49 Electric Propulsion

Introduction

Electrically powered aircraft convert electrical energy stored in batteries into mechanical power, driving an electric motor connected to a propeller or other propulsive system, thereby producing propulsive thrust for flight. Such aircraft may have higher net energy efficiency than fossil-fueled propulsion systems based on internal combustion engines (ICEs), including piston engines, turboprops, and turbofans. Indeed, reductions in net energy consumption for propulsion are highly desirable, with electrically powered aircraft potentially using less than half the primary energy input per unit of useful shaft power delivered compared with an ICE. However, for an airplane, what matters is not just the power or energy available or required for flight per se, but the power or energy available or required per unit mass, i.e., the specific power or specific energy, which ultimately governs payload and range capability.

Electrically powered aircraft have, until recently, been largely limited to small Unoccupied Aerial Vehicles (UAVs), or drones, many of which fall below the 55 lb (about 25 kg) FAA small-UAS limit, including payload. These aircraft are widely used for aerial photography, mapping, surveying, agricultural monitoring, and power line inspection. Many are hybrids capable of vertical takeoff and landing (VTOL) but cruise for most of the mission as fixed-wing aircraft, as shown in Figure 1. More recently, larger electrically powered aircraft have begun to enter limited niche service, especially as light-sport aircraft and flight trainers, while other electric and hybrid-electric concepts are being developed for short-range regional operations. These platforms benefit from the simplicity, quiet operation, and low maintenance requirements of electric propulsion, but the limited energy density of batteries continues to constrain flight time, range, and payload capacity, making electric propulsion much less practical for larger aircraft or long-duration missions.

The Censys Technologies Sentaero 6 is a good example of a modern, high-performance, hybrid VTOL/fixed-wing electric drone.

Continued research and development efforts by engineers are necessary to push the boundaries of electric motor and battery technologies, to realize the higher energy efficiencies possible with electrically powered aircraft, and to demonstrate their economic viability. An attractive byproduct of this technical effort is undoubtedly some reduction of greenhouse gas (GHG) emissions. However, as shorter-term goals, a combination of approaches, including sustainable aviation fuels (SAFs), improved and novel aircraft designs, hybrid-electric propulsion, and hydrogen fuel cells, will likely be necessary. In the meantime, engineers need to be well-versed in the fundamentals of this emerging and rapidly growing field of electric propulsion for aircraft.

Learning Objectives

  • Understand the environmental motivations behind electric aviation, including the impact of greenhouse gas emissions and the concept of carbon footprint.
  • Explain the meaning and significance of energy density in the context of battery-powered flight.
  • Identify the key capabilities and limitations of current battery technologies used in aviation.
  • Distinguish between hybrid-electric, battery-electric, and solar-electric propulsion architectures.
  • Know about the technical, operational, and regulatory challenges facing the development and certification of electric propulsion systems.

Why Electric Propulsion?

Batteries supply the energy required for an electrically powered aircraft through an electrochemical energy conversion process that generates electric current to drive an electric motor. The motor then converts electrical power into shaft power, driving a propulsor, such as a propeller, to do work on the air and generate thrust, as shown in Figure 2; however, other propulsion arrangements are possible. Batteries and electric motors are familiar technologies, having been around for centuries. However, over the last decade, substantial technical progress has made these essential elements increasingly viable for powering aircraft, and electrically powered airplanes are now beginning to enter limited operational service in niche roles. This progress has been driven mainly by higher battery energy density (i.e., more stored energy per unit weight) and improved electric motors (i.e., higher power output per unit weight).

An electric propulsion system consists of a set of batteries that serve as the energy source, supplying electrical current to an electric motor that drives a propeller.

Energy Efficiency

Electric vehicles (EVs), whether terrestrial or airborne, can achieve higher overall energy efficiency than vehicles powered by internal combustion engines (ICEs), although the comparison depends on the system boundaries considered, including electricity generation, distribution, storage, and onboard conversion losses. The foundational technologies for engineers to understand are the characteristics of electrical energy storage systems (e.g., batteries) and the means of converting electrical energy into mechanical work for propulsion (e.g., motors). Electric motors are generally much more efficient than ICEs at converting available onboard energy into mechanical shaft power. Typical internal combustion engines convert only a fraction of the fuel energy into useful shaft power, often on the order of 25% under practical operating conditions, whereas electric motors commonly achieve efficiencies of 80% or higher over much of their operating range.

Power-to-Weight Ratio

Another advantage of electric propulsion is that electric motors can have excellent power-to-weight ratios compared with internal combustion engines (ICEs). The disadvantage is that the energy source, namely the batteries, is heavy and has much lower energy density than fossil fuels. Consequently, a substantial battery mass may be needed to supply the energy required for flight. A further consideration is the need for cooling and power-management systems, which increase the net propulsion-system weight. Therefore, the overall energy balance must account for the trade-offs between motor efficiency, battery mass, cooling requirements, flight requirements, and operating costs. Regarding costs, the relatively low price of electricity, measured in US dollars per kilowatt-hour ($/kWh), is a significant advantage. However, this advantage must be balanced against the high cost of battery replacement, given the relatively limited cycle life of Li-ion batteries.

Electrical Infrastructure & Electric Costs

Engineers must also consider the infrastructure required to supply electrical power and the associated economic trade-offs. Electrification can also extend beyond propulsion, replacing traditional pneumatic and hydraulic aircraft systems with electrically driven alternatives. Nevertheless, system redundancy must also be considered. In the U.S., electricity is generated from a mix of sources, including natural gas, coal, nuclear energy, hydroelectric power, wind, solar, and biomass. Natural gas is now a major source of electricity because of its cost-effectiveness and efficiency, while coal use has declined substantially. Nuclear power supplies a significant fraction of the grid, and renewable sources, especially wind and solar, continue to expand.

Modern natural gas combined cycle (NGCC) power plants can achieve thermal efficiencies of about 60%, i.e., \eta_{\rm gen} \approx 0.60. Accounting for transmission and distribution efficiency, \eta_{\rm tran} \approx 0.95, battery charging and storage efficiency, \eta_{\rm bat} \approx 0.95, electronic speed controller efficiency, \eta_{\rm esc} \approx 0.98, motor efficiency, \eta_{\rm mot} \approx 0.95, and wiring efficiency, \eta_w \approx 0.95, the combined net efficiency is

(1)   \begin{equation*} \eta_{\rm net} = \eta_{\rm gen}\,\eta_{\rm tran}\,\eta_{\rm bat}\,\eta_{\rm esc}\,\eta_{\rm mot}\,\eta_w \approx 0.60 \times 0.95 \times 0.95 \times 0.98 \times 0.95 \times 0.95 \approx 0.50 \end{equation*}

or about 50%. This value is significantly higher than the 25–30% efficiency typical of gasoline engines converting fuel energy into shaft power and the 30–35% efficiency typical of diesel engines. However, conventional liquid fuels, such as gasoline, diesel, or Jet-A, also have upstream energy costs associated with extraction, refining, transportation, and distribution. Refining efficiencies are typically about 85–90%, so the overall well-to-propeller efficiency of fuel-powered aircraft is lower than the engine efficiency alone would suggest.

