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22nd century warp cores were designed as oblong cylinders connected by pylon conduits directly into the warp nacelles. (Star Trek: Enterprise) In the 23rd century, the warp core was not situated in the main engineering. The main warp reaction occurred in a dilithium crystal converter assembly which consisted of two flattened rounded nodules situated directly in front of the warp plasma conduits to the warp engines, which were behind a large metal grate. (Star Trek: The Original Series; ENT: "In a Mirror, Darkly, Part II") By 2270, most Federation warp cores were redesigned to consist of a large warp core unit in the secondary hull with matter and antimatter channeling into the core through vertical conduits, with the resulting energy directed to the nacelles through a horizontal conduit leading out from the rear of the core. (Star Trek: The Motion Picture)
Of the original Constitution-class warp core, only the dilithium crystal converter assembly and the warp engine plasma conduits were ever seen in Star Trek: The Original Series. The first season had a dilithium crystal energizer room only seen in "The Alternative factor". It Is likely the predecessor to the dilithium crystal converter assembly from seasons two and three. The tech evolved over the course of the series. The engine room was modified after season one to include the dilithium crystal converter. They are two round nodules with the crystal chamber in between. The warp plasma conduits were 8 tall glowing red tubes behind a safety grate at the back of the main engine room throughout the series. When Doug Drexler was called to design the detailed schematics of a Constitution-class starship, he included a vertical core from the dilithium crystal assembly intersecting a horizontal warp core that runs two decks below main engineering (X) The schematic made a prominent appearance on screen in ENT: "In a Mirror, Darkly, Part II". Star Trek: The Animated Series also featured a vertical component of the warp core, that extended from the dilithium crystal assembly.
As evidenced by the second draft script of ENT: "Broken Bow", the 22nd century warp core aboard an NX-class starship was originally designed to be vertical and extend through a deck, with a top which was high. A series of levers was at the bottom of the towering engine, and "pulsing pillar[s] of plasma" occasionally rose up through the warp core. Drawing inspiration from the engine of the Constitution-class USS Enterprise in Star Trek: The Motion Picture and motivated by wanting to clearly show the NX-class was a relatively early ship, Production Designer Herman Zimmerman suggested that the NX-class engine be of a horizontal configuration, an idea that was quickly approved by series co-creators and Executive Producers Rick Berman and Brannon Braga. (Star Trek: Communicator issue 135, p. 64; Star Trek: The Magazine Volume 2, Issue 7, p. 52) Changing the engine's orientation made the warp core look obviously different from its equivalents in later Star Trek chronology: warp cores that had typically been vertically positioned. (Star Trek: The Magazine Volume 2, Issue 7, p. 52) The "Broken Bow" script was changed to reflect the alteration and, in the revised final draft of the script, the warp core was described as extending "horizontally across the room."  Zimmerman noted, "We talked of a honeycomb design with multiple push and pull rods, accessible through openable doors." (Broken Bow, paperback ed., p. 269) However, the design of the warp core fell into place very quickly. Additionally, because it was to be represented as an engine which required a great deal of maintenance, the warp core was designed to incorporate enough controls and access panels that the crew could busy themselves with working on it. (Star Trek: The Magazine Volume 2, Issue 7, p. 52) Concerning how the warp core turned out, Zimmerman remarked, "It doesn't look like you can't understand it or that it wouldn't break down if all the components weren't working perfectly. So, it's a more realistic propulsion system than the fantastic propulsion system." (Broken Bow, paperback ed., p. 269)