Possible 'impossible' turn

Abstract

Turning back after engine failure during the takeoff phase of flight in a single engine aircraft is examined using a simplified analytical model. The important parameters are identified. The analysis shows that the optimum flight path is teardrop-shaped with a 45-deg bank angle at stall velocity during the turn. The effects of engine failure altitude, wind direction and velocity, climbout velocity, bank angle, and velocity in the turn on the required runway length are examined. The results show that the typical recommendations for general aviation single engine aircraft are not optimum. Nomenclature CD = drag coefficient Cf)(} = zero lift drag coefficient C, = lift coefficient Ci-max = maximum lift coefficient D = drag d = propeller diameter g = acceleration of gravity h — altitude / = advance ratio L = lift LID = lift-to-drag ratio n = propeller rpm R = turn radius RIC = rate of climb S = wing area t = time V = velocity Kruise = cruise velocity