## 4 Results for VNRS Efficiency at the Lateral Certification Point K\({}_{2}\)  
The noise calculation procedure described in Section 3 allows for the certification noise level of the next-generation SST to be determined for the given throttle schedule \(\tau\). If no VNRS is implemented, the distribution of EPNL values along the 450 m line is shown in Figure 5a and demonstrates a usual behavior with a distinct peak at a distance of about \(X=3500\) m from the brake release. The position of the peak is then taken as the position of the lateral certification point K\({}_{2}\), and the EPNL noise value at this point is understood as the noise level at the lateral point.  
Different curves in Figure 5 correspond to different values of \(\alpha_{0}\), which stands for the angle of attack after clearing the obstacle height, since \(\alpha_{0}\) is a control parameter of the problem. By changing the value of \(\alpha_{0}\), it is possible to achieve some reduction in noise at the lateral certification point. However, as can be seen from Figure 5b, this noise reduction at the lateral certification point is compensated with noise increase at the flyover certification point, so that the cumulative noise at both points does not demonstrate a dependence on the value of \(\alpha_{0}\).  
Let us now consider the case of thrust control, when the thrust is allowed to vary after clearing the obstacle height. The thrust setting \(\tau\) is defined as a function of the distance \(X\), determined by several independent coefficients. This is an intermediary approach between the \"simple\" programmed lapse rate, which corresponds to a single coefficient, and continuous thrust control with the number of coefficients equal to the number of trajectory discretization points.  
Figure 4: A block diagram of the modeling approach.  
The implementation of thrust control and the optimization of the function coefficients to ensure the minimum cumulative noise level at the lateral and flyover certification points lead to the thrust setting variation and the low-noise trajectory shown in Figure 6. In the figure, the reference case without VNRS (standard) and the case with VNRS (advanced) are compared.  
The results for noise levels with thrust control are shown in Figure 7 for the lateral certification point (distribution of EPNL along the sideline at 450 m), as well as for the cumulative certification noise at two measurement points. In this case, EPNL distribution over \(X\) becomes close to a noise plateau obtained in [12] and differs from the distinct noise peak observed in Figure 5a for the standard reference procedure without VNRS. The cumulative noise again does not depend on the value of \(\alpha_{0}\); however, the reduction in  
Figure 5: Results of noise calculations for the standard takeoff procedure: (**a**) distribution of the EPNL noise along the sideline at 450 m for different angles \(\alpha_{0}\); (**b**) cumulative noise levels at the lateral and flyover certification points.  
Figure 6: Implementation of VNRS: (**a**) thrust setting variation during takeoff, (**b**) takeoff trajectory.  
the cumulative noise level due to the implementation of the thrust control is present and can reach four EPNdB.