Slender shapes offering minimum drag in free-molecular flow

Analytical expressions are obtained for the optimum shapes which minimise the drag of a slender axisymmetric body in free-molecular flow, provided the drag expression is simplified using the slenderness assumption. The problem is formulated as one of Mayer type in the calculus of variations and solved by using the Buler-Lagrange equations together with the transversality condition. The shapes derived are optimum subject to constraints on thickness, length, wetted area and volume. In the particular cases solved any two of these four quantities are fixed while the remaining two are free. The expression for the shape of the body when thickness is free is obtained in closed form.