In my post number 10 in this thread I discussed problems with a well known theory to explain the many time, speed, and distance problems in various Star Trek productions. That theory was described in the booklet Introduction to Navigation , which was part of Star Trek Maps, 1980. The booklet explained there was a factor called the "Cochrane factor" modifying the spade that a starship using its engniens set at a specific warp factor would actually travel. And I then gave three reasons for considing this to be a flawed explaination of the many time, distance, and speed problems in various Star Trek productions. And then I said there was a much more obvious basic scientific flaw in that theory which I would give later and invited others to suggest it themselves. That was August 30, 2022, and nobody has responded by giving that flaw with the theory, so I guess it is now "later" and time fo rme to describe it. There are significant differences in the density of gas and dust in interstellar space. But that interstellar gas and dust is so rarified that it seems better to speak of its "thinness". Interstellar space is a hard vacuum, containing much less matter per cubic centimter than any vacuum produced in any Earth labatory. https://en.wikipedia.org/wiki/Interstellar_medium https://en.wikipedia.org/wiki/Molecular_cloud https://people.highline.edu/iglozman/classes/astronotes/interstellar.htm Interstellar gas and dust is much thinner than Earth's atmosphere. If you toward the horizon you are looking through more of Earth's atmosphere - more miles of gas and dust - than if you look stright up, and so the color of the air is different. The greater amount of air seen though when looking toward the horizon changes the colors of objects and mankes them dimmer. If you could look through a long enough column of Earth's atmosphere everying beyond a certain distance would be inivisible. Earth's air becomes opaque at a distance of hundreds of miles or kilometers. HIgh mountains can been seen at distances of hundreds of miles or kilometers from other high places, but in those cases part of the path of the light rays is through air much thinner than at sea level, which increases the visible distance. Answers to this question: https://worldbuilding.stackexchange...-world-and-no-obstacles-how-far-could-you-see say, for example, that at 250 miles only 1.8 percent of the light froman object will get through or that only 1 percent of light will pass thorugh 450 kilometers (279.617 miles) of pure nitrogen atmosphere. But light will pass through 250 thousand miles, or 250 million miles, or 250 billion miles, of interstellar space without significant blurring. It takes many light years of looking through an intersteller dust cloud for an object to be significantly blurred or even totally obscured. And the gravitational force of the matter in a cubic centimeter of interstellar space right next to an object should be extremely low. But the gravitational force of the matter in one cubic kilometer of interstellar space would be be one billion times as great. However, most of the mass of the Milky Way Galaxy is now believed to be dark matter. And most of the dark matter is believed to be some form of matter which doesn't interact with leetromagnetic enrgy, thus making it invisible, and also doesn't interact with itther matter and so shouldn't form denser clumps and less dense voids. Teh dark matter in the galaxy should have a rather smooth density gradient in contrast to normal matter, and since there is more of it than ordinary matter it should tend to smooth out the gravitaitonal effects of the differening densitys of ordinary matter. Returning to matter which can be seen: Since a parsec equals 3.26156 light years, a cubic parsec equals 34.695734 cubic light years. Thus there should be about 0.0017004 solar masses per cubic light year. Since the interstellar medium has only about 15 percent of the mass of the stars in the galaxy, the mass density of stars should be higher than the mass desnity of the interstellar medium in most locations in the galaxy. But of course the mass of the stars is not spread evenly through space but concentrated in stars which have very large volumes which are incredibly tiny compared to the vastness of interstellar space. Thus it seems that each star is surrounded by a polyhedron shaped volume of space where the star's gravity is stronger than the gravity of the nearest star in that direction. Since the strength of gravity falls off with the square of the distance, the ratio between the masses of the objects should found. The neutral point where the gravity of the two objects is equal should be farther from the more massive object than