The higher overall conversion efficiency of electric propulsion means that electrically powered vehicles can use less primary energy per unit distance traveled, depending on the electricity source and operating conditions. This advantage can reduce operating energy costs and emissions, especially when the electricity is generated from low-carbon sources. Therefore, the case for electric propulsion must be evaluated across the entire energy pathway, including generation, transmission, storage, onboard conversion efficiency, battery replacement costs, infrastructure requirements, and mission suitability.

What are greenhouse gases (GHGs)?

Greenhouse gases are gases that absorb and re-emit infrared radiation, thereby trapping heat in the atmosphere. This process is called the greenhouse effect. Without the natural greenhouse effect, Earth’s average surface temperature would be much lower, and life as we know it could not be sustained. However, human activities have increased the atmospheric concentrations of several greenhouse gases, strengthening the greenhouse effect and contributing to global warming and climate change. Important greenhouse gases include:

  • CO2: Carbon dioxide is a major greenhouse gas emitted by human activities, including the burning of fossil fuels, deforestation, cement production, and other industrial processes.
  • CH4: Methane is a potent greenhouse gas released from sources such as natural gas and oil production, livestock farming, landfills, wetlands, and the decomposition of organic waste.
  • N2O: Nitrous oxide is emitted from agricultural and industrial activities, fertilizer use, combustion of fossil fuels, and the treatment of wastewater and solid waste.
  • F-gases: Fluorinated gases include hydrofluorocarbons (HFCs), perfluorocarbons (PFCs), sulfur hexafluoride (SF6), and related compounds. Although present in smaller concentrations than CO2, many of these gases have very high global warming potentials and can remain in the atmosphere for long periods.

Energy Density of Batteries

When engineers discuss batteries for electrically powered aircraft, the term “energy density” inevitably comes up. In energy storage applications, the energy density is defined as the ratio of the energy stored to the volume or mass of the storage medium. To this end, energy storage performance is often quoted in terms of gravimetric specific energy, ED_g, and volumetric energy density, ED_{\cal{V}}. The former is energy per unit mass, while the latter is energy per unit volume. For any aircraft type, the weight of the energy storage medium is critical because increasing aircraft weight increases the lift required and, therefore, the induced component of the power required for flight. However, the total power required reflects contributions from both induced and parasitic power. Energy must be expended to transport stored energy, especially for batteries, which account for a significant fraction of the flight vehicle’s total weight.

An aircraft’s power and energy demands for flight are significantly greater than those of a terrestrial vehicle. Indeed, the power and energy required for a small aircraft are much higher than those of a road vehicle of the same gross weight, primarily because aircraft operate at much higher speeds and must continuously generate lift. Therefore, to make an airplane both practically and economically successful in carrying a payload over any required distance, high fuel energy density and low specific fuel (or energy) consumption of the engine or motor are crucial. For conventional aircraft propulsion using fossil fuels, such as Avgas or Jet A-1, the energy is stored in liquid form in the fuel tanks and released by combustion in the engine. For electric propulsion, energy is stored electrochemically in batteries and delivered as electrical power to drive an electric motor.

Gravimetric Specific Energy

The gravimetric specific energy of a battery is defined as the stored energy per unit battery mass, i.e.,

(2)   \begin{equation*} ED_g = \frac{\rm \small Energy~stored} {\rm \small Mass~of~energy~storage~system} = \frac{E}{M} \end{equation*}

where E is the stored energy and M is the mass of the battery or battery pack. Typical units are Wh/kg or kWh/kg. Notice that this quantity is defined per unit mass, not per unit weight. If energy were divided by weight instead, the result would differ by a factor of g.

Volumetric Energy Density

The volumetric energy density of a battery is defined as

(3)   \begin{equation*} ED_{\cal{V}} = \frac{\rm \small Energy~stored}{\rm \small Volume~of~energy~storage~medium} = \frac{E}{{\cal{V}}} \end{equation*}

where {\cal{V}} is the volume of the battery occupied by the stored energy.

Units of Energy Density

For energy storage devices, the available energy is often quoted in Watt-hours (Wh) or kilowatt-hours (kWh). A Watt-hour is a unit of energy equal to one Watt sustained for one hour. Notice that energy has units of work (i.e., force times distance) or base units of M L2T-2, which is equivalent to a Joule (N m) in SI units or foot-pounds (ft-lb) in USC units. One Watt is a Joule per second, so one Watt-hour equals 3,600 Joules of energy. In USC units, energy output can be expressed in horsepower-hours (hp h). However, this latter unit is rarely used, as the SI system is the international standard for quantifying electrical energy and power, even in the U.S.

Comparison with Fossil Fuels

The natural question is how these values compare with conventional fuels. The gravimetric energy density of jet fuel is approximately 11.9–12.5 kWh/kg, depending on formulation and grade, with a corresponding volumetric energy density of about 9.7 kWh/L. Aviation gasoline (Avgas) is similar, typically ranging from 12.2 to 12.8 kWh/kg. By comparison, lithium-ion batteries used in practical aircraft-level estimates have a gravimetric energy density of only about 0.22–0.25 kWh/kg, which is roughly 50 times lower than that of jet fuel. Their volumetric energy density is about 0.69 kWh/L, approximately 14 times lower than that of jet fuel. In absolute terms, this corresponds to about 43 MJ/kg for jet fuel, compared with roughly 0.8–1.0 MJ/kg for lithium-ion batteries at the cell level and closer to 0.5–0.9 MJ/kg at the pack level. Figure 3 illustrates that the mass, and therefore the weight, of the batteries is usually the more critical issue for an aircraft than their volume. However, both weight and volume remain important considerations in aircraft design.

Battery weight is a more critical issue for an aircraft than its volume, although both will involve design trades.

For the same stored energy, batteries require approximately 15 times the volume and about 50 times the mass of jet fuel. Therefore, for a given mission energy requirement, replacing a fossil fuel with batteries results in a disproportionate increase in aircraft gross weight, fundamentally altering the feasibility of the design. Therefore, one of the most significant challenges in the electrification of aviation becomes immediately apparent: the relatively low energy density of storage batteries compared with fossil fuels, together with the substantial weight penalty associated with storing that energy. For an aircraft, weight is critical and is one of the primary “killers” of performance, the other being aerodynamic drag. However, these penalties are partially offset by the higher energy conversion efficiency of an electric motor compared with an internal combustion engine (ICE). This advantage, however, must be evaluated at the system level, in conjunction with all components of the propulsion system, including the propulsor, whether a propeller, fan, or other device.

Considerations for Electric Propulsion

The uptick in interest and subsequent development of various forms of electric aircraft are driven by the general goals of improving energy efficiency and reducing greenhouse gas (GHG) emissions from aircraft. To the flying public, however, the cost of a ticket to fly from one place to another is what matters to them, not so much whether they may care to acknowledge that they will also generate a substantial carbon footprint in the process. Furthermore, the core technical issue for an airline is improving aircraft efficiency and reducing seat-mile costs, i.e., the cost of transporting one passenger one mile. The airlines will quickly align if this goal requires electric propulsion as the next step.

In the meantime, the International Civil Aviation Organization (ICAO) continues to advocate for stricter regulations that will reduce greenhouse gas (GHG) emissions from commercial aircraft. Regulations can help drive technical developments in the needed directions. Yet, it remains an economic and regulatory problem. To reach these goals, engineers must continue to address key issues and technologies in developing successful electrically powered aircraft.

