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Design and operational assessment of a low-boom low-drag supersonic business jet

There has been a worldwide interest to develop a supersonic business jet (SSBJ) for a minimum range of 4000 nm with low sonic boom intensity and high fuel efficiency. An SSBJ design model is developed in the GENUS aircraft conceptual design environment. With the design model, a low-boom low-drag SSBJ concept is designed and optimized. This article studies the design concept for its operational performances. The sustained supersonic cruise flight is studied to find out the fuelefficient Mach number and altitude combinations. The combined supersonic and subsonic cruise flight scenarios are studied to evaluate the feasibility of boom-free flight routes. The one-stop supersonic cruise flight scenario is studied to compare the fuel consumption and time advantage over subsonic airliners. The off-design sonic boom intensity is studied to explore the operational space assuming there would be a sonic boom intensity limit in the future. Through the studies, it is revealed that there is a corresponding most fuel-efficient operating altitude for a specific cruise Mach number. To operate the aircraft near the cutoff Mach number leads to both increases in the fuel consumption (6.3%–8.1%) and the mission time (11.7%–13.1%). The business-class supersonic transport (231 g/PAX/km) consumes nearly three times fuel as the economic-class supersonic transport (77 g/PAX/km), which is still far more than the economic-class subsonic transport (20 g/PAX/km). Off-design sonic boom intensity studies reveal different trends against the common understanding: the sonic boom intensity does not necessarily decrease as the altitude increases; the sonic boom intensity does not necessarily decrease as the Mach number decreases.


Introduction
The supersonic civil transport aircraft is unique in the civil aviation history. It has been over 50 years since the first flight of Concorde, which retired in 2003 due to the high operating costs and the rising environmental concerns (sonic boom, noise, emissions, etc.). It is widely recognized that the biggest challenges for civil supersonic transport are sonic boom disturbance and high fuel consumption. 1 There has been a renewed interest in designing environmentally friendly, economically viable, and technologically feasible aircraft for the next-generation supersonic civil transport, of which the pioneer is considered to be the supersonic business jet (SSBJ). 2 The supersonic business jet is smaller in size and mass, resulting in a lower sonic boom level. It is reasonable to assume that the business jet users (such as executives or heads of state) are more willing to pay for a time-saver. However, the future supersonic civil transport can be viable only if overland supersonic restrictions are relaxed or entirely lifted. 3 There have been studies on low-boom low-drag supersonic transport. 4,5 Accordingly, NASA is working on the experimental Quiet Supersonic Technology X-59 6 to support the potential change in Federal Aviation Administration regulations, which bans supersonic flight over land. Besides the sonic boom intensity, the supersonic aircraft are desired to be more efficient in fuel consumption, thus a lower operating cost and emissions. Japanese Aerospace Exploration Agency has been conducting experiments [7][8][9] to help develop the low-drag supersonic transport. Aerion Supersonic has been updating its supersonic natural laminar flow wing concept 10 to get a higher cruise aerodynamic efficiency. BOOM Technology 11 is developing a 55-seat supersonic passenger airliner with lower ticket price.
Currently, most of the efforts focus on the development of a technical feasible supersonic transport concept, few of them study the operational performance of a design. Gonzalez 12 studies the influence of the flight profile but puts main focus on the climb segments. Gonzalez-Gallego et al 13 study the trade-offs of subsonic and supersonic combined flight profiles, but their studies are based on a simple research model, and there is a lack of sonic boom performance assessment. Liebhardt et al 14 study the fullpermit, mixed-permit, and no-permit flight scenarios and conclude the cutoff Mach number is a valuable asset for supersonic operations. Li et al 15 study two different overwater routers for two different designs. The International Council on Clean Transport studies the environmental noise and emission standards of supersonic transport in the Stanford University Aerospace Vehicle Environment environment and suggests the policymakers to establish new environmental standards for supersonic transport. 16 For offdesign conditions, Lazzara et al 17 reveal the perturbations of the angle of attach and Mach number would have an impact on the ground boom signature. This article intends to show the feasibility of low-boom low-drag supersonic designs in a more general multidisciplinary perspective, to study the fuel conservation operating scenarios, and to explore the sonic boom avoidance or constrained overland flight profiles.
The structure of the article is as follows. The MDAO environment to design and analyze the supersonic concepts is described in Section 2. Section 3 presents the design results of a low-boom low-drag SSBJ and the design methods employed. The operational assessments of the SSBJ concept are detailed and discussed in Section 4. Finally, the conclusions and future work are drawn in Section 5.

