## 2 Description of the Noise Certification Procedure  
Noise certification of subsonic jet aircraft is defined by the ICAO [1]. An excellent and detailed description of the reference certification procedure, the constraints that must be met during the procedure, as well as its extension to the case of VNRS for supersonic aircraft, are provided in [12], so there seems to be no need to repeat it here. As a result, we limit our discussion to the most pertinent aspects of the study, such as different allowable positions of the lateral certification point. The takeoff reference profile of subsonic aircraft is provided in Figure 2, as specified by the ICAO [1]. For subsonic aircraft, the certification procedure requires that the maximum available thrust must be maintained before the pilot-initiated thrust cutback takes place (Point D). The cutback altitude should not be less than 210-300 m, depending on the number of engines; the procedure without thrust cutback is also allowed. The deflection angles of high-lift devices must be kept constant along the trajectory. The implementation of VNRS for supersonic aircraft implies relaxing these requirements. For instance, it is often supposed that soon after the obstacle height of 10.7 m (35 ft) is cleared, the automatic thrust control is enabled. It can be as simple as thrust reduction by several percent [6] or a sophisticated throttle schedule [12]. Similarly, an automatic control of high-lift devices can be implemented [11]. The final goal of these modifications consists of reducing noise, measured in the EPNL metric, at two certification points: flyover and lateral. The flyover point (K\({}_{1}\)) is positioned 6500 m behind the break release point on the extended runway centerline below the departure flight path. The lateral point (K\({}_{2}\)) is positioned on a line 450 m parallel to the runway centerline, where the highest EPNL is reached. The other allowable position of the lateral point (K\({}_{4}\)) will be discussed later. Thrust reduction at low altitudes capitalizes on noise reduction due to lateral attenuation when noise propagates from the aircraft to the lateral point over the ground. On the other hand, thrust reduction results in a lowering of the altitude of the aircraft over the first certification (flyover) point K\({}_{1}\), which leads to noise increase at the point. The (cumulative) certification noise at these two certification points is an arithmetic sum of EPN levels at the points, so it is an intricate balance between noise reduction at one point and noise increase at the other. Previous studies [8; 9; 10; 11; 12; 13; 14; 15; 16] have indicated that the effect of thrust reduction can lead to a reduction in cumulative noise. Control of high lift devices allows the aircraft to benefit from the maximum available lift-to-drag ratio, which results in altitude increase at the flyover point and thereby reduces noise. It should be noted that modeling of lateral attenuation is a formidable problem in itself. Five methods to predict lateral attenuation have been discussed in [11], which identified the disadvantages of each of them. It is expected that the uncertainty in modeling this effect has the largest impact on the thrust control schedules and their corresponding noise reduction potential [12]. Let us now consider the other position of the lateral point (K\({}_{4}\)), which is located on the extended centerline of the runway, 650 m vertically below the climb-out flight path at full takeoff power. It can be seen that this point is not affected by lateral attenuation at all. In addition, its position for a given departure trajectory is known beforehand so that it does not need determination of the maximum noise along the sideline. Its consideration in the context of SST noise studies is motivated by the concept of SST with turboprop buster engines [4].