In coaxial rotor helicopter systems, both rotors of the helicopter spin in opposite directions on the same vertical axis, requiring the bottom rotor to spin faster with a higher blade pitch angle and the top rotor to spin slower with a lower blade pitch angle. This was proven by Peters and Seidel [1]. As both blades are spinning, there is an induced flow of air between the rotors. The solution of the potential flow equations shows that the flow induced by the upper rotor on the lower is related to the adjoint velocity above the rotors and the time delays in the system. Therefore, the model used to determine the effects of the inflow will have both velocity states and co-states with included time delays. The time delays result from the effects of the vortex shed by the upper rotor, causing the induced flow on the upper rotor to decay with time as the flow on the lower rotor increases with time while the vortex moves downward. After the vortex has moved past the lower rotor, it decays again with an added time delay that matches that of the time it took to move between the two rotors. The main objective of this study is to determine how the velocity co-states affect the time delays on the Bode Plots for the transfer functions between rotor inputs and induced velocity on the two rotors. The computer language MATLAB and complex arithmetic are utilized in conjunction with Fourier Transforms to predict how the air will flow between the rotors when they are coupled through blade-element theory.

Document Type

Final Report

Author's School

McKelvey School of Engineering

Author's Department

Mechanical Engineering and Materials Science

Class Name

Mechanical Engineering and Material Sciences Independent Study

Date of Submission