Multidisciplinary design analysis and optimization environment
The research is conducted in a MDAO environment called GENUS. 18 It is the aim of the GENUS aircraft conceptual design environment to provide a modular, flexible framework both for designers to use existing and for researchers to develop new or use existing methods for aerospace vehicle design. GENUS is independent of commercial codes and is coded in Java, sequentially running on one single core. After evaluating various design systems, nine essential modules and a special module are identified, as shown in Figure 1. The environment can synthesize and analyze most aerospace vehicle concepts. The modules are linked together tightly, which makes the multidisciplinary design analysis and optimization possible. GENUS has shown its capabilities through a solar unmanned aerial vehicle (UAV) design, 19 a hypersonic transport design, 20 a blended-wing-body airliner design, 21 a conventional airliner design, 22 and a combat UAV design. 23

SSBJ design case
The main challenges for supersonic aircraft design are the sonic boom at ground level and low supersonic efficiency at cruise. The sonic boom can be avoided below the cutoff Mach number (around Mach 1.15); however, the time advantage at this Mach number is not evident. Through the previous studies, the authors have established multidisciplinary methodologies for supersonic transport, 24 validated the design model against different designs, 25 demonstrated the sonic boom can be shaped by tailoring the lift and volume distribution, 26 and proved the feasibility of low-boom and low-drag design optimization. 27 Therefore, all the previous efforts make the design of a low-boom low-drag SSBJ concept possible. Furthermore, this article will study the operational performances of an SSBJ concept to help gain more in-depth understanding on the supersonic transport, especially the sonic boom intensity and fuel efficiency. This part introduces the design from a multidisciplinary view.

Design mission
The mission module specifies the flight requirements for a design. These requirements are derived from the market or customer specifications. The mission requirements, shown in Table 1, for SSBJs have been analyzed by the authors in a review article, 1 considering the environmental impacts, technological challenges, and market analysis. They are assumed to be the appropriate initial requirements for environmentally friendly and economically viable SSBJs.

General geometry layout
The geometry parts are abstracted into the lifting surface and body component arrays. The lifting surface array is then specified as a wing, horizontal tail, vertical tail, or canard. The body component array is specified as a fuselage, engine pod, external tank, or tail boom. In this way, the geometry module can represent most of the configurations. The authors have analyzed several different wing and fuselage combinations in a previous study 26 and find that a low-boom low-drag design should have uniform longitudinal volume and lift distributions. The fuselage is expected to be slenderer, and a highly swept wing is expected to flat the lift distribution. A horizontal tail is preferred rather than the canard because the horizontal tail can help to reduce sonic boom signature in the aft part. The SSBJ concept geometry is shown in Figure 2.

