I understand that writers aren't perfect and need some wiggle room with regards to velocity, but a lot of that can be dealt with by the structure of the episodes. For example, if they're the only ship close enough to save someone, set the episode inside a single star system. If the crew have to get somewhere far away, either give them a "shortcut" (wormhole, etc) or make it clear that it will take them time to get there and cut to later. If an alien is chasing them, make it happen in open space so you don't have to worry about how long it takes to get from Planet A to Planet Z. The velocities don't have to be tricky if you don't structure the episodes in a way that accentuates these speed and distance related inconsistencies. Then, when you do have episodes that have specific velocities and distances, and you do it right, the viewers won'tl realize that you aren't putting in that much effort all the time.
I don't have a problem with warp factors per se. They are a very handy way to express a speed without actually giving an actual speed that might contradict something. I do think the new warp scale that made warp 10 equal to infinite speed was a mistake because it created this awkward situation where speeds had to get crammed into more and more decimals after 9. So instead of just picking a bigger warp number like 14 or 16, we got 9.95 or 9.9995. I think it would have been better to just stick with an open ended exponential function. That way you can just pick a bigger number for higher speeds. For example, Voyager could have a normal cruising speed of warp 9, an alien ship that is a lot faster than Voyager could have a speed of warp 11 and when Voyager used some fantastical new propulsion like slipstream, the crew could have said that they were going at the equivalent of warp 23. It would be more intuitive to the audience that the ship was going faster than before, more intuitive than 9.99995.
Come to think of it: why did they change the warp scale in TNG to include this warp 10 asymptote? I mean the real-world reason (not the in-universe one). Did they have any problems with the old TOS scale?
I think they wanted to avoid the ridiculousness of ever-increasing speed increments going all the way up to "Warp 43,835.9" or somesuch, as starship technology kept improving and ships kept going at more and more ludicrous speeds. Kor
^That would be my thought as well. But I doubt it really helped, instead we just got those 9.9... figures. And if I have to choose between 'warp 24' and 'warp 9.975', perhaps the first isn't so bad after all.
If you use the right exponential function, it would never get that high. Just warp 15 would be big enough. For example, if you use the formula, speed (in c) = 4^(warp - 1), warp 1 would be 1c but warp 14 would be a speed of just over 67 million times the speed of light. So yeah, you could do some pretty ludicrous speeds while still using fairly low warp factors. Even with better warp drives and faster speeds, there would never be any danger of warp factors getting too high.
In addition to what Mytran said, it might also have been the producers wanted to slow down travel and make the explored portion of the galaxy smaller for TNG. In TOS, speeds in open space were in the 400,000c to 800,000c ranges already and episodes like "The Alternative Factor" and "The Cage" and "The Paradise Syndrome" suggested that the Enterprise traveled far around the galaxy. It was like a reboot of a sorts and in many ways the tech capability in TNG were a step backwards so in my headcanon I treat TOS as a separate universe from TNG+Voy+DS9+Ent.
That could work, I suppose. Though you'd get negative factors for speeds slower than c/4 which might feel counterintuitive for those less technically inclined.. For example, I'd estimate I ride my bike at speeds somewhere around warp -12.
The formula is really only meant for speeds of c and higher. In fact, that is where warp factors become very handy. It is much easier to say "warp 14 ensign, punch it" than to say "set speed for 67,456,232c, ensign, punch it". For speeds less than the speed of light, I figure you don't need to use warp factors since those are speeds we can express today.
^I know, I wasn't being serious. Though I have to confess, 'warp factor minus infinity' sounds cooler than 'dead stop' :0 But, there are instances in Trek were warp factors lower than 1 are cited. For example in the Motion Picture and First Contact movies. Not many examples, though.
I've not come across that formula before - did you come up with it yourself? It does make for some slower lower warp speeds, but the higher ones certainly make space travel a little more plot-consistent! There are still a few oddities related to known speeds, however. That Which Survives for instance states that at Warp 8.4 they can traverse up to 990.7LY in 11½ hours - in fact it would be more like 304 hours (12.7 days). 11½ hours would require Warp 10.7 or thereabouts. Later in the episode they do indeed top Warp 14 which would wizz them back to the planet in just under 8 minutes, not long enough even for the ship to blow up! Voyager would of course get home in 3 months at Warp 9.975, but there's no indication she can sustain that speed and indeed is often seen "cruising" at Warp 6 which would better fit the 75 year stated journey. Tom Paris' boast that Warp 9.9 is "4 billion miles a second" is off by a factor of at least 10, but I have no problem with him mis-speaking in a moment of meeting REAL 20th century people, or just getting his metric-imperial measurements mixed up in his head. I totally get what you mean about Warp 15 being high enough though - Warp 16 calculates out at being a BILLION times lightspeed!
That chart is very cool. Yes, I came up with the formula myself. I wanted an exponential function to describe warp factors because I wanted super fast, even ludicrous, speeds but without crazy big warp factors. So the formula had to be a base integer raised to a power of warp. I also needed warp 1 = 1c, so the power had to be zero hence why the number is raised to a power of warp -1. This offsets the warp factor whereby a warp factor of 1 gives a power of 1-1 or 0 which I wanted. Any number raised to the power of 0 is always 1. I picked the base to be 4 just because it seemed to give reasonable speeds that I liked. I wanted ludicrous speeds to be around warp 14 or so. If you want the exponential function to be shallower (higher speeds to rise less sharply) you could go with a base of 2 or 3. If you want the exponential function to rise faster (higher speeds to rise even faster), you could use a base greater than 4. But 4 seemed like a reasonable compromise. With this formula, Star Trek could introduce better warp drives, exotic propulsion systems, even crazy fast speeds as much as the writers want and no matter how fast the ship gets, the warp factors would never get crazy.
I did these two warp scales a while back based on what has been shown in the series. One for TOS: and another for TNG+Voy. What's interesting is that in TNG+Voy there are way more examples of dialogue used to talk about high FTL speeds (faster than Warp 9) than slow FTL speeds. It is almost like the writers realized they needed to be more explicit about how fast things were once operating between Warp 9 and 10 or they weren't sure exactly what Warp 9.943 meant .
One problem with both the traditional TOS and TNG scale is that they don't work for most plots. Take answering distress calls. Unless the ship is basically in the system already, even at top speed the response could only be "Man, that sucks, tell them we'll be there next week to arrange for their burials. "
Or that ships are capable of doing "ludricous" speeds for short periods of time, even if that entails spending an extended period of time doing repairs & maintenance on the engines afterwards. Still, in cases of extreme emergency, this trade off is worth it Thanks for the feedback. I love messing around with the maths of Warp Factor velocities
https://www.trekbbs.com/threads/heres-my-warp-scale-excel-table.293802/ I still prefer my version of the Warp Factor Scale, it's at least consistent with no sudden change in formula after Warp 9.
You wouldn't say "67,456,232c" anymore than you'd say "Warp 8.7052356". You'd say something like "sixty million c". Also, remember that rounding Warp speeds leads to far greater inaccuracies than rounding the equivalent "times the speed of light" value, so "C" is better if you're rounding.