2.2.1 Past developments

Past development of commercial supersonicFootnote 1 aircraft had materialised in the commercialisation of the two aircraft – the French/British Aerospatiale/BAC Concorde and the Soviet Union’s TY 144. The Concorde entered commercial service in 1976 and retired in 2003. The TY 144 entered the commercial service in 1977 and retired in 1978^(8)–(11). Both aircraft had a similar design, technical productivity, operating costs, fuel consumption, related GHG emissions, and noise. However, regarding the latest four above-mentioned features, they had not fulfilled expectations of the main actors/stakeholders. The airfares had been based on the high operating costs, mainly influenced by the high fuel consumption. This had been additionally compromised by constraining the overland operations at the supersonic speed (M > 1) aimed at mitigating and/or avoiding excessive noise from the sonic boom(s). Under such circumstances, these aircraft had been inferior to their slower subsonic counterparts, the B 707 and the B 747, regarding the operational costs and consequently airfares^{(12)–(Reference Masefield14)}. Additionally, the accidents (crashes) of the Concorde (25 Jul 2000, Paris) and the TY 144 (3 June 1973, Paris Air Show) raised some concerns about their safety, which consequently speeded up their retirement⁽¹⁵⁾.

2.2.2 Past and current research and development

After the retirement of the Concorde and the TY144, research and development of supersonic aircraft continued. One of the earliest efforts dealt with identifying the relevant research topics regarding the design, economic efficiency, and safety of these aircraft. This was initially elaborated by improving the existing and developing some innovative research techniques^{(Reference Saltzman and Ayers27)}. This was followed by elaborating the concepts of commercial supersonic transport aircraft in terms of identifying new research opportunities regarding critical technologies and areas needing continuous development. These included the airframe design, control systems, engines, and materials, as well as the issue of reducing the sonic boom, fuel consumption and GHG emission, improving in-flight safety, and the certification requirements^{(28,Reference Williams29)} . Further research summarized the developments of the concepts of supersonic aircraft over the past 30 years, from the engineering, economic, and safety/environmental/social perspective^{(Reference Chambers30)}. This was certification by research on the possible introduction of LH₂ as fuel for commercial air transportation. It elaborated the necessary conditions for smooth transition from conventional (Jet A) to new (LH₂) fuel, including the necessary modifications of the aircraft design. This resulted in the development of the concept of both subsonic and supersonic aircraft powered by LH₂^{(Reference Sippel and Klevanski20),(Reference Westenberger31)}. In particular, comprehensive research on developing the concept of a large supersonic aircraft, including the overall long-term aspects related to the high-speed transport, was carried out. For example, two EC (European Commission) projects, LAPCAT and ATLLAS, developed the methodology for aircraft design including optimal integration of their airframe, engines, and materials. Additionally, some dedicated experiments were carried out to evaluate the overall feasibility of the proposed design under different operating conditions^{(24),(Reference Steelant25)}. RAMJET or SCRAMJET engines were also specifically explored as propulsion systems for supersonic aircraft, including the challenges in their development, technical/technological and operational feasibility^{(Reference Coen32),(Reference McClinton33)}.

As far as the most recent endeavours of the airspace industry are concerned, Boeing has announced the development of a hypersonic aircraft with the cruising speed of about M = 5. It is thought that it will be operational by the late 2030s⁽³⁴⁾. Additionally, three U.S.-based start-up companies, Aerion, Spike, and Boom, are developing the new supersonic aircraft expected to be operational in the mid-2020s (see Table AI-1)^{(22),(23),(Reference Fehrm35)}. The operational compatibility of the future supersonic aircraft has also been under scrutiny, with regard to the current and future ATC (air traffic control) system, and the corresponding flight operational rules and procedures. In particular, the prospective benefits and barriers to integrating these aircraft seamlessly in the U.S. NAS (National Airspace System) have been considered^{(12),(Reference Underwood21),(39)}.

Several research efforts have recently focused on the assessment of the potential market for the supersonic flights. One deals with the development of the air transport market, including its long-haul segment where the supersonic aircraft would most likely operate^{(Reference Reichmuth and Berster36)}. The other deals directly with the estimation of the global market potential for supersonic transportation by evaluating worldwide data on the premium ticket sales^{(Reference Liebhardt, Luetjens and Gollnick37)}.

One of the main concerns in developing the new concepts of supersonic aircraft has continued to be their economic efficiency. This has expected to be mainly influenced by the costs of substantial fuel consumption. The airfares based on such costs could make them eventually attractive primarily for business passengers with the presumably high value of their time. However, some research has indicated that if these aircraft were large and powered by LH₂ fuel charged at the reasonable prices, their costs and related airfares would be quite competitive to those of their current subsonic counterparts⁽²⁴⁾. Since the environmental and social impacts of supersonic aircraft powered by Jet-A fuel (kerosene) have expected to be substantial, the corresponding GHG emissions and their noise have been also under scrutiny. Some research has reviewed the environmental issues and challenges of relevance to the design of supersonic business jets. Due to the inherent interrelation of the above-mentioned performance, a multidisciplinary design, analysis and optimisation have been considered as necessary for creating “low-boom” “low-drag” supersonic aircraft^{(Reference Sun and Smith38)}. Additionally, a preliminary assessment of noise and GHG emissions by supersonic aircraft has indicated that their most likely design would not enable fulfilment of the current (2018/19) global standards for GHG emission of and local-airport noise. Particularly, according to the operating scenarios on the selected routes, their average fuel consumption and related GNG emissions (per passenger) would exceed those of their current subsonic counterparts several fold^{(Reference Kharina, MacDonald and Rutherford18)}. Also, the regulation of operations of the new supersonic aircraft, which is already underway, is primarily related to the sonic boom currently restricting their overland operation. One of these has been the U.S. FAA (Federal Aviation Administration) initiative for creating federal and international policies, regulations, and standards to certify the safe and efficient operation of civil supersonic aircraft^{(12),(Reference Norris and Warwick19),(39)}.

