Containing Aircraft Noise Levels at take-off: A Mathematical Programming Approach

The sustained growth of air transportation traffic along the last decades has induced increasing noise exposure for the areas surrounding large and medium airports. This study concentrates on the optimization of the take-off and departure flight phase for a transportation aircraft. A general aircraft trajectory generation problem is first formulated as an optimal control problem where a global cost, including noise penalties, is to be minimized. Since aircraft operators and communities have conflictive objectives, a noise index is introduced. Airlines operations costs and community noise levels are expressed as complex functions of the aircraft trajectory geometry resulting in a complex optimization problem. It is observed that flight dynamics present a differential flatness property and it is discussed how to take advantage of this to solve the trajectory generation problem and assess adequately the resulting surrounding noise exposure. Then, the case of a particular standard take-off/initial climb trajectory is considered. It appears that the noise level constraints turn the resulting mathematical programming problem numerically intricate and that this problem should be approached as a parameter optimization problem through a systematic evaluation process.