Many of us remember having to do time, distance and speed math problems in high school. How long will it take a vehicle at speed X to travel a distance Y, for example. Or if train A heads east as at speed C, and train B heads west at speed D, and if they are E miles apart when they both leave, when will the two trains pass each other? And no doubt high school kids varied greatly in how well they did in such questions and how much they liked or hated that type of math problem. And I kind of get the impression that many writers of Star Trek episodes, beginning with TOs and continuing with other series and movies, really hated those types of math problems and never bothered calculating the time it would take to travel from Earth to the star visited in the episode, if it was a real star, or to calculate how long it would take a starship to travel the distance mentioned in the episode. And I get the impression that few members of the production staff ever bothered to calculate whether the writer of an episode got the time, distance, and speed correct in their script and correct any errors that they found. And so, beginning with TOS, and continuing with other Star Trek productions, sometimes everything add ups and starships make voyages with travel times consistent with their stated speeds and either the TOS warp scale or the TNG warp scale. And sometimes a starship visits a star that it should not possibly be able to reach, and sometimes a star closer to Earth than many which have been visited is considered to be on the frontier of exploration. And some times a starship travels a distance tens or hundreds of times faster than it should be able to at the official warp scale for the era. In TOS the extreme example of a ship traveling much faster than the official warp scale is in "That which survives", where the Enterprise is thrown far from the planet Kirk has just beamed down to: Spock decides to return to the planet where Kirk's landing party is: Later: According to the official TOS warp formula found in writer's guides and The Making of Star Trek, warp factor 8.4 equals the speed of light multiplied by 8.4 cubed. Since 8.4 cubed is 592.704, warp 8.4 is 592.704 times the speed of light. One of the few things which scientific authorities have done to make things easier for science fiction writers is to define a light year as the distance which light (in a vacuum) travels in one Julian year of 365.25 days (instead of a Gregorian calendar year of 365.2425 days). A light day is the distance light travels in one day, a light hour is the distance light travels in one hour. Since there are 365.25 days in a year, and 24 hours in a day, there are exactly 8,766 light hours in a light year. So a distance of 990.7 light years equals 8,684,476.2 light hours. Traveling 8,684,476.2 light hours in 11.337 hours requires a speed of 766,029.47 times the speed of light. But the official formula makes warp factor 8.4 equal to 592.704 times the speed of light. So apparently Lt. Rahda calculated that the Enterprise would reach its destination 1,292.4317 times as soon as it would if it traveled the entire distance at the official speed of warp 8.4. And various fans have calculated that the Enterprise seems to exceed its official warp speed by about 1,292.4317 times in "That Which Survives" and publicized that in various publications since at least as early as the late 1970s forty years ago. So forget the number 47. 1,292.4317 should be the number that Star Trek fans should be obsessed with, and variations on 1,291.4317 should be used as a stardate, serial number on a part, "phone number" equivalent, year in the calendar of an alien planet, or other number, in various fan fictions, authorized novels, and official episodes and movies to show that the writers are aware of various problems in Star Trek. One common theory to explain how starships sometimes travel much farther and faster than they should according to the official warp speed formulas is that there is a factor which multiplies warp speed to many times greater than the speeds calculated by the official warp speed formula. But if that is the case, why wasn't the official warp speed formula changed by scientific bodies and/or Starfleet to reflect the actual warp speeds. If, for example, warp factor four always equals 200 times the speed of slight, why wasn't the official warp formula changed to make warp factor four be 200 times the speed of light? And one answer is possibly there are regions of "fast space" and "slow space" where warp speeds are multiplied by different amounts, so that the same warp factor will equal different speeds in different regions of space. For example, in one region of space warp factor four might equal 18,234.493 times the speed of light, in another 382.108 times the speed of light, in another 836.465 times the speed of light, etc.,etc., etc. If explored space includes many different regions where warp factors are multiplied by different amounts, the official warp scale might use the basic speeds which a warp factor would produce if there wasn't any multiplication factor involved. And as more and more Star Trek productions are produced, a three dimensional map of our local region of the galaxy could include more and more volumes of space labeled with how much they seem to multiply warp speeds according to the evidence of various episodes. And it seems to me quite possible that some regions of space might need to be much faster according to some episodes than they have to be according to other episodes. Thus there may be contradictions between various Star Trek productions in how "fast" or "slow" various regions of space should be. And another problem with that theory is that sometimes a starship travels a distance in a time that is reasonably consistent with the warp speed scale in use in that era. According to the theory of "fast space" and "slow space" that would require some regions of space to not multiply warp speeds at all. Voyages that take days or weeks in other regions of space might take years, decades, or centuries in that region of space. But what if in another Star Trek production a starship travels though that same region of space many times faster than its official warp speed? In my next post I will give an example of how a voyage at speeds close to the official warp scale messes up the theory of "fast" and "slow" regions of space where warp speeds are multiplied by different amounts.