We consider the issue of designing closed 3D UAV trajectories that allow for an energy efficient collection of data with aUAV-aided wireless sensor network. We consider a 3D wireless channel model and a realistic dynamical model for theUAV. The proposed trajectory is largely derived analytically, thus making its online calculation computationally tractable.We also show the importance of using realistic dynamical and energy models for the UAV in designing efficient trajectories. This is done mainly by showing that minimising the flying time of the UAV is not equivalent to minimising its energy consumption. Simulation results corroborate these findings.