A Study on the Conceptual Design of a 50-Seat Supersonic Transport

Abstract

The research and development of the next generation of supersonic transports (SSTs) meets economic and environmental problems. An SST encounters critical challenges, including the need for low fuel consumption, low noise, and low gas emissions. Currently, the feasibility of developing SSTs is increasing through the application of cutting-edge technologies, such as composite materials, advanced electric systems, sustainable aviation fuel, and innovative design methodologies. The object of this study was to perform the conceptual design of a 50-seat supersonic transport utilizing general conceptual design methods. In estimating weight and flight performance, statistical formulae were correlated with data from civil supersonic and subsonic jet transports. For wing sizing, carpet plots were created to explore the optimal combination of wing aspect ratio and wing loading. The results suggested that by utilizing advanced technologies, such as the use of a composite material for the structure, the maximum takeoff weight can potentially be reduced while still meeting design requirements. The constraint of climb gradient largely affects the maximum takeoff weight, and it is anticipated that flight performance at low speeds will be improved.

1. Introduction

Due to economic efficiency and environmental issues, supersonic transports (SSTs) have not been in operation since Concorde [1] was taken out of service in 2003. SSTs meet critical challenges such as low fuel consumption, low noise, and low gas emissions. On the other hand, several startup companies [2,3,4,5] are showing considerable interest and are actively working on the development of supersonic commercial and business jets. Over the past few decades, researchers have made considerable efforts to advance the next generation of supersonic civil transports [6]. NASA initiated the QueSST project aimed at developing technologies minimizing sonic booms, which could enable a resurgence of commercial supersonic flight within the next decade [7]. With the progress of technologies, such as composite materials and advanced design methodologies, the return of supersonic flight is anticipated in the future.

In the NASA High-Speed Research Program, Shields, E.W. et al. [8] developed conceptual designs for configurations carrying 250 passengers at a Mach 1.6 cruise speed with a range of 6500 NM. With sizing, an optimized configuration was obtained to have a wing area of 7700 ft² and a takeoff gross weight of 650,672 lb. Since 1997, Japan Aerospace Exploration Agency (JAXA) has conducted research to achieve economic viability and environmental compatibility to develop technologies for the next generation of supersonic transport [9,10,11]. Torenbeek, E. et al. [12] analyzed a supersonic commercial transport aircraft carrying 250 passengers and concluded that the Mach 1.6 design has a significantly longer range than the reference Mach 2.0 design with the same takeoff weight. Welge, H. et al. [13] developed conceptual designs and concluded that a 30- to 40-passenger concept aircraft could potentially approach the low-sonic-boom goals, and a 100-passenger (dual-class) concept could meet the stated fuel efficiency goals. Munoz, C.V. et al. [14] compared emissions and noise for the different aircraft–engine combination platforms with a low-to-medium-fidelity method. The authors studied the conceptual design of the SSBJ [15] and investigated the range extension of a 50-seat SST [16]. There has been much research work [17,18,19,20,21,22] focusing on concepts of civil supersonic transport in recent years.

For SST visibility, one of the fundamental basic issues is overall econometric viability, including vehicle and operational costs, i.e., achieving competitive and affordable costs in terms of a passenger seat-mile. In the conceptual design, overall SST issues, including the improvement of econometrics and fuel burn, may be taken into account with reasonable estimation. In this study, a conceptual design was developed by utilizing a conventional design method [23,24,25,26] in which lift and drag were efficiently predicted by aerodynamic theories and engine performance and component weight were estimated by statistical methods. Conceptual designs are usually implemented using linear methods with low fidelity in accuracy and require a short amount of time. After that, CFD (Computational Fluid Dynamics), which can conduct highly accurate calculations, is now often used in the preliminary design. On the other hand, CFD has problems such as a high computational cost, shape creation, mesh generation, the numerical accuracy of shock wave drag and sonic booms, and others.

The objective of this study is to develop a conceptual design of a 50-seat supersonic transport with a flight range of 3500 NM (nautical miles) and investigate its flight performance in each phase of operation. The overall geometrical configuration, engine specifications, internal cabin layout, and component weight are decided through an iterative process in which the flight performance is estimated and meet mission requirements and constraints.

2. Design Requirements of the 50-Seat SST

In this study, the primary design requirements of the 50-seat supersonic transport are outlined in

Table 1. Design requirements of 50-seat SST.

