Acceleration or power levels make far more sense than fixed multiples of C. The G solution also helps explain why Kirk so often left at Warp 1, too
Respectfully I disagree- the purpose of stating "warp speed" is to confer some kind of an integer of distance traveled per unit of time. Hence the use of the word "speed". Its a short form notation, that is all. Adding power indice co-efficients to a notation of speed, based on a hand drawn scale wasn't all that helpful IMHO, and frankly made what was already a mess a hopelessly complicated affair. The closest analogy I can come up with that makes any sense would be to rescale MPH to include the peak efficiency for shifting up to a different gear for maximum power. Not only do transmissions have different gear differentials, they have varied power ratios- so applying one scale over MPH wouldn't really make any sense. I think the same is true when applied to warp factors. That being said I understand that Gene Roddenberry wished to differentiate TNG from Franz Joseph's ST:TM and by association, TOS, because of their falling out, so those who developed the TNG scale for him did so as directed and dictated. At this point, it is what it is, 30 years on we just have to work within the framework as given. I have always thought that the Enterprise breaks orbit at Warp 1 because of the crowded nature of the inner solar system, be it due to gravitational field effects, or due to the bodies themselves being a navigational hazard, it's prolly easier to negotiate at lower warp speeds.
That presupposes that every course takes them parallel to the orbital planes of the planets and other debris. And even if that were really the case they'd just fly due south or north out of the solar system plane at whatever high warp speed they fancied and then change course accordingly, wouldn't they? It also doesn't explain the situations where they were not within a solar system at all (Arena, Galileo 7) and still set off at Warp 1
"We can have ya back on Vulcan in four days, Mister Spock" -- Montgomery Scott, Star Trek: The Motion Picture
Have they ever really mentioned speed that often in the films/TV shows? As has been mentioned we know that in TMP that they could reach Vulcan in 4 days and Vulcan has been established as being ~16ly from Earth so thats at least 4ly per day. But we don't know if that was at a crusing speed or maximum speed. And we are told in VOY Warp 9.9 is about 4 billion miles per second whis is around 21 472 times the speed of light. Simply put for better or for worse they move at the speed of the plot.
In TOS it was a relative fixture of the series- to the point of Scotty sweating bullets every time Kirk asked for Warp 8 speeds, to his disbelief when Nomad monkeyed with his poor Bairns and propelled the ship up to Warp 11 speed. If you want to get a general idea without going through and watching each epsiode how often warp speeds are cited, go to Google, type in the following search terms: "(name of episode)" transcript Star Trek, and then do a search on that page for "warp" and you will get the idea. If you go by the TMP Blueprints, the refit Enterprise would have a Max Safe Cruising Speed of 8 or 512c (on the stated cubed scale). To reach Vulcan, if it is 18 ly from Earth would take 12 days. At her Emergency Speed of Warp 12 or 1728c, she gets there in 3.8 days. I somehow doubt Scotty would actually be happy running the engines at her top rated speed for hours on end, let alone days, but that is the stated problem. Kicking it up to a fourth power, then a voyage of Warp 7 or 2401c would take only 2.73 days. Hmmmm. Exactly.
There are still people who use the words "weight" and "mass" interchangeably. The concepts are related, but the imprecision of language and expression means it keeps on being used even by people who should normally know better. Yes, that's all perfectly valid observation. The thing is, in space there is no such thing as "absolute speed." All speeds are relative. There's also the fact that any relative velocity will continue indefinitely whether the engines are active or not, so the entire concept of not being able to maintain a particular speed is just plain silly; if you need to travel at 1000c, just accelerate till you get to 1000c and coast the rest of the way (drag from the ISM shouldn't be so high that you couldn't sustain that speed at low power). Tying it to acceleration, on the other hand, solves a lot of plot problems, and also nicely explains why we can't ever seem to figure out what "speed" the ship is actually moving: it's because it isn't moving at a constant speed, but on a constant acceleration in an arbitrary direction. This would also finally explain to us what the hell "all stop" actually means for a starship. Because it's a space ship, turning off the engines wouldn't actually STOP the ship at all, it would just keep moving in whatever direction it was originally going. But stopping your acceleration puts you on the drift, which means you're coasting until you figure out what you need to do next (maybe reverse acceleration and move AWAY from your destination, or change course entirely). Celestial objects are so incredibly far apart that the odds of ACCIDENTALLY running into a planetary or asteroid body are astronomically small even at high warp. The plane of the solar system where most of those bodies are located is a very thin slice of an otherwise vast spherical region. If anything, you might need to worry about close-calls with other starships since everyone in the system will want to be moving along the planet of the ecliptic (because that's where all the planets and space stations will be anyway) but if you want to LEAVE THE SYSTEM, you can go in any direction you want and the planet of the system is no longer an issue. But warp factors being a unit of acceleration would mean the ship is simply leaving orbit. Accelerating constantly for about two hours at 1G would put you just outside the orbit of the moon and traveling at about 28% of the speed of light; call this "full impulse power," with the assumption that for anything faster than, say, 2Gs of acceleration, you're going to need to use the warp engines.
With some minor alterations, Star Trek Maps could provide a better system for warp speed and bridge the gap between TOS, TMP and TNG.
There may be a case that isn't how the fictional subspace physics works in Trek. Warp engines may need to continually operate at a certain energy output to maintain a particular warp factor and that a ship may gradually drop back to sublight if the warp engines are turned off. In such a scenario, a ship doesn't travel through space at warp as it pushes through the medium of subspace, which requires continual power to do so.
