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As mentioned, the nature of what a Warp Drive does is a scientific possibility and considered a possible near future tech with NASA working on a similar in principle Warp Drive (in Star Trek, the W...
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#2: Initial revision
As mentioned, the nature of what a Warp Drive does is a scientific possibility and considered a possible near future tech with NASA working on a similar in principle Warp Drive (in Star Trek, the Warp Drive creates a spacial distortion that makes space contract as the ship's bow moves towards it and expand as it moves astern. Thus, you do not violate FTL because you are really making the distance shorter, rather than going faster.). Impulse Drive may have a similar emerging tech inspiration behind it, but I'm not as familiar with it and Star Trek's use of it as a speed is a hard limit demarcation and avoids a hard science number so the ship moves at plot speed (i.e. Impulse is the fastest a ship can go without using warp, while the captain may use a fraction of impulse for a slower speed ("One Quarter Impulse" is a maneuverable in narrow passage speed, while Impulse seems to be able to cover the space of a solar system with reasonable time). It's likely that the "impulse drive" is an engine that can be adjusted for speed, and correlates to "Full Steam Ahead" in naval parlance. "Full Steam" is not a speed, but rather "the fastest the engines can move us" (in the U.S. Navy, the joke speed of "Full Bendix" to mean faster then "Full Steam." The lever on the bridge that functions (That round one that has a bar that surrounds the desired setting) as the method to adjust speed is made by a company called "Bendix", which does or did at one point stamp the company logo above the max setting. The joke being that the max speed is so desired that the helmsman adjusting the control broke past the "Full" setting and the highlighter is over Bendix logo... In some cases, the vehicle can actually go faster, if regulators are disabled. The regulators are there to prevent wear and tear, but if the choice is moving this ship at a speed that will break the engines faster or the ship is destroyed, it can be better to save the ship and put into safe port with an engine that needs to be replaced sooner than expected). Warp is used by other franchises and is described as functioning similar to Star Trek. The video game Stellaris used to have Warp as one of three possible FTL systems for ships (the other two were a series of Hyper-Lanes - extradimensional tunnels that connected each star to fixed stars, sort of like deep space 9's wormhole with a dash of Contacts ancient network or connections, implied to be built by something, but everyone who uses it only knows how to get to them and not how to make more routes... or who made them now - and Worm Hole generators - a "gate" station outside the ship could create an artificial wormhole to any star system in range... if the gate goes, the ships might be stranded if there is no other gate in range. A fourth system called "Jump Drives" could be researched later in the game, and basically acted as a teleportation system. Recent updates changed FTL so everyone starts with Warp Drive but alternatives exist and can be researched). The Stellaris FTL systems generally lined up with commonly used FTL drives that exist in scifi as it homaged a lot of the space opera genre tropes. Warp was Star Trek, Hyper-Lane was best aligned with Star Wars and Contact, Worm Hole Functioned the gates like Babylon Five, (though you didn't need an end gate), and Jump Drive functioned like Battlestar Galactica's FTL, with some in lore draw backs related to "Warp" from Warhammer 40,000 (each jump could trigger an endgame event featuring extra-dimensional aliens that emerged from the Jump Drive's tearing of realities.). The changes added two new systems with Natural Wormholes and "Jump Gates" with the former being a stable wormhole between two stars on the map and the latter being more like Babylon Five in that you needed an end point, but the end point was not fixed... if a gate existed in a system, it could send and receive from other systems friendly to you. Again, fans explained the FTL system lore in terms of other scifi fictional comparisons and even the developers described the systems by showing where the got inspiration. Because they were general descriptions and the actual working mechanics of FTL drives was never discussed, it wasn't an issue. "Warp" like Star Trek is fine. But your Warp Engines cannot use dilithium crystals to regulate the matter/anti-matter reaction that powered the drive. Your engine design is on you. Your scientific way around FTL is not. And you don't have to turn into a newt to go Warp 10 (though you should probably change your speed ticks in another way).