A numerical investigation of the dynamic Fluid Structure Interaction (FSI) of a yacht sail plan submitted to harmonic pitching is presented to analyse the system's dynamic behaviour and the effects of motion simplifications and rigging adjustments on aerodynamic forces. It is shown that the dynamic behaviour of a sail plan subject to yacht motion clearly deviates from the quasi-steady theory. The aerodynamic forces presented as a function of the instantaneous apparent wind angle show hysteresis loops. It is shown that the hysteresis phenomenon dissipates some energy and that the dissipated energy increases strongly with the pitching reduced frequency and amplitude. The effect of reducing the real pitching motion to a simpler surge motion is investigated. Results show significant discrepancies with underestimated aerodynamic forces and no more hysteresis when a surge motion is considered. However, the superposition assumption consisting in a decomposition of the surge into two translations normal and collinear to the apparent wind is verified. Then, simulations with different dock tunes and backstay loads highlight the importance of rig adjustments on the aerodynamic forces and the dynamic behaviour of a sail plan. The energy dissipated by the hysteresis is higher for looser shrouds and a tighter backstay.