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| Fig. 1: An example of a fully electric airplane. (Source: Wikimedia Commons) |
As electric cars become more and more prevalent, many have speculated that electric airplanes will be next. Indeed, airplanes are one of the biggest sources of pollution, creating a strong impetus for electrifying aircraft as a way to reduce emissions in 2018, aviation in the United States released 173,000,000 metric tons of CO2 equivalent, comprising nearly 3% of total emissions. [1] However, creating electric airplanes poses unique challenges when compared to electric cars. While some very small aircraft have been successfully powered with electricity, such as the plane in Fig. 1, larger, commercial planes appear to be much less viable
The primary obstacle in designing electric commercial aircraft is energy density. Currently, the industry standards for jet aircraft is a hydrocarbon fuel is Jet-A. While there are a large variety of jet fuels, such as JP-8 and Jet A-1, all of them have only negligible differences in specific energies, and are therefore interchangeable for our purposes. Generally, these jet fuels have a specific energy (energy per mass) of 43 MJ/kg. [2]
Meanwhile, current lithium-ion batteries have a specific energy around 0.9 MJ/Kg. While the technology has been improving, the theoretical upper limit of lithium-ion cells is only 1.44 MJ/kg to 1.8 MJ/kg. [3] Therefore jet fuels specific energy is nearly 50 times greater than that of current lithium ion batteries, and still 24 to 30 times greater than the theoretical upper bound.
Still, other types of batteries may offer more promise. Lithium Carbon Monofluoride (Li-CFx) batteries have been shown to offer a specific energy of 2.63 MJ/kg. [4] Furthermore, Lithium-Sulfur batteries have a theoretical upper bound of 9 MJ/Kg. [5] Unfortunately, while these batteries show promise in specific energy, they suffer from more fundamental problems, such as not being able to be re-charged. However, even if the problems with these high specific energy batteries were able to be overcome, they would still fall short of necessary energy per kilogram needed.
The most common commercial jet plane in the United States is the Boeing 737. More specifically, I will analyze a common variant of the 737, 737-400, a medium-sized, narrow-body aircraft used primarily for domestic flights (figures are rounded to the tens place). The 737-400 weighs 35,040 kg empty and has a maximum takeoff weight of 64,640 kg, leaving a useful load of 29,600 kg. At full fuel, the 737 carries 16,140 kg of usable fuel, leaving 13,460 kg for payload (crew, cargo, and passengers). [6,7]
Therefore, with 16,140 kg of jet fuel, the aircraft is carrying approximately 694,000 MJ of energy. In order to break-even, that is to say, to theoretically accomplish the same flight with no payload, an electric aircraft would need to store that amount of energy within 29,600 kg. Rough estimations already begin to show the scale of the problem:
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| Table 1: Estimated Mass Required to Match Energy Provided by Jet Fuel |
Therefore, current battery technology exceeds the useful load by a factor of about 26. Even the most theoretically energy dense batteries far from being a usable reality still exceed the useful load by almost three times.
Still, these results can be fine tuned by accounting for other factors. To the benefit of the case for electric aircraft, one can account for propulsive efficiency. While the hydrocarbon jet fuel is much more efficient at storing energy than batteries, electrical motors can be made more efficient at converting potential energy to propulsive energy. A jet engine can expect an overall efficiency of roughly 33% whereas a battery powered motor 73% efficiency, meaning that electrically powered aircraft may be 2.2 times more efficient. [8,9] Given this, we could expect that an electrically powered airplane would only need to carry 5/11 of the energy needed for a traditional jet. With this factored in, the electrical jet would only need to carry 315,000 MJ of Energy. Still, this is not nearly enough to make batteries a viable option. While a theoretical Li-S battery may be able to store that energy in 35,100 kg, this would still be 5,500 kg over the useful load. Current technology fairs significantly worse, still requiring 351,000 kg of mass to store the required energy.
Another obstacle for electrically-powered planes to surmount however, would be the lack of weight reduction due to inflight fuel burn. As a jet cruises, it burns fuel and therefore lightens its weight. This not only improves performance, but also relied upon in designing aircraft and airports. It follows that while a 737 has a maximum takeoff weight of 64,640 kg, its maximum landing weight is significantly less: 56,250 kg. Because battery discharge does not produce significant mass reduction, this should be taken as the true limit for an electric 737. This, of course, drastically harms the viability of electrically powered aircraft. Instead of useful load of 29,600 kg, an electric airplane would now only have 21,210 kg to work with. To compete with a traditional jet in terms of payload (13,460 kg) and range (315,000 MJ), an electric aircraft would now only have 7,750 kg for energy storage. To store the requisite 315,000 MJ, the battery would need a specific energy of nearly 41 MJ/kg, a physical impossibility for a battery.
While the success of electric cars may prompt some to think that electric aircraft are just around the corner, a closer look reveals significant problems. While some problems may be engineered-around max landing weights may be able to be increased by fortifying runways or redesigning landing gears the problem of energy storage is more fundamental: not even the upper theoretical limits allow for batteries to compete with hydrocarbons and current technology is nowhere close.
© Sam Segal. 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.
[1] "Inventory of U.S. Greenhouse Gas Emissions and Sinks, 1990 - 2018," U.S. Environmental Protection Agency, EPA 430-R-20-002, 2020.
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[3] A. Bills et al., "Performance Metrics Required of Next-Generation Batteries to Electrify Commercial Aircraft," ACS Energy Lett. 5, 663 (2020).
[4] F. C. Krause et al., "High Specific Energy Lithium Primary Batteries as Power Sources for Deep Space Exploration," J. Electrochem. Soc. 165, A2312 (2018).
[5] J.-W. Park et al. "Flexible High-Energy-Density Lithium-Sulfur Batteries Using Nanocarbon-Embedded Fibrous Sulfur Cathodes and Membrane Separators," NPG Asia Mater. 13, 30 (2021).
[6] J. Rustenburg, D. Skinn, and D. O. Tipps, "Statistical Loads Data for Boeing 737-400 Aircraft in Commercial Operations," Office of Aviation Research, DOT/FAA/AR-98/28, August 1998.
[7] D. Skinn, P. Miedlar, and L. Kelly, "Flight Loads Data for a Boeing 737-400 in Commercial Operation," Office of Aviation Research, DOT/FAA/AR-95/21, April 1996.
[8] H. Aygun and O. Turan, "Entropy, Energy and Exergy for Measuring PW4000 Turbofan Sustainability," Int. J. Turbo Jet Engines 38, 397 (2021).
[9] M. A. S. Eqbal et al., "Hybrid Propulsion Systems for Remotely Piloted Aircraft Systems," Aerospace 5, 34 (2018).
