When I look up the phrase 無駄足だった, I see it translated as "It was a Wild goose chase." I found this bizarre, since it seems like it would mean "It was a useless foot/leg." is this some sort of figure of speech that means the same or something similar to "wild goose chase" or am I missing something? Thanks for any help.
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1「せっかくそこまで足を運んだのに、そのかいがないこと。〈=無駄だった〉」 – blutorange Dec 01 '14 at 20:32
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I believe [無駄足]{むだあし} is derived from [無駄足]{むだあし}を[運]{はこ}ぶ ("move one's feet in vain"), which is one of a series of counterintuitive idioms Japanese vocabulary has.
- [小腹]{こばら}が[減]{へ}る "little stomach get empty"
actually describing "be a little hungry" (cf. [腹]{はら}が[減]{へ}る "be hungry") - [大]{おお}ぼらを[吹]{ふ}く "blow on a big conch"
actually, "blow on a conch loudly" or "tell a tall story" (cf. ほらを[吹]{ふ}く "talk big")
eventually [大]{おお}ぼら itself stands for "tall story". - [横車]{よこぐるま}を[押]{お}す "push a side cart"
actually, "push cart from the side" or "ram through"
eventually [横車]{よこぐるま}, "unreasonable demand". - [後ろ]{うしろ}[髪]{がみ}を[引]{ひ}かれる "be pulled by the rear hair"
actually, "be pulled by the hair from behind" or "too sorry to leave" - [無駄骨]{むだぼね}を[折]{お}る "break a useless bone"
actually, "break a bone in vain" or "make vain efforts" (cf. [骨]{ほね}を[折]{お}る "make efforts")
eventually [無駄骨]{むだぼね}, "vain efforts".

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2Or 無駄**に**足を運ぶ, to make every word's meaning traceable. "2 moras + 2 moras" way of contraction is very common in Japanese, as you know, and some of them date back to pre-modern era Japanese. e.g. 藪蛇 from 藪をつついて蛇を出す, 泥縄 from 泥棒に入られて縄をなう, 眉唾 from 眉に唾をつけたくなる, etc. I think 無駄足 exactly is on of these words. – isayamag Dec 02 '14 at 04:08