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Base drag effects on maximum lift-to-drag ratio airfoils at moderate supersonic speeds

Research paper by Robert E. Pritchard

Indexed on: 01 Feb '69Published on: 01 Feb '69Published in: Journal of Optimization Theory and Applications



Abstract

Maximum lift-to-drag ratio airfoils at moderate supersonic speeds are determined using Ackeret's linear theory for the forebody pressure coefficient and Chapman's experimental results for the base pressure coefficient. Two cases are investigated for both laminar flow and turbulent flow: (i) given length and thickness and (ii) given length and enclosed area.For case (i), it is shown that the maximum lift-to-drag ratio airfoil is identical with the minimum drag airfoil. Furthermore, for turbulent flow and given Mach number and Reynolds number, two critical values of the thickness ratio exist, τ1 and τ2. For τ≤τ1, the optimum airfoil is a diamond shape with a closed trailing edge and exhibits maximum thickness at midchord; for τ1≤τ≤τ2, the optimum airfoil is a diamond shape with a blunt trailing edge and exhibits maximum thickness between midchord and the trailing edge; finally, for τ≥τ2, the optimum airfoil is a wedge and exhibits maximum thickness at the trailing edge.For case (ii), it is shown that the maximum lift-to-drag ratio is identical with the minimum drag airfoil. Furthermore, for turbulent flow and given Mach number and Reynolds number, a critical value (A/l2)1 of the enclosed area ratio exists. ForA/l2≤(A/l2)1, the optimum airfoil is biconvex with a closed trailing edge and exhibits maximum thickness at midchord; forA/l2≥(A/l2)1, the optimum airfoil is biconvex with a blunt trailing edge and exhibits maximum thickness between midchord and the trailing edge.