The above-mentioned concepts of supersonic aircraft have been thought to carry out the long-haul flights with a rather positive balance between their effects and impacts. The effects have included travel speed, technical productivity, and economics. The impacts have included fuel consumption, GHG emissions, and noise. Some of these thoughts have also been systematically articulated as far-term (beyond the year 2035) research objectives of the two of the six strategic thrusts of the U.S. NASA strategic research program. The two relevant strategic thrusts have been “Innovation in Commercial Supersonic Aircraft” and “Transition to Alternative Propulsion and Energy”⁽¹⁶⁾. Consequently, the general requirements for design and operation of these aircraft have been as follows^{(4),(8),(16)–(23)}:

1. • Sufficient range for operating along the current and future long-haul, including the longest-haul non-stop routes;

2. • Flight costs and related air fares comparable to those of their subsonic counterparts and consequently attractive for both airlines and different categories of air passengers (low, medium, high income; business, leisure);

3. • Fuel consumption and related GHG emissions at the level at least neutral compared to their current subsonic counterparts; and

4. • Noise around airports and the sonic boom overland within the existing and forthcoming regulatory limits, the former similar to their subsonic counterparts.

The causal (regression) relationship between the technical productivity (TP), cruising speed (v), and capacity (S) of the past and current concepts of supersonic aircraft is estimated as follows (based on data in Table AI-1 (Appendix I)):

(2) \begin{align}&TP\left( {S,v} \right) = - 308.004 + 0.959 \cdot S + 0.307 \cdot v\nonumber\\ &t\left( { - 10.575} \right)\left( {6.442} \right)\left( {10.467} \right)\nonumber\\ &{R^2} = 0.987;F = 296.077;DW = 1.553;N = 10\,\,\left( {12 \lt S \lt 300;860 \lt v \lt 2867{\rm{ kt}}} \right)\end{align}

As can be seen, the aircraft capacity (S) and cruising speed (v) have very strongly influenced on technical productivity (TP). Again, this influence is about three times greater thanks to the seat capacity (coefficient at the variable (S)) than thanks to the maximum speed (coefficient at the variable (v)). Additionally, the influence of speed on the technical productivity (TP) is for more than four times greater than in the case of subsonic aircraft (see Eq. 1a).

In regard to economics, some estimates indicate that the price of currently developing Boom Aircraft will be about 200· 10⁶ $US and that of the previous EC LAPCAT Hydrogen Mach 5 Cruiser A2 640 · 10⁶ $\textrm{C}\kern-9.5pt{=}$ . Based on the advertised prices on particular long-haul routes, the average operating cost of Boom Aircraft could be less than about 1.5 - 1.8 /s-nm and that of the EC Hydrogen Mach 5 Cruiser A2 about 6.2 /s-nm (s-nm – seat-nautical mile)^{(Reference Kharina, MacDonald and Rutherford18),(22),(24),(Reference Steelant25)}. The fuel consumption, GHG emissions, and noise of these aircraft are expected to be in line with the above-mentioned requirements. In particular, the noise from the sonic boom is expected to be reduced to the level of about 70-80dB primarily through aircraft design and the increase in their cruising altitude, both of which could eventually allow for unrestricted overland operations⁽²²⁾.

3.3.1 Indicators of operational performance

The operational performance indicators are passenger demand, flight frequency on a route and network aircraft turnaround time on a route, transport work, technical productivity, and the size of the aircraft fleet.

Passenger demand and flight frequency on a route: The passenger demand on a network route (k) in the single direction, served by either category of aircraft during time (Δτ), is assumed to be (Q _k(Δτ)) ^{(Reference Liebhardt, Luetjens and Gollnick37)}. The flight frequency by either aircraft category to accommodate this demand can be estimated as follows^{(Reference Janić13)}:

(3a) \begin{equation}{f_k}\left( {\Delta \tau } \right) = {Q_k}\left( {\Delta \tau } \right)/({\lambda _k} \cdot {S_k})\end{equation}

k

route in the given network (k = 1,2,…, K);

Δτ

time interval in which the flights by either aircraft category are scheduled on route (k) (h, day, year);

$\lambda$ _k, S _k

average aircraft load factor and capacity, respectively, of a flight on route (k) carried out by either aircraft category ( $\lambda$ _k ≤ 1.0) (-; seats/dep);

K

number of routes in the network.

Aircraft turnaround time on a route: The turnaround time of an aircraft of either category on route (k) is expressed as follows:

(3b) \begin{equation}{\tau _k}\left( {{R_k}} \right) = {t_{0/k/1}} + {t_k}\left( {{R_{k/1}}} \right) + {t_{0/k/2}} + {t_k}\left( {D{R_{k/2}}} \right)\end{equation}

R _k/1, R _k/2

length of route (k) in direction (Reference Vuchic and Casello1) and (Reference Howard2), respectively (nm, km);

t _k(R _k/1), t _k(R _k/2)

flight time by aircraft category (i) in the direction (Reference Vuchic and Casello1) and (Reference Howard2), respectively, on route (k), (h);

t _0/k/1, t _{0/k /2}

handling time of an aircraft of either category at the apron/gate complex of the end airports, before operating on route (k) in direction (Reference Vuchic and Casello1) and (Reference Howard2), respectively, (h).

