I'm looking for examples of Warp Factors less than 1

[MrDowntempo]

This is for a personal project. Mainly I'm learning about Python programming, and using it to learn about curve fitting and all sorts of nifty mathy stuff. Right now, what I'm interested in, is Impulse speeds measured in warp factor, or some equivalent.

So of course, Warp 1, is the same as lightspeed, or C. And depending on the scale, it goes up from there. But we know that the scale can also go in the other direction, primarily because of Kirk ordering the ship to go warp factor .5 in the Motion Picture, and also saying it took 1.8 hours. Memory Beta has some calculations on how fast they assume that to be (based I think on the average distance to Jupiter) But I've been able to narrow that down, by using an astronomical calculator, and finding the average distance between Earth and Jupiter in the summer months (based on the look of San Fransisco in the opening scenes) of 2273 (based on Bones saying "It's been 5 years, Jim!") It comes out to about .41c, so we can conclude either from my calculations, or Memory Beta's that the scale isn't linear.

I would love love LOVE to find more data points like this. Whenever a speed is given as a Warp Factor less than 1, and can be compared to some other known unit (factor of light speed, kmph etc.) But So far I have been unable to find much.

In the original series episode, Elaan of Troyius, Kirk wants to take his sweet time, so orders Sulu to go Subspace factor .037 and then when asked to repeat it calls it SubLIGHT factor .037. Now maaaybe he just means .037c but (and I'm making a lot of assumptions here, because I must with the lack of data I've found) maaaybe that is also equivalent to Warp Factor .037, and I think it is, otherwise why would the number be so low? If Sublight Factor is used more often to define speeds below warp 1, you'd assume that warp 1 would be a really high number since it wouldn't be achievable. Instead, I think it's the same scale, Kirk is just making it a point to call it sublight to emphasize that we're traveling on Impulse. Based on that, and some very very back of the napkin math based on info about Elas and Troyius (the planets they travel between at that .037 speed) found in the Wikis, info about Binary Star orbits, habitable zone size, Hill Radii etc. I determined that those planets (take this with a planet sized piece of salt) are probably about 5.88 AU apart on average. I'm also assuming it takes 10 days based on the amount of outfit changes Elaan goes through (1 per day I assume), and the fact that someone in that episode was injured, and Bones says it'll take at least a week for them to recover, and we do see them walking about again near the last day. So ~5.88 au in 10 days, put Warp Factor .037 = to about .0034c

Speaking of Impulse, While I know FULL IMPULSE, is often given as .25c based on technical manuals, there's no relating that term to Warp Factor, so it's just not data I can use (yet) And I know some will mention that Full Impulse is the same as saying Full Steam Ahead, on a steamer ship, but I think it's more likely to assume that Full Impulse is just a colloquial way of saying .25c since we know different ships can travel faster than .25c on impulse alone. Still. Unless I can find something that says Full Impulse is also equal to Warp Factor .XXX I can't relate it to Warp Factor directly.

Another dead end I found the the Enterprise episode Singularity, where they travel on Impulse towards a black hole. Memory-Alpha calculated this roughly to 3mil KM in 2 Days, but at anything close to Full Impulse, 3Mil km could be traversed in minutes, so again, it's not something I can directly relate to the Warp Factor speed scale

There's a chart of Warp Speeds vs Time in the original series technical manual, and it has a section for less than warp 1. It makes literally no sense. The Axis are practically the same, and it's just not usable.

And that's all I've got beside Warp Factor 0 = 0c and Warp Factor 1 = c. I would kill for some more datapoints. I don't care if its TOS scale or TNG scale (probably doesn't matter much for < 1 WF), I don't care if its from apocrypha, some old technical manual, the Omnipedia, a retconned comic book, an early 80s table top RPG, or 90s video game. If I can get any data about warp factor's less than 1 in relating to light speed, or other real world units, I can put big enough error bars on it to be useful for me. Ultimately I'm trying to find the equation of the curve that passes through them.

