Economical assessment of commercial high-speed transport

The potential future market demand for a high-speed aircraft along with an estimate of the related costs and ticket prices have been assessed. To address the future demand for a high-speed aircraft, the eligible origin and destination city-pairs and the potential network for such a vehicle have first been identified. Then, the number of premium passengers flying this network, over the next 20 years, is forecasted. Based upon technical characteristics of the potential future high-speed aircraft, it is finally possible to determine the number of vehicles that would be necessary to accommodate this expected future demand.


Introduction
Despite the mothballing of Concorde [1], there is worldwide a regained interest in commercial high-speed transportation ranging from supersonic business jets (ref. HISAC, US, Russia), up to hypersonic speeds. As a matter of fact, during the last 10 years, the European Commission has co-funded long-term research projects on commercial high-speed transportation such as ATLLAS I and II [2,3], LAPCAT I and II [4][5][6][7], and FAST20XX [8]. In addition, national activities such as the ZEHST program in France [9] or the JAXA Hypersonic Transport (HST) in Japan [10] indicate the need and wish to establish the required basic technologies, as well as the design of conceptual vehicles to improve their overall performance. As the above projects have grown towards a certain maturity in conceptual layout and basic proof of technical feasibility, their performance figures in terms of ranges, speed, capacity, etc. allow to preliminary assess their economic viability in an operational environment. This was one of the goals set forward by the HIKARI project, a joint EU-JAPAN funded project to map a path for developing high-speed air travel.
The objective of this paper is to assess the potential future market demand for a high-speed aircraft and determine the costs and ticket prices of such a vehicle. The study is based on the methodology and results developed within the HIKARI project. To do so, this paper starts by determining the eligible origin and destination city-pairs (OD-CPs), the potential network (hereafter, HST network) for such a vehicle, and the expected number of premium passengers flying over the HST network during the next 20 years. Based upon general technical characteristics of the potential future highspeed aircraft, this work then estimates the number of vehicles necessary to accommodate this expected future demand and the related ticket prices. This paper concludes with the general terms for economic feasibility and with suggestions for follow-up studies.
From a policy and applied standpoint, estimating the demand and operating costs of a possible future high-speed aircraft is important, as it should provide insights about the economic viability of high-speed transport.

Market study methodology
To estimate the expected number of vehicles necessary to accommodate the forecasted demand for a potential future high-speed aircraft over the next 20 years, we follow five major steps: 1. Identification of the high-speed transport (HST) network, the eligible origin-destination (OD), city-pairs (CPs), and the expected number of first class and business (FC + B) passengers that are expected to fly the identified CPs in the coming 20 year time. 2. Determination of the expected future number of vehicles that would be necessary to accommodate the forecasted FC + B passengers, assuming an exogenous market share capture percent. 3. Estimation of the development and operating costs, based on the methodology developed by REL (2008).
Step 3 yields the derivation of the ticket price function, that is, the ticket price at which such a future vehicle could operate, as a function of the number of aircraft built. 4. Construction of a discrete choice model to estimate the market share that a high-speed aircraft could capture from existing commercial aircraft. More specifically, this market share depends on the flight time gain, relative to the subsonic aircraft, and the extra airfare that the passenger would need to pay to benefit from the flight time reduction. 5. Theoretical determination of the market equilibrium.
Specifically, by combining the previous 4 steps, step 5 solves for a. the market share that the high-speed vehicle could capture from the HST network; b. re-compute the expected number of vehicles necessary to accommodate this identified market; c. the ticket price at which such a vehicle could operate.
In the following paragraphs, we detail each of the previous steps.

Identification of the potential HIKARI Network and OD-CPs
To identify the potential HST network and the eligible OD-CPs in this network, we follow three steps. First, we forecast the expected future number of premium passengers, per OD-CP (the market size). Second, we construct valid itineraries (routes) 1 for each OD-CP. Finally, by predicting the percentage of travellers that are likely to select each itinerary, at each city-pair, we determine the demand for each itinerary, which in turn determines the shape of the potential future HST network.