The time (t _k(R _k/1)) or (t _k(R _k/2)) in Eq.3b is approximated as follows:

(3c) \begin{equation}{t_k}\left( {{R_{k/.}}} \right) = {t_{k/cl/.}} + {t_{k/cr/.}} + {t_{k/de/.}} + 1/2 \cdot {t_{k/LTO}}\end{equation}

t _k/cl/.

climbing time of a flight of either category operating on route (k) in the given direction (min);

t _k/cr/.

cruising time of a flight of either category operating on route (k) in the given direction (min);

t _k/de/.

descending time of a flight of either category operating on route (k) in the given direction (min);

t _k/LTO

LTO (Landing and Take-Off)Footnote 3 cycle of a flight of either category before and after operating on route (k) (min) (i = 1, 2).

The other symbols are analogous to those in the previous equations.

The detailed analytical models for estimating the flight time components in Eq. 3c are given in Appendix II.

Transport work, technical productivity, and size of the aircraft fleet: The transport work of the flight carried out on route (k) of the network by either category of aircraft during time (Δτ) is estimated as follows:

(3d) \begin{equation}T{W_k}\left( {{\rm{\Delta }}\tau } \right) = {f_k}\left( {\Delta \tau } \right) \cdot {R_k} \cdot {\lambda _k} \cdot {S_k}\end{equation}

where all symbols are analogous to those in the previous equations.

The technical productivity of the flight carried out on route (k) of the network by either category of aircraft during time (Δτ) is estimated as follows:

(3e) \begin{equation}T{P_k}\left( {\Delta \tau } \right) = {f_{k}}\left( {\Delta \tau } \right) \cdot {\lambda _k} \cdot {S_k} \cdot {\overline v _k}\left( {{R_k}} \right)\end{equation}

${\overline v _k}\left( {{R_k}} \right)$

average flight speed carried out by either aircraft category on route (R _k) in both directions (1) and (2) (km/h or kt).

From Eq. 3c, the average speed ${\overline {\rm{v}} _{\rm{k}}}\left( {{{\rm{R}}_{\rm{k}}}} \right)$ in Eq. 3e is expressed as follows:

(3f) \begin{equation} {\overline v _k}\left( {{R_k}} \right) = {R_k}/{\tau _k}\left( {{R_k}} \right)\end{equation}

From Eq. 3a and 3b, the required fleet of either aircraft category to serve the network under given conditions is expressed as follows:

(3g) \begin{equation}n\left( {\Delta \tau } \right) = \mathop \sum \limits_{k = 1}^K {f_k}\left( {\Delta \tau } \right) \cdot {\tau _k}\left( {{R_k}} \right)\end{equation}

The other symbols are analogous to those in the previous equations.

3.3.2 Indicators of economic performance

The indicators of economic performance are flight cost, cost of passenger time, and contribution to GDP (gross domestic product).

Flight cost: The total cost of a single flight carried out by either category of aircraft on route (k) of the network can be estimated as follows:

(4a) \begin{equation}{C_{k/T}} = {C_{k/F}} + {C_{k/o}}\end{equation}

where

C _k/F

fixed cost of a flight carried out on route (k) ($US/flight);

C _k/o

is the variable, i.e., operating cost of a flight carried out on route (k) ($US/flight).

The fixed cost (C _k/F) in Eq. 4a can be estimated as follows⁽⁴²⁾:

(4b) \begin{equation}{C_{k/F}} = \left( {\frac{{P \cdot ADR}}{{\mathop \sum \nolimits_{k = 1}^K {f_k}\left( {UL} \right)}}} \right) = \left[ {\frac{{P \cdot (100 - RV/UL)}}{{\mathop \sum \nolimits_{k = 1}^K {f_k}\left( {UL} \right)}}} \right]\end{equation}

P

aircraft price including the capital maintenance costs during its useful life ($US/aircraft);

ADR

aircraft annual depreciation rate (%);

RV

aircraft residual value (%);

UL

aircraft useful life (years);

f _k(UL)

number of flights carried out on network route (k) during the aircraft’s useful life.

The other symbols are analogous to those in Eq. 3a.

The operating cost (C _k/o) in Eq. 4a includes the cost of fuel, crew, maintenance, insurance, fees (airport, ATC), and others (www.PlaneStats.com). For the flights carried out by the subsonic aircraft this cost is usually estimated by the empirical data. For the flights carried out by the supersonic aircraft, this cost can be approximated by using the corresponding available data in combination with an analogy with the cost of their subsonic counterparts⁽²⁴⁾. From Eq. 4a, the average cost is expressed as follows:

(4c) \begin{equation} {\overline C _k} = {\frac{{C_{k/T}}}{{R_k} \cdot {\lambda _k} \cdot {S_k}}} = {\frac{{C_{k/F}} + {C_{k/o}}}{{R_k} \cdot {\lambda _k} \cdot {S_k}}}\end{equation}

${\overline c _k}$

average cost of a flight carried out on route (k) of the network ($US/p-km).

The other symbols are analogous to those in the previous equations.