Aerodynamics
The main aerodynamic analysis tool is panel aerodynamics (PANAIR). 28 PANAIR can predict inviscid subsonic and supersonic flows of arbitrary configurations by solving a linear partial differential equation numerically. There are several studies 29-31 on supersonic transport applying the PANAIR method, and its accuracy is believed to be sufficient for conceptual design. For aerodynamic analysis, PANAIR can provide lift coefficients and induced drag coefficients. The drag components for supersonic flight are denoted by equation (1) where C D is the total drag coefficient, C D F is the friction drag coefficient, C D wave is the supersonic wave drag coefficient, and C D LV is the lift-induced vortex drag coefficient. The form factor method 32 is modified to calculate the zero-lift skin friction and form drag. The result comes from the contribution of each component, as shown in equation (2) where N is the number of geometric components used to model the configuration, FF j is the form factor of component j, C F j is the skin friction coefficient of component j, S wet j is the wet area of component j, and S ref is the reference area of the total aircraft. The supersonic area rule 33 is applied to calculate wave drag due to volume, as indicated in equations (3) and (4). For accurate wave drag calculation, the Mach plane crosssectional area intersecting with the geometry is required where θ is the angle between the Y-axis and a projection onto the Y-Z plane of a normal to the Mach plane, l is the  overall aircraft length, and AðxÞ is the ray tube area at longitudinal coordinate x.
The drag components and drag polar are plotted in Figure 3, and the surface pressure distribution is given in Figure 4.

Propulsion system
The propulsion module uses the NASA EngineSim model 34 to build a rubber engine system. There are four types of engines that EngineSim can design: a turbojet, a turbojet with afterburner, a turbofan, and a ramjet. EngineSim calculates these engines based on the geometry, material properties, flight conditions, throttle setting, and so on. A low-bypass turbofan engine, which is the design for the SSBJ concept, is within the design capability of EngineSim. The design parameters, cruise thrust and specific fuel consumption (SFC) of the engine are shown in Table 2.

Performance
The performance module is designed to flexibly assemble different segments, which consist of various types of climb, cruise, and descent methods. Each segment consists of a number of control points, which are continuous in the Mach number, angle of attack, aerodynamic coefficients, etc. To keep the continuity between segments, the end point of the last segment is set to be the starting point of the next segment. In the later operational assessments, the supersonic and subsonic cruise segment combination and one-stop profile are manipulated in this module.

Sonic boom near-field pressure
The Whitham theory 35 is used for the near-field pressure calculation. The equivalent area due to volume and where A e ðx,θÞ is the equivalent area at coordinate x and angle θ, A v ðx,θÞ is the Mach plane cross-sectional area at coordinate x and angle θ, β ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , q ∞ is the ambient dynamic pressure, and Lðx,θÞ is the lift on a spanwise strip per unit chordwise length.
The F-function derives from the equivalent area, as shown in equation (6) FðxÞ ¼ 1 2π where FðxÞ is the F-function. In this research, the F-function is decomposed to F-function due to volume and F-function due to lift, as indicated by equation (7). This helps to study their individual effects on sonic boom intensity, as plotted in Figure 5 Fðx,θÞ ¼ F volume ðx,θÞ þ F lift ðx,θÞ where F volume is the F-function due to volume and F lift is the F-function due to lift. The near-field pressure is then calculated based on the Whitham theory, as shown in equation (8) δpðxÞ where δp ¼ p À p 0 , p 0 is the ambient pressure, γ is the ratio of specific heat, M is the flight Mach number, and r is the radius in polar coordinate. The near-field pressure is optimized through the shaped sonic boom technology by varying the wing and tail planes' geometry and positions with essential performance constraints. The F-functions and near-field pressure are plotted in Figure 5.

Sonic boom ground signature
The waveform parameter method 36 is based on geometrical acoustics. This method calculates the sonic boom signature directly with distance steps along a ray, which is more suitable for automatic computation. It is reprogrammed in Java and implemented as a special module method. A weakness of the method is that the code expects one shock formation or coalescence at a time. For a complex signature with large numbers of points specified, there is a big chance of failure. This becomes a problem when using computational fluid dynamics data as F-function inputs. The ground sonic boom signature is plotted in Figure 6. It can be seen that the peaks of the near-field pressure and the ground signature are corresponding, which is very important for the lowboom design and analysis.

