Development of Response Surface Equations for High-Speed Civil Transport Takeoff and Landing Noise

As an element of a design optimization study of high speed civil transport (HSCT), response surface equations (RSEs) were developed with the goal of accurately predicting the sideline, takeoff, and approach noise levels for any combination of selected design variables. These RSEs were needed during vehicle synthesis to constrain the aircraft design to meet FAR 36, Stage 3 noise levels. Development of the RSEs was useful as an application of response surface methodology to a previously untested discipline. Noise levels were predicted using the Aircraft Noise Prediction Program (ANOPP), with additional corrections to account for inlet and exhaust duct lining, mixer-ejector nozzles, multiple fan stages, and wing reflection. The fan, jet, and airframe contributions were considered in the aircraft source noise prediction. Since takeoff and landing noise levels are a function of both engine design variables and flight path variables, several possible approaches to the problem were considered. The first method would have required developing an RSE which is a function of low-speed aerodynamics and engine design variables, by using the Flight Optimization System (FLOPS) computer program to calculate the takeoff performance and passing the flight path to ANOPP. The second method required development of an RSE which is a function of engine cycle variables and flight path variables. The latter approach was chosen for this study, primarily for its simplicity and ease of integration of the final RSEs into FLOPS. Pareto plots are provided showing the estimated effect of each of the variables on the variation in the noise levels. Screening studies showed that the variation in sideline noise was dominated by jet parameters-such as mass flow, area, total pressure, and suppressor area ratio-while fan variables and climb velocity played a smaller role. Takeoff noise was similarly affected, except that the sensitivity to the jet variables was diminished, and cutback altitude was shown to have a significant effect. Approach noise was controlled almost completely by fan variables. The most important variables were chosen for each of the three noise levels, and separate response surface equations were developed for two-, three-, and four-stage fans using a central composite design of experiments (CCD) matrix. The resulting RSE coefficients are given, along with plots for the prediction profiles for each equation. The sideline and takeoff noise RSEs all exhibited good fit with the data, and the trends were as expected. The approach noise RSEs exhibited lower R² values, indicating a poorer fit with the data. It was determined that this behavior was caused by correlation in the design matrix, resulting in significant errors in the estimation of the second-order RSE coefficients. Problems with the approach RSEs were eliminated when their development was repeated using a face-centered form of the CCD. Based on the results of this study, recommendations are made for any future studies in this area.