Market size
We focus on international long haul, 2 premium air passengers, as of 2012. More specifically, our database contains premium air passenger between city-pairs, all over the world.
Relying on Airbus GMF 20-year air traffic forecast at CP level, 3 we then forecast the expected number of premium passengers, per OD-CP, in 2032. In particular, we restrain to international long-haul OD city-pairs, with at least 3200 monthly, bi-directional premium passengers in 2032.

Itinerary construction
Once the size (number of passengers) of each market (OD-CP) has been forecasted, the next step is to construct valid itineraries (routes) for each OD-CP. Following Grosche [11], we assume a set of rules for itinerary building, 4 as follows.
Number of stops Passengers want to minimize their travel time and to increase the convenience of their journey. Thus, if there are too many stops in an itinerary, it is unlikely to be chosen by the passenger. The maximum number of stops s max is the number of stop threshold, above which we exclude those itineraries, with more stops than the threshold. Because multiple stops with only one HIKARI leg would outweigh the time gain of a high-speed aircraft, we choose s max = 1.
Detour Each non-direct itinerary implies a detour compared to the direct itinerary between two cities, e.g., to exclude overland flight. A maximum detour factor d max indicates to what extent the great circle (GC) total distance of the sequence of connecting flights in the non-direct itinerary, dist cnx , can exceed the direct distance, dist dir , between the origin and destination cities: dist cnx ⩽ d max × dist dir . The detour factor leads to a pre-selection of possible HST itineraries. From the analysed trajectories, we found that the most appropriate value is d max = 1.4, i.e., the great circle (GC) distance of the connecting leg and the HST leg can be at most 40% larger than the direct OD GC distance. The value of the detour factor is in line with the detour factor calibrated by Grosche [11].
Connection time For simplicity and because we assume a full and optimized connectivity between connecting leg and HIKARI leg, the connection time t cnx is set at 2 h. Table 1 summarizes the selected values of the parameters.

HST network forecast
Once itineraries for each OD-CP have been built, the share that each itinerary has on the market (OD-CP) is determined based on the elapsed flight time. Intuitively, the longer the flight time of a given itinerary, the less likely it is that a passenger would select such an itinerary. The demand for each itinerary is determined by multiplying the percentage of passengers expected to travel on each itinerary by the expected market size, i.e., the number of OD-CP air passengers. The aggregation of itineraries and OD-CP determines the shape of the expected future HST network.

Expected future number of aircraft based upon an exogenous market share capture
Relying on the HST network, we then compute the expected future number of high-speed vehicles that would be necessary to accommodate the forecasted FC + B passengers, assuming an exogenous market share capture per cent. To do so, a parametric space consisting of different classes was proposed, based on the capabilities and operational requirements for the HST aircraft worked out in the different European and Japanese projects [2-7, 9, 10]. Specifically, the parametric space boiled down to the following classes for consideration: Importantly, step 2 does not take into account any constraint on the ticket price or other external variables affecting the market share.
To avoid sonic boom or ground overpressure produced over land, as it is standard in the industry, we constraint the aircraft to cover a maximum stretch of 400 km subsonically (Mach ≈ 0.80) after take-off and prior to landing. Adding the time to accelerate and decelerate to the subsonic cruises, one dwells already 51 min flying subsonically with a corresponding range of 966 km.
Based on the latter, the flight time formula for each cluster becomes Finally, regarding eligible airports to be considered as hubs in the HST network, we assume that they must satisfy the following conditions: Airport's distance to the coast is smaller than 400 km. This is to comply with sonic boom constraints overland 5 .
Each airport in the HST network has at least three HST legs.