That assumes that warp fields and the nature of subspace operate in a manner in accordance with Einstein's Theory of Special Relativity- which in Star Trek, by inference of the violation of c as the absolute universal speed limit and constant casts this argument as a red herring. The prime issue pertaining to the use of Relativistic style effects and mechanisms is that Roddenberry and co. threw those particular features of realistic space travel out the window on Day 1. TMoST I believe covers that in some detail, but as I recall it was felt that trying to explain Relativistic effects (time dilation being the most obvious issue) would only get in the way of having to tell the story (likewise the invention of the transporter as a time saving, narrative device). As a result, the system you are trying to ascribe these constants and constraints to already hold them in strict abeyance. I could perhaps see that maintaining a warp field at a certain power level to maintain that speed, being below what was required in getting to that speed (effectively accelerating or "charging" the warp field "up" would have a greater requisite power consumption than to simply maintain it), but at no time have we _ever_ seen a starship "coast" after attaining that velocity. Simply put, a starship still has to output power from its M/AM reactor to maintain whatever velocity attained, that is the constant of fictional warp drive we have always seen, and while it may be silly, that is what you have to work with. You propose an interesting thought - I will think on this further and consider it. This assumes that the system is generally Sol-like, and while we can assume that the majority of systems are similar, that is not necessarily always the case. Given that, objects in the outer solar system (the Oort cloud) are fairly inconspicuous, and there are alot of them, colliding with one would generally be bad. I would think it might be a good thing to keep Sulu on a tight leash even though he might be hell-bent-for-leather to go to Warp 12 for this very reason. Likewise, a single particle of gas and dust striking a ship's hull at c will definitely have a detrimental effect on its occupants and systems- hence the use of the Navigation Deflector System, but even given that technology, I think that Standard Operating Procedures for Starfleet Vessels would have something along the lines I have stated, to err on the side of caution. This is my opinion, and it may change, but for now, I see no reason to doubt my position.
One thing about Mr. Scott's statement in TMP is that we don't know exactly what it means. Kirk was suggesting they give the Enterprise a proper shakedown, which Mr. Scott agrees they need one. It could be that it will take a few days to get the shakedown finished and Scott's apologizing to Mr. Spock by saying they can get it done and him home in just four days, rather than Mr. Scott boasting about his engine's speed, which is what we use to think, with the Warp Factor 12 speed giving in a lot of reference material just so Enterprise could reach a planet ~16 light years away within four days using the warp factor cubed system. If Mr. Scott is apologizing to Mr. Spock, than USS Enterprise can go a lot faster than the old Warp Factor Cubed system in TMP.
Here's a little something I have worked on for a few days. Its a TNG Warp Scale calibrated to V = C * W^4 up to Warp Factor 9, and in which Warp 9.9 is equivalent to 21473c and Warp Factor 10 is infinity. 9 = 6561c 9.1 = 7105.002398771584c 9.2 = 7725.482477363039c 9.3 = 8444.49687978731c 9.4 = 9295.360380768241c 9.5 = 10331.723127446336c 9.6 = 11647.869244249454c 9.65 = 12462.935725731591c 9.7 = 13431.91673832336c 9.8 = 16144.362830154689c 9.9 = 21473.813066394923c 9.925 = 24008.911171124742c 9.95 = 27978.853637798755c 9.975 = 36074.751122697446c 9.99 = 50090.689815142876c 9.999 = 112844.5406589971c 9.9999 = 253265.7906607502c 9.99999 = 568195.1218775817c 9.999999 = 1274675.7831192315c
That scale works well for Tom Paris' boastful comment about the ship's speed (he is the pilot, after all!) However, it doesn't cover the problems with all the mentions of "parsecs" in the show. Unless a parsec isn't what we think it is?
There is certainly the argument to be made that by the 23rd/24th centuries it's lost its original meaning and is just a generic term for a "largish" distance. In several of the examples I listed above that could fit quite well
Are you sure 12 decimal places is enough accuracy? We want to be precise, after all. Those microseconds are important.
A microsecond can save your life! You can do loads in a few microseconds- you can smash an atom, start a nuclear chain reaction or even bound quarks into hadrons..
At this speed, Voyager could have covered seventy thousand light-years in twenty days. So why even try for warp ten? Just have Paris throttle back slightly short of ten.
If we accept that episode at face value (ugh), then I don't think this actually makes any sense. Since Warp 10 is literally infinite velocity, it can't be any form of acceleration that actually achieves it; it would have to be a discontinuous jump that would suddenly place the ship at warp 10 once certain prerequisites were achieved. That is, the fact that the shuttle could travel at warp 9.99 and warp 10 doesn't necessarily mean that it could travel at any given warp velocity between the two. And the fact that they don't do that is at least circumstantial evidence in favor of the idea that they couldn't.
I am not quite familiar with the Star Trek Maps interpretation of warp dynamics and travel, so if you could provide a few pointers I would be greatly appreciative. Exactly- at very high percentage points of 9, you don't really need to hit 10 to get back to Earth in a jiffy- the further to the right of the decimal place you go from Warp 9 the faster you go. I think it would have been easier just to say, "Tom, take us to Warp 36.." and have the same effect, so to speak, but whatever. I am pretty convinced that the whole reason that the TNG scale exists is a combination of Roddenberry trying to completely render Franz Joseph materials obsolete and inapplicable to what at the time was "new" Trek, and to also add a bit of "realism" to how warp mechanics worked by adding power indice co-efficients to each warp factor and scaling it so that Warp 10 is akin to c- something unattainable.