Pilot + Crew	2 + 2
Seat	50
Range [NM]	3500
Altitude [ft]	50,000
Cruise Mach	1.6
$S_{FL}$ [ft]	<6000
$S_{TOFL}$ [ft]	<6000

. The aircraft can carry a maximum of 50 passengers, and its operational range of 3500 nautical miles allows it to cross the Atlantic Ocean, enabling travel from New York to London or Paris. Its cruise speed was set at Mach 1.6 so as to provide a competitive flight time advantage over subsonic jets. To operate in small key business airports, the field lengths of both takeoff and landing did not exceed 6000 ft.

The SST design was required not only to minimize shock wave drag and reduce viscous drag during supersonic cruising but also to improve the lift-to-drag ratio during takeoff and landing. As suggested in ref. [10], a cranked arrow wing was appropriate for achieving high aerodynamic efficiency within the operational Mach number range. The cranked arrow wing features inboard and outboard wings with highly sweptback supersonic leading edges. The layout of the 50-seat SST is illustrated in Figure 1. In this study, a cranked arrow wing was adopted, two jet engines were mounted at the rear, and the fuselage was area-ruled to mitigate wave drag in supersonic flight.

3. Layout of the Cabin

The fuselage design is highly restricted by the requirements to mitigate sonic booms and wave drag. Usually, the area rule of supersonic theory is applied to minimize wave drag, and the vehicle’s volume and lift distribution are taken into account to mitigate the sonic boom caused by shock waves. Typically, a large fineness ratio of the fuselage is essential to effectively reduce wave drag during supersonic flight. On the other hand, the distribution of the fuselage’s cross-sectional area and its length must be designed with careful consideration of the cabin size, which is dependent on the specified number of seats. The cabin size is determined by the fuselage’s cross-sectional geometry and the longitudinal layout of the seat rows. Meanwhile, the external shape of the fuselage should be marginally larger in size than the interior shape to allow for the structural framework. Therefore, the overall dimensions must be compact to reduce weight and aerodynamic drag, while also being spacious enough to ensure passenger comfort. The number of seats across determines the number of rows, which in turn affects the cabin’s length. In this study, to prevent the cabin from being excessively long or short, the final layout of the cabin is limited to three seats across and 17 rows with a single aisle, as illustrated in Figure 2.

The cabin length is related to the seat pitch and the number of seat rows. As supersonic transports typically possess a longer fuselage than their subsonic counterparts, a seat pitch of 38 inches is selected to afford passengers a luxurious spacing comparable to that of business class. The seat dimensions are based on the economy class standards of Japan Airlines Co., Ltd., Tokyo, Japan.

The cross-section of the cabin layout is shown in Figure 3. The layout was decided by referencing existing aircraft, such as the Saab 2000, along with Concorde and others. A minimum area for the cabin cross-section is preferred to mitigate wave drag. The final dimensions of seat and cabin are outlined in

Table 2. Dimensions of seat.

backrest height	0.80	m
seat surface height	0.45	m
seat height	1.25	m
seat width	0.63	m
backrest width	0.50	m
pitch	0.97	m

and

Table 3. Dimensions of cabin of 50-seat SST.

cabin width	2.40	m
cabin height	2.20	m
aisle width (A in Figure 3)	0.52	m
aisle height (B in Figure 3)	2.03	m
overhead locker to floor (C in Figure 3)	1.64	m

, respectively. The super ellipse was adopted as the cross-sectional shape. To facilitate the use of existing service carts, the aisle width was selected with reference to that of narrow-body aircraft like the Airbus A320 series. The dimensions of hand luggage, such as suitcases, were set according to the Japan Airlines guideline, which dictated a height of 45 cm, a width of 35 cm, and a depth of 20 cm for aircraft with under 100 seats. Two toilets and two galleys are set up at both the back and front of the cabin, on the side of the two seats.

The structural framework was assumed to have a thickness of 100 mm. The dimensions of the fuselage are shown in

Table 4. Dimensions of fuselage.

Fuselage diameter	2.60	m
Nose length	21.0	m
Tail length	24.0	m
Cabin length	20.0	m
Fuselage length	65.0	m
Thickness of structural framework	0.10	m

. Here, the external fuselage diameter was defined as the average of the external width and height. The distribution of fuselage diameter will be designed to mitigate wave drag at supersonic cruising. The shape of the nose and tail of the SSBJ [27] was referred to.

