Computation of Variable Noise Reduction System Efficiency for Supersonic Civil Aircraft During Takeoff

Abstract

The noise of next-generation supersonic civil aircraft can become a significant nuisance for the population in the vicinity of airports. This study investigates the efficiency of the noise control approach for a notional supersonic civil aircraft at takeoff, based on the implementation of a variable noise reduction system (VNRS) with thrust control. Noise levels are computed with a decoupling approach, where the engine noise data and the flight trajectory are calculated independently. It is shown that implementation of the VNRS for the supersonic civil aircraft could lead to a reduction in the certification noise levels at the lateral and flyover measurement points by about 4 EPNdB. The effect of VNRS on noise levels for two allowable positions of the lateral certification point (on the sideline and on the extended runway centerline) is considered and compared for the first time. It is found that the cumulative noise reduction at the flyover and lateral certification point due to the VNRS is larger by 0.8 EPNdB for the position of the lateral certification point on the sideline than for the position on the extended runway centerline.

1. Introduction

The renewed interest in civil supersonic transport (SST) leads to growing concerns about high levels of community noise, i.e., noise around airports produced by such aircraft. Community noise is airport-dependent but can be related to the certification noise metric defined by the International Civil Aviation Organization (ICAO) [1]. Typically, the lower certification noise of an aircraft leads to lesser noise exposure around the airport.

Subsonic aircraft has achieved impressive reductions in their certification noise levels during the last several decades, primarily due to using higher-bypass-ratio turbofan engines. However, such engines have larger diameters that limit their application for SST because of the increased drag at cruise with supersonic speeds. This contradiction in requirements for SST engines constitutes one of the major problems for next-generation SST design: low noise levels at landing and takeoff regimes imply high bypass ratios, while aerodynamic efficiency and low fuel burn at supersonic cruise require low-bypass-ratio engines. There are a number of available technologies for noise reduction, which include technologies for turbofan noise reduction at the source [2] and technologies relying on installation effects such as shielding [3]. However, they are not sufficient to ensure that SST complies with the current noise certification requirements for subsonic aircraft, which is a necessary condition for public acceptance of SST. As a result, a different approach has to be proposed for SST to achieve substantial noise reduction.

One approach to reducing the certification noise of next-generation SST consists of transferring a portion of the turbofan engines’ thrust at takeoff to buster engines [4]. The idea is to reduce the speed of the turbulent jet, which is a dominant noise source for low-bypass-ratio turbofan engines. This allows for achieving significant noise reduction because the jet noise level is proportional to the eighth power of jet speed in accordance with Lighthill’s theory [5]. The thrust deficit due to this jet speed reduction at takeoff is compensated for by turboprop buster engines, which have lower noise levels than those of high-speed jets. When the aircraft reaches a certain altitude and flight Mach number, the thrust of the turbofan engines is increased, while the blades of the turboprop buster engines are folded to avoid deterioration of aerodynamic characteristics of the aircraft at high flight speeds. It is envisioned that transferring a large portion of thrust to the buster engines (35% or more) would allow such an SST to comply with the existing noise regulations for subsonic aircraft [4].

Another approach to certification noise reduction consists of using advanced takeoff procedures [6]. Whereas the reference certification procedure for subsonic aircraft prescribes that a significant part of departure flight has to be performed at maximum thrust, with the constant configuration of high-lift devices (HLD), etc., this approach proposes to modify the requirements for next-generation SST. It capitalizes on the excess thrust capability of SST engines at takeoff: in contrast to subsonic aircraft, supersonic aircraft have more thrust available than is necessary for a safe takeoff. As a result, it is possible to change the engine operation or airframe configuration in order to reduce noise during the departure procedure. To make the idea viable it has to be ensured that the control of engine thrust, or airframe configuration is fully automatic, so that it is performed not only during the aircraft certification but is reproduced in day-to-day operations of the aircraft as well. The aircraft subsystems that realize this automatic control are called variable noise reduction systems (VNRS) [7]. The major objective of the present study is to assess the VNRS efficiency in terms of noise reduction for SST.

