In order to overcome the efficiency problem of the conventional gradient-based optimal design method,a highly-efficient viscous adjoint-based RANS equations method is applied to the aerodynamic optimal design of hovering rotor airfoil.The C-shaped body-fitted mesh is firstly automatically generated around the airfoil by solving the Poisson equations,and the Navier-Stokes(N-S)equations combined with Spalart-Allmaras(S-A)one-equation turbulence model are used as the governing equations to acquire the reliable flowfield variables.Then,according to multi-constrained characteristics of the optimization of high lift/drag ratio for hovering rotor airfoil,its corresponding adjoint equations,boundary conditions and gradient expressions are newly derived.On these bases,two representative rotor airfoils,NACA0012 airfoil and SC1095 airfoil,are selected as numerical examples to optimize their synthesized aerodynamic characteristics about lift/drag ratio in hover,and better aerodynamic performance of optimal airfoils are obtained compared with the baseline.Furthermore,the new designed rotor with the optimized rotor airfoil has better hover aerodynamic characteristics compared with the baseline rotor.In contrast to the baseline airfoils optimized by the finite difference method,it is demonstrated that the adjoint optimal algorithm itself is practical and highly-efficient for the aerodynamic optimization of hover rotor airfoil. In order to overcome the efficiency problem of the conventional gradient-based optimal design method, a highly-efficient viscous adjoint-based RANS equations method is applied to the aerodynamic optimal design of hovering rotor airfoil. The C-shaped body-fitted mesh is automatically generated around the airfoil by solving the Poisson equations, and the Navier-Stokes (NS) equations combined with Spalart-Allmaras (SA) one-equation turbulence models are used as the governing equations to acquire the reliable flowfield variables. multi-constrained characteristics of the optimization of high lift / drag ratio for hovering rotor airfoil, its corresponding adjoint equations, boundary conditions and gradient expressions are newly derived. Of these bases, two representative rotor airfoils, NACA0012 airfoil and SC1095 airfoil, are selected as numerical examples to optimize their synthesized aerodynamic characteristics about lift / drag ratio in hover, and better aerodynamic performance o f optimal airfoils are obtained compared with the baseline. Future revised, the new designed rotor with the optimized rotor airfoil has better hover aerodynamic characteristics compared with the baseline rotor. contrast to the baseline airfoils optimized by the finite difference method, it is demonstrated that the adjoint optimal algorithm itself is practical and highly-efficient for the aerodynamic optimization of hover rotor airfoil.