Cost and ticket price estimation
The ticket cost model estimation is based on the LAPCAT concept, with development and production costs estimated by REL [12]. In that study, the basic cost estimations were taken from [13] for the development and production of aerospace equipment in the USA along with modifications and cross × (GC distance − 966 km) + 51 60 . 5 As robustness check, we also considered 300 km. reference from [14,15] to consider technology evolution. This study found an initial development cost of €22.6bn and a first unit price of €979 m (2006 prices) which is taken as a starting base for the present economic study and methodology. These figures have been uprated, in line with the cost of investment goods in the French aerospace sector to 2012 prices. The combination of an assumed 90% learning factor, 6 as well as financial assumptions (including a 15 year asset life and 5% interest rate) yields a relationship between the production run and the aircraft purchase cost.
Operational costs have subsequently been added. The key cost concept here is fuel, assumed to be 170,000 kg of hydrogen per one-way trip from Europe to Australia for a 300 seat vehicle, costing €4.49 per kg to produce in 2012 prices. This assumption is based on the theoretical efficiency of hydrogen produced via electrolysis. No differentiation on hydrogen consumption based on the different classes of vehicles has been introduced.
Maintenance costs are assumed to be 0.005% of the purchase price of the plane per one-way trip, with an additional once a year service costs of 10% of the purchase price. Finally, there are indirect costs associated with running an airline such as slot fees, head office functions, etc. These are estimated at €30.7 m per annum, uprated from REL's 2006 estimate, in line with the French aviation sector Gross value added (GVA) deflator.
These costs are then combined with assumptions over the working time of the aircraft and passenger load. Two single flights per aircraft and per day are assumed, with 30 days per year down time, yielding 550 flights per annum. In addition, a load factor of 75% is supposed. Finally, each ticket is marked up by 5% on cost price to yield ticket price.
To sum up, the previous assumptions jointly deliver the relationship between numbers of aircraft produced and ticket price.

Market share capture model
To estimate the market share that a high-speed aircraft could capture from the expected future premium air passenger market, we solve the theoretical problem of an individual, who wants to travel by air and has to decide between a subsonic and a high-speed aircraft. More specifically, we suppose that his random utility depends linearly on the flight time and the airfare he pays for the trip [16]. Assuming that the error in his random utility function is distributed logistic, it is possible to show that the probability that he prefers the high-speed aircraft takes the following form (see Appendix B for a derivation): where Prob HST i is the probability that an individual i chooses the high-speed transport, time ratio is the proportion between travel time of high speed and subsonic aircraft, while fare ratio corresponds to the ratio between airfare in a high speed and a subsonic aircraft.
To calibrate the value of the coefficients o , 1 , and 2 , we use Concorde data between 1984 and 2002. More specifically, due to data availability, the Concorde routes used for the calibration were London-Washington and New York-Paris.

Theoretical equilibrium determination
By combining the previous steps, we compute the equilibrium in the market, which is defined as a vector: More specifically, to determine the equilibrium, the following system of three equations, with three unknowns (Ticket price * , Market share * , Number of aircraft * ) is to be solved: with a, b, and c fixed parameters, summarizing technical requirements, such as load factor, aircraft capacity, speed (time ratio), etc. It shows that over the next 20 years, air traffic is expected to grow at a 4.7% annual pace. According to Airbus GMF [17], Asia-Pacific will lead air traffic growth, representing 34% of world RPK (Revenue Passenger Kilometre) in 2032. Together with Europe and North America, these three regions will represent ~ 75% of 2032 world RPK. Because the potential future demand for a high-speed aircraft targets premium passengers, and since the evolution of the share of these passengers on total air passengers have been very stable at around 8% over the last 10 years, we assume that this ~ 8% share of premium passengers will remain constant over the next 20-35 years. Reinforcing the Prob HST i = 1 1 + e o + 1 * time ratio+ 2 * fare ratio , E * = (Ticket price * , Market share * , Number of aircraft * ).

Step 1: Identification of the potential HST network and OD-CPs
(1) Ticket price = f (Number of aircraft, a), previous assumption, the proportion of international tourists, with business as purpose of visit, has also remained very stable over the same period.
To characterize the HST network and the eligible OD-CPs, we focus on four dimensions: • Identification of HST hubs. • Expected traffic growth over the eligible OD-CPs. • The resulting HST network. • Distribution of premium passengers in the HST network, by distance.

Identification of HST hubs
We identify 56 HST hub cities, all of which satisfy the constraints stated in Sects. 2.2 and 2.3. These HST hubs are used to build valid itineraries for each OD-CP. The names of the cities, abbreviations, and distance to the coast for each city are displayed in the appendix. Interestingly, the constraint distance to the coast (300 or 400 km) does not significantly alter the number of eligible HST cities. More specifically, assuming a 300 km distance constraint, the number of HST hubs reduces to 52, 4 cities less than if supposing 400 km. Finally, it is worth to highlight that all the HST cities are already aviation mega cities, according to the GMF definition, namely, cities which handle more than 10,000 long-haul passengers per day (both premium and economy passengers). by distinguishing between region pairs. It also displays the compounded annual growth rate, per region pair, over the period. Figure 4 depicts the expected future HST network, which comprises 151 countries, 1095 country-pairs, 506 cities, 4768 OD city-pairs, and 18,810 routings.

