The performance of wind propulsion systems is evaluated in unsteady inhomogeneous winds with tools that are routinely used to predict the performance of wind turbines and which give access to the unsteady aerodynamic forces acting on the wingsail. A rigid wingsail exposed to a realistic atmospheric surface layer wind is used as a testbed. For this case, we show that standard deviations of the aerodynamic driving force are larger than 15%-20% of the mean values when the true wind velocity is larger than the ship speed. We also show that the mean aerodynamic driving forces computed by averaging the unsteady driving forces are only slightly smaller than the ones computed on the mean wind despite the strongly nonlinear dependence of the unsteady forces on the wind velocity and direction.