4. Initial Sizing

The flight profile of an SST may be split into several phases, as shown in Figure 4. The civil transport must meet specified airworthiness regulations with regard to the flying qualities and flight performance.

The weight ratios of the phases of cruise, alternate airport, and loiter were obtained using the Breguet equation, as shown in Equation (1).

$$R={\displaystyle \frac{V·{\eta }_j}{c_j}}·{\displaystyle \frac{L}{D}}\mathit{ln}\left({\displaystyle \frac{W_{initial}}{W_{final}}}\right)$$

(1)

where the specific fuel consumption $c_j$ and installation efficiency ${\eta }_j$ of the jet engine were calculated by an empirical method [28]. The bypass ratio $BPR=3$ was assumed according to the authors’ discussion [16].

As shown in

Table 5. Aircraft weight ratio of each phase.

Phase	Flight Status	Weight Ratio	Fraction
1	Engine start and warm-up	$W_1$/$W_{TO}$	0.990
2	Taxi	$W_2$/$W_1$	0.995
3	Takeoff	$W_3$/$W_2$	0.995
4	Climb	$W_4$/$W_3$	0.980
5	Cruise	$W_5$/$W_4$	0.630
6	Descent	$W_6$/$W_5$	0.985
7	Alternate airport	$W_7$/$W_6$	0.959
8	Loiter	$W_8$/$W_7$	0.968
9	Landing and engine shut down	$W_9$/$W_8$	0.992

, the weight fractions of each phase were assumed according to Roskam’s suggestions [25] for estimation by using the weight and statistical data of existing subsonic and supersonic civil aircraft [25]. In each flight phase, the weight of fuel consumption was calculated as a weight decrement. As a result, the fuel weight used in flight was finally decided to satisfy the block range.

First, $W_{OE}$ was estimated by using existing aircraft data. An approximate formula, i.e., Equation (2), was obtained by fitting the weight data of subsonic transports [29] and supersonic airplanes (Chapter of [25]) that existed in the past and performing collation with that of Concorde, as shown in Figure 5.

$$W_{OE}=2.995{W_{TO}}^{0.8489}$$

(2)

The ratio of fuel weight ($W_F$) and the maximum takeoff weight ($W_{TO}$) was determined to match the flight range with the specified payload. Then, $W_{TO}$ was calculated by iteratively solving the weight equation, Equation (3), while satisfying Equation (2).

$$W_{TO}={\displaystyle \frac{W_{PL}}{1-\left(\frac{W_F}{W_{TO}}\right)-\left(\frac{W_{OE}}{W_{TO}}\right)}}$$

(3)

These values were eventually decided to satisfy the specified mission and constraints. The initial weights of the 50-seat SST are shown in

Table 6. Initial weights of the 50-seat SST.

MTOW	$W_{TO}$	171,176	lbf
Fuel weight	$W_F$	77,228	lbf
OEW	$W_{OE}$	82,998	lbf

. As a result, the estimated values show that $W_{OE}$ and $W_F$ account for approximately 45.7% and 47.6% of $W_{TO}$, respectively.

Furthermore, any aircraft must be designed to meet all criteria at several flight conditions. For a jet-powered aircraft, the relations of the wing loading ($W/S$) and thrust-to-weight ratio ($T/W$) were obtained by estimating the results of flight performance at takeoff, landing, climb, and cruise. Then, Roskam’s method (Chapter 3 of [25]) was used to estimate the field lengths of takeoff and landing.

The length of runway available was assumed to be 6000 ft. The total FAR25 field length for takeoff ($S_{TOFL}$) was calculated by the following empirical equation. The coefficient was correlated with statistical data of existing jet-powered transports. $S_{TOFL}$ is inversely proportional to the maximum lift coefficient at takeoff ($C_{LmaxTO}$), which is desirable to be as large as possible.

$$S_{TOFL}=40.3·{\displaystyle \frac{{\left(\frac{W}{S}\right)}_{TO}}{\sigma C_{LmaxTO}{\left(\frac{T}{W}\right)}_{TO}}}<6000 \mathrm{f}\mathrm{t}$$

(4)

where $C_{LmaxTO}$= 0.9, 1.1, 1.3, and 1.5 were assumed to discuss the total FAR25 field length.