Batteries

Batteries are a crucial component of an electric aircraft, providing the electrical energy required for flight. Li-ion batteries are widely used; however, all battery types are heavy, and battery technology still has a long way to go before it can achieve the energy densities required for aircraft. Engineers are also developing alternative battery architectures and chemistries to enhance energy storage capabilities.

Motor Specific Power

Electric motors convert electrical energy into shaft torque, which then drives a propulsion system. They can be of various types, such as brushed or brushless, synchronous, or induction motors. Electric motors can be 90% or more efficient, with the remaining 10% loss primarily because of thermal losses, making further efficiency improvements challenging. However, advances in the power-to-weight ratio of motors, the metric that matters for aircraft, remain feasible. These gains are driven by improvements in materials (for example, high-temperature permanent magnets and high-permeability electrical steels), power electronics (wide-bandgap semiconductor inverters), novel motor topologies (such as axial-flux designs), and enhanced thermal management methods (including liquid cooling), which together can push the specific power of electric motors beyond 10 kW/kg.

Thermal Management

Thermal management systems are essential for maintaining optimal operating temperatures in batteries, motors, and other electrical components. The electrical current draw can be high during takeoff, climb, and other high-power operating conditions, and the batteries can become excessively hot. Batteries exhibit some internal resistance, which can cause heating during both charging and discharging, especially at high discharge currents. Therefore, proper cooling or thermal mitigation measures must be implemented to ensure optimal performance and prevent overheating or other temperature-related issues. A worst-case scenario is overheating, which can cause a failure or a fire, both of which are catastrophic for an aircraft. Designing these cooling systems for high specific power requires careful trade-offs between heat-rejection capacity, system weight, and airframe integration.

Charging Infrastructure

Electrically powered aircraft require suitable airport charging infrastructure for recharging their batteries. These charging stations must be capable of accommodating an aircraft’s high-power, rapid-charging requirements. Merely extending the existing infrastructure for fast-charging electric vehicles, which is increasingly available at gas (petrol) stations and parking lots worldwide, cannot be considered a viable solution for aviation. Airport charging for electric aircraft must be designed as dedicated megawatt-class hubs with on-site energy storage or renewable buffering and requires substantial grid reinforcement to recharge large battery packs within the short turnaround times demanded by commercial aircraft operations.

Costs

Li-ion batteries are expensive in terms of specific energy and replacement costs, which are also tied to the number of usable recharge cycles, typically 2,000-3,000 cycles, even for the best batteries. Battery costs have declined substantially, with non-aviation Li-ion battery packs now well below their 2010 costs. However, aviation-qualified battery systems remain more expensive because they require additional containment, monitoring, thermal management, redundancy, certification testing, and documentation. Therefore, aviation battery costs should be treated separately from high-volume automotive pack prices. Additionally, it is essential to consider that the total cost of implementing Li-ion batteries in aviation encompasses not only the battery itself but also system integration, battery monitoring systems, safety measures, and associated paperwork. Reducing aviation battery costs will require a combination of technological advancements, economies of scale, and industry investments. Indeed, continued basic research into battery technology will be crucial for achieving significant cost reductions in the future.

Electric Motors

An electric motor is a relatively simple electromechanical machine, at least in principle, that converts electrical energy into rotational mechanical energy at its shaft, producing the torque required to do work. Electric motors operate through the interaction between the magnetic field and the electric current in wire windings to generate torque at the motor’s shaft, as shown in Figure 4 for a brushed motor. Electric motors used in aviation must be designed to achieve a high power-to-weight ratio, as with any other propulsion system.

An animation of the rotor rotation inside the magnetic field of a simple electric motor. The torque at the shaft can be used to produce useful work.

One significant benefit of electric motors over other methods of producing rotational torque, such as ICEs, is their much higher energy efficiency. Typically, electric motors are over 90% efficient, whereas internal combustion engines (ICEs) are 30%-50% efficient. Electric motors are also lightweight, compact, and mechanically simple, and can provide almost instant increases in power when required. The power output of electric motors is often quantified by specific power, usually expressed in kW/kg, a power-per-unit-mass metric commonly used in aircraft design. Today’s high-performance electric motors can achieve specific powers of about 5–8 kW/kg, with specialized aviation designs potentially reaching or exceeding 10 kW/kg. Such specific powers are significantly higher than those achievable with an ICE.

Specialized electric motor types, such as brushless and radial-flux designs, offer advantages over conventional motor designs. One newer design of particular importance for aviation applications is the axial-flux motor, as shown in Figure 5; its main advantages are higher power density and electrical efficiency. Axial-flux motors are also compact, making them suitable for applications with limited space, such as aircraft. In addition, multiple motor units can be stacked to achieve the desired net power output.

A 261 kW (350 hp) direct-drive axial flux motor designed specifically for aviation applications.

Battery Design

Electrically powered aircraft and their operation set unique and stringent requirements for battery design. The batteries must be lightweight, compact, rechargeable quickly, and capable of delivering high current and power to meet requirements across all phases of flight, particularly during takeoff and climb. They must also have protections to ensure safe operation and thermal control.

Rechargeable lithium-ion (Li-ion) batteries are the most widely used battery type today; see Figure 6. Before that, nickel-cadmium (Ni-Cd) batteries were commonly used. Li-ion batteries have become ubiquitous, powering everything from smartphones and laptop computers to electric cars and even airplanes, mainly because they have high specific energy among commercially mature rechargeable battery types. As previously discussed, specific energies are expressed as gravimetric (kWh/kg) or volumetric (kWh/L) energy densities, both of which are important for aviation applications.

Rechargeable Li-ion batteries are the most widely used battery type today.

Over the last two decades, advances in battery chemistry, materials, and manufacturing have substantially increased the energy density of Li-ion batteries at the cell level. The specific gravimetric energy of commercial Li-ion cells has increased from roughly 80 Wh/kg in early applications to about 250–300 Wh/kg for many high-energy cells, with higher values reported for specialized or developmental cells. At the pack level, after accounting for packaging, protection, wiring, cooling, and battery-management hardware, the usable specific energy is lower, typically closer to 0.20–0.25 kWh/kg for practical aircraft-level estimates. However, as previously discussed, these values remain low compared with Avgas or Jet A-1 fuel, which have a specific (mass) energy nearly 50 times higher, at about 12,000 Wh/kg, and a volumetric energy density nearly 14 times higher, at about 9,700 Wh/L.

Further gains in battery cell‐level energy density now seem more incremental as material limits are approached. Current research focuses on high-nickel layered oxides (>90% Ni), silicon-dominated anodes, and solid-state electrolytes, which together may enable energy densities of 500–600 Wh/kg. Alternative chemistries, such as lithium-sulfur and lithium-air, hold promise but face significant challenges in terms of cycle life, safety, and manufacturability. Even with these next-generation cells, the substantial energy gap between electrochemical storage and hydrocarbon fuels poses significant challenges for the electrification of aviation.

What is lithium?

