In many japanese sci fi series (Yamato, Macross, etc.) when a spaceship is going to take off they say something similar in romaji to "hashin!" . When I look for how to say take off in japanese I find words like 飛び立つ (Tobitatsu ), 踏み切る (Fumikiru ) , but nothing similar to "hashin". How does exactly this word sounds (romaji/hiragana) and how do you write it with kanjis? You can listen it here:
It's 発進｛はっしん｝ that means indeed "take off / launch / departure".
To break it down, you can see how this word is composed by the kanji 発 (that means departure) which you can indeed find in many related words, and the kanji 進 that means to advance, progress.