There are several studies that considered the implementation of different VNRS for supersonic aircraft noise reduction [8,9,10,11,12,13,14,15,16,17]. An overview of their results is provided in

Table 1. An overview of the results of previous studies of VNRS implementation for SST.

Paper	Aircraft	MTOM, kg	Number of Engines	HLD Control	Noise Reduction due to VNRS
Grantham and Smith (1981) [8]	AST-105-1	311,164	4	Yes	5 EPNdB
Olson (1992) [9]	AST-105-1	311,164	4	No	4.3 EPNdB
Mirzoyan and Khaletskii (2023) [10]	SBJ	55,000–77,000	2-3	No	18 EPNdB
Berton (2023) [11]	STCA	55,000	3	Yes	5.2 EPNdB
Voet et al. (2024) [12]	STCA	55,000	3	No	10.6 EPNdB
Muñoz et al. (2023) [13]	SSAL	156,492	4	No	3 EPNdB
Graebert et al. (2024) [14]	SBJ	41,697	2	No	5.5 EPNdB
	SSAL	144,277	4	No	14 EPNdB
Bertsch et al. (2024) [15]	TWO	55,412	2	No	5.1 EPNdB
	THREE	51,000	3	No	4.9 EPNdB
Akatsuka (2024) [16]	S3	66,600	2	Yes	2.1 EPNdB
Horton and Busch (2024) [17]	STCA	55,000	3	Yes	5.3 EPNdB

; since all of the studies used thrust control, it is not specified in Table 1.

Table 1 demonstrates that the obtained effect of VNRS implementation for SST varies significantly for different studies and aircraft concepts. The importance of the aircraft concept on VNRS efficiency was also highlighted in [18]. There, a reduced-order model for SST takeoff noise was proposed that showed a difference of 19.2 dB in the noise reduction potential through VNRS implementation between the reference Mach 1.4 aircraft and a Mach 2.2 aircraft.

These studies computed aircraft noise with semi-empirical models for different noise sources (jet noise [19], fan noise [20], etc.), based on engines’ parameters at a given point of the takeoff trajectory. A significant amount of attention has been paid to uncertainties [16,21] and sensitivities to the parameters [22] of these models. Such an approach is excellent for the reference certification procedure [23] or for “simple” advanced takeoff procedures (a programmed lapse rate) [6], when a constant thrust reduction is applied soon after clearing the obstacle height. However, optimization for SST takeoff trajectories with this approach has proven to be a formidable and complex task. The complexity of the problem makes it error-prone, which leads some authors to recommend cautiousness when modeling the flights for the novel SST concepts [15].

The studies on SST noise modeling also mention an approach that relies on the so-called noise–power–distance (NPD) data [24]. The approach is used primarily for the computation of noise around airports and scenario assessment, rather than noise at the certification measurement points. In the absence of experimental data for the NPD characteristics of SST, they can be obtained via computation with semi-empirical models [21] for different noise sources and then used for assessing the noise contour areas [15,25]. In the context of the certification noise, it can be said to start, in a sense, with an answer, because rudimentary noise characteristics for each airplane are given as tabular lookup data [11].

There is, however, a different approach that does not seem to be considered in the previous studies on SST noise reduction with VNRS, but which is commonly used for the optimization of trajectories and high-left-devices configuration for subsonic aircraft. The approach decouples engine noise modeling from trajectory computation. It uses engine noise data obtained for a number of thrust values, typically from static engine tests on open test rigs (Figure 1a) or, less frequently, from tests of engines installed on an aircraft (Figure 1b) as one-third octave noise spectra for a range of azimuthal observation angles. The static noise data can be interpolated for different thrusts, thus providing noise level SPL as a smooth function of frequency, azimuthal angle, and thrust. In conjunction with a simple interpolation of the engine thrust as a function of flight speed and altitude at takeoff, it allows for significant simplification of the optimization procedure.

The decoupling approach thus relies on experimental data for engine noise that are obtained independently of the flight parameters of aircraft. Although the noise sources of aircraft engines in static conditions can be different from those in flight conditions [28], it is the static condition data that are used at the later stages of aircraft design. As a result, the methods of estimating certification noise levels based on such kind of data are very reliable and mature. The present study intends to capitalize on this experience of calculating certification noise of subsonic aircraft at the later design stages and implement it for assessment of VNRS efficiency.