As mentioned above, in combination with the route length, the average cost ( ${\overline c _k}$ ) in Eq. 4c can be considered as the basis for setting up the airfares.

Cost of passenger time: Using supersonic instead of subsonic flights is expected to bring savings in the passenger time and related costs. These average savings by a flight of either category carried out on route (k) can be estimated as follows:

(4d) \begin{equation}{\overline c _{k/sv}} = \left[ {{\alpha _k} \cdot \left( {t_{k/1}^* - t_{k/2}^{\ast}} \right)} \right]/\left( {{R_k} \cdot {\lambda _k} \cdot {S_k}} \right)\end{equation}

${\rm{t}}_{{\rm{k}}/1}^{\rm{*}}{\rm{t}}_{{\rm{k}}/2}^{\ast}$

flight time on route (k) by subsonic (i = 1) and supersonic (i = 2) aircraft, respectively, (h) $({\rm{t}}_{{\rm{k}}/1}^{\rm{*}} > {\rm{t}}_{{\rm{k}}/2}^{\ast})$ ;

α _k

average value of time of a user/passenger travelling on route (k) ($US/h-p).

The other symbols are analogous to those in the previous equations.

Contribution to GDP: The average contribution of the subsonic or supersonic flight(s) carried out in the network to the GDP is estimated as follows:

(4e) \begin{equation} {\overline r _{GDP}} = \left( {GDP/{V_{RPK}}} \right)\end{equation}

${\overline r _{GDP}}$

average GDP generated by commercial air transportation in the given region ($US/p-km);

GDP

total GDP generated by commercial air transportation in the given region during the specified period of time ($US/year);

V _RPK

output of commercial air transportation in the given region during the specified period of time (RPK/year) (RPK - revenue passenger kilometre).

Overall social-economic feasibility: The overall social-economic feasibility of the subsonic or supersonic flight(s) carried out on route (k) of the network is estimated as the difference between its total cost and contribution to GDP. From Eq. 4 (c, d, e) and 5 d (see below) this equals:

(4f) \begin{equation}\Delta {c_k} = {\overline r _{GDP}} - \left( {{{\overline c }_k} + {{\overline c }_{k/sv}} + {{\overline c }_{k/e}}} \right)\end{equation}

${\overline {\rm{c}} _{{\rm{k}}/{\rm{e}}}}$

average cost of GHG emissions of a flight carried out on route (k) of the network ($US/p-km).

The other symbols are analogous to those in the previous equations.

If (Δc _k) is positive, the flight on the route (k) is overall social-economically feasible, and vice versa.

3.3.3 Indicators of environmental performance

The indicators of environmental performance are fuel consumption, emissions of GHG, and contribution to the global warming and climate change.

Fuel consumption: The fuel consumption of subsonic flights in the network is estimated by using the available empirical data. That of the supersonic flights is estimated by the analytical models considering the mechanical forces acting on the aircraft during the particular phases of flight—climb, cruise, and descend—and the corresponding energy consumption. The summed quantity is then increased for the factor including the fuel consumed during the LTO cycle(s). In general, in each of the above-mentioned flight phases the fuel consumption is estimated as follows:

(5a) \begin{equation}FC = \left[ {\left( {1/\eta } \right) \cdot T \cdot r} \right]/{e_f}\end{equation}

T

thrust force during the given phase of flight (N) (N - Newton);

r

distance along which the thrust force (T) is applied (m, km, nm);

e _f

specific energy of the fuel used (J/kg) (J - Joule);

η

propulsion efficiency of the aircraft engines during the given phase of flight (η _to < 1.0).

After expanding Eq. 5a in Appendix III for the particular flight phases - climbing (cl), cruising (cr), descending (de), and (LTO) cycle, the total fuel consumption of a flight carried out by supersonic aircraft on route (k) of the network can be estimated as follows:

(5b) \begin{equation}F{C_k} = F{C_{k/cl}} + F{C_{k/cr}} + F{C_{k/de}} + \left( {1/2} \right) \cdot F{C_{k/LTO}}\end{equation}

GHG emissions: GHG emissions by subsonic aircraft can be estimated by using available empirical data. Based on Eq. 5b, the GHG emissions by both subsonic and supersonic flight are estimated as follows:

(5c) \begin{equation}E{M_k} = F{C_k} \cdot \mathop \sum \limits_{m = 1}^M {e_m}\end{equation}

FC _k

fuel consumption by a flight carried out on route (k) by either category of aircraft (kg, ton);

e _m

emission rate of the (m)-th GHG from burning the given type of fuel (kg or ton of GHG/kg or ton of fuel);

M

number of different GHG emitted by burning the given type of fuel.

If internalised, the total and average cost of GHG emissions of a flight carried out on route (k) by either category of aircraft can be estimated as follows:

(5d) \begin{equation}{C_{k/e}} = F{C_k} \cdot \mathop \sum \limits_{m = 1}^M {c_{e/m}} \cdot {e_m}\quad \text{and} \quad {\overline c _{k/e}} = \frac{{{C_{k/e}}}}{{{R_k} \cdot {\lambda _k} \cdot {S_k}}}\end{equation}

c _e/m

unit charge of the (m)-th GHG ($US/kg, $US/ton).

The other symbols are analogous to those in the previous equations.

