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The supersonic tube vehicle is a new idea in high-speed transport, a vehicle that operates within a hydrogen atmosphere and, because of the low density of hydrogen, would increase sonic speed and dramatically decrease drag relative to air[1]. A hydrogen atmosphere requires that the vehicle operate in a hydrogen-filled tube or pipeline. To prevent leakage of air into the tube, hydrogen pressure is slightly above outside air pressure, and the tube serves as a phase separator.

The proposed supersonic tube vehicle (STV), a cross between a train and an airplane, is multi-articulated, runs on a guideway within the tube, is propelled by contra-rotating propfans, and levitates on hydrogen aerostatic gas bearings. The front locomotive and first railcar of a train are shown in the cutaway drawing below. Vehicle power is provided by onboard hydrogen-oxygen fuel cells. Hydrogen fuel is breathed from the tube itself, liquid oxygen (LOX) is carried onboard, and the product water is collected and stored until the end of a run. Breathing fuel from the tube solves the problem of hydrogen-storage, a major challenge of contemporary hydrogen fuel-cell vehicles.

Supersonic tube vehicle (STV) in its hydrogen tube
Cutaway CAD model shows contra-rotating propfan propulsion and levitation on aerostatic gas bearings. Fuselage outer diameter is 2.69 m, and tube inside diameter is 5.00 m. Tube hydrogen pressure is slightly above outside air pressure.

Analysis of the Concept

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The speed of commercial aircraft is practically limited by the speed of sound in air, 346 m/s at 298 K, and jet transports typically operate around Mach 0.8. As an airplane enters the transonicregion, parts of its surface are subsonic and, because air-stream velocity increases along curvature of its surface, some parts are supersonic. Air becomes strongly compressible near the speed of sound, and the supersonic parts emanate shock waves approximately normal to the surface. The shock waves increase drag (wave drag) and decrease lift; as speed of the aircraft varies, movement of the waves on the surface causes buffeting [2][3]. Wave drag gives rise to a power peak at Mach 1 called the “sound barrier.”

Because of the high speed of sound in hydrogen, it delays the onset of the sound barrier. Mach 1.2 in air corresponds to only Mach 0.32 in hydrogen. Thus, the vehicle could reach MA = 1.2, that is, be supersonic with respect to air, while remaining subsonic in the hydrogen atmosphere. A hydrogen atmosphere offers several advantages over air as the operating fluid for a vehicle: high speed of sound results in a high transonic speed, low fluid density ρ gives low pressure drag, low viscosity μ gives low viscous or skin-friction drag, and high thermal conductivity facilitates heat rejection to the operating fluid (see Table 1).

Table 1: Properties1 of Hydrogen versus Air
Properties Hydrogen Air Hydrogen Value/Air Value
Speed of Sound, m/s (km/h) 1,310 (4,720) 346 (1,246) 3.8
Density (ρ), g/L 0.082 1.16 0.071
Viscosity (μ), μPa-s 9.0 18.6 0.48
Thermal Conductivity, mW/m-K 187 26.2 7.1
1 At pressure P = 1 bar and temperature T = 298-300 K [4]

Two somewhat analogous applications exist: (1) Hypersonic rocket sleds reduce drag and aerothermal effects by being rammed at high speed into a disposable polyethylene tunnel inflated with helium [5]. Vehicle drag is an increasing function of fluid density, and the density of helium (0.164 g/L) is only 14% of the density of air [6]. The current world land speed record of 289 thousand m/s (10,400 km/h = 6,450 mi/h) used such a technique. However, because the sled’s speed far exceeds the speed of sound in helium (965 m/s), the object of the technique, unlike ours, is not to delay the onset of the sound barrier. (2) Cryogenic hydrogen gas has been proposed as a wind tunnel gas to increase the effective Reynolds numbers of test bodies [7].

Potential benefits of the proposed transport system include: (1) energy-efficient, supersonic transport from city center to city center with zero emissions and negligible acoustic noise to the environment, (2) operation independent of the weather, (3) low infrastructure cost compared to similarly routed long-stator maglev systems [8], and (4) a solution to the hydrogen storage problem for long-range hydrogen-fueled vehicles. At first thought, hydrogen safety would seem to be an issue, but the system risk is similar to that of a natural-gas pipeline and can be satisfactorily managed [9]. The principal challenges facing the system are: (1) high absolute infrastructure cost, (2) maintenance of adequate hydrogen gaps in the aerostatic levitation and guidance system, and (3) possibly dynamic instability of the levitated vehicle.