Lithium is a chemical element with the symbol Li and atomic number 3. It is the lightest metal and belongs to the alkali metal group in the periodic table. Lithium is highly reactive and has a silvery-white appearance. It is commonly found in small amounts in the Earth’s crust and primarily obtained from spodumene, petalite, and lepidolite. Lithium has numerous industrial and commercial applications, including rechargeable lithium-ion batteries.

Batteries also have an energy conversion efficiency. Battery energy conversion efficiency is the extent to which a battery converts its stored chemical energy into usable electrical energy during discharge. For modern lithium-ion batteries, discharge efficiency is typically 90–95%, meaning most of the stored energy can be delivered to an electrical load. If charging losses are included, the net efficiency is about 85–95%. Efficiency varies with temperature, discharge rate, and battery age. Remember that in electric aircraft, this battery efficiency is only one component of the total system efficiency, which also includes losses in the motor, electronics (e.g., the Electronic Speed Controller [ESC]), wiring, and the propeller.

Battery Concerns for Aviation

Several key concerns regarding the use of batteries on aircraft include installation losses, thermal effects, longevity, safety concerns, and associated costs. To address these concerns, the aviation industry is actively researching and developing advanced battery technologies, enhancing safety protocols, and integrating electric and hybrid-electric propulsion systems into aircraft. These efforts aim to harness the benefits of battery technology while mitigating the associated risks and challenges to enhance aviation’s safety, efficiency, and sustainability.

Installation Losses

The electrical metrics quoted for Li-ion batteries are usually more optimistic than “pack-level” metrics, which must account for installation losses. These losses include the “hidden” weight of wiring from the batteries to the motor, insulation, structural materials, and the required cooling systems. These added components increase the installed system weight but do not increase the stored energy capacity. Such considerations can increase the installed battery pack or propulsion system weight by at least 20% relative to the cell-only battery mass. Therefore, in aircraft design, allowances for such factors must be incorporated into the weight estimates and performance evaluations of electrically powered aircraft.

High Discharge Rates

For electrically powered aircraft, battery discharge rates are significantly higher than those of electric road vehicles. One problem is that they also become hotter upon rapid discharge. Heat generation reduces battery life and requires specialized cooling systems to mitigate temperature rise. Aircraft batteries will likely go through multiple deep discharges and thermal cycles per day. The high power demands of takeoff and climb-out will result in exceptionally high battery discharge rates and thermal management issues, which, if not appropriately controlled, can significantly reduce the number of duty cycles a battery can achieve.

Safety Issues

Li-ion batteries can be hazardous if not carefully monitored and protected by temperature, voltage, and current sensors that track each battery cell’s condition, for example, via a battery management system. Because a typical battery pack for an aircraft may have tens or hundreds of individual cells, as many protection sensors and circuits are required. The reported incidents involving Li-ion batteries in aviation have been attributed to cell faults, overcharging, overheating, manufacturing defects, or external damage, any of which can lead to thermal runaway. Thermal runaway is a chain reaction within a battery pack in which exothermic reactions in one cell spread to neighboring cells, potentially causing a fire or explosion of the entire battery pack. If not catastrophic, this situation can still pose significant risks to an aircraft and its occupants.

Hidden Carbon Footprint

The carbon footprint of Li-ion battery production is a crucial consideration when evaluating the overall emissions of electric propulsion systems. Battery production entails environmental and climate-related issues. Lithium extraction and processing occur in several countries, and some extraction methods have been heavily criticized for causing environmental damage. Lithium, a silvery metal, is not easily obtained from mining and requires 500,000 gallons of water to extract one ton of lithium from the earth. This water becomes contaminated and cannot be released back into the environment without treatment.

The carbon footprint associated with manufacturing Li-ion batteries is challenging to quantify and may be substantial. However, carbon savings will likely offset it in the long run. GHG emissions from battery production are typically 60 kg CO2/kWh. However, it is worth noting that the emissions from battery production are a one-time upfront cost, whereas fossil-fueled aircraft emit GHGs throughout their operational life. The continued decarbonization of the electric grid through solar and wind energy will also play a crucial role in reducing the overall carbon footprint of electric aviation.

Battery Replacement Cycles

The frequency of battery replacements for an electrically powered aircraft still needs to be determined. Most research on battery aging has focused on automobiles, many of which have reached the end of their useful lives. Battery usage in an electric aircraft will differ from that in electric road vehicles, partly because of higher energy and current draw rates and the resulting thermal effects.

Without specific battery age modeling for aircraft, a Li-ion battery typically has a lifespan of 3,000 duty cycles. This lifespan corresponds to an aircraft performing four daily flights for about two years. Once this lifespan is reached, the battery must be sent to a recycler and replaced. It is likely that future certification requirements, such as under FAA or EASA rules, will require that the batteries be replaced more frequently than 3,000 cycles to ensure a safe operational life without the possibility of failure, i.e., a standard regulatory safe-life policy used for many other aircraft components.

At a battery recycler, Li-ion battery packs are first discharged and dismantled to remove housings, wiring, electronics, copper, aluminum, and steel. The remaining cells are usually shredded or crushed under controlled conditions to produce a mixed powder containing the active electrode materials. This powder is then processed to recover lithium, nickel, cobalt, manganese, copper, aluminum, and graphite. These recovered materials can then be refined and reused in new batteries or other industrial products.

Future of Battery Technology

Lithium battery technology has seen significant advancements, with a notable increase in energy density since 2010 and a doubling in the last fifteen years, as shown in the timeline in Figure 7. This upward trend is attributable to improvements in materials, design, and manufacturing processes. Innovations such as solid-state electrolytes, silicon anodes, and advanced cathode materials have played vital roles in enhancing the performance and energy density of lithium batteries. These advancements have helped extend battery life, reduce charging times, and increase overall efficiency, which is crucial for applications such as electric aircraft propulsion, electric road vehicles, portable electronics, and other forms of energy storage.

Lithium battery technology continues to improve, with notable increases in energy density and reductions in costs since 2017. It is not yet certain that the trends will continue.

Further developments in battery technology aim to achieve gravimetric energy densities of up to 1 kWh/kg by the year 2050. In the short term, commercially produced high-energy, state-of-the-art Li-ion cells using cathodes of lithium-nickel-manganese-cobalt-oxide or lithium-nickel-cobalt-aluminum-oxide can achieve energy densities of about 250–300 Wh/kg, with higher values reported for specialized or developmental cells. Further research and commercial development of lithium batteries could achieve a cell-level capacity of up to 1 kWh/kg by 2030. However, achieving Li-ion battery energy densities exceeding 500 Wh/kg will require substantial advances in battery technology and may necessitate the development of alternative battery chemistries. Based on the current pace of battery research and the time required to translate this research into production batteries, energy densities greater than 500 Wh/kg may still be a decade or more away.

The cost of lithium batteries has also declined significantly over the past decade. According to various industry reports, the cost of lithium-ion battery packs has fallen from around $1,100 per kWh in 2010 to less than $150 per kWh in recent years, with some projections suggesting costs could drop below $100 per kWh in the near future. These cost reductions make lithium batteries more viable for a range of applications, not only in aviation and aerospace.

Where does the electricity come from when I plug my electric vehicle into an outlet?