Contribution to global warming and climate change: The GHG emitted by subsonic or supersonic flight powered by either type of fuel (Jet A or LH₂) contribute to global warming and climate change. Each GHG has its GWP (global warming potential) estimated for the future long-term period (for example, 100 years ahead)^{(Reference Derwent, Simmonds, O’Doherty, Manning, Collins and Stevenson43),(44)}. Based on Eq. 5c, the GWP of any subsonic or supersonic flight carried out on route (k) can be estimated as follows (tons of GHG/flight):

(5e) \begin{equation}GW{P_k} = E{M_k} \cdot \mathop \sum \limits_{m = 1}^M GW{P_m}\end{equation}

GWP _m

Global Warming Potential of the (m)-th GHG (-).

The other symbols are analogous to those in the previous equations.

The relative savings in GWP by carrying out the supersonic (i = 2 - LH₂ fuel) instead of the subsonic (i = 1 - Jet A fuel) flight(s) on route (k) of the network are estimated as follows:

(5f) \begin{equation}\Delta GWP\left( k \right) = \left( {1 - \frac{{GWP\left( {k,2} \right)}}{{GWP\left( {k,1} \right)}}} \right) \cdot 100\end{equation}

All symbols are analogous to those in the previous equations.

3.3.4 Indicators of social performance

The indicators of social performance are noise, congestion and delays, and safety.

Noise: The noise produced by the subsonic aircraft around airports has been permanently regulated and used as the criteria for their (noise) certification⁽⁵⁾. The noise by the forthcoming supersonic aircraft, in addition to that around airports, has been and will continue to be the subject to specific regulation along the (overland) segments of air routes due to the sonic boom^(12),(39). This noise by a supersonic flight passing above an observer on the ground can be estimated as follows⁽⁴⁵⁾:

(6a) \begin{equation}{L_2} = {L_1} - 20 \cdot log\ {d_1}/{d_2}\end{equation}

L ₁, L ₂

noise at the reference distance (d ₁) and at the distance (d ₂) of an observer on the ground from the noise source, i.e. the flying over aircraft, respectively (dBA) (d ₁, d ₂ - nm, km).

The distance (d ₁) is very close to the noise source, i.e. the flying over aircraft. The distance (d ₂) is estimated as follows⁽¹¹⁾:

(6b) \begin{equation}{d_2} = H/\sin \theta \quad \text{and}\quad \theta= \sin^{-1}(1/M)\end{equation}

H

altitude of supersonic flight (m, ft);

Θ

Mach angle (°);

M

Mach number (M > 1).

At present, the costs of noise as an externality by supersonic aircraft are quite uncertain and are therefore not elaborated in the given context.

Congestion, delays and safety: Both categories of flights are carried out under the equivalent operational conditions at all airports of the network. As mentioned above, they are assumed to be “ultimately” free from the substantial congestion and delays. The same applies to their safety, i.e. the risk of and actual occurrence of the air traffic incidents/accidents. Therefore, the corresponding indicators of this performance and related costs/externalities are not elaborated.

4.1.1 Infrastructural performance

The indicators of infrastructural performance are represented by the characteristics of the existing air route network shown in Fig. 3 and given in Table 1.

Figure 3. Simplified geographical scheme of the air route network consisting of 25 world’s longest routes in the given example (period: the year 2018) ⁽⁶⁵⁾.

Figure 4. Simplified layout of supersonic aircraft in the given example (LAPCAT Hydrogen Mach 5 A2 concept) ^{(24),(Reference Steelant25)}.

Table 1 Characteristics of the existing long-haul air route network and subsonic non-stop flights in the given example (Fig. 2) (Period: the year 2018) ⁽⁶⁵⁾)

The same network is assumed to be operated exclusively either by the above-mentioned subsonic aircraft or their supersonic counterparts in the year 2050.

4.1.2 Technical/technological performance

The fleet of subsonic aircraft contains the average aircraft type based on Eq. 1 (a, b, c). The simplified layout of considered supersonic aircraft is shown in Fig. 4 (the EC’s LAPCAT Hydrogen Mach 5 A2 concept)^{(24),(Reference Steelant25),(Reference Coen32)}.

Table 2 Some design characteristics of subsonic and supersonic aircraft in the given example ^{(24),(28),(Reference Coen32)}

^a Averages of the aircraft types operating on 25 longest routes in the given example^{(62),(63)(Reference Janić64)};

^b Based on the EC Hydrogen Mach 5 Cruiser A2 ^{(Reference Janić13),(24),(Reference Steelant25)};

^c Based on ${\left( {L/D} \right)_{max}}=4 \cdot (1+3/M)$ (M is Mach number) ⁽⁷²⁾.

Additionally, the design-related characteristics of an average subsonic and supersonic aircraft belonging to the corresponding fleets are given in Table 2. On the one hand, these characteristics can be considered as inputs; on the other, they can represent indicators of technical/technological performance of the network and flights.

4.1.3 Operational performance

The inputs for estimating the indicators of operational performance of the network are synthesised from the relevant empirical data (subsonic flights) and the hypothetical “what-if” operational scenario-based data (supersonic flights) given in Table 1 and 2.

4.1.4 Economic performance

Flight cost: The inputs for estimating the total operating cost of subsonic flight(s) are derived from Eq. 1b. The inputs for estimating the total operating cost of supersonic flight(s) operated at the speed M = 2.4 are derived as follows.