Feasibility is shown by comparing the hydrogen tube vehicle with a mid-sized turboprop airliner, the Bombardier Dash 8 Q400. Based on aerodynamic analysis of the Q400, the tube vehicle will require 2.0 MW of net power to run at 1,500 km/h, which is supersonic with respect to air. It requires 2.64 h to travel from New York City to Los Angeles, consuming 2,330 L of onboard LOX during the trip. Part of the feasibility analysis shows that it is possible to package the fuel-cell stack, LOX system, and water holding tank, along with other components, within each locomotive. Compared to the Q400, the supersonic tube vehicle would be approximately twice as fast, require one-third the power, and consume one-tenth the energy to make the transcontinental trip.

In comparison with jet airplanes, the supersonic tube vehicle would be faster, more energy efficient, and operate independent of the weather. Principal challenges facing the system are: (1) high absolute infrastructure cost, (2) maintenance of adequate hydrogen gaps in the aerostatic levitation and guidance system, and (3) possibly dynamic instability of the levitated vehicle.

Speed and Energy

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This section tests the hypothesis that the STV will be simultaneously fast and energy efficient. Because “fast” and “efficient” are relative descriptions, the hypothesis is tested by comparing the theoretical speed and energy consumption of the STV with those of four conventional long-haul passenger transport modes: road, rail, maglev, and air. If the STV is shown not to be simultaneously fast and energy efficient, then pursuing costly development of hardware prototypes, as an early step toward commercialization, would not be warranted.

Empirical data are obtained for typical examples of vehicles serving each long-haul passenger mode and include Prevost X3-45 and other intercity coaches for road transport, Siemens ICE 3/Velaro high-speed train for rail, Siemens/ThyssenKrupp Shanghai Transrapid for maglev, and Bombardier Q400 turboprop and Boeing 747 fanjet aircraft for air transport.

Studies show that the STV is capable, in principle, of cruising at Mach 2.8 and concurrently consuming less than half the energy per passenger of a Boeing 747 at a cruise speed of Mach 0.81.

The vehicles representing the transport modes analyzed are specific but typical instances of classes of vehicles. The results comparing practical cruise speed and energy consumption of the five modes of transport are collected in Tables 1 and 2, respectively. Empirical energy results for aircraft are based on more than 28 000 data points, and because they represent all flights of three carriers during three months and over a large geographical region, sampling error is negligible. Limitations in the available categories of data parameters, however, cause estimated statistical-bias errors of 1-3 % [10].

Table 2 – Practical cruise speeds Vc
Mode Vc km/h
STV 3500
Airplane 910
Maglev 500
High-Speed Train 350
Coach 150

The practical limits of speed in Table 2 are usually determined not by theoretical capability but by such factors as high energy consumption due to poor aerodynamics, poor-quality infrastructure, sharing the infrastructure with slower vehicles, and ground-level acoustic noise. A dedicated highway infrastructure, with banked curves and noise barriers, could raise the road-vehicle cruise speed to the limit imposed by standing waves in pneumatic tires (see [11], Eq.1). Likewise, a dedicated railway infrastructure could raise rail speed to a limit imposed by Klingel oscillations (see [12], Eq. 2) or catenary-wire travelling waves. Aircraft are the only mode of the five that already has an infrastructure in place allowing operation at the theoretical limit of speed.

For speed, the five modes rank as shown in the continued inequality

STV >> airplane > maglev > train > coach (1)

In theory, the STV can cruise at Mach 2.8 relative to air outside the tube, whereas the Boeing 747-400 can cruise at Mach 0.85 at 10 600 m. The Concorde supersonic transport cruised at Mach 2.2 at an altitude of up to 18 900 m.

