Airfoil Profiles for Minimum Pressure Drag at Supersonic Velocities - Application of Shock-Expansion Theory, Including Consideration on Hypersonic Range
Abstract
A theoretical investigation is made of airfoil profiles at supersonic velocities to determine the shapes having minimum pressure drag at zero lift for various given auxiliary conditions. Shock-expansion theory is employed, thereby extending the applicability of the results through the hypersonic range. Curves are presented for Mach numbers of 1.5, 2, 3, 4, 6, 8, and infinity which enable the shape and the drag of an optimum profile to be determined readily if the base pressure is known from experiments. Examples are presented of optimum profiles determined with the aid of experimental base pressure data. Variations in profile shape are investigated to provide information on the degree to which deviations in shape from the optimum can be made without resulting in a significant drag increase. A comparison of optimum profiles determined by the shock-expansion method of this report with corresponding profiles determined by the linearized-theory method of a previous report shows only small differences in shape at Mach numbers up to infinity even though the linearized theory at high supersonic Mach numbers breaks down completely insofar as the drag of the profile is concerned. The experimentally observed dependence of base pressure on trailing-edge thickness is found to have a significant effect on the shape and drag of optimum profiles of small thickness ratio. Curves are presented which show that for thin airfoils the use of a trailing-edge thickness considerably greater than the theoretical optimum can result in an excessive drag penalty at moderate supersonic Mach numbers, though not at hypersonic Mach numbers.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 17, 1952
- Accession Number
- ADA377157
Entities
People
- Dean R. Chapman
Organizations
- National Aeronautics and Space Administration