Distribution of premium passengers in the HST network, by distance
We now look at the distribution of the forecasted premium passengers by distance, as plotted in Fig. 5, on the basis of the Great Circle distance. For the real distance flown, the GC distance should roughly be multiplied with an Extended Range Factor (ERF) to indicate the range that the aircraft should technically be capable of covering to realize the different OD-CP legs.
As shown in Fig. 5, the distribution of premium passengers is skewed to the right (skewness coefficient of 0.92), with two peaks corresponding to the intervals 6000-6500 and 9500 − 10,000 km for GC distance. Moreover, the long right tail of the premium passenger distribution underlines the potential for high-speed aircraft, as its flight time gain relative to the subsonic aircraft increases with distance.
It is now possible to relate Figs. 2, 3, and 5 to investigate the sensitivity of the predicted premium passengers to different assumptions on the threshold distance to consider for international long-haul traffic. 7 Figure 6 displays the reduction in the expected premium passengers if instead of considering a GC distance of 3700 km, we were to assume 5000, 7000, or 10,000 km (GC distance).

Step 2: Determination of the expected number of aircraft, assuming an exogenous market share capture
Step 2 computes the expected number of high-speed aircraft necessary to accommodate the forecasted demand, assuming an exogenous market share capture. 8 We first do it for cluster 1 (which aircraft has an average speed of 4260 km/h) and then for cluster 2 (with an average speed of 7100 km/h). figures is the assumption on yearly utilization hours: 3150 h per year (left) versus 5000 h (right). Combined, they show, as expected, that a higher utilization of the high-speed aircraft results in less forecasted vehicles to accommodate the same premium passenger demand. Figure 8 also displays the forecasted demand for a highspeed aircraft, as a function of market share, but instead assuming an aircraft capacity of 300 seats. It compares the situation with 3150 yearly utilization hours and 5000 yearly utilization hours.

Results for cluster 1
Importantly, the few predicted vehicles under the assumption of 300 seats are due to the manner we compute expected future vehicles. More specifically, we assume that if annual forecasted premium passengers on a given route are not enough to fill the annual theoretical seats that would be offered by such a vehicle on the same route, the route is discarded.
Overall, Figs. 7 and 8 show that there exists a market for a potential future high-speed aircraft. However, the size of this market, as measured by the number of forecasted high-speed aircraft in 2032, strongly depends on the assumptions taken. As an illustration, assuming an aircraft capacity of 100 seats and a potential market share between 10 and 20%, the number of expected aircraft ranges between 50 and 276 vehicles.
The significant variability of the results is the reason why in the next subsection, we investigate how results change when the aircraft speed change, relative to the baseline scenario. The baseline scenario is characterized by the following parameters: an average speed of 4200 km/h, an aircraft capacity of 100 seats, 3 weekly frequencies, 3150 yearly utilization hours, and a load factor of 75%.

Results for cluster 2, relative to cluster 1
Figures 9 and 10 compare the results of cluster 1 and cluster 2, in terms of the forecasted number of aircraft. They assume 3 weekly frequencies and a load factor of 75%. Figure 9 supposes an aircraft capacity of 100 seats, whereas Fig. 10 assumes an aircraft capacity of 300 seats. A higher vehicle speed, relative to cluster 1, leads to less forecasted aircraft. Intuitively, flying faster results in less yearly utilization hours and, therefore, results in a lower number of required high-speed vehicles.