Table 3 – Normalized energy consumption
Mode ENd [kJ (seat km)-1] V0 a [km/h] ENV [kJ h (seat km)-1]
Airplane
Boeing 747-400 1530 870 1.76
Bombardier Q400 1450 480 3.02
Coach 254 110 2.32
Maglev 227 430 0.527
Train 184 300 0.612
STV 130 1500 0.0865

a V0 is the fixed vehicle speed at which the un-normalized energy consumption E0 was measured or calculated. Speed of 870 km/h for the Boeing 747 at altitude of 10 700 m (see Table 5) corresponds to Mach 0.81.


As shown in Table 3, under conventional seat-distance energy normalization, the STV at 1500 km/h consumes 8 % of the energy consumed by the Boeing 747-400 at 870 km/h (Mach 0.81). Because energy consumption due to parasitic drag rises as the square of speed, at 3500 km/h (Mach 2.8), the STV would consume 44 % of the energy of the Boeing 747 at Mach 0.81. Surprisingly, the Nd-normalized energy consumption for the 371-seat Boeing 747-400 airplane is only slightly greater than the value for the 74-seat Bombardier Q400. The larger airplane has higher drag and hence raw energy E0, due to higher parasitic and induced drag, but it has a disproportionately larger number of seats, evidently because its ratio of length to cross-sectional area is greater. Because the value for either airplane greatly exceeds the Nd-normalized energy consumption of the other four modes, we will not separate the two in ranking Nd-normalized energy consumption, as given in the continued inequality

Airplane >> coach > maglev > train > STV (2)

Introduction of NV-normalized energy consumption, which compensates for an Nd-normalized bias against fast vehicles, changes the energy consumption ranking. Now, because of greater speed, the 747-400 experiences about half the NV-normalized energy consumption of the Q400. Indeed, the Q400 has the highest energy consumption of the five modes, whereas the 747-400 has lower normalized energy consumption than the coach. The STV at 1500 km/h consumes 3 % of the NV-normalized energy consumed by the Q400 turboprop at 480 km/h, and its energy consumption is 16 % of that for the next most energy-efficient mode, the maglev train. Because of the large difference in energy consumption of the two airplanes, denoting the Q400 as “turboprop airplane” and the 747-400 as “fanjet airplane,” they are separated for ranking of NV-normalized energy, as given in the continued inequality

Turboprop airplane > coach > fanjet airplane > train > maglev >> STV (3)

In view of the above, road transport is very energy intensive, especially with NV-normalization, because of (a) losses in rolling resistance, which increase linearly with weight and more than the second power of speed, (b) poor aerodynamics, and (c) slow speed enforced by low-speed infrastructure. Because of the first-power dependence of rolling resistance on vehicle weight, truck freight would fare worse than the normalized energy-consumption results in Table 3. Maglev and high-speed trains are close in energy consumption: The maglev is higher under Nd-normalization but lower under NV-normalization. This is understandable because advantages of one offset advantages of the other: Maglev has negligible guideway friction but requires levitation power. Energy consumption of air transport is high because of induced drag, which increases as the second power of weight. Indeed, normalized energy consumption of air cargo is about 50 times greater than conventional freight railways [13]. Because the STV operates in a low-density, low-drag hydrogen atmosphere and has low levitation-energy requirements [14], it consumes the least normalized energy of the five modes of transport.

The study shows that (a)the STV is theoretically the fastest and (b)it is the least energy consuming of the five modes of transport. This result is well-summarized by the finding that at 3500 km/h the STV would consume 44 % of the energy per passenger of the Boeing 747 at 870 km/h. It is the concurrence of high speed and low energy consumption – demonstrated by empirical comparison with four conventional modes of transport – that make the STV a potentially attractive passenger transport mode. Its most fitting application, similar to that of the supersonic Concorde, is operations where time minimization is important.

In conclusion, with respect to speed, aircraft are the closest of the modes to the supersonic tube vehicle. In theory, the STV can cruise at Mach 2.8 relative to air outside the hydrogen tube. The Boeing 747, in comparison, can cruise at Mach 0.85, and the supersonic Concorde could cruise at Mach 2.2.

