  We determine the parametric hull of a given volume which minimizes the total
water resistance for a given speed of the ship. The total resistance is the sum
of Michell's wave resistance and of the viscous resistance, approximated by
assuming a constant viscous drag coefficient. We prove that the optimized hull
exists, is unique, symmetric, smooth and that it depends continuously on the
speed. Numerical simulations show the efficiency of the approach, and complete
the theoretical results.