from the less massive object by the square root of the mass difference. If one object is 100 times as massive as the other one, the netural point between the two objects should be 10 from the more massive one than from the less massive one. Thus the neutral point between the two objects wil be 10/11 of the total distacne from the more massive object and 1/11 of the total distance from the less massive object. I note there are degrees of uncertainty in the masses and distances of the following objects, thus making the distances to their neutral points slighty uncertain. Alpha Centauri A & B have a combined mass of about 1.988 the mass of the Sun. The square root of 1.988 is 1.4099645. So the neutral point between the Sun and Alpha Centauri is 1/2.4099645 of the 4.37 light years between them, or 1.8133044 light years from the Sun. Sirius A & B have about 3.081 the mass of the Sun. The square root of 3.081 is 1.7552777. So the neutral point between the Sun and Sirius is 1/2.7552777 of the 8.60 light years between them, or 3.1212822.light years from the Sun. There are many stars and star sytems much more massive than Alpha Centauri or Sirius, up to about 50 times as massive, but they are so far away their neutral points are much farther from the Sun than those of Alpha Centauri or Sirius. K type main sequence stars with masses from 0.59 to 0.88 the mass of the Sun are about 3 to 4 times as abundant as G type stars like the Sun, and M type main sequence stars with masses from 0.079 to 0.57 the mass of the Sun are probably the majority of stars in the Milky Way. So most stars and star systems are less massive than the Sun. For example, Barnard's Star has a mass of 0.144 the mass of the Sun. THe Sun is 6.944444 times as massive as Barnard's star. The square root of 6.9444444 is 2.6352313.. So the neutral point between the Sun and Barnard's Star should be 2.6352313/3.6352313 of the 5.9629 light years between them or 4.3225914 lightyears from the Sun. The Hyades star cluster has about 400 times the mass of the Sun. The square root of 400 is 20. So the neutral point between the Sun and the HYades about 153 light years away is 1/51 of the distance, or 7.2857 light years from the Sun. A giant molecular cloud has 10,000 to 10,000,000 times the mass of the Sun. TheTaurus molecular cloud is about 430 light years from Earth. If it has a mass 10,000 times that the Sun, the squae root of 10,000 is 100. Thus the neutral point between the Taurus molecular could and the Sun would be 1/101 of the 430 light year distance, or 4.257387 light years from Earth. If the Taurus molecular cloud has 10,000,000 times the mass of the Sun, the square root of 10,000,000 is 3,162.2776, so the neutral point between the Sun and the Taurus Molecular cloud would be 1/3,163.2776 of 430 light years, or about 0.135923 light years from Earth. One of the milky Way's satellite galaxies, the Sagittarius Dwarf Spheroidal Galaxy, has a mass of 400,000,000 solar masses. The square root of 400,000,000 is 20,000. So the neutral point between the Sun and that dwarf galaxy is 1/2,0001 of the 65,000 light years between them or 3.2498375 lightears from the Sun. The large Magellanic Cloud has a mass of 138,000,000,000 solar masses. The square root of that is 371,483.512. The neutral point between the Sun and the Large Magellanicloud is about 1/371,484.512 of the approximately 163,000 light years between them, or 0.1638 light years from the Sun. The Andromeda Galaxy has a mass of 1,500,000,000,000,000 solar masses. The square root of 1,500,000,000,000,000 is 1,224,744.871 . Thus the neutral point between the Sun and is 1/1,224,745.871 of the 2,500,000 light years between them, or 2.0412 light years. The supermassive black hole at the center of galaxy M87 has a mass of 6,500,000,000 solar masses. The square root of 6,500,000,000 is 80,622.57. Thus the neutral point between the Sun and that black hole is 1/80,623.57 of the approximately 53,500,000 light years between them, or 663.577 light years. The Galaxy M87 has a mass of at least 2,400,000,000,000 solar masses. The square root of 2,400,000,000,000 is 1,549,193.3. Thus the neutral point between the Sun and M87 is 1/1,549,194.3. of the approximately 53,500,000 light years between them, or 34.534 light years. The galaxy M87 is at the center of the Virgo Cluster of galaxies. The Virgo Cluster has a mass of 1,200,000,000,000,000 solar masses. The square root of 1,200,000,000,000,000 is 34,641,016.15. Thus the neutral point between the Sun and The Virgo Cluster is 1/34,641,017.15 of the 53,500,000 light years between them, or 1.5444 light years. Despite being about 21.4 times as far away as the Andomeda Galaxy, the Virgo Cluster has a stronger