However, the STV is much lower in normalized energy consumption than high-speed airplanes. Under conventional seat-distance energy normalization, the STV at 1500 km/h, the lowest supersonic speed in air at sea level, consumes 8 % of the energy per passenger of the Boeing 747-400 at 870 km/h. At 3500 km/h (Mach 2.8), the STV would consume 44 % of the energy of the Boeing 747 at 870 km/h (Mach 0.81). With seat-velocity normalization, the STV at 1500 km/h consumes only 3 % of the energy consumed by the Q400 turboprop at 480 km/h. The aircraft empirical energy results are based on large data sets (more than 4700 points for the 747 and more than 23 700 for the Q400), with negligible sampling errors but estimated statistical-bias errors of 1-3 %. Thus, the aircraft empirical results are as statistically sound as one can expect [15], and the STV theoretical results are based on aerodynamic analysis undertaken by two mathematical methods [16], [17]. Of the five transport modes compared, only air transport has an infrastructure in place that allows vehicles to reach their theoretical limit of speed. Because of its predicted high speed and concurrent low energy consumption, the STV’s most attractive role is long-distance passenger transport, and its closest competitor is the supersonic jet transport.

The STV is a promising new idea in transport, but much fundamental knowledge is needed to fully understand the aerodynamics of vehicles operating in a hydrogen atmosphere within a tube, and many technical challenges confront the practicality of aerostatic gas-bearings as levitation devices. Research on the important issue of total cost – infrastructure, operating, maintenance, and social cost – is underway and later studies will also address the critical and complex issue of STV hazard analysis.


Notes

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  1. ^ Miller 2008, pp.1995-2006
  2. ^ Anderson 2001
  3. ^ Kermode 2006
  4. ^ Lide 2008
  5. ^ Minto 2004
  6. ^ Lide 2008
  7. ^ Haut 1977
  8. ^ Final report 2004
  9. ^ Miller 2008
  10. ^ Boyd Group International 2009
  11. ^ Miller 2009
  12. ^ Miller 2009
  13. ^ Hirst 1973
  14. ^ Miller 2008
  15. ^ Boyd Group International, 2009
  16. ^ Miller 2008
  17. ^ Miller 2009a

References

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  • Hirst, Eric (1973). "Energy-intensiveness of transportation". Journal of Transportation Engineering, ASCE. 99 (1): 111-122. doi:10.1061/TPEJAN.0000294.
  • Miller, Arnold R. (2008). "Hydrogen tube vehicle for supersonic transport: Analysis of the concept". International Journal of Hydrogen Energy. 33 (8): 1995-2006. doi:10.1016/j.ijhydene.2008.01.030.
  • Miller, Arnold R. (1–3 April 2009), "Supersonic hydrogen tube vehicle: Speed and energy comparisons with road, rail, air, and maglev transport", Proc of HYPOTHESIS VIII, Lisbon, Portugal {{citation}}: Missing or empty |title= (help)CS1 maint: date format (link) CS1 maint: location missing publisher (link)

Miller, A. R., “Beyond aircraft: Supersonic hydrogen tube vehicle.” In: Proceedings of the World Hydrogen Technologies Convention, New Delhi, India, 25-28 August 2009a.

  • Anderson, David (2001). Understanding Flight. New York: McGraw-Hill. p. 320. ISBN 0071363777. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  • Kermode, A.C. (2006). Mechanics of Flight (11th ed.). Harlow, England: Pearson-Prentice Hall. p. 512. ISBN 1405823593. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  • Lide, editor-in-chief, David R. (2008). CRC Handbook of Chemistry and Physics (88th ed.). Boca Raton, FL: CRC. p. 2640. ISBN 978-0849304880. {{cite book}}: |last= has generic name (help)
  • Minto, David (2004), "CTEIP Funded advances in hypersonic testing at the Holloman High Speed Test Track.", Proceedings of the 24th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, American Institute of Aeronautics and Astronautics publication, Portland, Oregon, pp. 2004–2740 {{citation}}: Missing or empty |title= (help)CS1 maint: location missing publisher (link)
  • Haut, R.C.; Adcock, J.B. (1977). "Cryogenic hydrogen as a wind tunnel test gas". Journal of Aircraft. 14 (12): 1155-1156. doi:10.2514/3.58907.
  • Final report on the National Maglev Initiative, Washington, DC: National Transportation Library, US Department of Transportation, 6 December 2004
  • Analysis Review: Fuel consumption of Boeing 747-400 and Bombardier Q400 passenger airplanes(report commissioned by Vehicle Projects Inc, Golden, CO, USA)., Evergreen, CO: Boyd Group International, 11 June 2009



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