Identifying the Safe Area for Thrown Ice from a Wind Turbine

Throwing ice from a large and modern wind turbine located in frigid regions can result in significant human and financial damages due to its high velocity and long range. Consequently, the trajectory, rotation, velocity, and kinetic energy of thrown ice from a horizontal axis wind turbine are investigated while the movement of a thrown ice is simulated in three dimensions, including both rotation and translation. A method for calculating Euler angles is presented inversely, followed by the derivation of the equations of translation and rotation using Newton's second law and Euler's laws of motion, which make it possible to calculate and plot the position of any desired point on the ice at any given moment which fills a gap in the references. The calculations are conducted using a ballistic model with an average drag coefficient. The obtained ordinary differential equations (ode) are solved numerically using the 4th-order Runge-Kutta method, the results are verified with existing references, while applying lift in the equations and solving the nonlinear differential equations, comparing the movement of the ice under conditions where lift is considered versus when it is neglected has been done for the first time. Furthermore, the concept of terminal velocity is described, and the value of this velocity and the time it takes to reach it for the specific flying ice are provided. Lastly, various parameters, such as a change in angular velocity, drag coefficient, local wind velocity, and the concept of apparent mass and its effect on the movement of the thrown ice as well as the presence of lift force on the distances of ice impact with the ground are examined, and unsafe areas around the wind turbine by considering changes in influencing parameters where the probability of ice-ground collision exists are identified.