Shockless airfoils with thicknesses of 20.6 and 20.7 percent chord analytically designed for a Mach number of 0.68 and a lift coefficient of 0.40

A 20.8 percent-thick airfoil shape was designed to have shockless inviscid flow at a Mach number of 0.68 and a lift coefficient of 0.40. In order to determine the actual airfoils which would yield this same shockless flow when viscous effects are included, boundary layer displacement thicknesses were subtracted from the inviscid shape for Reynolds numbers of 100 and 35 million. This process yielded airfoils with thicknesses of 20.7 and 20.6 percent, respectively. Subtraction of boundary layer displacement thicknesses for Reynolds numbers below 35 million yielded nonphysical airfoils, that is airfoils with negative thicknesses near tHe trailing edge. The pitching moment about the quarter-chord point at the design condition was -0.082 for the inviscid shape and, consequently, for both airfoils. Off-design calculations for the two airfoils were made using a computer program which provides for the interaction of the inviscid flow and boundary layer solutions. The pressure distributions of the airfoils were shockless for conditions from the design point to lower Mach numbers and lift coefficients. No boundary layer separation was predicted except in the last 3 percent chord on the upper surface.