The price of a supersonic aircraft including the capital maintenance cost during the life-cycle is assumed to be: P = 450 · 10⁶ $US. This is similar to that of the A380 aircraft^(46),(47). The aircraft residual value at the end of useful life of: UL = 20 years is assumed to be: RV = 10%, which gives ADR (Annual Depreciation Rate): = 4.5%/year⁽⁴²⁾. The inputs for estimating the variable cost component are as follows: the fuel cost - 1.00 and 0.85 $US/kg of LH₂⁽⁴⁸⁾; the crew cost - 2000 $US/h. The fixed, fuel, and crew costs are assumed to account for 70% of the total operating cost⁽⁴⁹⁾. The inputs for both subsonic and supersonic flights are adjusted to the prospective conditions in the year 2050.

Cost of passenger time: The inputs for estimating the prospective savings in the cost of passenger time if using supersonic instead subsonic flights are represented by the average value of passenger time of: α _k = 74 $US/h-p. Based on 50% medium and 50% high income passengers, both performing 50% business and 50% leisure trips. This value is assumed to be also relevant in the year 2050 (h - hour; p - passenger)^(50),(51).

Contribution to GDP: The inputs for estimating the average contribution of commercial air transportation to GDP are obtained from the long-term annual forecasts for global commercial air passenger transportation and its contribution to GDP⁽⁵²⁾. For the year 2050, GDP ₂₀₅₀ = 5.4 · 10¹² $US/year and V _RPK/2050 = 14.1 ·10¹² RPK/year, which gives: ${\bar r_{GDP/2050}}$ = (GDP/V _RPK)₂₀₅₀= 5.59 · 10¹² $US/14.1 · 10¹² RPK = 0.3965 $US/p-km.

4.1.5 Environmental performance

Fuel consumption: The regression equation in Eq. 1c and the inputs in Table 2 are used for estimating the fuel consumption of subsonic flight(s). The inputs in Table 2, 3, and 4 are used in the corresponding models (Appendix III) to estimate the fuel consumption of the supersonic flight(s).

Figure 5. Indicators of economic performance: The average operating cost of particular categories of flights carried out on an average route of the network in the given example (period: the year 2050).

Table 3 Characteristics of supersonic flight(s) in the given example

^a Take-off speed is 185 kt; the landing speed is 175 kt; the speed at FL10 is 250 kt (FL10 = 10000ft);

^b the rate of climb: R/C (h) = 9000 - 0.1308 $\cdot$ H; the rate of descend: R/D(H) = - 8000 + 0.1154 $\cdot$ H (based on Concorde and TY 144) (H is the altitude (10³ feet));

^c the climb/descend time: $t\left( {{H_1},{H_2}} \right) = \left( {1/b} \right) \cdot \left\{ {\ln \left[ {a\left( {{H_1}} \right) - b \cdot {H_2}} \right] - \ln \left[ {a\left( {{H_1}} \right) - b \cdot {H_1})} \right]} \right\}$ (H₁, H₂ is the initial and the end altitude, respectively) ⁽⁸⁾;

^d attack angle is = 4⁰;

^e At FL 60-65 (10³ft);

^{f (28)};

^{g (24);(Reference Steelant25)}.

Table 4 Characteristics of aircraft fuels, emissions of GHG, costs/externalities, and GWP (Global Warming Potential) in the given example ^{(66),(Reference Janić67)}

^a Direct combustion;

^b engine power is 45–100%; PM - Particulate Matters;

^c carbon dioxide equivalent;

^d global warming potential (values for 100-year time horizon) ^{(Reference Derwent, Simmonds, O’Doherty, Manning, Collins and Stevenson43),(44)};

^e high impact ^{(48),(Reference Kuchemann73)};

^f high Impact ⁽⁷⁴⁾.

GHG emissions, contribution to global warming and climate change, and costs/externalities: The inputs for estimating GHG emissions of both subsonic and supersonic flights relate to the characteristics of Jet A and LH₂ fuel, their contribution to global warming and climate change and the related costs as externalities is given in Table 4. The related cost of emissions of particular GHG is adjusted for the year 2050.

4.1.6 Social performance

The cruising altitude ranging as: H = 36 - 60·10³ ft and speed of M = 2.4 are used as the “what-if” scenario-based inputs for estimating the level of noise produced by supersonic flight(s) as experienced by an observer on the ground.

4.2.1 Infrastructural and technical/technological performance

As mentioned above, the indicators of infrastructural and technical/technological performance are not particularly elaborated. They are assumed as given in the inputs for estimating those of the other performances.

4.2.2 Operational performance

The inputs in Tables 1, 2, and AI-1 (Appendix I) are used for estimation of the indicators of operational performance as given in Table 5.

Table 5 Indicators of operational performance of an average route of the network in the given example: Transport work, productivity, and required fleet of particular aircraft categories (period: the year 2050)

^a Based on the aircraft capacity of $\textrm{S} = 300$ seats/dep and load factor $\lambda = 0.7$ ;

^b includes the standard LTO cycle of t_LTO $=34.38$ min (Masiol and Harrison, 2014) (h - hour);

^c based on the average route length of $\textrm{R}=6532\,\textrm{nm}$ (12097km) (Table 1) and the average flight duration t(R);

^d based on the aircraft handling time at the origin and the destination airport of $\tau_{0}=1\,\textrm{h}$ ;

^e based on the aircaft availability of $\textrm{U}=90\%$ /year and the daily frequency of ${\rm{f}}(\Delta \tau ) = 1$ dep/day;

^f based on the flight frequency of ${\rm{f}}(\Delta \tau ) = 1$ dep/day.