A majority of electricity in the U.S. is still generated from fossil fuels, mainly natural gas and coal, although their combined share is now closer to 60% than 80%. Oil contributes only a very small fraction of U.S. electricity generation. Wind energy has experienced substantial growth in the U.S., now accounting for approximately 10% of total generation, and is expected to continue to grow. Solar power now accounts for a growing share of total electricity generation and is expected to continue increasing rapidly. Hydroelectric power accounts for roughly 7%. Biomass (such as wood, agricultural residues, and dedicated energy crops) and geothermal energy account for less than 1% of the total energy mix. Therefore, when you plug your airplane in for a recharge in the U.S., you still generate a substantial carbon footprint. Germany is a global leader in renewable electricity adoption, with renewables now supplying more than half of its electricity.

Power Chain Efficiency & Weights

It is essential to understand better how the power and associated weight of an electric aircraft compare with those of a “traditional” fossil-fuel-powered aircraft. A modern turboprop or turboshaft engine can have a shaft thermal efficiency of approximately 50%, meaning that about 50% of the fuel energy is converted into useful work at the engine shaft. A piston engine (sometimes called a piston-prop or piston aero-engine) has a lower net efficiency of about 35%. However, an electric motor’s net mechanical and thermal efficiency is much higher, approximately 90%, meaning that the motor converts 90% of the available energy into usable power. Therefore, one may be tempted to replace an ICE and its fossil fuel supply with an electric motor and a battery “because it is more efficient.” However, this decision requires a deeper justification through analysis.

Motor Efficiency & Weight

A turboshaft or turboprop has, on average, a shaft-specific power of about 1.32 kW/kg (0.8 hp/lb) to 1.97 kW/kg (1.2 hp/lb). For piston-prop engines, shaft-specific powers range from about 0.33 kW/kg (0.2 hp/lb) to 0.66 kW/kg (0.4 hp/lb). Yet these values remain substantially lower than those of electric motors, which typically achieve specific powers of 5-8 kW/kg. A nominal value of 5 kW/kg represents 2020 motor technology. While the values for an electric motor are desirable, a propulsion system for an aircraft must also be evaluated relative to the weight of the energy source carried on board, which is stored in the batteries.

Battery Efficiency & Weight

One kilogram of Avgas or Jet A-1 fuel stores approximately 12 kWh of chemical energy, approximately 50 times more than a Li-ion battery pack, which stores only about 0.25 kWh/kg. With a representative turboprop or turboshaft efficiency of 50%, Jet-A can deliver about 6 kWh of shaft energy per kilogram of fuel. For a piston-prop engine running on Avgas at about 35% efficiency, the corresponding useful shaft energy is approximately 4.2 kWh/kg. However, even at 90% motor efficiency, a Li-ion battery with a pack-level specific energy of 0.25 kWh/kg delivers only about 0.225 kWh/kg of shaft energy, which is much lower than that available from hydrocarbon fuel.

Net System Efficiency

At this point, it is possible to achieve greater engineering clarity regarding the energy and weight tradeoffs of an ICE propulsion system versus an electric propulsion system, at least for electrifying an existing aircraft with an ICE. The foregoing values are summarized in the table below, illustrating the high conversion efficiency of an electric motor but the poor energy-to-weight ratio of the battery-based propulsion system. The primary reason for this outcome is that the batteries’ high weight reduces the usable shaft energy per unit weight of the onboard energy source.

Type Efficiency Specific power (kW/kg) Fuel/energy type Fuel/energy storage medium Energy density (kWh/kg) Available shaft energy (kWh/kg)
Piston engine 32 – 35% 0.33 – 0.66 Gasoline/petrol Avgas 12.2 – 12.8 4.2
Turboprop 45 – 50% 1.32 – 1.97 Jet fuel Jet A or Jet A-1 11.9 – 12.5 6.0
Electric motor 90–95% 5.0 – 8.0 Batteries Li-ion 0.22 – 0.25 ~0.225

For example, consider replacing a 150 kW (200 hp) piston-prop engine on a relatively small airplane with a 400 kg (882 lb) payload when carrying a full load of Avgas. If the engine has a mass of approximately 136 kg (300 lb), an equivalent electric motor would have a mass of approximately 20 kg (44 lb), as shown in Figure 8. Delivering 150 kWh of shaft energy for one hour with a piston-prop engine operating at about 35% efficiency requires about 430 kWh of fuel energy, corresponding to roughly 36 kg (79 lb) of Avgas. However, operating a comparable electric motor at the same shaft power for one hour would require at least 667 kg (1,471 lb) of Li-ion batteries, about 19 times the corresponding fuel weight. Similar arguments can be made for turboprops or turboshafts, in general.

Retrofitting an existing aircraft, in this case a general aviation (GA) airplane, with an electric propulsion system is illogical because it would likely result in no payload. A solution is a ground-up redesign of the entire aircraft.

Again, while an electric motor’s low weight and high efficiency are desirable, the challenges of simply retrofitting an existing aircraft with an electric propulsion system become apparent, even though it may seem like a good idea on the surface. The power-to-weight ratio, or more specifically, the propulsion system’s energy-to-weight ratio, including the weight of the energy source, is crucial for an airplane. A solution is a ground-up redesign of the entire airplane, starting from the propulsion system and designing the airframe around it.

Check Your Understanding #1 – Retrofitting a turboprop with an electric motor & battery pack

A turboprop engine has a rated power of 746 kW and a mass of 227 kg without the propeller. Estimate the mass of an equivalent electric motor plus the needed mass of batteries to run this electric motor at the same rated shaft power as the turboprop for one hour. Assume the turboprop has an efficiency of 50%, the electric motor is 90% efficient, the electric motor has a specific power of 8 kW/kg, and the battery pack has a gravimetric energy density of 0.256 kWh/kg.

Show solution/hide solution.

The turboprop delivers a rated shaft power of 746 kW and has a mass of 227 kg. An equivalent electric motor must deliver the same shaft power. If a high-performance electric motor has a representative power-to-weight ratio of about 8 kW/kg, then the required motor mass is

    \[ M_{\rm mot} = \frac{746}{8} = 93.3~\mbox{kg} \]

which is significantly lighter than the turboprop engine.

To run this motor for one hour at a shaft power of 746 kW requires a shaft energy of

    \[ E_{\rm shaft} = 746 \times 1 = 746~\mbox{kWh} \]

Because the electric motor efficiency is 90%, the battery must supply

    \[ E_{\rm bat} = \frac{746}{0.9} = 828.9~\mbox{kWh} \]

Assuming a battery gravimetric energy density of 0.256 kWh/kg, the required battery mass is

    \[ M_{\rm bat} = \frac{828.9}{0.256} = 3,\!238~\mbox{kg} = 7,\!139~\mbox{lb} \]

Therefore, the total mass of the electric motor plus batteries would be

    \[ M_{\rm total} = 93.3 + 3,\!238 = 3,\!331~\mbox{kg} = 7,\!342~\mbox{lb} \]

For comparison, if the turboprop thermal efficiency is 50%, then the required fuel energy to deliver 746 kWh of shaft energy is

    \[ E_{\rm fuel} = \frac{746}{0.5} = 1,\!492~\mbox{kWh} \]

Using a jet-fuel energy density of about 12 kWh/kg, the corresponding fuel mass is

    \[ M_{\rm fuel} = \frac{1,\!492}{12} = 124.3~\mbox{kg} = 274~\mbox{lb} \]

This comparison shows that while the electric motor itself is much lighter than the turboprop engine, the battery mass required to supply the necessary energy is overwhelmingly greater than the corresponding fuel mass, highlighting the fundamental limitation imposed by the low energy-to-weight ratio of current battery technologies. Therefore, with current battery technology, such a retrofit is difficult to justify except for short-duration experimental flight testing or research applications.

