Kinematic Modeling of Separation Compression for Paired Approaches to Closely-Spaced Parallel Runways
In a simultaneous paired approach to closely-spaced parallel runways, a pair of aircraft flies in close proximity on parallel approach paths. The longitudinal separation between the aircraft must be maintained within a range that avoids wake encounters and, if one of the aircraft blunders, avoids collision. To increase operational availability, the approach procedure must accommodate a mixture of aircraft sizes and, consequently, approach speeds. In these procedures, the slower aircraft is placed in the lead position. The faster aircraft maintains separation from the slow aircraft in a dependent operation until final approach and flies independently afterward. Due to the higher approach speed of the fast aircraft, longitudinal separation will decrease during final approach. Therefore, the fast aircraft must position itself before the final approach so that it will remain within the safe range of separation as separation decreases. Given the approach geometry and speed schedule for each aircraft, one can use kinematics to estimate the separation loss between a pair of aircraft. A kinematic model can complement fast-time Monte-Carlo simulations of the approach by enabling a tailored reduction in the variation of starting position for the fast aircraft. One could also implement the kinematic model in ground-based or on-board decision support tools to compute the optimal initial separation for a given pair of aircraft. To better match the auto-coupled flight of real aircraft, the paper derives a kinematic model where the speed schedule is flown using equivalent airspeed. The predicted time of flight using the equivalent airspeed kinematic model compares well against a high-fidelity aircraft simulation performing the same approach. This model also demonstrates a modest increase in the predicted loss of separation when contrasted against a kinematic model that assumes the scheduled speed is true airspeed.