In this paper, a 3-D model of a Magnus effect-based airborne wind energy system adapted from flight dynamics is proposed. The model is derived from first principles where the forces acting on the system are presented. In order to validate our aerodynamic model, a study of lift and drag coefficients is presented for the rotating cylinders in high Reynolds number regime. The proposed 3-D model is validated by simulation, controlling the system in crosswind trajectories. The performance of the system power production is also assessed and compared to a simplified static model.