1. Introduction An Aircraft Noise Pollution Model for Tra jectory Optimization ATALAY BARKANA, Member, IEEE DMMA Eski§ehir, Turkey GERALD COOK, Member, IEEE University of Virginia Clarlottesville, Va. 22903 Abstract The mobility of our society makes effective and efficient operation of our air terminals a necessity. For this reason, landing trajectories must be optimized. One important factor in the performance index is aircraft noise received by people residing near the terminal. This paper develops a mathematical model of this noise effect so that it may be included in the performance index. The model yields the boundary on the ground inside of which the noise level is at or above 70 dB. This area can be weighted with the population density. The model compares very favorably with available data. With the emphasis today's society places on mobility, it is very important that our transportation systems operate in a very effective manner. lt is also important that these transportation systems cause as little annoyance as possible to the other activities of society. For these reasons research is being done on optimizing landing trajectories of short- haul passenger aircraft, i.e., aircraft used primarily for trans- porting passengers between cities less than 200 miles apart. Criteria for these optimization studies include passenger comfort, fuel consumed, time spent during the landing maneuver, and aircraft noise received by those residing near the terminal. The first two items need no explanation. The third term, time spent during the landing maneuver, is some- what a measure of terminal congestion given a specified schedule of arrivals. Thus, it is desired to get the planes down quickly to minimize this congestion and alleviate the air traffic controllers' problems. The final term is a very important one. If the existing terminals are to be used at their full capacity, landings will be frequent. This being the case, consideration must be given to bothersome noise re- ceived by the residents in the near-terminal area, and efforts must be made to minimize this effect insofar as is reason- ably possible. Noise is therefore included in the perform- ance criterion. Zalovik and Schueter [1] reported experiments on in- creasing landing glide slope angle from 30 to 60. Here dis- crete sensors were used to measure the noise level at various points along the ground track. No effort was made to mathematically model the noise emission. Lee et al. [2] developed graphical and analytical methods for determining contours of constant noise level. These models have no roll dependence which seems to be a significant deficiency. In addition, the analytical method fails when the aircraft is in level flight. Jacob [3] performed optimization studies on landing trajectories. He assumed motion was restricted to a vertical plane and penalized only for the maximum per- ceived noise level along the ground track of the glide slope. This work makes no attempt at treating three-dimensional flight trajectories and their noise effect. Obtaining a work- able accurate mathematical model of the noise term is the subject of the present paper. 11. Noise Data Manuscript received November 28, 1974. Copyright 1976 by IEEE Trans. Aerospace and Electronic Systems, vol. AES-12, no. 2, March 1976. The research on which this paper is based was supported by NASA, Langley Research Center Contract No. NASA 1-10210-8. Simulation data based on a Boeing 737-200 JT8 D-7 was supplied to the authors by the NASA Langley Research Center. Fig. 1 defines the geometry for these data. The noise level at the observer was calculated for each ten-degree increment as 0 varied from +800 to -80°, i.e., as the aircraft moved by in level flight. Tabulations of these noise levels were supplied for elevation angles of be = 0, 7.18, 14.47, 30, and 90 degrees; range at closest point of approach of CPA = 400, 800, 1600, 3200, 6400, and 12 800 ft; and thrust levels of T= 3962, 5028, 9482, and 12 356 lbs. Using the data for a given thrust setting and a given eleva- tion angle, one can construct a plane at this angle with IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-12, NO. 2 MARCH 1976 109