Symmetry unbreaking in the shapes of perfect projectiles

We study the shapes of perfect projectiles: Bodies of prescribed volume that are designed to suffer minimum fluid drag in steady flight. Perfect projectiles have a surprising property: Although the flow of fluid around the body of the projectile is fore-aft asymmetric at moderate flow speeds, the shape of the body that minimizes drag is nonetheless highly symmetrical. We show that perfect projectiles are weakly asymmetric and that their asymmetry grows with the cube of the projectile size for sufficiently small projectiles. The persistence of apparent fore-aft symmetry is speculated to be a signature of the linearity and reciprocity of the drag-determining features of the flow around the projectile. (C) 2008 American Institute of Physics.