gravitational influence in the Milkly Way Galaxy, and because of its great distance there is little variation in the strength of that gravitational influence in different parts of the Milky Way. The Virgo Cluster is at the center of the Virgo Supercluster - maybe. There is a new theory that the Virgo supercluster doesn't exist and its parts are all part of an even greater group of galaxies called the Laniakea supercluster. The center of the Laniakea Supercluster is about 250 million light years away. Since I haven't found it's mass, Idon't know where its neutral point withthe Sun is, but it is possible that some distant superclouster has a neutral point closer to the Sun than the Virgo Cluster does.. The center of the Milky Way Galaxy is about 25,000 to 27,500 light years from the Sun. One object at the center is the supermassive black hole Sagittarius A* with a mass of about 3 to 4 million solar masses. Teh squae root of tht mass is about 1,732.05 to 2,000. Thus the neutral point between the Sun and Sagittarius A* is about 13.75 to15.877 light years from the Sun. Of course there are billions of stars in the central bulge of the galaxy. Take the central one billion (1,000,000,000) stellar masses of the galaxy. The square root of one billion is 31,622.7766, Thus the neutral point between the Sun and the central one billion solar masses of the galaxy is 1/31,623.7766, of the 27,500 light years between them, or 0.86959 light years. Take the central ten billion (10,000,000,000) stellar masses of the galaxy. The square root of ten billion is 100,000. Thus the neutral point between the Sun and the central one billion solar masses of the galaxy is 1/100,001, of the 27,500 light years between them, or 0.27499 light years. Take the central hundred billion (100,000,000,000 stellar masses of the galaxy. The square root of one hunded billion is 316,227.766. Thus the neutral point between the Sun and the central one hunred billion solar masses of the galaxy is 1/316,228.766. of the 27,500 light years between them, or 0.08696236 light years. The central 100 billion stellar masses of the galaxy is about 10,000 to 1,000,000,000 times the masses of clusters and gas clouds with masses of 100 to 10,000,000 solar rmasses. Thus the neutral points between such clustres and gas clouds and the s cene rof the galaxy, it they are about 27,500 light years from the center of the galaxy, should be betwoon 1/31,623.7766 and1/101 of htt distance, or about 877496.4387 0.86959 to 272.2772 light years from those objects. The total mass o the Milky Way Galaxy is about 890,000,000,000 to 1,540,000,000,000 solar masses. If half that mass or 445.000,000,000 to 770,000,000,000 solar masses is considered to have a center point 27.500 light years from Earth, and the square root of that mass range is between 667,080 to 877,496. Thus the neutral point between the Sun and and the center of half the Galxy's mass would be about 0.03133 to 0.041224 light years from the Sun. So the average star's gravity should be the strongest gravity only to a dstance of 0.2 light year or less, a volume of 0.0331 cubic light years or less. With about 100,000,000,000 to 400,000,000,000 stars in the galaxy, the totla volume where the grvitational pull of stars are greater than the gravitational pull of the galactic center should be only about 3,351,000,000 to 13,404,000,000 cubic light years. If the galactic disc is 1,000 light years thick and has a radius of 50,000 light years it wuld hve a total volume of about 7,853,980,000,000 cubic light years. Thus the total volume of space where the gravity of individual stars is greater than the gravity of the galactic center should be about 0.000426 to 0.001706 of the total volume of the galactc disc. So for most of a starship's interstellar voyage, where it its not passing close to a star, the local curving of space due to gravity should be dominated by the gravity of the center of the galaxy. And that gravity will get stronger or weaker very slowly as the starship travels closer to or farther from the galactic center. And there will also be smaller but significant gravitational forces caused by distant galaxies and galaxy clusters, which change even slower as the starship travels. So the local concentrations of matter within the space that a starship is travelling will not curve space as much as the gravity of very distant objects and space curvature will change only slowly and slightly as a starship travels distance of a few tens or hundreds of light years. [added Sept. 15, 2022] And In my post number 23 I describe the locations of various patches of "fast space" and "slow space" necessary to explain the distacne, speed, and time paraxes in Star Trek.
