Optimal Cruise Airspeed in the Presence of Wind Uncertainty

Aircraft ground speed during the cruise phase of flight is particularly sensitive to changes in wind speed and direction. These highly variable wind conditions are typically forecast on an hourly basis and in many cases only provided to aircraft prior to their departure. Thus the total flight time and the corresponding time of arrival are difficult to predict and control. We propose an approach to determining the airspeed such that there is a very high probability of achieving the required time of arrival (RTA) at a future point in the cruise phase while at the same time minimizing the fuel that is consumed in the interim. In the proposed approach, the cruise phase is divided into several segments and the historical correlations between the forecast winds in the segments are used within the context of a stochastic programming (SP) and receding horizon control (RHC) framework to determine the aforementioned optimum airspeed. Through a numerical study, we observe that fuel consumption decreases as the number of look-ahead segments is increased, albeit with non-linearly increasing computational time, and increases as the number of segments is increased from 8 to 14 segments.