Robustness check: sonic boom and flight path deviations
As a robustness check, we revise the distance computation considering the particularities of the high-speed aircraft with respect to constraints imposed by sonic boom. More specifically, the model so far uses great circle distance to compute the distance between city-pairs. However, because of the sonic boom and the need to avoid flying over highly populated areas, the GC distance may not be adequate for many HST legs.
To conduct the robustness check, first, all the HST legs in the eligible network have been classified in 28 traffic flows. An example of a big traffic flow is North America, west side, to Europe. Second, we identify representative citypairs for each big traffic flow. Finally, we compute extended range factors (ERFs) 9 for 7 representative city-pairs, which are applied to all CPs belonging to each of these big traffic flows. For the remaining 21 traffic flows, a weighted average ERF is applied to all CPs belonging to these traffic flows. Figure 11 displays the 28 traffic flows, used to group the ~ 4800 OD city-pairs, together with the city centres in each traffic region and the 7 ERFs used to recalculate the distance. For the remaining 21 traffic flows, the weighted average ERF is 1.118.
With the new flight distance, we recomputed the forecasted number of aircraft. The baseline scenario continues to be characterized by the following parameters: An average speed of 4200 km/h, an aircraft capacity of 100 seats, 3 weekly frequencies, 3150 yearly utilization hours and a load factor of 75%. We extend this baseline scenario, by allowing for an aircraft capacity of 300 seats. Figure 12 displays the results for cluster 1. Intuitively, the reduction in the forecasted number of aircraft is due to the assumption that the distance of the connecting leg and the HST leg has to be at most 40% larger than the direct OD distance. More specifically, when taking into account the flight path deviation, due to the sonic boom, ~ 3000 routings over 18,810 are discarded, because they no longer satisfy this assumption. This in turn yields to a reduced number of forecasted high-speed vehicles. Figure 13 displays the results for cluster 2.
To conclude, the procedure presented here enables us to have a better assessment of the true distance that a highspeed aircraft would need to fly to overcome regulatory restrictions. Nevertheless, in terms of forecasted number of aircraft, its impact is negligible, regardless of the vehicle speed considered.  assumptions underlying these estimates (other than the number of seats per plane) are the same as discussed above. 10 As displayed in the figures, there is a sharp fall in the cost per ticket when moving from 0 to ~ 15-20 vehicles. This is driven by two factors, namely, the development costs being spread between ever more units and the "learning factor" pushing down unit costs, as the production run is doubled from 1 to 2 units, 2 to 4, etc. However, both drivers become proportionately less important after around 20 units or so, as the impact of an extra unit on per vehicle development costs diminishes and the intervals between doubling production runs widen dramatically. At this point, the ticket price hits a lower bound, determined by variable costs such as the fuel bill per plane, and maintenance and other overheads. More specifically, in the case of a 300-seater vehicle, the lower bound is around €5000 per one-way trip, whereas in the case of a 100-seater vehicle, it is three times as much.

Step 4: Construction of the market share capture model
We calibrate the coefficients o , 1 , and 2 , as defined in Sect. 2.4, using Concorde data between 1984 and 2002. The values of the calibrated coefficients are given in Table 2. Figures 15 and 16 display the estimated theoretical probability that an individual chooses a high-speed aircraft. As already explained, this probability depends on the flight time gain, relative to the subsonic aircraft, and the extra airfare that the passenger would need to pay to benefit from the flight time reduction. Because this probability function is calibrated using Concorde data, Figs. 15 and 16 only provide a local approximation to the true probability. For a fare ratio  The previous figures show that if the high-speed aircraft is able to reduce the flight time by 75%, relative to a subsonic aircraft, while the ticket price increases by 400% (fare ratio of 4), the market share that the high-speed vehicle would capture is only ~ 5%. Given the assumed average speed of 4260 km/h in cluster 1, the 75% time reduction is consistent with this cluster. 11 In addition, a fare ratio of ~ 4 is aligned with OE's ticket price estimation, assuming an aircraft capacity of 100 seats and provided an average FC + B ticket price of €4300 is supposed. 12 Assuming a constant 75% time reduction, an aircraft capacity of 300 seats and knowing that a bigger aircraft implies a lower ticket price, the market share of the high-speed vehicle would increase to ~ 13%, provided the fare ratio equals 2.3. 13 It would reach the ~ 26%, if instead the fare ratio equals 1.2.
Regarding cluster 2, with an average speed of 7100 km/h, the expected market share would be ~ 5% if the vehicle capacity has 100 seats; ~ 14% if 300 seats and a fare ratio of 2.3 and finally, ~ 27%, provided 300 seats and a fare ratio of 1.2 are supposed. Table 3 summarizes the previous results.   (1), assuming 100 and 300 seats, respectively, and cluster 1. Importantly, Fig. 17 supposes that the development and production costs E * = (Ticket price * , Market share * , Number of aircraft * ). for a 100-seater aircraft are 20% lower than for the 300 seater. 14 Otherwise, there would be no equilibrium found for the case of 100 seats. Figures 17 and 18 show that regardless of the aircraft capacity considered, there are two equilibria, that is, a low and a high equilibrium. The low equilibrium is characterized by a high-ticket price, low market share, and few forecasted aircraft, whereas the high equilibrium yields a lower ticket price, a higher market share, and more forecasted aircraft, relative to the low equilibrium. 15 What is crucial for this exercise is the ticket price determination, which in turn depends on the development and production costs, at which an aircraft manufacturer would be able to produce such a high-speed aircraft. Figures 19 and 20, in turn, depict the theoretical equilibrium vectors for cluster 2, assuming 100 and 300 seats, respectively. As before, Fig. 19 assumes that the development and production costs for a 100-seater aircraft are 20% lower than for the 300-seater. 16

