Modeling a Gliding Turn-Back Maneuver (“Impossible Turn”) Following an Engine Failure

In aviation, the “impossible turn” refers to a single-engine fixed-wing aircraft attempting to return and land in the opposite direction on its departure runway following the loss of engine thrust at low altitude after takeoff. The Federal Aviation Administration (FAA) suggests that “considerable luck” is required to successfully complete this maneuver without stalling or impacting short of the runway, yet offers little specific guidance to pilots on when such a maneuver is feasible. Furthermore, the altitude loss associated with this maneuver is highly dependent on environmental factors such as the density altitude and the headwind component, making the real-time viability assessment in an actual emergency difficult, even for an experienced pilot. To analyze this return maneuver, a five-degree-of-freedom (5-DOF) time-based Python simulation is developed. The simplified maneuver model consists of four flight phases: (1) a constant bank-angle turn, initiated after some reaction time following the engine failure, involving a greater-than-180-degree heading change to establish the aircraft on an intercept course with the runway centerline; (2) a wings-level, constant-airspeed glide; (3) a second turn to align with the runway centerline; and (4) a final glide to the runway threshold. The geometry of this maneuver is defined by several pilot-controllable parameter inputs: the glide/turn airspeeds, the intercept angle to the runway, and the turn bank angles. The simulation is generalizable to any single-engine fixed-wing aircraft as the only necessary aerodynamic inputs are the Oswald efficiency and the minimum drag coefficient, both of which can be derived from manufacturer-provided or experimentally obtained engine-out glide data. The simulation also considers the effects of wind, runway length, and density altitude, outputting the minimum and, if applicable, maximum altitudes at which a return maneuver can be performed in the case of an engine failure. The simulation results are compared against the performance of a Cessna 172S Skyhawk using both the X-Plane 12 flight simulator and real-world simulated engine-out return maneuvers. Additionally, optimization results indicate that minimizing altitude loss requires bank angles exceeding 45 degrees at low airspeeds, making pilot skill the primary limiting factor. However, with constraints on allowable bank angles and airspeeds, the program can provide preflight guidance on when the maneuver may be considered and executed safely in the event of an engine failure after takeoff.