As can be seen, the flight time by the supersonic aircraft operating at a speed of M = 2.4 would be almost two times shorter than that of their subsonic counterparts. Consequently, thanks to the shorter route turnaround time, the required fleet of supersonic aircraft would be lower by about 46%. The transports work on an average route and consequently in the network would be equal for both categories of flights. This is mainly due to the equal flight frequencies, seat capacity, load factor, and the average route length. However, thanks to the higher cruising speed, the technical productivity of supersonic flights would be about 2.9 times greater than that of their subsonic counterparts.

4.2.3 Economic performance

Flight cost

The total operating cost of a subsonic flight is derived from Eq. 1b and the adjustments reflecting the expected conditions in the year 2050, as follows: C(R, S) ₂₀₅₀= [(a ₀+ a ₁·R + a ₂· S) ₂₀₁₉· t (R)] [(1 – p _fc) + p _fc· (1 + i _r) ³⁰· (1 – r _fc)] = [(177.479 + 0.301 ·6532 + 21.965 ·300) · 16] · [(1-0.4) + 0.4 · (1 + 0.012)³⁰ · (1 – 0.4)] = 131761 $US/flight. The average cost per flight is equal to: ${\overline c _{ - /2050}}$ = C(R, S) ₂₀₅₀/(R · $\lambda$ · S) = 131761/(6532 · 1.852 · 0.7 · 300) = 0.052 $US/p-km (p _fc = 0.4 is the share of fuel cost in the total aircraft operating cost in Eq. 1b^(49),(53)); r _fc = 0.4 is the cumulative rate of improvement in aircraft fuel efficiency in the year 2050 vs 2019/2020^{(Reference Gareth54)}; i _r = 1.2% is the annual rate of increasing prices of crude oil, which proportionally influences an increase in the price of Jet-A fuel during the period 2018/19-2050⁽⁵⁵⁾.

The total cost of a flight carried out by supersonic aircraft is estimated as follows:

The fixed cost of the fleet of 24 aircraft (M = 2.4) in Table 5, carrying out 329 flights/year on each of 25 routes of the network in Table 1, is estimated as follows: C _F/2050 = [24·(450·10⁶) · 0.045]/(329·25) = 59088 ($US/flight)⁽²⁴⁾, the crew cost: c _cw/2050 = 2000 $US/h · 8.681 h = 17362 $US/flight⁽⁵⁶⁾, and the fuel cost: c _fc/2050 = 93516 kgLH₂/flight · 1$US/kg LH₂ = 93516 $US/flight (see also below)⁽⁴⁸⁾. If the above-mentioned (three) cost components are assumed to account for about 70% of the total flight operating cost, the corresponding total cost will be: C _T/2050 = (C _F/2050 + c _cw/2050+ c _fc/2050)/0.7 = (59088 + 17362 + 93516)/0.7 = 242809 $US/flight. The average cost of single flight carried out on the route: R = 6532 nm (12097 km) (by the aircraft of: S = 300 seats and load factor: Λ = 0.70 is equal to: ${\overline {\rm{c}} _{ - /2050}}{\rm{}}$ = C _T/2050/(R · $\lambda$ · S) = 242809/ (6532 · 1.852 · 0.7 · 300) = 0.096 $US/p-km. If the fuel cost is 0.85 $US/kgLH₂⁽⁴⁸⁾, the corresponding average cost of the supersonic flight would be: ${\overline {\rm{c}} _{ - /2050}}$ =155939/(6532 · 1.852 · 0.7 · 300) = 0.061 $US/p-km. Figure 5 shows these average cost per flight.

As can be seen, at the frequency of 1 flight/day, the average operating cost of the supersonic flight, depending on the fuel cost, would be between 18% (0.85 $US/kgLH₂) and 85% (1 $US/kgLH₂) higher than that of the subsonic flight. This example indicates that the supersonic flights would generally be economically inferior to their subsonic counterparts under the given conditions.

Cost of passenger time: The cost of passenger time and the potential savings in this cost by using the supersonic instead of the subsonic flight(s) are given in Table 6.

Table 6 Indicators of economic performance of an average route of the network in the given example: Cost of passenger time and its potential savings at particular categories of flights (period: the year 2050)

^a Based on 50% medium- and 50% high-income passngers on board and their 50% business and 50% leisure trips ^(50),(51);

^b based on the route length of $\textit{R}=12097\,\textit{km}$ (6532nm), the aircraft seat capacity of $S=300$ seats/dep, and the load factor of $\lambda=0.7$ ;

^c based on 25 flights/day in the network.

As can be seen the cost of passenger time would be about 50% lower for the supersonic flights. The corresponding savings in this cost would be about 4.5 /p-km.

4.2.4 Environmental performance

The fuel consumption of subsonic flights in the given example is derived from Eq. 1c, while respecting the prospective improvements in the aircraft fuel efficiency of r _fc $\,{\approx}\,$ 0.4 by the year 2050^{(Reference Horton57)}. Consequently, the fuel consumption of a flight carried out by an aircraft with a seat capacity of S = 300 seats along the route R = 12097km (6532nm) would be FC ₂₀₅₀(R) = 55.3 tons/flight (Jet A fuel). Under the same conditions, by applying the models in Appendix III to the inputs from Table 4, the average fuel consumption of the supersonic flight is estimated as: FC ₂₀₅₀(R) = 1.02 (FC _cl+ FC _cr+ FC _de) = 1.02 · (9245 + 76089 + 6339) = 1.02 · 91687 $\,{\approx}\,$ 93516kg/flight (LH₂). In this case the factor 1.02 is applied to include the fuel consumed during the LTO cycle. The inputs in Table 4 and the above-estimated fuel consumption are used for estimating GHG emissions and their absolute and relative contribution to global warming and climate change as shown in Fig. 6 (a, b).