Operational assessments
This section gives several trade-off studies of a 10-passenger SSBJ concept in terms of the operational performance. Since the cruise segment has the biggest influence on the mission performance, it is mainly studied in this part. First, the sustained supersonic cruise flight is studied to find out the most fuel-efficient Mach number and altitude combination. Then, different combinations of supersonic and subsonic cruise flights are studied to gain understanding of the boom-free flight routes. Third, the one-stop supersonic cruise flights are studied to compare the fuel consumption and time advantage over subsonic airliners. Last, the offdesign sonic boom intensity study explores the operational space assuming there is an acceptable sonic boom intensity limit in the future.  The overall fuel consumptions at Mach numbers and altitude combinations are plotted in Figure 8. It can be seen from the figure that for each cruise Mach number, there is a range of altitudes where the fuel consumption is at its lowest. This gives the corresponding fuelefficient altitudes for different operational Mach numbers.
Here is the explanation for the results in Figure 8. As indicated by equation (9), for the same range and mass, the fuel is proportional to the factor SFC=Mach × L=D × a 0 . For the altitudes (11,000-19,000 m) studied, the speed of sound is the same. Therefore, the fuel consumption is dominated by the factor SFC=Mach × L=D where SFC is the specific fuel consumption, a 0 is the ambient sound speed, and L=D is the lift to drag ratio.
The fuel consumption factors are plotted in Figure 9, which shows the same results as Figure 8.  The above trade-off studies indicate that there is a fuelefficient altitude for a specific cruise Mach number. For example, the fuel-efficient altitude for Mach 1.20 is between 11,000 m and 13,200 m. For a fixed design, there can be a more detailed plot to indicate the most efficient cruise altitude for each Mach number, as illustrated by Figure 10. There is an operational feasible zone with the maximum fuel capacity limit. However, the design point is not actually the most fuel-efficient combination of Mach and altitude. If the design point changes, the whole operational plot will change accordingly. Further work still requires to explore the coordination of the design point and the most fuel-efficient point.

Combined supersonic and subsonic cruise flight
For a specific design, there is an operational scenario to meet the current regulations that ban civil supersonic flight  overland. That is to fly at supersonic speeds over sea to maintain the speed advantage and to fly below the cutoff Mach number (around Mach 1.15) over land to avoid sonic boom. In practice, this flight profile can be applied to, for example, a trans-Atlantic route where the initial and final flights are over land. The trans-Atlantic route is one representative case for the 4500 nm range. It is also one of the busiest routes for business travel and the route that Concorde operated. The purpose of this section is to study the performance of the supersonic and subsonic combination flight profile that comply the current regulations, which ban supersonic flight overland.
The SSBJ10 design mission total range is 4500 nm, of which 1000 nm is subsonic cruise range. The subsonic flight is at the normal subsonic airliner cruise altitude (around 11 km). A cutoff supersonic Mach number 1.15 and a low supersonic Mach number 1.20 are also studied.  Figures 11 (a) and (b), respectively.
The overall performance at different Mach numbers is plotted in Figure 12. It can be noticed that the subsonic cruise segment leads to a reduction in the total fuel consumption (5.0%-6.8%). However, there will be a significant mission time increase (20.8%-28.5%). The low supersonic cruises (near the cutoff Mach number) lead to increases both in the mission time (11.7%-13.1%) and the fuel consumption (6.3%-8.1%), resulting in a shorter mission range. Therefore, it is advised not to cruise the supersonic aircraft near the cutoff Mach number region, if the design point is not in that region.
From the above analysis, it can be seen that the supersonic and subsonic cruise combinations are fuel-  efficient. The subsonic cruise range and Mach number with the maximum design fuel capability are plotted in Figure 13. Though the complex of the transonic flow might influence the accuracy of the results, a low supersonic cruise subsegment is beyond the operational feasible zone. For different subsonic subsegment range mission, there is a corresponding fuel-efficient Mach number.

