|Fig. 1: Concept to replace gas turbine with HTS motor (Source: N. Kau. Adapted from Wikimedia Commons.).|
According to BP's 2017 Statistical Review of World Energy, the world consumes 96.6 million barrels per day with global oil reserves at 1706.7 billion barrels.  While the automotive industry diversifies to include electric vehicles amongst their products, one can only wonder what will happen to the aviation industry once oil reserves run dry.
One possible solution that researchers are exploring is superconducting turbines powerful enough to run off electricity generated from hydrogen fuel cells. Here we discuss superconductivity use as a motor, the current designs, and the associated concerns.
In 1957 three American researcher, John Bardeen, Leon Cooper, and John Schrieffer, established the BCS (an acronym for the first three letters of their last names) theory of superconductivity. According to their theory, electrons in a solid, group in to pairs called Cooper pairs. These electrons pair up due to interactions with the vibrations of the lattice. [2,3] These pair of electrons then moved inside the solid without friction. However, the electron-electron interaction is relatively weak and can be easily broken up by thermal energy existing within the system. Therefore, below a certain critical temperature, materials exhibit a phenomenon of precisely zero electrical resistance and current can circulate in the material without dissipation of energy. Resulting in incredibly efficient motor solution for flight. Additionally, there have been discoveries in materials which behave as superconductors at unusually high temperatures called high-temperature superconductors (HTS).
Because superconductors can carry very high current density with no resistance, this enables for very light machines. Superconducting motors utilize HTS windings in leu of traditional copper coils. These HTS wires can thus carry much larger currents, therefore generating stronger magnetic fields within the same volume. Furthermore, an electric motor using conventional magnets could weigh up to five times as much as a traditional turbine engine. Superconducting motors however, could be far lighter and more efficient. 
Current aircraft propulsion systems are based on gas turbines. These turbines work by generating thrust through the exhaust of hot pressurized gas and through the rotation of a fan. The turbine can be summarized in two stages: a low-pressure stage and a high-pressure stage.  The low pressure-stage rotation speed is limited by the tip speed of the fan blade. However, the turbine naturally wants to reach higher RPMs and thus consequently by limiting the efficiency.  Thus by replacing the gas turbine with a HTS motor to generate all the thrust through the rotation of the fan would prove advantageous.
Of the currently existing superconducting machines, most are of small form validating special designs.  The three major types of superconducting machines are ones of high power or torque density motors/generators, linear motors, and high-speed machines. Most notable of the high power or torque density motors/generators is AMSC's 36.5 MW, 120 RPM motor and Siemens's 4 MV A, 3600 RPM generator. Oswald's 10kN, 70 mm displacement stands out for linear motors and GE's HIA 4MV A, 16 kRPM for high speed machines. 
While HTS make for lighter, more efficient motors, the associated mass gain from a necessary electrical energy storage system cannot be ignoredr. At cruising altitude, a Boeing 747 uses around 4 liters of jet fuel per second.  JP-8 has an energy density of 4.2 × 107 joules/kg, so the corresponding energy consumption is
Now consider the current commercial lithium ion battery technology in a Tesla Model S. The current model boasts a 100 kWh capability that weighs approximately 540 kilograms. Therefore, the battery within the Tesla Model S has a specific energy of just above 185 Wh per kilogram or 6.67 × 105 joules per kilogram. A Boeing 747-400 has a maximum takeoff weight of 4.13 × 105kg, with 1.63 × 105kg being jet fuel.  To replace JP-8 with Tesla's lithium ion battery that can store the same amount of energy would weigh 1 × 107kg. Or in other words, the battery alone would weigh as much as 25 fully loaded Boeing 747s.
A glaring concern associated with electric aeropropulsion is the associated energy storage. A storage solution takes the form of cryogenically stored hydrogen; hydrogen can be converted into electrical energy through fuel-cell systems. Furthermore, they cryogenically stored hydrogen can serve a second purpose of cooling the superconductors. Although this solution seems like two birds with one stone, pressurized hydrogen carries its own inherent risks. This is a risk that should be taken into account when choosing hydrogen as an energy storage solution. There is also an associated mass gain with using hydrogen fuel cells. If we arbitrarily assume that a Boeing-747 consumes approximately 10 kilograms of JP-8 on takeoff, the corresponding power is 4.2 × 108 Watts. Hydrogen, which has an energy density of 1.42 × 108 joules per kilogram, for the same power requirement has a mass flow of 2.95 kg/sec. Oxygen, which has an energy density eight times of hydrogen, would thus have a mass flow of 23.7 kg/sec. Therefore the total mass flow within the fuel cell is approximately 118.4 kg/sec. This is more than 10 times more in mass flow to use hydrogen fuel as compared to traditional jet fuel JP-8.
Lastly, similar with many other HTS technologies, there comes a high maintenance cost associated with using HTS. Thus at the current status quo, it would be extremely difficult to realistically achieve a cost competitive application. 
With oil reserves predicted to run dry in the next 50 years, HTS motors pose a potential solution to the crisis the aviation industry faces. While HTS motors may seem like an attractive new technology to replace traditional gas turbines, the economic feasibility of this technology will ultimately determine its place in the years to come.
© Nicholas Kau. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 BP Statistical Review of World Energy 2017," British Petroleum, June 2017.
 C. Kittel, Introduction to Solid State Physics, 8th Ed. (Wiley, 2004).
 M. Tinkham, Introduction to Superconductivity, 2nd Ed. (Dover, 2004).
 W. D. Chalmers, On the Origin of the Species Homo Touristicus (IUniverse, 2011).
 C. A. Luongo et al., "Next Generation More-Electric Aircraft: A Potential Application for HTS Superconductors," IEEE 5153109, IEEE Trans. Appl. Supercond 19, 1055 (2009).
 P. J. Masson et al., "HTS Machines as Enabling Technology For All-Electric Airborne Vehicles," Supercond. Sci. Tech. 20, 748 (2007).
 P. M. Grant and T. P. Sheahen, "Cost Projections For High Temperature Superconductors," Electric Power Research Institute, September 1998.
 "747-500 Airplane Characteristics for Airport Planning," Boeing Corporation, D6-58326-1, December 2002.