Dynamic soaring is an exquisite flying technique to acquire energy from the atmospheric wind shear. In this study, we performed a nonlinear controllability analysis of an unmanned aerial vehicle (UAV) under dynamic soaring conditions is performed. We formulated dynamic soaring as an optimal control problem. The controllability of the UAV along the optimal soaring trajectory was then analyzed. We analyzed the nonlinear controllability characteristics of generic flight dynamics in the presence and absence of wind shear to provide a controllability explanation for the role of wind shear in the physics of dynamic soaring flight. It is found that the wind shear is instrumental in ensuring controllability as it allows the UAV attitude controls (pitch and roll) to play the role of thrust in controlling the flight path angle.