Hybrid-Electric Propulsion

Electric aviation includes all-electric aircraft, which rely solely on batteries or fuel cells, and hybrid-electric designs that combine internal combustion engines (ICEs) with electric motors. Hybrid power systems offer certain advantages while mitigating the limitations of purely electric propulsion. Hybrid architectures can offer a practical compromise by leveraging the high energy density and long-range capabilities of fossil fuels, while also benefiting from the efficiency and reduced emissions of electric propulsion.

In many cases, the ICE drives a generator that powers electric motors, or both the engine and motor contribute directly to propulsion. This flexibility can allow the ICE to operate closer to its optimal efficiency while also enabling quieter, lower-emission operation during selected phases such as taxi, descent, or low-power maneuvering. Hybrid systems may also recover limited energy during descent or ground operations. However, the practical benefit is much smaller than that for road vehicles because aircraft have relatively limited opportunities for braking energy recovery. As such, hybrid-electric propulsion represents a viable near-term bridge between conventional combustion-powered aircraft and fully electric flight.

Several prototype and demonstrator aircraft illustrate the application of these principles. The Ampaire Electric EEL is a retrofitted Cessna Skymaster, as shown in Figure 9, that uses a parallel hybrid drivetrain, allowing both the piston engine and electric motor to provide propulsion. Diamond Aircraft’s DA40 hybrid demonstrator combines a small rotary engine with electric propulsion components to explore serial hybrid configurations. These and other projects signal growing interest in hybrid-electric aviation, particularly for short-range and regional flight operations where endurance and reliability are key considerations.

The Ampaire Electric EEL, a hybrid-electric version of the Cessna 337 Skymaster, first flew in 2019.

Power System

Hybrid propulsion systems can employ different configurations. For example, they can use an ICE to generate electricity, which powers electric motors for propulsion, as shown in the schematic in Figure 10. This combination enables the ICE to operate at its most efficient power output while reducing emissions relative to direct propulsion. Hybrid systems may also use limited energy recovery during descent or ground operations, although the opportunities are much smaller than for road vehicles. These hybrid power systems have been used in automobiles for many years.

A hybrid electric/ICE propulsion system is a suitable option when excess power is required, such as during takeoff and climb.

The two main types of hybrid-electric propulsion systems for aircraft are serial and parallel hybrids. In the serial hybrid, an ICE generates electrical energy that charges a battery and/or powers the electric motor, which in turn spins the propeller. In the parallel combination, an ICE drives the propeller directly, with an electric motor adding shaft power during takeoff and climb.

While hybrid systems entail performance and weight trade-offs, their primary benefit is that they can offer many of the advantages of electric propulsion while mitigating their drawbacks, as illustrated in Figure 11. As such, hybrids are an excellent near-term solution before all-electric aircraft become feasible. Hybrid propulsion systems may also alleviate some certification challenges for a pure-electric aircraft, but this remains to be seen.

Some hybrid systems could address the stark dichotomy in power-to-weight ratios between fossil-fuel and electric propulsion.

Power & Flight Analysis

At any instant during flight, the total propulsion power must be supplied by a combination of engine output and battery discharge, i.e.,

(4)   \begin{equation*} P_{\mathrm{ICE}}(t) + P_{\mathrm{batt}}(t) = P_{\mathrm{req}}(t) \end{equation*}

where {P_{\mathrm{ICE}}(t)} is the shaft power provided by the engine, P_{\mathrm{batt}}(t) is the useful shaft-equivalent power provided by the battery-electric branch after electrical and motor losses, and P_{\mathrm{req}}(t) is the shaft power required by the propulsion system to sustain flight at an airspeed V_{\infty}(t). Battery terminal power must be corrected for the relevant electrical and motor efficiencies before being added to shaft power.

Over the full mission duration T_{\mathrm{mission}}, the total required energy is

(5)   \begin{equation*} E_{\mathrm{req}} = \int_0^{T_{\mathrm{mission}}} P_{\mathrm{req}}(t)\, dt \end{equation*}

and the energy provided by the hybrid system must satisfy

(6)   \begin{equation*} E_{\mathrm{ICE}} + E_{\mathrm{batt,use}} \ge E_{\mathrm{req}} \end{equation*}

Here, {E_{\mathrm{ICE}}} is the total shaft energy from the internal combustion engine, and E_{\mathrm{batt,use}} is the useful shaft-equivalent energy supplied by the battery-electric branch after the relevant electrical and motor losses.

The engine energy is derived from fuel combustion, i.e.,

(7)   \begin{equation*} E_{\mathrm{ICE}} = \eta_{\mathrm{ICE}} \, Q_{\mathrm{fuel}} = \eta_{\mathrm{ICE}} \, m_{\mathrm{fuel}} \, q_{\mathrm{LHV}} \end{equation*}

where q_{\mathrm{LHV}} is the lower heating value of the fuel, m_{\mathrm{fuel}} is the fuel mass consumed, and \eta_{\mathrm{ICE}} is the shaft efficiency of the engine. The instantaneous fuel power conversion is given by

(8)   \begin{equation*} P_{\mathrm{ICE}}(t) = \eta_{\mathrm{ICE}} \, \overbigdot{m}_{\mathrm{fuel}}(t) \, q_{\mathrm{LHV}} \end{equation*}

The total fuel mass consumed is

(9)   \begin{equation*} m_{\mathrm{fuel}} = \int_0^{T_{\mathrm{mission}}} \overbigdot{m}_{\mathrm{fuel}}(t) \, dt \end{equation*}

The stored battery energy is

(10)   \begin{equation*} E_{\mathrm{batt}} = ED_g \, M_{\mathrm{batt}} \end{equation*}

where ED_g is the gravimetric energy density of the battery, typically in Wh/kg, and {M_{\mathrm{batt}}} is the battery mass. The useful shaft-equivalent battery energy is then

(11)   \begin{equation*} E_{\mathrm{batt,use}} = \eta_{\mathrm{batt}} \, E_{\mathrm{batt}} \end{equation*}

where \eta_{\mathrm{batt}} represents the applicable battery, electrical, and motor-chain efficiency for this branch.

The propulsion power required at a given airspeed V_{\infty}(t) is

(12)   \begin{equation*} { P_{\mathrm{req}}(t) = \frac{D(t)\, V_{\infty}(t)}{\eta_p} } \end{equation*}

with the aerodynamic drag being given by

(13)   \begin{equation*} D(t) = \frac{1}{2} \, \varrho_{\infty}(t) \, V_{\infty}(t)^2 \, S \, C_D(t) \end{equation*}

Here, \eta_p is the propulsive efficiency, \varrho_{\infty} is the ambient air density, S is the wing reference area, and C_D is the drag coefficient. Again, careful optimization of aerodynamic design, wing loading, battery capacity, and fuel allocation is essential to achieving efficient, long-range, or long-endurance hybrid-electric flight.

