A bird's wings are articulated to its body via highly mobile shoulder joints. The joints confer an impressive range of motion, enabling the wings to make broad, sweeping movements that can modulate quite dramatically the production of aerodynamic load. This is enormously useful in challenging flight environments, especially the gusty, turbulent layers of the lower atmosphere. In this study, we develop a dynamics model to examine how a bird-scale gliding aircraft can use wing-root hinges (analogous to avian shoulder joints) to reject the initial impact of a strong upward gust. The idea requires that the spanwise centre of pressure and the centre of percussion of the hinged wing start, and stay, in good initial alignment (the centre of percussion here is related to the idea of a ‘sweet spot’ on a bat, as in cricket or baseball). We propose a method for achieving this rejection passively, for which the essential ingredients are (i) appropriate lift and mass distributions; (ii) hinges under constant initial torque; and (iii) a wing whose sections stall softly. When configured correctly, the gusted wings will first pivot on their hinges without disturbing the fuselage of the aircraft, affording time for other corrective actions to engage. We expect this system to enhance the control of aircraft that fly in gusty conditions.