The approach speed $V_A$ for landing was limited by the maximum length of the airport runway. The relation was expressed by an empirical equation.

$$S_L=0.27{V_A}^2<6000 \mathrm{f}\mathrm{t}$$

(5)

According to this relation, $V_A$ must be less than 149 knots. Then, the wing loading was calculated by the definition of lift coefficient for different conditions of landing.

$${\left({\displaystyle \frac{W}{S}}\right)}_{TO}\le {\displaystyle \frac{\frac{1}{2}·\rho ·{V_A}^2·C_{LmaxL}}{\left(\frac{W_L}{W_{TO}}\right)}}$$

(6)

The criterion of one-engine-inoperative (OEI) climb was the following equation. The thrust-to-weight ratio ($T/W$) must be large enough for safety even if one engine is inoperative.

$${\left({\displaystyle \frac{T}{W}}\right)}_{TO}\ge {\displaystyle \frac{N_{eng}}{L_p\left(N_{eng}-1\right)}}\left(\gamma +{\displaystyle \frac{1}{L/D}}\right)$$

(7)

where the number of engines $N_{eng}$ = 2, lapse rate $L_p$ = 0.8, and climb angle $\gamma$ = 0.024 are given.

At cruising, the thrust was required to satisfy the aerodynamic conditions.

$${\left({\displaystyle \frac{T}{W}}\right)}_{TO}\ge {\displaystyle \frac{\left(\frac{W_{cr}}{W_{TO}}\right)}{L_{pcr}}}\left\{{\displaystyle \frac{q\left(C_{Do}\right)}{\left(W_{cr}/W_{TO}\right){\left(W/S\right)}_{TO}}}+{\displaystyle \frac{{\left(W_{cr}/W_{TO}\right)\left(W/S\right)}_{TO}}{qe\pi AR}}\right\}$$

(8)

For supersonic aircraft, a large sweep angle of the wing is usually adopted to reduce wave drag and results in a low aspect ratio ($AR$) related to the Mach number of supersonic cruise. On the other hand, $AR$ is required to be large enough for subsonic flight. Before the wing size was determined, trial calculations were conducted to set the range of $AR$ and wing loading, and then $AR=3.57$ was initially assumed for the wing in this study.

The above results are summarized in Figure 6. The shadow side of each line is the range not satisfying the requirement. Constraints of $S_{TOFL}$ for different $C_{LmaxTO}$ values and $S_L$ for different $C_{LmaxL}$ values are plotted. It was observed that $T/W$ was reduced with an increase in $C_{LmaxTO}$ and $C_{LmaxL}$. According to the existing data [25], $C_{LmaxTO}=1.3$ and $C_{LmaxL}=1.6$ were assumed in the initial design. The initial design was chosen to minimize $T/W$ and satisfy all criteria at the same time. As a result, in the process of the initial sizing, the design point was determined as shown in Figure 6, i.e., ${\left(T/W\right)}_{TO}=0.478$ and ${\left(W/S\right)}_{TO}=76.5$ lbf/ft². The initial design results are summarized in

Table 7. Initial sizing result.

Wing loading [lbf/ft2]	${\left(W/S\right)}_{TO}$	76.5
Thrust-to-weight ratio	${\left(T/W\right)}_{TO}$	0.474
Wing area [ft2]	$S$	2238
Maximum takeoff thrust [lbf]	$T_{TO}$	81,172
Lift coefficient at takeoff and landing	$C_{Lmax,TO}$	1.3
	$C_{Lmax,L}$	1.6

. Then, the wing area and engine thrust were estimated.

5. Refinement of the Initial Design

After the initial sizing, the design was refined to obtain the main specifications and flight performance in detail. The thickness of the wing and tail was assumed to be 3%, and the volume coefficients of horizontal and vertical tails were based on statistical data of jet-powered aircraft.

