Influence of the Path Pitch Angle on the Flyability and Mode of Motion of Propeller Airplanes

This study examines the distance that an airplane is able to fly on inclined trajectories at various angles when it starts at different altitudes. It clearly exhibits the dependence of the airplane’s performance, when it climbs or descends, on the angle of inclination of the path and on the variations in initial weight, altitude, and power available. The results are obtained by solving the airplane’s equations of motion with the airplane’s dynamic constraints. Different specific dynamic behaviors of the airplanes are shown to occur within particular ranges of the inclination angle. Two remarkable behaviors, which have not been discussed before, are exhibited, namely the existence of a “relative ceiling” in ascending trajectories and that of a “maximum gliding altitude” in descending trajectories. These are specific altitudes that delimit the ranges of altitudes from which the airplane always attains the same terminal speed and reaches the same final altitude, whatever its initial altitude. Finally, it is shown how a feasibility matrix can be constructed, with which one can rapidly determine if a considered trajectory is flyable or not. This matrix requires only a small amount of memory storage and could reside on board essentially any airplane. The results of the study are illustrated with two very different airplanes: a Cessna 182 Skylane and a Silver Fox-like small UAV.