Analysis and Evaluation of Supersonic Underwing Heat Addition

The linearized theory for heat addition under a wing has been developed to optimize wing geometry, heat addition, and angle of attack. The optimum wing has all of the thickness on the underside of the airfoil, with maximum-thickness point well downstream, has a moderate thickness ratio, and operates at an optimum angle of attack. The heat addition is confined between the fore Mach waves from under the trailing surface of the wing. By linearized theory, a wing at optimum angle of attack may have a range efficiency about twice that of a wing at zero angle of attack. More rigorous calculations using the method of characteristics for particular flow models were made for heating under a flat-plate wing and for several wings with thickness, both with heat additions concentrated near the wing. The more rigorous calculations yield in practical cases efficiencies about half those estimated by linear theory. An analysis indicates that distributing the heat addition between the fore waves from the undertrailing portion of the wing is a way of improving the performance, and further calculations appear desirable. A comparison of the conventional ramjet-plus wing with underwing heat addition when the heat addition is concentrated near the wing shows the ramjet to be superior on a range basis up to Mach number of about B. The heat distribution under the wing and the assumed ramjet and airframe performance may have a marked effect on this conclusion. Underwing heat addition can be useful in providing high-altitude maneuver capability at high flight Mach numbers for an airplane powered by conventional ramjets during cruise.