The component weights were estimated by the empirical methods summarized in Roskam’s book (Chapter 5 of [26]). The structure weights of the wing, tail, fuselage, and gear were calculated by the GD method; the weight of the nacelle was calculated by the Torenbeek method; the weight of the power plant and equipment was calculated by the Jenkinson method; and the weight of the operating item was calculated by the Howe method. In order to apply these methods to the supersonic transport, coefficients were modified to correlate with existing data of SST and subsonic jet transports. As an example, the weight estimation formulae for the wing and fuselage are shown in Equations (9) and (10) below.

$$\begin{array}{l}{W}_{wingestimation}\\ =0.00642{{S_w}^{0.240}AR{·M}^{0.430}\left(W_{TO}{N}_{ult}\right)}^{0.909}{\left(\lambda \right)}^{0.210}{\displaystyle \frac{1}{{\left[100{\left(\frac{t}{c}\right)}_m\right]}^{0.380}{\left(\mathit{cos}{\Lambda }_{\frac{1}{2}}\right)}^{1.54}}}\end{array}$$

(9)

$$W_{festimation}=15.65{\left({\displaystyle \frac{q_D}{100}}\right)}^{0.283}{\left({\displaystyle \frac{W_{dg}}{1000}}\right)}^{0.95}{\left({\displaystyle \frac{L}{h}}\right)}^{0.474}$$

(10)

Furthermore, the next-generation SST will largely adopt an advanced composite structure to reduce weight and enhance strength. So, each component weight was multiplied by a fudge factor for different composite structures or advanced system technologies. The fudge factors were set at 0.75 for the wing and tail, 0.80 for the fuselage, 0.95 for the nacelle, and 0.95 for the equipment, as suggested by Raymer [24]. The weight of the jet engine was estimated by a statistical formula suggested by Roskam [25].

With the consideration of advanced technology, all component weights were recalculated. A breakdown of the weight is shown in

Table 8. Weight breakdown of the refined initial design (unit: lbf).

${\mathit{W}}_{\mathit{E}}$	${\mathit{W}}_{\mathit{c}\mathit{r}\mathit{e}\mathit{w}}$	${\mathit{W}}_{\mathit{O}\mathit{P}}$	${\mathit{W}}_{\mathit{t}\mathit{f}\mathit{o}}$	${\mathit{W}}_{\mathit{O}\mathit{E}}$	${\mathit{W}}_{\mathit{P}\mathit{L}}$	${\mathit{W}}_{\mathit{F}}$	${\mathit{W}}_{\mathit{T}\mathit{O}}$
73,101	820	2048	825	76,794	10,950	77,227	164,971

, where $W_{OE}$ = 74,964 lbf, $W_F$ = 77,227 lbf, and the weight ratio $W_{OE}/W_{TO}$ = 0.466 and $W_F/W_{TO}$ = 0.468. It was found that the total weight was reduced by 6205 lbf as compared with the initial design results (Table 6) of the conventional aircraft, and the wing loading was decreased. The results show that the composite structure has a significant effect on weight reduction. Therefore, the wing specifications were modified as $W_{TO}$ = 164,971 lbf, which corresponded to $W/S$ = 73.7 lbf/ft². These results are shown in Table 8.

Aerodynamic performance was calculated by aerodynamic linear theories and statistical methods, which are usually used in conceptual designs. The drag of components was estimated by aerodynamic theories and empirical methods. Based on the results of the weight and geometry, the flight performance of the 50-seat SST was estimated for each flight phase, including cruising, takeoff, and landing. The methods of references [24,25] were applied for the induced drag $C_{Di}$, friction drag $C_{Df}$, wave drag $C_{Dwave}$, miscellaneous drag $C_{Dmisc}$, and maximum lift $C_{Lmax}$ of takeoff and landing. The drag coefficients were estimated by Equations (11) and (12). The details of each component can be found in (Chapter 12 of [24]).

$$C_D=C_{D0}+C_{Di}=C_{D0}+{\displaystyle \frac{C_L^2}{\pi ARe}}$$

(11)

$$C_{D0}={\displaystyle \frac{\sum \left(C_{fcomp}{·S}_{wetcomp}\right)}{S_{ref}}}+C_{Dmisc}+C_{Dwave}+C_{DL\&P}$$

(12)

Friction drag was estimated by flat plate boundary layer theory with the assumption of a 5% laminar flow region on the fuselage surface, 10% laminar regions on the horizontal and vertical tails, and full turbulence on the nacelle and wing. For convenience of discussion, full turbulence is assumed on the wing surface at first, and the effect of laminar flow will be investigated later. The wave drag was estimated by applying the theory of supersonic axisymmetric bodies to the equivalent volume distribution of the 50-seat SST.

