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| Fig. 1: A Boeing 747 taking off at Toronto Pearson Airport in 2015. (Source: Wikimedia Commons) |
As electric automobiles become more popular in an effort to reduce gasoline consumption, and thus to reduce the amount of carbon in the atmosphere from burning fossil fuels, another natural extension of electric transportation is electric flight. While solar and battery powered flight have been considered and employed for the purposes of the unmanned aerial vehicle, the scenario of an electrically powered commercial plane is considered less frequently, likely because of the challenges presented. [1] Therefore, it is important to establish where current battery technology lies in making this possibility a reality. To this end, we use a transcontinental flight as a prototypical example, as the two most populous cities (New York City and Los Angeles) lie on opposite sides of United States. As an aside, a similar length of flight is required to get from North America to Europe (Newfoundland to the U.K.), but we use a transcontinental North American trip as our benchmark.
This problem involves both airplane technology and battery technology. First, we state the current status of commercial battery technology. The value we use corresponds to commercially available Li-ion batteries. These batteries have been reported to have an energy density (ρE) of [2,3]
| ρE,Li-ion | = | 0.1 kWh kg-1 = 3.6 × 105 J kg-1 |
We can use a Boeing 747 (See Fig. 1) as a prototypical example for calculating how much energy a plane needs to fly 4000 km. A Boeing 747-100 consumes 149,700 pounds of jet fuel (jet A-1 or JP8 fuel) for a flight of 3000 nautical miles. [4] Other parameters of the Boeing 747- 100 are displayed in the second column of Table 1. In SI units, this translates to a Boeing 747-100 consuming 67,903 kg of jet fuel for a flight of 5556 km.
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| Table 1: Parameters for a selection of Boeing airplanes. For the analysis here, a Boeing 747-100 is used, which has its parameters listed in the second column. [4] | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
We can convert the amount of fuel from kilograms to Joules by multiplying the mass by the energy density of jet fuel (ρE,A-1 = 4.3 × 107 J kg-1) [5]
| E | = | m ρE,A-1 | = | 67903 kg × 4.3 × 107 J kg-1 | = | 2.9 × 1012 J |
Now we can find the amount of energy used per kilometer by dividing the total number of Joules used in the flight by the distance of the flight. From this, we obtain a ratio of Energy/Distance
| Energy Distance |
= | 2.9 × 1012 J 5556 km |
= | 5.22 × 108 J km-1 |
Now we can take the distance from New York City to Los Angeles, which is about 4000 km, and find the amount of energy it would take to complete this flight with a Boeing 747-100:
| ENYC-LA | = | Distance × | Energy Distance |
= | 4000 km × 5.22 × 108 J km-1 | = | 2.1 × 1012 J |
The maximum weight of the fuel (assuming no passengers) is the difference between the empty fuel weight (526,500 lb = 238,816 kg) and the max takeoff weight (735,000 lb = 333,390 kg). Calculating this difference results in a value of mfuel = 94,576 kg. We can then find how much energy is in a "full tank" of Li-ion batteries by multiplying together the allowed weight of fuel and the energy density of the Li-ion batteries
| ELi-ion | = | mfuel ρE,Li-ion | = | 67903 kg × 3.6 × 105 J kg-1 | = | 2.4 × 1010 J |
Now that we have computed both the total amount of energy it takes to fly a Boeing 747-100 from NYC to LA and the amount of energy batteries can supply as a replacement fuel, we notice that the energy it takes to get from NYC to LA is greater than energy that the batteries can supply by about two orders of magnitude:
| ENYC-LA | = | 2.1 × 1012 J | ≫ | ELi-ion | = | 2.4 × 1010 J |
Although this does not take into account more minute details of energy expenditure during flight (such as length of taxiing phase, etc.), this calculation demonstrates the inability of batteries to provide sufficient energy for flight.
From the calculations and analysis presented here, we conclude that in its current state, battery technology cannot be used for a North American transcontinental electric plane. Hybrid systems and alternate fuels, including solar panels, hydrogen fuel, electrical storage, and synthetic fossil fuels, may be better alternatives to using purely electrical storage and should be investigated further. From an energetic point of view, synthetic jet fuel is the most promising avenue for commercial flight in the future. [5]
© Mark Zic. 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] X.-Z. Gao et al., "Reviews of Methods to Extract and Store Energy for Solar-Powered Aircraft," Renew. Sustain. Energy Rev. 44, 96 (2015).
[2] I. Buchmann, Batteries in a Portable World: A Handbook on Rechargeable Batteries for Non-Engineers, 3th Ed. (Cadex Electronics Inc., 2011).
[3] A. P. Brdnik et al., "Market and Technological Perspectives for the New Generation of Regional Passenger Aircraft," Energies 12, 1864 (2019).
[4] "747 Size Comparison," Boeing (2007).
[5] P. Kallio et al., "Renewable Jet Fuel," Curr. Opin. Biotechnol. 26, 50 (2014).