Conclusions and way forward
The market study shows that there is a market for a potential future high-speed transport aircraft. The following paragraphs and Table 4 summarize the main results obtained in this paper: 1. Ticket prices decrease with aircraft capacity; with these obtained prices, the HST is economically competitive with the classically used aircraft with respect to premium passengers for 300-seater aircraft. For 100 seaters, equilibrium is found at a 2.3 higher ticket price. 2. The results of the theoretical equilibrium determination show a trade-off between market share and aircraft units. More specifically, while the equilibrium market share is at most 10% for the 100-seater and 26% for the 300-seater aircraft, the number of deployed aircraft with the former (100-seater) is 77 compared to 54 for the latter (300-seater aircraft). 3. There is a negligible preference for a higher speed (cluster 2) on the market share over the lower speed (cluster 1) 4. Relying on Concorde data set, the market share is at best limited to 32%. As the 300-seater passenger aircraft has equilibrium points (up to 26%) close to this maximum, the share would actually be larger if the limitation of 32% would be lifted and hence the number of aircraft.
We envision three venues of future research. The first one and most immediate is to extrapolate our results to consider a 2050 time frame. Actually, the HST projects LAPCAT, HIKARI, and ATLLAS concluded that the related technology maturity should allow the high-speed aircraft to be ready for operational use by ~ 2050. At least a preliminary assessment of the potential future market for a high-speed aircraft is, therefore, strongly desirable.
A second venue of future research is to conduct a dedicated survey to premium and tourist passengers rather than using a market share capture model calibrated on Concorde data. Such a technique could improve the value of time estimation, being more suitable for the HST context. Finally, the performance and capabilities of the high-speed transportation have been performed on overall values of the conceptual designs provided by the consortium. Making a dedicated assessment with the actual capabilities for each of the conceptual HST aircraft will indicate which of the designs and deployed technologies should be followed to assure the best value for the market considering the thermal and structural paradoxes [18,19] and environmental considerations [20].

Appendix B
To derive the probability that individual i chooses the highspeed aircraft, we write a parametric model of passenger demand. Specifically, we assume that individual i derives utility U ij from flying high-speed or subsonic, with j indexing the two alternative choices the passenger can make. Furthermore, we assume that U ij has two components, namely,  Theoretical equilibrium determination, 300 seats, cluster 2 a deterministic part, which we denote as V j , and a random component ij that is unobservable to the modeller, which we assume to distribute logistically.
The utility U ij thus writes Since ij distributes logistically, the probability that individual i chooses mode j then becomes where P ij denotes the probability of choosing mode j (HST say) (see Train [17] for a formal derivation).
To estimate this model, without loss of generality, we assume that the deterministic part of the utility V j is a linear function of measurable attributes, namely, the time ratio (TR) and the fare ratio (FR). V j writes with a j , b j , and c j being to be estimated parameters that capture passengers' preferences over these attributes. Substituting the previous expression for V j in P ij and rearranging yields Eq. (2.4).