At takeoff, the ICAO defines the certification noise at two measurement points, lateral and flyover [1]. All the above studies consider the lateral certification point the point located on a line 450 m parallel to the runway centerline; this measurement point is used for the certification of subsonic jet aircraft. However, there is another position for the lateral certification point, which is used for the certification of propeller-driven subsonic aircraft. It is located on the extended runway centerline below the departure flight path, where the aircraft altitude at full thrust is 650 m. As an example of the SST concept with turboprop buster engines [4] shows, it is not immediately obvious which position of the lateral point should be preferred.

The current efforts of researchers and the industry aim at achieving compliance of next-generation SST with the current ICAO regulations for subsonic aircraft noise (so-called Chapter 14 norms). If the certification noise levels for SST with or without VNRS prove to be lower at one position of the lateral point than at the other, this can be used to demonstrate lower certification noise levels without additional effort. Therefore, it is of interest to consider SST noise levels for both allowable positions of lateral certification points, as well as the efficiency of VNRS for noise reduction in both positions.

Thus, the contribution of the paper is twofold: firstly, it provides an assessment of VNRS efficiency for SST noise reduction at takeoff with the decoupling method, and secondly, it compares these results for two possible choices of the lateral certification point. It has to be stressed that the study focuses on VNRS efficiency and does not involve an investigation of the aircraft’s compliance with Chapter 14 norms.

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 (K₁) is positioned 6500 m behind the break release point on the extended runway centerline below the departure flight path. The lateral point (K₂) 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 (K₄) 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 K₁, 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 (K₄), 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]. However, it is also expected that the efforts on VNRS development for supersonic aircraft, such as the automatic control of high-lift devices, will lead to wider implementation of VNRS for subsonic aircraft as well, including propeller-driven aircraft.

Since there seems to be no accepted interpretation of how the certification point should be defined for a VNRS-equipped aircraft, for the purpose of this study, the lateral point K₄ is defined as the point on the extended runway centerline, corresponding to the flight altitude of 650 m. Thus, by analogy with the other position of the lateral certification point (K₂), the requirement of full takeoff power (the maximum available thrust) is excluded from the definition. However, to make the comparison of points K₂ and K₄ more representative, the study will limit their consideration to the case when the distance X₄ from the point of brake release to point K₄ is less than the distance X_D to Point D, where the pilot-initiated cutback is initiated:

X₄ < X_D

(1)

It allows the VNRS efficiency for cumulative noise reduction at these points to be compared in a consistent manner.

3. Description of SST and Its Departure Noise Modeling

The study considers a next-generation SST configuration (Figure 3) with a maximum takeoff mass of 72 tons, powered by three engines with a bypass ratio of 2.5 at takeoff. It has a seating capacity of 20 passengers and is designed for a cruise speed of M = 1.8, a flight range of 7400 km, and a balanced field length of 3200 m. Its takeoff thrust-to-weight ratio is 0.52, takeoff wing load is 450 kgf/m², and the maximum lift-to-drag ratio of the aircraft at takeoff is L/D = 6.5 [30].

As has been noted in the Introduction, in this study, the modeling of aircraft noise involves decoupling of engine noise data determination from flight trajectory calculations. This is commonly performed for subsonic aircraft when the static acoustic test data are available for aircraft engines. At the moment, it seems that such data are absent for engines of next-generation SST, which makes the researchers, and the industry rely on the simulation results based on semi-empirical models of powerplant noise sources.

The SST configuration used in this study has been developed with a view to an existing subsonic donor engine (Figure 1b), which has the same bypass ratio of 2.5 and can produce the same thrust at takeoff that is required for the SST departure procedure. Indeed, it is likely that engines of future SST will be different from their subsonic analogs with the same thrust and bypass ratio. However, SST engines are still under development, and how their acoustic characteristics differ from the engines for subsonic aircraft is one of the uncertainties of the SST research. Since the objective of the study consists of the assessment of VNRS efficiency for noise reduction, and not in determining the compliance of the SST with Chapter 14 norms, it was deemed possible to use the experimental acoustic data of the subsonic engine for noise calculations of the SST at takeoff [27]. Such an approach ensures that all the noise sources of the engine are accounted for and allows the uncertainties associated with engine cycle modeling to be excluded from the analysis of VNRS efficiency.

