at the high end Warp 8+. For years, I've struggled with coming up with something "better", if only to use in fiction stories. I've even considered dropping the Warp Factor usage and simply described speed in light-years per hour, with 60-80 being very near the top end. Of course, being that specific can lead to plot/story problems, which is probably why Roddenberry invented the Warp system to begin with.
http://www.starfleetgames.com/documents/Warp_Speed_in_SFU.pdf
I like this idea a lot. But it would make more sense if the emblem was used only for Engineering and not as a catch-all for the other support services (security, commo, etc.)
Ahh SFB. I haven't played that game in ages.
Yeah, TOS's vagueness to the speed of warp factors worked in their favor to tell stories. Of the stories where we can derive speed from distance and time there is a pattern found where they are either fast or slow depending on terrain.
So if you were to write your own fiction, you could calibrate Warp 8 in interstellar space to 80 LY/hour and Warp 8 when <2 AU from a sun/star to 0.001 LY/hour as a starting point. As ships at Warp 8 get closer to the star/planet, expect the LY/hour to slow down to the point where it might be just going the equivalent of supersonic speeds or as the ship passes 2 AU leaving a star system the ship's speed ramps up from 0.001 LY/hour to 80 LY/hour. I don't think the transition is gradual though and more like a sharp transition since the Enterprise "snapped like a rubber band" in "Tomorrow is Yesterday".
Other than that all warp factors above and below are open to interpretation, IMHO. It wasn't stated or demonstrated that Warp 4 is half of Warp 8, etc
Yeah, TOS's vagueness to the speed of warp factors worked in their favor to tell stories. Of the stories where we can derive speed from distance and time there is a pattern found where they are either fast or slow depending on terrain.
So if you were to write your own fiction, you could calibrate Warp 8 in interstellar space to 80 LY/hour and Warp 8 when <2 AU from a sun/star to 0.001 LY/hour as a starting point. As ships at Warp 8 get closer to the star/planet, expect the LY/hour to slow down to the point where it might be just going the equivalent of supersonic speeds or as the ship passes 2 AU leaving a star system the ship's speed ramps up from 0.001 LY/hour to 80 LY/hour. I don't think the transition is gradual though and more like a sharp transition since the Enterprise "snapped like a rubber band" in "Tomorrow is Yesterday".
Other than that all warp factors above and below are open to interpretation, IMHO. It wasn't stated or demonstrated that Warp 4 is half of Warp 8, etc
Hmm, we do see a trend from at least four patches in The Cage to three during the series to one in TMP, so perhaps some organizational consolidation of departments occurred?
So Warp 13 from TNG: All Good Things would net you 53,582,633c (144+233)³, which would get you from one side of the Milky Way to the other in about 16 hours and from one end of the 7,000LY Federation to the other in 75 minutes.
Hmm...that's not as insane as I was expecting. Not sure that fits the plot of the episode exactly. Maybe toss in a divisor? Maybe something like (Fn-1 + Fn)³ / n².
Okay, maybe not n², that would make the lower warps far too slow. Maybe (Fn-1 + Fn)³ / Fn-1?
I'm not well versed enough in geometry to BS a reason for any of this. I'm just trying to massage a curve into something that has a low r-square value vs my expectations and preconceived notions.
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I still prefer my way, Take the TNG scale, chop off the hand drawn curve after Warp 9.
Keep using the same formula for Warp 0-9 and scale onto infinity.
It's super simple and inherently has major backwards compatibility.
Gets rid of the ever increasing decimal place that isn't intuitive to most people other than Trekkies like us.
Keep using the same formula for Warp 0-9 and scale onto infinity.
It's super simple and inherently has major backwards compatibility.
Gets rid of the ever increasing decimal place that isn't intuitive to most people other than Trekkies like us.
Maybe Security guys thought it represented a seatch pattern.
More generally, the Sgt. G Fibonacci Warp Scale is very interesting, but only really applicable to some of the anomalously high speeds, especially for TOS with its factor-cubed background info scale. Capable of warp nine in later TOS unaided, even the cube of that doesn't touch actual figures given in the episodes, whereas the Fibonacci version goes too high compared to later shows.
The Enterprise NX-01 regularly demonstrated speeds of 1000-1500c with her warp five engine, and of course Voyager suggested Warp 9.9 equalled 21,500c. In between are various TNG-era examples suggesting common cruising speeds of 3000c and warp nine being around 9000c, as per examples I use at my site. Outliers exist, of course, but that rough scale seems to reflect the preponderance of examples.
(It is worth noting that, much as I am loathe to accept "warp highways", where default speeds are increased like an aircraft riding the jet stream, they do have utility.)
There is a ton of excellent work in this thread cataloging actual warp velocity examples with supporting info:
http://www.starfleetjedi.net/forum/viewtopic.php?f=8&t=6329
What a super useful list!
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@DSG2k - Ditto
I didn't have the motivation or time to research non-TOS speeds but this list gives a nice starting point to research speed data that it's on my reading list. Similar threads
