Revisiting Spanwise Loading Theory for Tailless and Flying-Wing Aircraft

Flying-wing and tailless UAVs can integrate the lifting surface, structure, payload volume, propulsion, and control surfaces into a compact airframe with fewer nonlifting components. Their design places special demands on the spanwise loading because the wing must also provide trim, structural efficiency, and control without a conventional empennage. A unified closed-form framework was developed that relates the prescribed spanwise circulation distribution to the induced velocity, local and integrated induced drag, wing-root bending moment, span-resizing trade, and geometric twist required to realize the loading. Closed-form twist relations were derived for both constant-chord and linearly tapered wings. For fixed lift and span, elliptical loading remains the minimum-induced-drag solution. The Prandtl-type loading has higher integrated induced drag but produces outboard upwash and local negative induced drag, allowing differential outer-wing lift to contribute to proverse yaw. The same inboard lift redistribution reduces root bending moment, allowing span or aspect ratio to be increased at the same idealized root bending moment.