In general, noise modeling of the next-generation SST in this study is performed in such a manner as to minimize the uncertainties of noise calculation methods. For instance, although one engine of the next-generation SST is located above the fuselage, so that its noise can be shielded by the airframe, no correction for the shielding has been implemented. The under-the-wing engines of the next-generation SST have long inlets that can result in significant noise reduction, especially after acoustic liners are installed inside the inlet ducts. However, sound propagation in such long and curved ducts with impedance walls is not sufficiently understood at the moment, so no additional correction for this effect has been used as well. Such assumptions are intended to allow for isolating (decoupling) the effect of VNRS by engine thrust control from the effects of installed engine noise modeling.

Airframe noise is considered an important noise source of subsonic aircraft at approach [32]. During takeoff, the contribution of airframe noise is small even for subsonic aircraft; the available estimates show that airframe noise of SST at takeoff is small as well [14,17,21]. In [21], it was obtained that the airframe noise of the SST is smaller than engine noise by 27.9 EPNdB at the lateral certification point K₂, and by 23.7 EPNdB at the flyover certification point K₁. Similarly, in [17] it was shown that the airframe noise is less than engine noise by 15 EPNdB and 25 EPNdB at the flyover and lateral certification points, respectively. Although the authors of [14] did not provide quantitative estimates of airframe noise, their calculations led to the conclusion that this noise source was insignificant compared to engine noise. Therefore, no attempt has been made to account for the effects of airframe noise during the certification departure procedure of the SST in this study.

On the other hand, the effects of noise propagation from the aircraft to the certification measurement points have to be rigorously simulated, because the implementation of VNRS for SST noise reduction to a large extent relies on and benefits from these effects, especially the effect of lateral attenuation discussed in Section 2. Therefore, noise propagation modeling includes spherical spreading, Doppler shift and convective amplification, atmospheric absorption (ISO 9613-1:1993) [33], lateral ground attenuation [34], and ground reflection [35]. It can be seen that the effects of ground reflection and lateral attenuation are calculated independently, which is a standard practice. Recently, a novel method was proposed in [36] to account for both these effects simultaneously. In appendices of [36], detailed descriptions of a ground reflection method and a lateral attenuation method are conveniently provided. However, the authors of the present study do not have previous experience in the implementation of the novel method, nor have they validated it in the experiments; therefore, it has been decided to perform the present study with the use of the standard calculation methods for ground reflection and lateral attenuation.

The resulting approach for noise calculation is very robust and is based on a reliable set of data, as well as on the validated and widely used methods for prediction of noise propagation from the source position to the measurement points.

Validation of the approach to model SST noise was performed in the context of modeling the noise of a Supersonic Technology Concept Airplane (STCA) developed by NASA [37] (p. 40). TsAGI used SOPRANO software v.4.0 [38] to calculate STCA noise for the reference departure procedure, and its results generally agreed with those provided by NASA and JAXA [39] (

Table 2. Comparison of calculation results for STCA certification noise (in EPNdB).

	NASA	TsAGI	JAXA
Flyover	84.4	84.3	83.5
Lateral (K2)	97.2	95.4	96.7
Approach	95.9	98.8	97.0
Cumulative	277.5	278.5	277.2

).

The flight trajectory of the SST at takeoff is calculated based on a set of two-dimensional flight dynamics equations that describe the horizontal and vertical motion (X, H) of the aircraft as a function of time t. The rate equations for the position vector (X, H), velocity V, and the climb angle γ are given by

$$\begin{array}{c}{\displaystyle \frac{dV}{dt}} = {\displaystyle \frac{g}{W}}\left[T\cos \left(\alpha + \delta \right) - D - F_{\mathit{fric}} - W\sin \gamma \right],\\ {\displaystyle \frac{d\gamma }{dt}} = {\displaystyle \frac{g}{VW}}\left[T\sin \left(\alpha + \delta \right) + L - W\cos \gamma \right],\\ \begin{array}{cc}{\displaystyle \frac{dH}{dt}} = V\sin \gamma ,& {\displaystyle \frac{dX}{dt}} = V\cos \gamma \end{array}\end{array}$$

(2)

where g is the acceleration due to gravity, T is the full thrust of the engines, W is the weight of the aircraft, D is the aerodynamic drag of the aircraft, L is the lift force of the aircraft, F_fric is the rolling friction force, H is the flight altitude, X is the distance from the brake release, α is the angle of attack, δ is the angle of the thrust vector direction.