Figure 6. Indicators of environmental performance of particular categories of flights carried out on an average route of the network in the given example (period: the year 2050) a) fuel consumption, emissions of GHG, and GWP; b) savings in the contribution to GWP.

Figure 6a shows that the average fuel consumption by the supersonic flight would be about 70% higher than that of the subsonic flight. The corresponding GHG emissions would be also higher by about 19%. At the same time, the GWP of the subsonic flight would be about 16 times higher than that of its supersonic counterpart (CO₂ and H₂O dominate in Jet-A and H₂O in LH₂ fuel). Figure 6b shows that despite the higher fuel consumption and related GHG emissions, the supersonic flight(s) could substantially contribute to savings (about 94%) in the overall GWP and consequently global warming and climate change, both compared to their subsonic counterparts.

4.2.5 Social performance

The noise generated by the supersonic flight(s) operating on an average route of the network is shown in Fig. 7 (a, b).

Figure 7. Indicators of social performance: Relationship between the noise levels generated by supersonic flight (M = 2.4) passing above an observer on the ground in the given example (period: the year 2050). a) Noise vs cruising altitude; b) noise vs distance from an observer on the ground.

Figure 7a shows that the noise produced by a supersonic flight passing above an observer on the ground would decrease with the increase of the cruising altitude. Figure 7b shows that increasing the distance between the overflying aircraft and an observer on the ground, due to an increase of the cruising altitude, would contribute to the decreasing of the experienced noise of an observer on the ground. The levels of noise generally between 83 and 88 dBA do not reflect barely audible explosion (physical phenomenon) and have been the subject of undesirable psychological reactions. As such, these noise levels appear to be about 6-13% above U.S. NASA’s suggested tolerable levels from the sonic boom, set at about 78 dB⁽³⁹⁾. Additionally, the size of the area covered by the noise from the Mach cone needs to be taken into account. Both these are and will certainly be used as inputs in considering the possible noise constraints on operations of the supersonic aircraft^{(12),(39),(58)}.

4.2.6 Some derived indicators of performance

Aircraft design: The maximum take-off weight, payload including only the passengers and their baggage, and the fuel consumption allow for the estimation of some the design-related derived indicators of the technical/technological performance of both subsonic and supersonic aircraft. These are expressed by the ratios such as: PL/MTOW (Payload/Maximum Take-Off-Weight), FW/MTOW (Fuel Weight/Maximum Take-Off-Weight), and PL/FW (Payload/Fuel Weight) as shown in Fig. 8.

Figure 8. Some (design-related) derived indicators of technical/technological performance of subsonic and ssssupersonic aircraft in the given example (Period: the year 2050) ^{(24),(28),(Reference Coen32),(62),(63)}.

As can be seen, the particular ratios would be quite different for subsonic and considered supersonic aircraft. For example, the ratio PL/MTOW is about 21% for subsonic and 8% at supersonic aircraft. (Full payload for supersonic aircraft: 31500kg; 1 passenger + baggage = 105kg^{(Reference Baxter and Bardell59)}). The ratio FW/MTOW is about 45% for subsonic and 23% for supersonic aircraft, the latter also influenced by the fuel type. Finally, the rate PL/FW is about 46% for subsonic and 34% for supersonic aircraft, the latter again influenced by the fuel type.

Economics and environment: The derived indicators of economic and environmental performance of an average route and the entire network are considered through the relationship between the flight operating cost, the cost of GHG emissions, i.e. externalities, and the savings in the cost of passenger time, as shown in Fig. 9 (a, b).

Figure 9. Indicators of the economic performance: The average costs of particular categories of flights carried out on an average route of the network in the given example (period: the year 2050).

Figure 9 shows the difference between the average total cost and its components of the subsonic and supersonic flight on an average route of the network. As can be seen, the average total cost would be lower for the supersonic than for the subsonic flight, by about 20%. This would be achieved thanks to its lower externalities and higher potential savings in passenger time despite the higher operational costs. Consequently, this example indicates that internalising all costs of the particular actors/stakeholders involved in both the demand and the supply side of the given air route network could eventually make supersonic flights economically feasible under the given conditions.

The overall social-economic feasibility: The relationship between the average total monetary contribution to the GDP and the average total cost of both subsonic and supersonic flight(s) carried out on an average route of the network is shown in Fig. 10.

Figure 10. Indicators of social-economic performance: The average contribution to GDP and the average total costs of particular categories of flights carried out on an average route of the network in the given example (period: the year 2050).

As can be seen, in the cases of both subsonic and supersonic flights the average contribution to GDP would be overall higher than the average total cost thus making their difference generally net positive. This difference would be about 5% greater for supersonic flights compared to subsonic flights. The above figures indicate that supersonic flights could eventually be overall social-economically feasible but only under the considered circumstances.

The above-mentioned results enable synthesising some qualitative pros and cons of supersonic flights, relevant for the particular actors/stakeholders involved, which are summarised as follows:

These pros and cons indicate that the full implementation of the future supersonic commercial flights is and will remain a challenge for all above-mentioned main actors/stakeholders involved.