  We consider Newton's problem of minimal resistance, in particular we address
the problem arising in the limit if the height goes to infinity. We establish
existence of solutions and lack radial symmetry of solutions. Moreover, we show
that certain conical parts contained in the boundary of a convex body inhibit
the optimality in the classical Newton's problem with finite height. This
result is applied to certain bodies considered in the literature, which are
conjectured to be optimal for the classical Newton's problem, and we show that
they are not.