What Might be of use, is that chart from an Episode of Enterprise I see referenced a lot, but in higher resolution than I can find on the Wikis. But any direct references with numbers would be ideal.

Thanks for any help you can offer!

 

[NCC-73515]

DIS S4 and PIC S2 travelled at Warp 0.001

 

[blssdwlf]

The Motion Picture as far as I can tell is the only time we hear of Warp factors less than 1.

"Full impulse" equaling 0.25c originated from the TNG:Tech Manual however as you observed 0.25c isn't corroborated in the episodes or movies.

Also keep in mind that each series treats impulse and warp speeds differently.

Good luck!

 

[SchwEnt]

Do Warp Factors less than one follow the same formula?

Common formula for Warp Factors cubed times lightspeed
(i.e. Warp Factor 3 equals 3x3x3 times lightspeed. Warp Factor 3 equals 27 times lightspeed).

Would Warp Factor .5 equal .5x.5x.5 times lightspeed?
Warp Factor .5 equals .125 times lightspeed?

If ship speed is to be .125 c... is there a difference between Warp Factor .5 and one-quarter impulse?

 

[David cgc]

Do Warp Factors less than one follow the same formula?

Common formula for Warp Factors cubed times lightspeed
(i.e. Warp Factor 3 equals 3x3x3 times lightspeed. Warp Factor 3 equals 27 times lightspeed).

Would Warp Factor .5 equal .5x.5x.5 times lightspeed?
Warp Factor .5 equals .125 times lightspeed?

If ship speed is to be .125 c... is there a difference between Warp Factor .5 and one-quarter impulse?

I actually had this exact same thought in another thread a week or two ago and did some quick estimations. The upshot was with the possible range of distances between Earth and Jupiter, and the fact that we know how long it took to get from one to the other (no more than 1.8 hours, possibly much less depending on exactly how long it took before the ship accelerated), Warp 0.5 is definitely closer to half the speed of light than 0.5^3 times the speed of light. 0.125 c is much too slow to make the trip in the time available.

 

[Henoch]

So of course, Warp 1, is the same as lightspeed, or C.

Depends on your formula , me personally for TOS, I have Warp 1 at 18.65 c in normal interstellar space ("calm" space between stars once you leave a star's heliosphere which is an effect of its magnetic field.) This is based on Gene Roddenberry's early concept that the Enterprise's max. speed is 0.73 lightyears per hour (lys/hr).

I use the warp speed equation v=c(wf^3)x, where x is a multiplier factor based off the space/subspace environment. Solving for x at Warp Factor (wf)=7 and v = 0.73 lys/hr (or ~6400 lys/yr) for the ship’s maximum speed which I assume to be Warp Factor 7 during the Cage era, gives 6400=c(7^3)x or x = 18.65.

Of course, x can be adjusted by the speed of plot for any story. My examples:

• Pushing through a star's heliosphere/magnetic field, x drops to 1.
• Close approach to the star or even planets drops x even farther to ~0.2 as another example.
• In strong magnet space storms, wormholes, etc. and depending on the direction the ship encounters the those magnetic potentials, x could reach upward to 10,000's .

Back on topic, during TOS, impulse commands like full impulse were never equated to a speed. To me, full impulse sounds like "run the impulse engines at full power" which gives the ship its highest acceleration rate or thrust that probably peaks at some percent of c but we never learn what this peak speed is. Several of us on this site also believe that impulse can exceed the speed of light using technobabble theories such as using the ship's inertial dampening system, structural integrity field, main deflector, or running impulse power through the warp engines, etc. to either reduce the ship's mass or compress space in front of the ship.

From the first TOS movie, Warp 0.5 might mean that impulse power is also being run into the warp engines to create a weak warp field that slightly compresses space-time somewhat, which makes impulse speed higher than just the thrust from the impulse engines by themselves. For example, normal full impulse might give 0.25c max., but full impulse with warp engines might give 0.5c. YMMV .

