There are cresent kicks in some Shorin-ryu Kushanku and in wado-ryu Seisan. What is the purpose of these? I have found, even performing the cresent kicks that, they are akward, slow, lack power even at lower heights, and to quote Geoff Thompson, from his book "Real Kicking" "Hightly decorative, highly impractical (sorry); I have to say that I'm of a similar mindset" I often see silly applications that result in using cresent kicks to knock weapons out of the attackers hand, but I've pressure tested this and usually it ends up with you getting stabbed several times, in the leg, but I could be missing something. I think on some fundamental level it could represent a sweep and it has been stylistically altered and over time has became a cresent kick. They seem like they are outliers in within the kata. Most kicks are delivered low, are simple, front kick, side kick, and importantly, when the oppenent is already in a vunerable position, at least this is how I interpret kicking within the context of self-defence and the kata. Even nidan geri is more effective than the cresent kick, I've used it in the street, like a right idiot I must add, and it put the person down. He deserved it yadda yadda. Now, just because I personally find this kick useless as a chocolate fire-guard doesn't mean that it is. I could be very wrong, or just really terrible at this kick. I could be missing some fundamental aspect of it, I don't think that I am, but I acknowledge that I could be wrong.