Extraction and Solution of the Gyroplane Trim Equations

A. Osaji*, 1, §, H. Farrokhfal2
1 Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran
§ Present Address: No 71, Farhang Avenue, Roodsar, Guilan, Iran
2 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

© 2009 Osaji and Farrokhfal.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran; Tel: +98-142 6211577; E-mail:


Extraction and solution of the gyroplane trim equations are the goal of this paper. At first according to forces and moments acting on gyroplane and the different parts of gyroplane, the six equations of the rigid body will be extracted. Because of the trim conditions, angular velocity and linear acceleration are considered to be zero. Then the energy balance equation will be derived by modeling forces and velocities. The energy balance equation shows the advancing efficient power, which is derived from the engine, is equal to all depleted powers (induced power, profile power, main rotor power, parasite power, climb power) by the gyroplane. Then by modeling non-dimensional velocities in the parallel and perpendicular directions of the main rotor reference plane, the main rotor momentum equation will be extracted. The forces of each different parts of the gyroplane will be derived according to the trim control parameters in the body axes. They will be assigned into the rigid body equations of motion. By solving the rigid body, energy balance and main rotor momentum equations, for several flight scenarios, the pilot trim control parameters (containing thrust, angle of attack for reference plane, pilot blade pitch angle and Rudder angle) will be obtained.