6. Optimum Wing Sizing

For optimization of wing sizing, two major variables were investigated to satisfy mission requirements. The baseline shape was set as the refined design with aspect ratio $AR$ = 3.57 and wing loading $W/S$ = 73.7 lbf/ft². A parametric study was conducted to obtain an optimum design. The aspect ratio and wing loading were set in the range of $AR$ ± 20% and $W/S$ ± 20%, respectively. The sizing matrix is shown in

Table 9. Wing sizing matrix.

		$\mathit{W}/\mathit{S}$ [lbf/ft2]
		59.0	73.7	88.5
$AR$	2.86	①	②	③
	3.57	④	⑤	⑥
	4.28	⑦	⑧	⑨

, and case ⑤ is the baseline configuration.

The purpose of wing sizing was to minimize $W_{TO}$ with the following constraints and criteria:

• Takeoff field length $S_{TOFL}$ ≦ 6000 ft;
• Landing field length $S_{FL}$ ≦ 6000 ft;
• Range ≧ 3500 NM;
• Gradient of second segment climb (SSC) $\gamma$ ≧ 0.024.

Flight performance was calculated as described above. It was assumed that high-lift devices were used at takeoff and landing. According to the initial results, the maximum takeoff lift coefficient was set to be 1.3, and the maximum landing lift coefficient was set to be 1.6, as shown in Figure 6.

Then, the optimal combination of wing aspect ratio and wing loading was explored. A carpet plot of the 50-seat SST was drawn for potential regions of $W/S$ and $AR$ with constraint lines as shown in Figure 7. It was observed that $W_{TO}$ was increased with a decrease in $W/S$ and significantly increased with an increase in $AR$. The optimum design must have the smallest weight, and in the meantime, it must satisfy all of the constraints. Then, the values of optimal $W/S$ and $AR$ were calculated by interpolation from the carpet plot shown in Figure 7.

The optimum design was found to have the minimum $W_{TO}$ under all of the constraints in Figure 7. Because the optimum design was calculated by interpolation, which generated some differences as compared with the values estimated by the methods used above, the solutions of $W/S$, $AR$, ${\left(T/W\right)}_{TO}$, and $W_F/W_{TO}$ were slightly adjusted to decide the final design. The main characteristics and shape parameters of the final design are shown in

Table 10. Characteristics of the final design.

$\mathit{A}\mathit{R}$ [-]	$\mathit{W}/\mathit{S}$ [lbf/ft2]	$\mathit{L}$ [m]	${\mathit{W}}_{\mathit{T}\mathit{O}}$ [lbf]	${\mathit{W}}_{\mathit{O}\mathit{E}}$ [lbf]	${\mathit{W}}_{\mathit{F}}$ [lbf]	${\mathit{T}}_{\mathit{T}\mathit{O},\mathit{m}\mathit{a}\mathit{x}}$ [lbf]	$\mathit{C}\mathit{G}$ [m]
2.95	62.7	65	161,953	73,677	79,326	80,847	41.0

and

Table 11. Shape parameters of the optimum design.

	$\mathit{A}\mathit{R}$ [-]	$\mathit{b}$ [m]	$\mathit{S}$ [m2]	$\mathit{M}\mathit{A}\mathit{C}$ [m]	${\mathit{\Lambda }}_{\mathit{L}\mathit{E},\mathit{i}\mathit{n}}$ [deg]	${\mathit{\Lambda }}_{\mathit{L}\mathit{E},\mathit{o}\mathit{u}\mathit{t}}$ [deg]	$\mathit{\lambda }$ [-]
Wing	2.95	26.6	240.1	10.95	77	55	0.11
Horizontal tail	2.5	13.61	74.1	5.90	55	55	0.332
Vertical tail	1.5	7.64	38.9	5.60	55	55	0.294

, respectively. The final design of the wing had the aspect ratio $AR$ = 2.95 and wing loading $W/S$ = 62.7 lbf/ft². To meet the specified range and satisfy the criterion required by the second segment climb of FAR25.121 ($\gamma \ge 0.024$), the fuel capacity and ${\left(T/W\right)}_{TO,max}$ were adjusted to 47.8% and 49.9%, respectively. As compared with the initial weight, the MTOW was reduced by 9233 lbf, while the fuel was increased by 2098 lbf.

During cruising, 80.8 of % fuel was used, and the lift gradually changed with the weight decrease due to the fuel consumption. Here, the design lift was set to the weight ($W_{cruise}$ = 124,323 lbf as shown in

Table 12. Conditions of the final design.