Solar-Electric Propulsion

Solar-electric propulsion is becoming an increasingly viable means of flight. Solar-electric airplanes use photovoltaic (PV) power systems to sustain flight, converting incident solar irradiance into usable electrical energy with lightweight, high-efficiency PV panels (cell arrays). For aviation use, the PV panels are made to be lightweight and flexible. They are typically integrated into the curved upper surfaces of the wings and fuselage, covering as much area as practically possible. Modern PV technologies used in aerospace applications typically achieve efficiencies of 20–25%. Under favorable peak irradiance conditions, the PV electrical power generated is typically about 200–250 W/m^{2}, with a panel-specific power that may approach about 1 kW/kg for lightweight aerospace panels. Mission-average values are usually lower because of the incidence angle, time of day, atmospheric conditions, and aircraft attitude. A typical installation on small airplanes and drones can produce several kilowatts (Note: 1 kW ≈ 1.34 hp), which can drive electric propulsion systems and charge onboard batteries.

By harnessing sunlight with solar arrays and onboard energy storage, a solar-powered airplane may fly for tens of hours or even several days without refueling, producing no direct in-flight greenhouse gas emissions. This type of airplane is ideal for applications such as continuous environmental monitoring, disaster response, and high-altitude communications relays. Solar energy can also be used to extend the flight time of various types of drones and other UAV systems, provided the PV electrical power captured is sufficient to offset the drivetrain-corrected shaft-power penalties associated with the extra weight and drag of the PV panels. Therefore, to ensure the feasibility of solar installations for a given aircraft application, a careful trade study should be conducted as part of the design process.

History

Research into solar-powered electric flight began in the early 1970s with small, remotely-piloted airplanes, such as the AstroFlight Sunrise, which demonstrated that lightweight PV panels could supply electrical power to propulsion motors in flight. In 1981, the Solar Challenger, a crewed airplane, crossed the English Channel using only solar energy for propulsion, demonstrating the viability of solar-electric flight. In the late 1990s and early 2000s, the NASA Pathfinder, Pathfinder-Plus, and then Helios prototypes demonstrated solar-powered electric flight at very high altitudes, with Helios approaching 30 km, thereby helping introduce the concept of high-altitude pseudo-satellites (HAPS) for telecommunications and Earth observation.

Solar Impulse 2, as shown in Figure 12, circumnavigated the globe entirely on solar power, validating high-efficiency solar cell arrays, ultra-light composite structures, and high aspect ratio wing designs in a single integrated system. The airplane had a single pilot and featured a 72 m (236 ft) wing span, a mass of about 2,300 kg (5,071 lb), approximately 17,000 solar cells distributed over the upper surfaces, a PV efficiency of {\eta_{\mathrm{PV}} \approx 0.23}, and a battery capacity of 68 kWh (245 MJ). By balancing structural weight with ultra-light composites, very low wing loading, and efficient electric motors and propellers, the airplane required only modest cruise power. It could sustain flight during nighttime hours on its stored electrical energy.

Solar Impulse 2 circumnavigated the globe on solar-only power, completing the around-the-world trip in 17 stages over almost 17 months.

Photovoltaic (PV) Cells

Key to the success of solar-powered airplanes is the amount of energy captured from photovoltaic (PV) cells, which are connected in series and parallel combinations to form a PV array or panel, as shown in Figure 13. PV cells use the photovoltaic effect, in which sunlight is directly converted into electrical energy. Each PV cell consists of a p-n junction, formed by combining two types of semiconductor materials: a p-type layer, which contains an abundance of holes (positive charge carriers), and an n-type layer, which has an excess of electrons (negative charge carriers). When sunlight strikes the cell’s surface, photons with sufficient energy excite electrons in the semiconductor lattice, freeing them from their atomic bonds and generating electron-hole pairs. The built-in electric field at the p-n junction drives electrons toward the n-side and holes toward the p-side, establishing a voltage difference across the layers. This potential difference drives a direct current (DC) through the load when the cell is connected to an external circuit.

Photovoltaic (PV) cells operate based on the photovoltaic effect, in which sunlight is directly converted into electrical energy.

For aviation applications, PV panels are manufactured using lightweight, thin, flexible materials, allowing them to conform to and be attached to curved aerodynamic surfaces such as wings and fuselages. The instantaneous PV electrical power output of a PV array can be expressed as

(14)   \begin{equation*} P_s (t) = \frac{d E_s(t) }{dt} = \eta_{\mathrm{PV}} \, A_p \, G(t) \, f_\theta(t) \end{equation*}

where {\eta_{\mathrm{PV}}} is the photovoltaic efficiency, G(t) is the incident solar irradiance (in units of W/m2), and A_p is the exposed collection area of the PV panels (units of m2). A larger, more efficient solar panel will capture more energy and deliver greater power for propulsion. Notice that the area of the solar panel, A_p, may be either less than or greater than the wing reference area S, depending on how much of the airframe surface is covered. The wing reference area S is the planform area, whereas A_p is the actual exposed collection area of the PV panels. In practice, the design goal is often to maximize A_p by covering as much of the exposed upper surfaces of the airplane’s wing and fuselage as possible with PV panels.

The term f_\theta(t) in Eq. 14 accounts for the effective orientation of the PV array relative to the Sun. For a single flat panel, f_\theta=\cos\theta, with \theta = 0 when the exposed collection area is directly facing the Sun’s rays. For panels distributed over curved wing and fuselage surfaces, f_\theta should be interpreted as an area-weighted effective incidence factor for the array rather than as a single geometric angle for every cell. In practice, the useful mission-average value \langle f_\theta \rangle is often between 0.4 and 0.8, depending on the time of day, latitude, flight direction, and aircraft attitude. Under clear-sky conditions near noon at mid-latitudes, G \approx 1,000~\mathrm{W/m^{2}}. The mission-average PV electrical power density harvested can be written as

(15)   \begin{equation*} p_{s} = \eta_{\mathrm{PV}} \,\langle \, G \, f_\theta \rangle \end{equation*}

This value of p_s is an electrical power density, not the incident solar irradiance itself. The total mission-average PV electrical power harvested is, therefore, P_{s_{\rm avg}} = p_s \, A_p. Under clear-sky conditions near noon with nearly normal solar incidence, the harvested PV electrical power density p_s may approach 200–250 W/m{^2}. Mission-average values are lower after accounting for the incidence factor, time of day, atmospheric conditions, and aircraft attitude.

A larger array of solar panels will capture more energy and provide more power for propulsion and battery charging. However, the weight of the PV installation is a major consideration, especially for a drone. For aviation, PV panels or modules are often manufactured as thin laminates, so the effective material density of the laminate can be estimated from its areal mass density and thickness, i.e.,

(16)   \begin{equation*} \varrho_{\mathrm{eff}} \approx \frac{m_s}{t_p} \end{equation*}

where m_s is the areal mass density of the PV laminate and t_p is its thickness. For example, with a quoted areal density of 0.4 kg/m^{2} and a thickness of 0.4 mm for a thin PV panel, then

(17)   \begin{equation*} \varrho_{\mathrm{eff}} \approx \frac{0.4}{4 \times 10^{-4}} \approx 1,000~\mathrm{kg/m^3} \end{equation*}

which is comparable to the material density of most plastic sheets.