 

[Kamen Rider Blade]

Depends on your formula , me personally for TOS, I have Warp 1 at 18.65 c in normal interstellar space

Spoiler: SxS Comparison of the TOS & TNG Warp Scales

From what I can tell, Warp 1 is the same, on both scales.

 

[MrDowntempo]

Yeah, I know the scales are different pass warp 1, but I'm not sure if that hold for impulse speeds as well. I like to imagine Full Impulse is colloquial meant to mean Set impulse to our target speed of .25c since that jives with the tech manual, and the fact that all ships have different max impulse speeds. I'm willing to fudge away acceleration as needed.

I've also seen others play with the warp scale with scaling factors like that. Warp 1 = 1c though is just too intuitive for me to let go of.

I appreciate the replies I've gotten so far. But am still specifically looking for data points. And instances, canonical, or apocryphal that could be put into a graph or table of warp factors under 1 against multiples of light speed.

Meanwhile, in an attempt to pursue this goal further, I re-watched ENT:First Flight, grabbed 2 screenshots, and fudged around with them in a popular open source image manipulation program to correct for perspective and lens distortion. Did a little sharpening and tweaked the curves to bring out the chart as well. This is the best I could manage:

It's not perfect, but the best I could manage with my limited experience. The Y-axis is clearly logarithmic, but the X-axis, with 21 units between 0 and warp 1 is pretty odd.

 

[Jedi Marso]

It's all made up technobabble, and ultimately all speeds conform to one curve: the speed of plot. Trying to make something actual or scientific out of what Hollywood writers have come up with over the last 50 years is a fruitless exercise.

Yet...

It hasn't stopped 3-4 generations worth of ST fans from trying, so go for it, baby, and have FUN!

 

[Henoch]

Note the light blue area on the graph. To me, it looks like a variable range around the "ideal" warp curve. If so, then Warp Factor 1 can vary between roughly 0.6c and 60c. Also note that the title of the graph at the bottom is "<can't read>DISTORTION IN WARP FACTORS"; that sounds like the speed can be distorted at each Warp Factor. Distorted by what is not provided. YMMV .

 

[UssGlenn]

Man, the TNG scale is still slow. Takes a full day to get to the next star over. So much for stars flying past the window.

 

[MrDowntempo]

Note the light blue area on the graph. To me, it looks like a variable range around the "ideal" warp curve. If so, then Warp Factor 1 can vary between roughly 0.6c and 60c. Also note that the title of the graph at the bottom is "<can't read>DISTORTION IN WARP FACTORS"; that sounds like the speed can be distorted at each Warp Factor. Distorted by what is not provided. YMMV .

That's a very good and valid point. Of course there's no usable legend for that is meant to be, but that's certainly the most likely way to interpret it. Still, there's a big circle at Warp 1 and 1c, which implies that's the ideal uhh.. target. And yeah. I couldn't make out the bottom label any better than that. I assume its Time Distortion? But it's hard to say for sure. Could be space distortion, or timespace distortion? Neither is really helpful though, nor looks like it lines up with the last letter of the unreadable word.

 

[blssdwlf]

@Henoch - how are you getting 0.6-60c for Warp 1 on that diagram? It seems to only span 0.6-9c?

 

[Henoch]

@Henoch - how are you getting 0.6-60c for Warp 1 on that diagram? It seems to only span 0.6-9c?

Oopsie, my bad reading log scales. It spans 0.6 to ~5.4c. Can't be 9c; you may be misdirected by the horizontal solid line at ~8c (not 10c), and the blue area is below that line. Here's how I read it:

I also think the blue variable zone may only be applicable for the region of space they currently are in (Sol Solar System, maybe even tighter, around Earth orbit), and it could be smaller or bigger for other regions of space with different environments. YMMV .

 

[Timelord79 (he/him)]

Man, the TNG scale is still slow. Takes a full day to get to the next star over. So much for stars flying past the window.

