CORRECTION... I no longer believe in my "successful model." MacKay also published a model http://arxiv.org/abs/0910.5834 based on pelvis bone "sag distance" relative to pelvic breadth being equal for all size people, but that makes no sense to me. Relative sag seems irrelevant evolutionarily. Breaking your pelvis does matter. It is about strength, not relative sag distance. So... now I'm back to not believing in any model including any of my own. So then, examining MacKay's model, he actually models the human body as height=z > breadth=x > depth (front to back) = y. The pelvis is assumed to have (up to constant factors) breadth (hip to hip) x, height z, and thickness (front to back) y. The load on the pelvis as a torque-moment (standing stationary) then is BodyWeight*x, which is x*y*z*x. Everything will be up to constant factors. The ability of the pelvis to withstand that load without cracking is proportional to I/z where I=area moment of inertia=y*z^3. Hence we'd want x*y*z*x and y*z*z to be proportional, i.e. z = x^2. If instead of standing stationary we sprint using my sprinting model, the max load on the pelvis as a torque-moment then is BodyWeight*x*sqrt(z), which is y*x^2*z^(3/2). The ability of the pelvis to withstand that load without cracking again is proportional to y*z^2. Hence we'd want these to be proportional, i.e. z^(1/2) = x^2 or z = x^4. Meanwhile MacKay finds z = x^1.5 using his relative sag criterion which I claim makes no evolutionary sense. MacKay then offers arguments about bipedal balance and heat conservation that perhaps y and z should be proportional. It has in fact been argued one of the great evolutionary wins of humans is that they can SHED heat well, which is why we are not covered with fur, hence can outrun prey without dying of heat stroke ("persistence hunting" via long distance running). Humans are actually one of the best animals at long distance running. This is exactly the opposite of MacKay's heat argument and I suppose would tell us that y should be proportional to x not z? Be nicer if we had data on that. With y propto z we then would find: MacKay fixed-relative-sag Model: weight = height^(8/3) * Stationary standing break-strength model: weight = height^(5/2) * Sprint break-strength model: weight = height^(9/4) With y propto x instead, we then would find: MacKay fixed-relative-sag Model: weight = height^(7/3) * Stationary standing break-strength model: weight = height^2 Sprint break-strength model: weight = height^(3/2) assuming I have not made more mistakes. I starred(*) the ones seeming not absurdly in disagreement with real data. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)