## 5 Results for VNRS Efficiency at the Lateral Certification Point K\({}_{4}\)  
Let us now consider the other position of the lateral certification point (K\({}_{4}\)), which is defined as the point on the extended runway centerline that corresponds to the aircraft altitude \(H=650\) m. To make the comparison between points K\({}_{4}\) and K\({}_{2}\) more representative, the additional constraint by Equation (1) is imposed on the position K\({}_{4}\) of the lateral certification point. Unlike position K\({}_{2}\) of the lateral certification point, where lateral attenuation is relied upon for noise reduction; noise propagation to position K\({}_{4}\) does not involve the effect of lateral attenuation. As a result, noise reduction with VNRS at this point is determined primarily by the reduction in thrust used for reaching the altitude of 650 m. If control of high-lift-devices position is implemented as VNRS, it allows the SST to remain in a configuration with maximum \(L/D\) during takeoff that permits further thrust reduction and thus leads to noise abatement. Taking into account the uncertainty associated with the definition of this certification point, no optimization of flight trajectory has been carried out to minimize noise at the point with VNRS. Instead, noise calculation was performed at this position of the lateral certification point for the standard takeoff procedure, as well as for the advanced takeoff procedure obtained for noise minimization at position K\({}_{2}\). The results then were compared with the data for position K\({}_{2}\) to answer the following questions:  
1. Are the noise levels of the SST at both positions of the lateral certification points similar for the standard takeoff procedure? 2. Does the implementation of thrust control affect the noise level at position K\({}_{4}\), and if so, is the effect significant? However, as can be seen from Figure 6b, the requirement of Equation (1) is not met with the optimized trajectory of the SST. This could be fixed by performing optimization of thrust control for the position K\({}_{2}\) of the lateral certification point, as has been performed in Section 3, but with an additional constraint given by Equation (1). Nevertheless, such  
Figure 7: Results of noise calculations for the advanced takeoff procedure: (**a**) distribution of the EPNL noise along the sideline at 450 m; (**b**) cumulative noise levels at the lateral and flyover certification points. an optimization could be considered unrepresentative, because it would account for both positions of the lateral certification point: K\({}_{2}\) via the choice of the cost function, and K\({}_{4}\) via the constraint of Equation (1). As a result, another SST was considered that has the same aerodynamic and engine parameters, but with the maximum takeoff mass reduced by 10 tons. The improved thrust-to-weight ratio allows for a faster climb of such an SST, which enables it to comply with Equation (1). For this SST the same calculations of the standard and advanced takeoff procedures were performed for both positions (K\({}_{2}\) and K\({}_{4}\)) of the lateral certification point, as well as for the cumulative noise. The results of these calculations are provided in Figure 8.  
It can be seen that for this aircraft an implementation of VNRS leads to cumulative noise reduction of about three EPNdB (Figure 8a). Since the noise level at the flyover certification point does not depend on the choice of the position for the lateral certification point, a comparison of the results of Figure 8a for position K\({}_{2}\) and Figure 8b for position K\({}_{4}\) shows that the standard takeoff procedure produces very similar noise levels at these positions, with an average difference smaller than 0.1 EPNdB. Implementation of thrust control results in a significant noise reduction of 2.2 EPNdB for position K\({}_{4}\), as can be seen from Figure 8b. Nevertheless, this is less than the reduction of three EPNdB observed for position K\({}_{2}\) of the lateral certification point.