TITLE AND SUBTITLE A Method for Designing Blended Wing - Body Con gurations for

A procedure for tailoring a blended wing-body con guration to reduce its computed wave drag is described. The method utilizes an iterative algorithm within the framework of rst-order linear theory. Four computed examples are included. In each case, the zero-lift wave drag was reduced without an increase in drag due to lift. Introduction In the initial rough-cut state of supersonic conguration design, the requirement for low wave drag is a prime consideration. Often, at this stage in the design process, linear codes are used to compute the lift and the drag due to lift (ref. 1) as well as the zero-lift drag (ref. 2). Reference 2 includes a design option for tailoring the fuselage of a con guration to obtain low zerolift wave drag. However, this procedure has several weaknesses. It is applicable only if the con guration has a fuselage that is de ned by circular cross sections. The procedure is based on the zero-orderaccuracy Eminton-Lord theory (ref. 3), by which the computed drag is independent of Mach number. This independence is inconsistent with the rst-order theory (ref. 4) that is used in the analysis phase of the program to compute drag from the equivalent area distributions obtained from Mach plane slices. Finally, the procedure does not account for the volume that is required to ll the gap that occurs between the fuselage and the wing when these two components are input separately in the wave-drag geometry format. This paper describes a method for tailoring a blended wing-body con guration for low wave drag. The method utilizes Mach plane slice area distributions and so is consistent with the wave-drag analysis. Furthermore, since for a blended wing-body the fuselage geometry is not input as a separate component to the wave-drag program, there is no requirement to account for the fuselage-wing gap. The method designs for low drag at zero lift in accordance with the rst-order analysis procedures of reference 2, and then the methods of reference 1 are used to ensure that this tailoring does not increase the drag at the design lift coe cient. Symbols B base area of body of revolution Bb equivalent base area corresponding to displacement e ect of jet exhaust CD;wl drag coe cient due to lift at design lift coe cient CL lift coe cient CD;w0 zero-lift drag coe cient Dw zero-lift wave drag E(x) error distribution L length of equivalent body M Mach number MSAD Mach slice area distribution q dynamic pressure S synthesized distribution obtained by averaging individual equivalent area distributions Sr cross-sectional area of body of revolution S equivalent area|area of Mach plane slice at polar angle through con guration, projected onto Y Z-plane T thickness along centerline section V volume; volume parameter X = x=L x; y; z Cartesian coordinates Dw;i wave-drag component corresponding to i set of Mach plane slices ; dummy integration variables angle between Y -axis and projection of Mach plane slice normal vector onto Y Z-plane Analysis Linear Wave-Drag Equations Reference 4 shows that the linear theory approximation to the wave drag of a general, slender, nonlifting con guration is Dw = Z 2 0 dDw d d (1) where dDw d is the wave drag associated with the set of Mach plane slices. These are the Mach planes whose surface normal vectors project onto the Y Z-plane at angle to the Y -axis. (See g. 1.) 1 Equation (1) is approximated by the sum of a nite number of Mach slice drag components: Dw 1 n n X i=1 Dw;i (2) The increments Dw;i are de ned by the formula Dw;i = q 2 Z L