Lift and drag forces depend on velocity V and angle of attack α:

$$\begin{array}{cc}L = C_L\left(\alpha ,{\theta }_{\mathit{flaps}}\right){\displaystyle \frac{1}{2}}\rho V^2,& D = C_D\left(\alpha ,{\theta }_{\mathit{flaps}}\right){\displaystyle \frac{1}{2}}\rho V^2\end{array}$$

(3)

where ρ(H) is the air density, while coefficients C_L and C_D are considered known for a given aircraft configuration defined by the position of high lift devices θ_flaps [40].

In addition, an additional assumption is made that the available engine thrust is a linear function of the aircraft velocity V and altitude H in the considered range of these parameters, so that

$$T = \tau T_0\left(1 - aV\right)\left(1 - bH\right)$$

(4)

where T₀ is the engine thrust under static conditions at the sea level. Thrust setting coefficient τ is introduced to account for thrust control by an automatic VNRS or by a pilot at the cutback point.

The certification procedure described in Section 2 imposes a number of constraints that the variables of Equations (2)–(4) have to meet, which were conveniently tabulated in [12]. The present study also preserves the constraint that the indicated speed must be kept constant after clearing the obstacle height and before reaching the pilot-initiated cutback point. The condition of constant indicated speed is related to the flight speed V by the following expression:

$${\displaystyle \frac{dV}{dt}} = -{\displaystyle \frac{V^2}{2\rho }}{\displaystyle \frac{d\rho }{dH}}\sin \gamma ,$$

(5)

which can be used for simplification of the first equation of (2).

Equations (2)–(5) are solved with TsAGI in-house code that was developed and extensively used for determining the optimal deflection of high-lift devices θ_flaps to minimize the certification noise of subsonic aircraft [41]. It has been compared with SOPRANO [38] results and agrees well both for subsonic and supersonic aircraft. For the purposes of the present study, it has been modified to allow for variable thrust control. The position of high-lift devices θ_flaps, is kept constant during the departure procedure in the same manner as is done for subsonic aircraft; thus, the considered VNRS is limited to variations in thrust.

The resulting trajectory is represented as a number of segments, and for each segment, aircraft noise is calculated based on the available engine noise data. Under the assumption that the aircraft noise source is compact, the noise is propagated from the position at the takeoff trajectory to the certification microphones. Certification regulations [1] require that the temporal resolution for the measured signal at the microphone should be not less than 0.5 s, so the condition has been always checked, and the number of segments has been increased if necessary to ensure a time step Δt < 0.5 s. Based on the calculated time series at the microphone, the effective perceived noise level (EPNL) was computed.

A block diagram of the modeling approach used in the study for the calculation of certification noise of the SST is provided in Figure 4. Its input data consist of:

• Aerodynamic characteristics of the aircraft, such as C_L and C_D, for different angles of attack and flap deflection angles.
• Engine performance characteristics, such as thrust T, for different flight velocities and altitudes.
• Engine noise matrices, i.e., one-third octave noise spectra for a range of azimuthal observation angles and different thrusts.
• Parameters for calculation of noise propagation and loudness: coefficients for atmospheric absorption, coefficients for ground reflection, and noy tables.

4. Results for VNRS Efficiency at the Lateral Certification Point K₂

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 τ. 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 K₂, 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 α₀, which stands for the angle of attack after clearing the obstacle height, since α₀ is a control parameter of the problem. By changing the value of α₀, 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 α₀.

Let us now consider the case of thrust control, when the thrust is allowed to vary after clearing the obstacle height. The thrust setting τ 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.

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 α₀; however, the reduction in the cumulative noise level due to the implementation of the thrust control is present and can reach four EPNdB.

