Accession Number : AD0277290

Title :   OPTIMUM SLENDER BODIES OF REVOLUTION IN NEWTONIAN FLOW

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH

Personal Author(s) : MIELE,ANGELO

Report Date : APR 1962

Pagination or Media Count : 1

Abstract : The problem of minimizing the drag of a slender body of revolution in Newtonian flow at zero angle of attack is considered. A generalized closed form expression is obtained for the optimum shape which is valid regardless of the conditions imposed on the diameter, length, ettedAREA, AND VOLUME. This expression contains as particular cases those valid when any two of these four quantities are fixed while the remaining are free. A 3/4-power law, which previous authors had recognized to be a good approximation to the exact variational solution in Newtonian flow, is found to be a rigorous solution of the Euler-Lagrange equations if the slender body approximation is used. For the cases considered, analytical expressions are derived for the thickness ratio and the drag coefficient. Also, to verify the minimal properties of the solutions obtained, the optimum shapes are compared. This comparison can be reduced to the bare essenti ls if an appropriate quality coefficient is introduced for the drag. Only in the case where the diameter and the length are given is the quality coefficient proportional to the drag coefficient. Otherwise, it generally involves the product of powers of three dimensionless integrals associated with the drag, the wetted area, and the volume. (Author)

Descriptors :   *BODIES OF REVOLUTION, AERODYNAMIC CHARACTERISTICS, DIFFERENTIAL EQUATIONS, DRAG, HYPERSONIC CHARACTERISTICS, INTEGRAL EQUATIONS, MATHEMATICAL ANALYSIS

Distribution Statement : APPROVED FOR PUBLIC RELEASE