	Weight [lbf]	Altitude [ft]	Velocity [knot]	Mach Number [-]
cruising	124,323	50,000	918	1.6
takeoff at $W_{TO}$	161,953	0	131	0.199
SSC at OEI	161,953	0	131	0.199
landing at $W_{TO}$	161,953	0	118	0.179

) of the fuel used for cruising divided by half of the total fuel. The polar curve of lift and drag coefficients is shown in Figure 8. The cruising conditions and drag breakdown of the final design are shown in Table 12 and

Table 13. Breakdown of the drag coefficients of the final design at cruising.

${\mathit{C}}_{\mathit{D}\mathit{f}}$	${\mathit{C}}_{\mathit{D}\mathit{W}}$	${\mathit{C}}_{\mathit{D}\mathit{m}\mathit{i}\mathit{c}\mathit{s}}$	${\mathit{C}}_{\mathit{D}\mathit{i}\mathit{n}\mathit{t}}$	${\mathit{C}}_{\mathit{D}0}$	${\mathit{C}}_{\mathit{D}\mathit{i}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	$\mathit{L}/\mathit{D}$
0.0090	0.0024	0.0004	0.0006	0.0125	0.0025	0.0150	0.1103	7.347

, respectively. The overall flight performance parameters, such as takeoff and landing lengths, range, and climb gradient, are summarized in

Table 14. Flight performance of the final design.

${\mathit{R}}_{\mathit{s}\mathit{u}\mathit{p}}$ [NM]	${\mathit{S}}_{\mathit{T}\mathit{O}\mathit{F}\mathit{L}}$ [ft]	${\mathit{S}}_{\mathit{F}\mathit{L}}$ [ft]	$\mathsf{\gamma }$ [-]
3500	4709	5670	0.024

. It was shown that all of the design requirements were satisfied.

Besides weight reduction, aerodynamic performance plays a very important role for an SST. Because a large $C_{Lmax}$ is required for either a short $S_{TOFL}$ at takeoff (see Equation (4)) or a short $S_{FL}$ at landing (see Equation (5)), efficient high-lift devices must be adopted. According to Equation (7), the improvement of $L/D$ has a large effect on the reduction in the engine thrust at landing, thus having a large effect on $W_{TO}$.

For the fuselage, the weight Equation (10) and the drag show that an increase in the fuselage length has no significant effect on the maximum takeoff weight $W_{TO}$ and the friction drag coefficient $C_{Df}$. On the other hand, an extra-long nose is usually adopted to reduce sonic booms for an SST, but it may result in a large increase in wave drag.

Further discussion was conducted to investigate the effect of laminar flow on the wing. The laminar flow region was assumed to be 0~15% on the wing surface. As shown in Figure 9, it was observed that the $L/D$ was largely improved, and the flight range was increased by 142 NM. This indicates that the design of a laminar flow wing plays an important role in improving aerodynamic efficiency during supersonic cruising.

7. Conclusions

In this study, a conceptual design was conducted for a 50-seat SST to explore a feasible solution. The SST was required to cruise at Mach 1.6, carry a maximum of 50 passengers, and have an operational range of 3500 nautical miles. It results that the final solution has a maximum takeoff weight of 161,953 lbf and satisfies the constraints of takeoff and landing. As compared with the initial weight, the MTOW was reduced by 9233 lbf, while the fuel was increased by 2098 lbf. In the refinement and optimum design, the weight and flight performance in flight phases were estimated, and wing sizing was conducted by the carpet plot method to reduce the maximum takeoff weight. The main results are as follows:

• According to the weight estimation, the maximum takeoff weight may be largely reduced by advanced technology, such as using composite material for the structure.
• The final design was decided using a carpet plot with the minimum value of the maximum takeoff weight and satisfaction of design requirements.
• As a result of wing sizing, the constraint of climb gradient largely influenced the maximum takeoff weight. It is anticipated that flight performance at low speed will be enhanced by the use of high-lift devices.
• The laminar flow had a considerable impact on the improvement of aerodynamic efficiency during supersonic cruising.

This research will be continued to optimize the SST for low-drag and low-sonic-boom design. The accuracy of aerodynamic estimation should be improved, and the effect of sonic booms should be taken into account in the design process.