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I used to go NOWHERE when I just used my legs but shoulder injuries are the main one that swimmers have to deal with so I'd hate to rely on it too much. I, also, agree that using the kickboard puts you in a totally unnatural position so I don't ever do that. I do, however, swim on my back and have developed a pretty good kick. I could swim laps just about forever this way and can keep up with the slower swimmers just with my legs.
Gotta go but, if this doesn't make sense, let me know and I'll explain.
(I smell a SWIMMING area:p)