A study of aircraft cruise

The long range aircraft cruise problem is analyzed using a model intermediate in complexity between energy model and point mass model. It is shown that this formulation imbeds the classical steady state cruise as the central member along with several other oscillatory extremals. The oscillatory cruise trajectories are shown to exist if the Hessian of the function QD/VT with respect to altitude and airspeed is positive definite. An expression for predicting the frequency of oscillation is developed. Qualitative effects of increasing the vehicle thrust and improving the L/D are discussed. Numerical results for two fighter aircraft and a transport aircraft are given. While oscillatory cruise mode exists for the two fighter aircraft, steady state cruise at full throttle is found to be optimal for the transport aircraft. A second variation analysis to bring out the reason for fuel savings is developed. It is shown that whenever the Hessian of the function QD/VT is positive definite, the second variation will be zero along the classical steady state cruise arc, indicating that a neighboring extremal is competitive. Comparisons with the previous point mass and energy modeled results are given.