Helicopter blade flapping with and without small angle assumption in the presence of dynamic stall

The flapping equation for a rotating rigid helicopter blade is typically derived by considering (1) small flap angle, (2) small induced angle of attack and (3) linear aerodynamics. However, the use of nonlinear aerodynamics such as dynamic stall can make the assumptions of small angles suspect as shown in this paper. A general equation describing helicopter blade flap dynamics for large flap angle and large induced inflow angle of attack is derived. A semi-empirical dynamic stall aerodynamics model (ONERA model) is used. Numerical simulations are performed by solving the nonlinear flapping ordinary differential equation for steady state conditions and the validity of the small angle approximations are examined. It is shown that the small flapping assumption, and to a lesser extent, the small induced angle of attack assumption, can lead to inaccurate predictions of the blade flap response in certain flight conditions for some rotors when nonlinear aerodynamics is considered.