In my post number 22 I criticized the theory that the gravitational force and spce curvature in different regions of space could affect the speed of warp travel. I showed that in our part of the galaxy the gravity of distant objects such as the center of the galaxy and distant galaxies and galxy clusters dominates the gravitaitona forces in most of the space between stars, and such gravitational forces will change only slightly in interstellar voyages of tens or hundreds of light years. Thus it would be hard to find small regions of space except within a fraciton of a light year of a star, where there would "fast space" or "slow space" changedng the spwed of warp travel. And you can't find a long line of stars spearated by a half a light year anywhere near Earth. And the thought has occured to me that possibly some people might not appreciate how small the regions of "fast space" and "slow space" would have to be to solve the distance time, and speed problems in productions. So maybe I should give some examples of the scale of the patches of "fast space" and "slow space" necessary for explaining some of the disance, speed, and time problems in Star Trek, if those problems are explained by starships travelling faster in regions of space than in others. [Added 09-22-22] I found the equitorial coordinates and distances of various stars mentioned in Star Trek producitons.. And I used this site http://www.robertmartinayers.org/tools/coordinates.html to convert their equitorial coordinates into modern galactic coordinates. I think that galactic orordinates are more useful for science fictiton purposes. Galacticc coordinates use the equitorial plane of the galaxy as the equator. The modern Galactic coordinates use the direction of the center of the galaxy and the supermassive black hole Sagittarius A* as the zero of galactic longitude. You should picture a map of the galactic disc as seen from above, about 100,000 Light years (LY) in diameter, with the central point of the galaxy in the center. I think that most astronomers orient their galacitc maps with the dot representing the Sun and Earth directly below the center of the galaxy and about halfway out to the rim, and I guess that we might as well picture it that way. The real stars mentioned in are mostly tens, or hundreds, or up to a few thousand, light years from Earth. So the center of the galaxy shoudl be outside the borders of a map of real Star Trek stars, but a line can point from Earth to the center of the galaxy. The direction to the center of the galaxy is galacitic longitude 0, toward the top of the map. Galactic longitud eincreases in a counterclockswise direction, with longitude 90 directly left of the Sun, longitude 180 at the bottom, opposite to the glactic center, longitude 270 directly right of the Sun, and increasing until longitude 360 is the same as longitude 0, pointing to the galactic center. The coordinates and distances of stars can be used to calcuate their positions in 3 D space. [End of addition 09-22-22] In "The Cage"/"The Menagerie" the Enterprise was travelling from Rigel VII to the Vega Colony when it diverted to Talos IV 18 light years off its route. The posiiton of Rigel (Beta Orionis) in space is given by its astronomical coordinates, (its direction as seen from Earth) and its distance from Earth. In the equatorial coordinate system Rigel has Right Ascension 05 h, 14 m, 32.049 s, and Declination - 8 degrees, 12', 14.78". Using this program: http://www.robertmartinayers.org/tools/coordinates.html I convert those coordintates into galactic longitude of 209.2432 degrees and galactic lalitude of -25.2472 degrees, more useful for science fiction writers. Rigel is about 800 to 900 light years from Earth. Vega, Alpha Lyrae, is at Galctic longitude 67.4482 and latitude 19.2372 and a distanc eof 24.04 plus or minus 0.04 light years from Earth. Thus it must be slightly farther from Rigel than Earth is. According to this program https://www.wolframalpha.com/widgets/view.jsp?id=1ece06643e87f3c4d90813af5ee12223 Rigel is 863 light years from Sol (the Sun) and 883.6 light years from Vega. Since they were going to drop off wounded crewmembers at the Vega Colony, there should be a lot of "fast space" between Rigel and the Sun and Vega. But there should be some "slow space" between Rigel and the Sun to explain why they headed to Vega a little father away. And maybe a smaller patch of "Slow space" between Earth and Vega to explain why they weren't going to turn at Vega to go on to Earth. Altair is at galactic longitude 47.7441 and latitude - 8.9092 and is about 16.73 plus or minus 0.05 light years (LY) from the Sun. It is about 14.8 LY from Vega. Since the Enterprise is heading for Altair in "Amok Time" there probably isn't much "slow space" between, Altair, the Sun, Vega, and wherever Vulcan is. If Vulcan is at 40 Eridani as is often supposed, there should be mostly "fast space" in the 29.69 light years between Altair and Keid (40 Eridani). 