One method that gives good proportion for a "mansard" is what I call "inverted layout." ...with the lower slope at two-to-one (rise-to-run) and the upper slope is its inverse: one-to-two.
This is what I was referring to... it's basically half an octagon and does very much resemble a half circle as Chris mentioned. Whatever you want to call this roof style, this "inverted" method gives nice proportions, I think...
