ON SLENDER BODIES OF MINIMUM DRAG IN NEWTONIAN FLOW
Abstract
In recent papers the problem of minimizing the pressure drag of slender bodies in Newtonian flow was considered in general and, then, solved for those particular cases in which, of the four geometric properties being considered (thickness, length, enclosed area, and moment of inertia of the contour for two-dimensional shapes and diameter, length, wetted area, and volume for axisymmetric shapes), two are prescribed and the remaining two are free. The analysis is here extended to the class of problems in which three quantities are prescribed and the remaining is free. After the variational problem is reformulated in order to account for the fact that the pressure coefficient must be nonnegative every where, special attention is devoted to those particular cases in which two of the three prescribed quantities are the thickness and the length. In each case, a one-parameter family of extremal solutions is obtained, the parameter being related to the three prescribed quantities. Furthermore, each of the extremal solutions contains three classes of body shapes: an infinitely thin plate or a spike followed by a regular shape, a regular shape only, and a regular shape followed by a constant thickness contour or a cylinder. In all of the cases considered, analytical expressions are obtained for the geometry of the optimum shapes and the associated drag coefficients.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1963
- Accession Number
- AD0403016
Entities
People
- David G. Hull
Organizations
- Boeing