Linearization of Aircraft Landing Equations of Motion with Airframe Flexibility Effects

The conventional approach in aircraft landing loads analysis, such as for shock absorber development, is using a nonlinear set of equations and a modal representation of the airframe. For preliminary shock absorber design studies, a linearized set of equations may provide a highly efficient simulation method to limit the parameter space of linear shock absorber models. This article develops a set of linearized equations of motion to simulate the landing touchdown event while capturing airframe flexibility effects using a transfer function. The linearized flexible model demonstrates the ability to generally capture flexibility effects and output responses of interest with a significantly reduced simulation time compared to both fully flexible and nonlinear reduced-order models. The linearization of a Fiala tire model is accomplished by scaling the longitudinal tire stiffness such that the peak tire drag force matches that of the nonlinear model, and the vertical tire stiffness is obtained from a linear regression of a nonlinear vertical force versus deflection curve through an expected range of tire deflection.