5. Results for VNRS Efficiency at the Lateral Certification Point K₄

Let us now consider the other position of the lateral certification point (K₄), 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 K₄ and K₂ more representative, the additional constraint by Equation (1) is imposed on the position K₄ of the lateral certification point.

Unlike position K₂ of the lateral certification point, where lateral attenuation is relied upon for noise reduction; noise propagation to position K₄ 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 K₂. The results then were compared with the data for position K₂ 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 K₄, 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 K₂ of the lateral certification point, as has been performed in Section 3, but with an additional constraint given by Equation (1). Nevertheless, such an optimization could be considered unrepresentative, because it would account for both positions of the lateral certification point: K₂ via the choice of the cost function, and K₄ 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 (K₂ and K₄) 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 K₂ and Figure 8b for position K₄ 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 K₄, as can be seen from Figure 8b. Nevertheless, this is less than the reduction of three EPNdB observed for position K₂ of the lateral certification point. It is thought that the resulting difference of 0.8 EPNdB in noise reduction with thrust control for the positions K₂ and K₄ is caused by the effect of lateral attenuation, which is present for position K₂ and absent for position K₄.

However, it should be repeated that the advanced takeoff trajectory was optimized for position K₂ of the lateral certification point, whereas no optimization was performed for position K₄. It can be expected that optimization of the advanced takeoff trajectory for position K₄ will lead to further noise reduction at position K₄, so it is likely that the cumulative noise reduction for optimized trajectories will be similar for positions K₂ and K₄.

6. Conclusions and Future Work

The study investigates the efficiency of the noise control approach for a notional supersonic civil aircraft at takeoff, based on the implementation of VNRS with thrust control. Noise levels are computed with a decoupling approach, wherein the engine noise data and the flight trajectory are calculated independently. For the purposes of this study, experimental data of static noise tests (one-third octave spectra over a range of azimuthal angles for different thrusts of the subsonic donor engine) were used to obtain the powerplant noise levels of the aircraft at all points of its takeoff trajectory. However, the data can be obtained numerically as well, based on the semi-empirical models of different engine noise sources (jet noise, fan noise, core noise, etc.)

An in-house code for optimization of high-lift device deflection angles to minimize the certification noise levels of subsonic aircraft was modified to allow for automatic thrust control. The modified code was used to compute the standard and advanced (i.e., with variable thrust) takeoff procedures and for optimization of thrust control for the certification noise at the lateral and flyover measurement points.

It is shown that implementation of such a VNRS for supersonic civil aircraft could lead to the reduction in the certification noise levels at the lateral (on the sideline at 450 m) and flyover measurement points by about four EPNdB. This noise reduction is a result of an intricate balance between noise reduction at the lateral point due to lateral attenuation and noise increase at the flyover point due to a decrease in flight altitude over that point.

The effect of VNRS on noise levels for the other allowable position of the lateral certification point (on the extended runway centerline) is considered for the first time. Its consideration in the context of SST noise studies is motivated by the concept of SST with turboprop buster engines [4]. However, it is also expected that the efforts on VNRS development for supersonic aircraft, such as the automatic control of high-lift devices, will lead to wider implementation of VNRS for subsonic aircraft as well, including propeller-driven aircraft. It is highlighted that additional clarity from regulatory authorities on the definition of the lateral certification point on the extended runway centerline may be needed.

It is obtained that the reduction in the cumulative certification noise at the flyover and lateral point due to the VNRS is larger by 0.8 EPNdB for the position of the lateral certification point on the sideline than for the position on the extended runway centerline. It is likely that the difference is caused by the effect of lateral attenuation for the former case. However, the thrust control used for noise calculation at the advanced takeoff procedure was the same for both positions of the lateral certification points, and thus it was not optimized for noise abatement at the lateral point along the extended runway centerline. Optimization of the advanced takeoff procedure for this position will lead to further noise reduction at the point, so that the cumulative noise reduction for optimized trajectories will be similar for both positions of the lateral certification point. Such a study can be performed when more regulatory certainty on the certification point in the context of VNRS implementation becomes available. The current status of the results of the study lead to the tentative conclusion that position K₂ for the lateral certification point provides lesser certification noise levels for SST.