40 Eridani is at galactic longitude 200.7488 and - 38.0476 latitude and is 26.333 plus or minus 0.006 LY from the Sun. In "Amok Time" Admiral Komack says: So there is probably mostly "fast space" between Altair and the Klingon Empire where ever it is. The next episode "Who Mourns for Adonais?" is set at Pollux (Beta Germinorum). Pollux is at galactic longitude 192.2293 and latitude 23.4063 and is 33.78 plus or minus 0.09 LY from Earth. Kirk says: Pollux is 33.78 LY from Earth, so there should be a lot of "slow space" between them. Pollux is also 29.77 LY from 40 Eridani, the possible star of Vulcan, 48.95 LY from Vega, 48.19 Ly from Altair, and 23.76 light years from Capella, so there should be a lot of "slow space" betwen Pollux and those stars too. In "Friday's Child" the Federation and the Klingons negotiate for mining rights at Capella IV, which thus should have mostly "fast" space between it and the Federation and the Klingon Empire. Capella is at galactic longitude 162.5885 and 4.5665 latiude and is 42.919 plus or minus LY from Earth and about 23.76 LY from Pollux. In "Where No Man Has Gone Before" the Enterprise is headed for the edge of the galaxy. The edge of the galaxy is of course in every direction from Earth, a distances between about 500 and 75,000 LY for the Galactic disc and several hundred thousand LY for the galactic halo. When they reach the edge of the galaxy: There must be a lot of really "fast space" between Aldebaran and the edge of the galaxy at least about 500 LY, and possilby many thousands, from Aldebaran, if Dr. PIper thinks Kirk hasn't met Dehner yet! Aldebaran (Alpha Taurii) is at galactic longitude 181.1291 and latitude -20.0595 and is 63.5 plus or minus 1.0 LY from the Sun. To be continued. is at galactic longitude and latitude and is plus or minus LY from the Sun. is at galactic longitude and latitude and is plus or minus LY from the Sun. is at galactic longitude and latitude and is plus or minus LY from the Sun. is at galactic longitude and latitude and is plus or minus LY from the Sun. is at galactic longitude and latitude and is plus or minus LY from the Sun. is at galactic longitude and latitude and is plus or minus LY from the Sun. is at galactic longitude and latitude and is plus or minus LY from the Sun.
In TOS the crew scans their flight path to evaluate gravimetric, space density, radiation, energy polarity as well as for space weather so in-universe there is some interaction with all those things that they are checking against. It might not make sense in real-world but real-world and Star Trek don't always align, IMHO. Adding in a later movie like "Generations" we also saw that the destruction of the Amargosa star altered gravitational forces that impacted starships traveling through the sector. Again, Star Trek may not be playing by real world rules given how fast gravity propagated in the movie.
Apparently, like radio waves, gravity waves travel faster than light in subspace. I have long theorized that the subspace dimension is the domain/source of gravity. YMMV
IIRC, "The Cage" + "The Menagerie" and "A Piece of the Action" showed that radio waves are still light-speed
Odd that the SS Columbia didn't have subspace radio 31 years prior to TOS. Maybe its subspace radio was damaged by the same event that destroyed the ship and only its emergency "distress" radio survived? We do know that the Federation did exist 100 years prior to TOS, but it didn't have subspace radio back then, so, that explains the old style conventional radio from the SS Horizon. Back then, it must have been faster to deliver your reports in person via FTL ships than radio...unless the explorer ships carried FTL postal probes for long range communication.
Yeah, it makes the most sense that their subspace radio was damaged resulting in using an old-fashioned lightspeed radio distress signal to send for help. Agreed. And it may have take decades before the "outer reaches of the galaxy" upgraded to subspace radios versus the core worlds so yeah, FTL postal probes and FTL ships probably did most of the long-range comms.
