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well, i am a big 'fan' of middle age history and all i know is this:
the longbow first appeared with the pagans (saxons, angles, vikings,e.t.c.) as a simple solution to the problem that a small selfbow (crafted from a peice of wood) could not draw back to the chin, and was made of ash, elm, or yew. when the normans conqured england, william the conquerer demanded the entire saxon army give him their weapons, but not their bws, as archers posed little threat during the invasion of england. this made the longbow the simbol of free english. it was realised that yew was by far and away the best wood of them all, because it had a band of stretchy sapwood on the outside (back of the bow) and heartwood on the inside (belly of the bow) but as and elm were still used as they were more common (over here in britain ash wood is dead easy to find) and they were incredibly powerful.
your bow will almost certainly by asmetric because symmetric longbows are cut from branches about the thickness of logs, and are about 90-180 lbs draw weight.
it should be the length of your armspan, not your height. your bow should be cut from the wood like so the back is sapwood and the belly is heartwood
and being short is not important, a longbow is tailor made to fit the persons size. keep in mind they quite often look ridiculously thin but don't worry they are meant to be.
remember, a longbow is long in proportion to your size, not to other bows. tools i would recommend are:
(well, that's what i use and it works very well.)
oh btw in england is illegal to cut yew trees, dating back to the 14th century when longbows were very important.