Gust Load Alleviation (GLA) is an important aspect of flight dynamics and control that reduces structural loadings and enhances ride quality. In conventional GLA systems, the structural response to aerodynamic excitation informs the control scheme. A phase lag, imposed by inertia, between the excitation and the measurement inherently limits the effectiveness of these systems. Hence, direct measurement of the aerodynamic loading can eliminate this lag, providing valuable information for effective GLA system design. Distributed arrays of Artificial Hair Sensors (AHS) are ideal for surface flow measurements that can be used to predict other necessary parameters such as aerodynamic forces, moments, and turbulence. In previous work, the spatially distributed surface flow velocities obtained from an array of artificial hair sensors using a Single-State (or feedforward) Neural Network were found to be effective in estimating the steady aerodynamic parameters such as air speed, angle of attack, lift and moment coefficient. This paper extends the investigation of the same configuration to unsteady force and moment estimation, which is important for active GLA control design. Implementing a Recurrent Neural Network that includes previous-timestep sensor information, the hair sensor array is shown to be capable of capturing gust disturbances with a wide range of periods, reducing predictive error in lift and moment by 68% and 52% respectively. The L2 norms of the first layer of the weight matrices were compared showing a 23% emphasis on prior versus current information. The Recurrent architecture also improves robustness, exhibiting only a 30% increase in predictive error when undertrained as compared to a 170% increase by the Single-State NN. This diverse, localized information can thus be directly implemented into a control scheme that alleviates the gusts without waiting for a structural response or requiring user-intensive sensor calibration.