It worked well enough for a certain other sci-fi universe... https://reddwarf.fandom.com/wiki/Post_pod
In addition to space lanes…another alternative to explaining newer ships finding old colonies and vessels much farther out might be to introduce “warp staging” where you have nested ringships launch in “terrain.” Each old ship is a one way trip…but does leave behind ring segments that are like catapults. Early warp voyages were like Moonshots. I have argued that sublight ships can still be of use. Say you have a planet 10 ly out from where you are now….and you are hauling freight only. You launch 20 ships at half light-speed. After awhile, you have a network where a ship reaches port every six months…though the travel time is 20 years each way…time dilation not being much of a factor. But once you figure out what each planet needs—you send the same thing. Eventually, you expect a ship every six months that made a 10 ly trip effectively FTL. Biolation sleep for biologicals Now, when a true warp ship like the TOS Enterprise shows up…it’s a big deal. Frontier feeling. Your grandpappy did a one way moonshot…frontier life is all you know…there is this fool Mudd selling crap—and ZIP! Where did that..that STARSHIP come from?
So you believe that subspace radio uses ordinary radio waves sent through subspace? And presumably faster than light space radar would send ordinary radio waves through subspace, and phaser beams would use ordinary electromagnetic radiation sent thorugh subspace in order to travel faster than light. But as I remember, there was a scene in one of the over 150 TNG episodes where someone, possibly LaForge, spoke of the electromagnetic and subspace spectrums. This implies that subspace radiation is separate from electromagnetic radiation and isn't merely electromagnetic radiation sent through subspace. I was quite surprised by that scene. The USS Horizon didn't have subspace radio about 100 years before TOS. In "A Piece of the Action": The Romulan War was fought about 100 years before TOS. In Balance of Terror": So the Romulan war should have happened after the voyage of the Horizon, sometime after subspace radio was invented. But the Horizon was a Federation ship, before the Romulan War, which seems to have been fought by Earth and allies and not by the Federation. And in Star Trek: Enterprise Captain Archer often has subspace radio communications with Earth. The Romulan War seems to be fought after .Star Trek: Enterprise, except for the last episode, the much derided "These Are The Voyages" which happens after the Romulan war and during the foundatin of the Federation. So obviously a complicated explanation would be needed to make TOS and Star Trek: Enterprise happen in the same alternate universe, making it seem likely they do happen in different alternate universes as many fans claim.
Stardates may be late linked to pulsars to know where you are…each universe’s pulsar a little different? Shades of Niven’s “All the Myriad Ways” style. You can’t go home quite…but get close. I could see Q going over “historical recordings” explaining hiccups to the crew of the U.S.S Relativity…
Other than Speed of Plot, Some series did atleast try for the most part, to keep with the speed of warp speed, Enterprise was going roughly 1 ly per day, and 3 months out they were 90-100 ly away from Earth, so more or less accurate, atleast they tried for the first season, by season 4 it was very much speed of plot. as for a real world explanation? I'd say a combination of alot of factors. Space weather, going through varying density of interstellar medium, warp may be affected by larger gravitational bodies like if a black hole was near by. Might have charted "Short Cuts" like subspace corridors, stable short range wormholes. in all, fun to theorize.
Fascinating read. A quick thought without on-screen evidence: Could the factor that causes variation in warp sped be impulse speed? Like warp is a factor (how much you bend space-time) on your actual impulse speed. So if different ships have different impulse capabilities and use different impulse settings at different occasions then the same warp speed would mean different real speed. In addition, brining impulse in would also require us to consider the time required to accelerate - and decelerate!. Nearer destinations could be slower to reach than fares ones, because you can‘t accelerate to full speed before having to decelerate?