One-stop supersonic cruise flight
This part studies the long-range (more than the SSBJ design range 4500 nm) flight mission operated by sustained subsonic flights and one-stop supersonic flights. The representative routes for this operation would be the trans-Pacific routes, where the refueling stop can be Honolulu or Adak. Figures 14 (a) and (b) illustrate a 7000 nm one-stop mission profile of the supersonic flight over time and over range, respectively. The time lapse for refueling is assumed to be 60 min.
The results of fuel consumption and mission time are given by Figure 15. Not surprisingly, the subsonic airliner has the lowest fuel consumption (20 g/PAX/km). The business-class supersonic transport (231 g/PAX/km) consumes three times as much as a supersonic airliner (77 g/PAX/km), which is close to a business-class subsonic airliner (81 g/PAX/km). The advantage of supersonic flights is also quite obvious, saving about half (47%-53%) of the journey time.

Sonic boom intensity
This section studies the off-design sonic boom intensity of a fixed design at different Mach numbers and altitudes. The overall sonic boom performance is plotted in Figure 16. Here are two trends that against the common understanding. First, the sonic boom intensity does not necessarily decrease as the altitude increases. Second, the sonic boom intensity does not necessarily decrease as the Mach number decreases.  To explain the reason, the factors that influence the sonic boom intensity directly are investigated. From boom generation equation (7), the F-function due to volume and F-function due to lift have direct impact on the near-field pressure, which then influence the sonic boom intensity on the ground.
The lift coefficients at different Mach numbers and altitudes are plotted in Figure 17. These are the required C L to maintain level flight at different flight conditions. As the altitude increases, the air density decreases; therefore, the required C L increases. The same principle applies to the Mach numbers.
The impact of C L on the lift distribution and F-function due to lift are then plotted in Figures 18 (a) and (b), respectively. It can be understood that, for a fixed design, the lower the Mach number, the higher the C L . A higher C L   then leads to a higher peak in the F-function due to lift, which is then added to the total F-function.
On the other hand, the volume distributions vary with Mach numbers, as plotted in Figure 19(a). That is because the cross-sectional Mach plane angles are different at different Mach numbers. The F-functions due to volume, as shown in Figure 19(b), are then slightly different. All these differences are then added to the total F-function.
F-functions at different Mach numbers are plotted in Figure 20, which indicates the near-field pressure levels according to equation (8). The ground sonic boom intensity will have the same peaks as known from Section 3.7.
From the above analysis, it can be seen that the sonic boom intensity for a fixed design is more complex. This section can help the designer to get a more in-depth   understanding of the sonic boom feature of a supersonic aircraft. Figure 21 indicates the operational flexible zone under the assumed sonic boom limit of 1.0 psf (47.85 Pa).

Conclusions and future work
Through the study, a supersonic transport model is demonstrated in a multidisciplinary design analysis and optimization (MDAO) aircraft conceptual design environment. Within this model, the design of SSBJ concept is designed and optimized, and the operational performances of the specific design are assessed.
The purpose of this article is to study the operational performances of a fixed supersonic transport, which is seldomly studied before. First, the sustained supersonic flights indicate there is an operational flexible zone limited by the maximum fuel capacity. For a cruise Mach number, there is a corresponding most fuel-efficient operating altitude. Further work still requires to explore the coordination of the design point and the most fuel-efficient point. Second, the combined supersonic and subsonic flight scenarios show that a high subsonic cruise subsegment can help to meet the current civil supersonic flight regulations and reduce the fuel consumption by 5.0%-6.8%. However, the low supersonic (around cutoff Mach) cruise subsegments are both fuel-inefficient (6.3%-8.1% increase) and time-inefficient (11.7%-13.1% increase). Therefore, it is advised not to cruise near the cutoff Mach number region, if the design point is not in that region. Third, the one-stop supersonic flight scheme can gain 47% to 53% time advantage over subsonic flight for long-range mission, which is attractive for high-end passengers. However, the supersonic transports, especially the business  class, have tremendous fuel consumption (231 g/PAX/km) comparing to the subsonic economy class (20 g/PAX/km). New environmental standards will be required for the return of supersonic transport. Last, the off-design sonic boom performance is quite different from the common understanding. The sonic boom intensity does not necessarily decrease as the altitude increases and does not necessarily decrease as the Mach number decreases.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.