An aerodynamic model for 6-DOF flight motion of windborne debris of square plates

Abstract

Plate-type debris is a typical type of windborne debris, often originating from roof tiles and shingles. Numerical simulation using aerodynamic models provides a practical method to predict trajectories of windborne debris. In this paper, we first propose a revised model for the 3-degree-of-freedom (3-DOF) flight motion of square plates in winds by integrating experimental data from previous studies. Thereby, we divide the aerodynamic force and moment into a translational part and a rotational part. In addition, we propose conditions of autorotation in the revised model. The calculation of the rotational force and moment depends on whether these conditions are fulfilled. The revised model is validated by comparing the numerical results with experimental results of plate trajectories. Next, based on the revised model for the 3-DOF motion, we propose an aerodynamic model for the 6-DOF motion by incorporating the findings about the rotational force and moment, which were obtained from the authors’ previous study on the 6-DOF motion of square plates. Based on these findings, the model is developed in the way that the direction of the rotational force depends on the relative wind velocity and the angular velocity of plate, and the direction of the rotational moment depends on the translational moment. By doing so the proposed model in this paper avoids directly using a database of aerodynamics, which is large and difficult to obtain. Validation using the experimental results of plate trajectories shows that the proposed model, which has a relatively simple form, performs generally well.