Nice to hear a fresher theory on Warp Speed. Possible on-screen support: From WNMHGB: SPOCK: Decoding memory banks. I'll try to interpolate. The Valiant had encountered a magnetic space storm and was being swept in this direction. KIRK: The old impulse engines weren't strong enough.From Balance of Terror: KIRK: Yes, well gentlemen, the question still remains. Can we engage them with a reasonable possibility of victory? SCOTT: No question. Their power is simple impulse. KIRK: Meaning we can outrun them?The two entries imply that the Enterprise has a more advanced form of impulse. The Valiant had old impulse. The Romulan has simple impulse. It is clear that the Enterprise is much faster/powerful than both. Using your first part of your theory, maybe the Romulans do have warp drive boosted with simple impulse while the Enterprise has warp drive plus advanced impulse.
It's an interesting theory but Distance to destination does not appear to affect the real speed (how much room to accelerate and decelerate) as we have: - "Bread and Circuses" showcasing a short trip covering 1/16th of a parsec that occured in less than a minute (~300,000c) - "By Any Other Name" where a super far trip covering millions of light years take hundreds of years (~9,000c) If distance was a factor then the average speed in "By Any Other Name" should be much higher than "Bread and Circuses" but it isn't. And impulse doesn't appear to be automatically contributing to the operation of warp but it can be additive to it. "The Ultimate Computer" SPOCK: Hit in engineering section. Possible damage to her impulse engines. She's still maneuverable on warp drive."The Corbomite Maneuver" KIRK: Maximum acceleration when I give the word. SULU: Yes, sir. KIRK: Engage. SULU: It's a strain, Captain. Engines are overloading. KIRK: More power. SPOCK: We're superheating. Intermix temperature, seven thousand four hundred degrees. Seven five, seven six, eight thousand degrees. KIRK: Shear away, Mister Bailey. SPOCK: Two thousand degrees above maximum. Eight four, eight five, eight six. She'll blow soon! KIRK: Now, Mister Sulu. Impulse power too.
Yes, I was trying to think of a reference for running warp drive without impulse engines, but even then, this event is not 100% conclusive since her impulse engines were only "possible damage". This event I did think of, but disregarded it since it was a static thug-of-war and not a speed event, but I do see that the ship is first pulling only with warp drive, then adds in impulse power at the end implying that warp drive doesn't need impulse power (but it doesn't say impulse engines) to operate. Does the ship normally operate the impulse engines using warp power while also under warp engine drive is the question? One good reference dispels this theory, "Obsession" SCOTT: Captain, while we're waiting I've taken the liberty of cleaning the radioactive disposal vent on number two impulse engine, but we'll be ready to leave orbit in under half an hour. ... SCOTT: Captain, we can't maintain warp eight speed much longer. Pressures are approaching the critical point. KIRK: Range, Mister Chekov? CHEKOV [OC]: Point zero four light years ahead. Our phasers won't reach it, sir. SPOCK: We are barely closing in on it, Captain. We could be pursuing it for days. KIRK: If necessary. Do what you can to increase our speed, Scott. SCOTT: Aye, sir. KIRK: Extreme magnification, Mister Chekov. CHEKOV: Magnification twelve. There, sir. Got it. KIRK: Spock, how do you read that? SPOCK: Conflicting data, Captain. It seems to be in a borderline state between matter and energy. Elements of both. It could possibly use gravitational fields for propulsion. KIRK: And you don't find that sophisticated, Mister Spock? SPOCK: Extremely efficient, Captain. Whether that indicates intelligence is another matter. CHEKOV: Open hatch on impulse engine number two. Mister Scott was doing an AID clean-up on it. KIRK: We won't be using the impulse engines. Turn the alarm off. The Enterprise is at very high warp speed and Kirk said they won't be using the impulse engines, so, theory busted.
@Henoch - we do have this line from "Elaan of Troyius"... "Elaan of Troyius" CREWMAN: We're only running on impulse engines now. Ordinarily, we use the warp engines exclusively. I think I've settled on that thrusters are the base propulsion and impulse and warp are the multipliers. Impulse engines generate a magic field and the thrusters accelerate/decelerate. Warp engines generate a magic field and the thrusters accelerate/decelerate. FWIW, I think SNW is combining the idea that the thrusters and impulse are one system as "impulse thrusters" and it is what accelerates/decelerates when warp is engaged.