I never assumed it’s stars literally flying by.
Cause that would cause a bunch of scaling issues with perspective and parallax.
I just take it as a visual distortion of the surrounding space from the warping of space time.
Similar to distortions you could observe near a black hole.
Basically gravitational lensing effects.

 

[blssdwlf]

Oopsie, my bad reading log scales. It spans 0.6 to ~5.4c. Can't be 9c; you may be misdirected by the horizontal solid line at ~8c (not 10c), and the blue area is below that line. Here's how I read it:

I also think the blue variable zone may only be applicable for the region of space they currently are in (Sol Solar System, maybe even tighter, around Earth orbit), and it could be smaller or bigger for other regions of space with different environments. YMMV .

No worries. It was under 10c so I wasn't sure where you got 60c

Yeah, I'm thinking also that the variable zone depends on the region of space the ship is in.

 

[Cyfa]

This may be pretty useless as there were no distances mentioned, but in Lower Decks: "A Mathematically Perfect Redemption" (S3), Peanut Hamper speculates that her make-shift ship will hit "warp factor point zero two or point zero three". Then, when she gets it going, she doubts it will make warp one (although she's cut off before she finishes saying "one", so I'm guessing that's what she was going to say), but it achieves warp speed nevertheless.

 

[MrDowntempo]

This may be pretty useless as there were no distances mentioned, but in Lower Decks: "A Mathematically Perfect Redemption" (S3), Peanut Hamper speculates that her make-shift ship will hit "warp factor point zero two or point zero three". Then, when she gets it going, she doubts it will make warp one (although she's cut off before she finishes saying "one", so I'm guessing that's what she was going to say), but it achieves warp speed nevertheless.

Haha! Yeah, that was a good bit, but not usable for my purposes since it seems like it does hit Warp 1, and there's nothing much to compare it too to get an actual speed. At least its confirmation that warp values less than 1 are still a valid measurement in later stardates.

I also rewatched the Star Trek reboot. They show the warp factor with 3 decimal digits on the main screen when going to warp. But it scales up quite a bit faster than the ship does which is unfortunate. I might rewatch the 2 sequels to see if I can see it used again.

 

[Henoch]

I couldn't make out the bottom label any better than that. I assume its Time Distortion? But it's hard to say for sure. Could be space distortion, or timespace distortion? Neither is really helpful though, nor looks like it lines up with the last letter of the unreadable word.

I'm fairly sure the word previous to DISTORTION is FIELD based on the "D" plus "L" would be the only other letter that fits based on the gap between letters. So, probably "<something> FIELD DISTORTION IN WARP FACTORS".

There is a plot for speed below Wf 1 on the Chart; I find it odd that there are 21 divisions on the Wf scale between what I assume to be zero and Wf 1.

 

[MrDowntempo]

I'm fairly sure the word previous to DISTORTION is FIELD based on the "D" plus "L" would be the only other letter that fits based on the gap between letters. So, probably "<something> FIELD DISTORTION IN WARP FACTORS".

There is a plot for speed below Wf 1 on the Chart; I find it odd that there are 21 divisions on the Wf scale between what I assume to be zero and Wf 1.

That Does make sense! And I think can just be interpreted as warp factor? Anywho. I'm still looking for more data points because, I'm Ideally trying to find the equation of the curve there. I don't think it's linear, and I don't think it's the same as the equation above warp 1. Here's what I've got so far. I probably need to change my initial guess function to either another piecewise (ugh, don't wanna, would need more data points and they're already rare) or another technique. The software I'm using (MatPlotLib and SciPy's Curve_Fit) doesn't allow me to set explicit min and maxs at the points, only the standard deviation, which I can estimate using the range rule. Also the scale isn't logarithmic in the chart (been having some trouble there), and that's why the ENT:First Flight data points get wider as they get closer to warp 1.

I've got some ideas about how to fit the curve better, and not ignore the Motion Picture data point, but ideally, I just need more data.

The Full Impulse line is just there because I didn't know what else to do with that data yet.