Power Control System

Because solar irradiance is inherently variable and flight conditions can vary with time of day, cloud cover, and aircraft attitude, solar-powered aircraft require a dedicated Energy Management System (EMS) to balance power generation, storage, and consumption, as shown in Figure 14. The EMS continuously monitors energy flows to propulsion, avionics, and payloads, while coordinating with onboard batteries to buffer periods of low solar input. In this way, the EMS acts as the supervisory controller, ensuring that energy availability matches mission requirements while preserving overall efficiency.

Representative power system for a solar-powered airplane.

A central element of the EMS is the Maximum Power Point Tracker (MPPT), a DC–DC converter that optimizes the operating point of the photovoltaic (PV) panels. Because PV arrays exhibit nonlinear current-voltage characteristics, with a single point at which power output is maximized, the MPPT continuously adjusts its duty cycle to maintain this optimum under changing irradiance and temperature conditions. By working in conjunction with the battery management system, the MPPT enables efficient storage of excess energy during peak sunlight and its subsequent release during low-light conditions, ensuring the aircraft maintains reliable operation and maximum electrical efficiency throughout the mission.

Power & Flight Analysis

The analysis of a solar-electric airplane is relatively straightforward, as it is based on achieving a suitable energy balance for flight. For continuous flight on solar power, the instantaneous electrical power balance requires that the PV electrical power harvested plus the net battery power must equal the total electrical power required by the propulsion system and onboard systems, i.e.,

(18)   \begin{equation*} P_s (t) + P_{\mathrm{batt}}(t) = P_{\mathrm{elec}}(t) \end{equation*}

where P_s (t) is the PV electrical output from the solar panels, P_{\mathrm{batt}}(t) is the net battery power, positive when discharging and negative when charging, and P_{\mathrm{elec}}(t) is the total electrical power required by the propulsion system, avionics, payloads, and other onboard systems. Power is the time rate of change of energy, so

(19)   \begin{equation*} P_s (t) = \frac{dE_s (t)}{dt} \end{equation*}

where E_s(t) is the cumulative electrical energy harvested from the PV array.

The power required for flight will depend on the aircraft’s true airspeed {V_{\infty}}, its in-flight weight W, as well as flight altitude and temperature through their effect on the ambient density \varrho_\infty, i.e., a density-altitude effect. Because both parasite and induced drag vary with \varrho_\infty, the shaft power requirement varies accordingly. If P_{\rm req} denotes the shaft power required by the propeller, then the corresponding electrical power drawn from the PV/battery bus is approximately

(20)   \begin{equation*} P_{\mathrm{elec,prop}} = \frac{P_{\rm req}}{\eta_{\mathrm{drive}}} \end{equation*}

where \eta_{\mathrm{drive}} includes the motor, controller, wiring, and related electrical losses between the electrical bus and the propeller shaft, but does not include the propeller efficiency \eta_p, which is already included in P_{\rm req}. The total electrical power requirement also includes avionics, payload, and other onboard electrical loads. The solar-electric power system is not affected by density altitude in the same way as the aerodynamic power required for flight. However, the PV output can still vary with altitude, atmospheric clarity, cloud cover, incidence angle, and cell temperature. The available energy from the battery may also depend on temperature because of changes in internal resistance and electrochemical efficiency.

For continuous flight, which may in some cases extend over a day-night cycle, the total harvested PV electrical energy must cover both the electrical energy required during daylight and that demanded at night, i.e.,

(21)   \begin{equation*} \int_{t_{\mathrm{sunrise}}}^{t_{\mathrm{sunset}}} P_s(t)\, dt \;\ge\; E_{\mathrm{req,day}} \;+\; \frac{E_{\mathrm{req,night}}}{\eta_{\mathrm{batt}}} \end{equation*}

where E_{\mathrm{req,day}} and E_{\mathrm{req,night}} are the electrical energy demands of the propulsion system and onboard systems during the daylight and nighttime portions of the mission, respectively. Defining the daily harvested PV electrical energy as E_s and the battery capacity as E_{\mathrm{batt}}, the electric airplane design constraints become

(22)   \begin{equation*} E_s \ge E_{\mathrm{req,day}} + \frac{E_{\mathrm{req,night}}}{\eta_{\mathrm{batt}}} \qquad \text{and} \qquad \eta_{\mathrm{batt}}\,E_{\mathrm{batt}} \ge E_{\mathrm{req,night}} \end{equation*}

where \eta_{\mathrm{batt}} is an effective battery storage efficiency that accounts for the losses associated with charging, storing, and discharging the energy needed for nighttime flight.

These basic energy balance relations apply to all types of solar-electric aircraft. Still, the design implications differ depending on whether it is a pure solar airplane, in which the solar array is the primary mission energy source and the battery stores energy for low-sunlight or nighttime operation, or a solar-augmented airplane, in which PV modules provide supplemental energy to reduce the net battery discharge rate and extend flight endurance and/or range.

Pure Solar Flight

For a pure solar-powered airplane, the PV electrical energy harvested during the daylight portion of the mission must be sufficient to cover daytime propulsion and onboard electrical loads, while also storing enough usable energy in the batteries to sustain flight during periods of low or zero solar input. In this case, the feasibility condition is stringent because the daily solar energy balance must close over the entire mission cycle. The battery supplies energy for nighttime propulsion and buffers diurnal fluctuations. Its nominal stored energy is

(23)   \begin{equation*} E_{\mathrm{batt}} = ED_g \, M_{\mathrm{batt}} \end{equation*}

where ED_g is the gravimetric energy density and {M_{\mathrm{batt}}} is the battery mass. If ED_g is given in Wh/kg, then E_{\mathrm{batt}} is obtained in Wh; multiplication by 3,600 converts this value to joules. The efficiency \eta_{\mathrm{batt}} accounts for charge/discharge losses, so the effective available energy is \eta_{\mathrm{batt}} \, E_{\mathrm{batt}}. Modern lithium-ion batteries typically achieve values of ED_g \approx 250~\mathrm{Wh/kg} with efficiencies of \eta_{\mathrm{batt}} \approx 0.95.

Solar-Augmented Flight

For a solar-augmented airplane, the situation is different. The battery is fully charged on the ground to supply the mission’s primary stored energy, while the PV panels reduce the net battery discharge rate, thereby extending flight endurance or range. The instantaneous electrical power balance still holds, i.e.,

(24)   \begin{equation*} P_s (t) + P_{\mathrm{batt}}(t) = P_{\mathrm{elec}}(t) \end{equation*}

where P_s(t) is the PV electrical output from the solar panels, P_{\mathrm{batt}}(t) is the net battery electrical power, positive when discharging and negative when charging, and P_{\mathrm{elec}}(t) is the total electrical power required by the propulsion system, avionics, payloads, and other onboard systems. The solar input P_s (t) need not cover the entire electrical power requirement. To this end, a PV electrical power density p_s can be defined as

(25)   \begin{equation*} p_s = \frac{P_s}{A_p} \end{equation*}

where A_p is the exposed collection area of the PV panels. However, solar augmentation is beneficial only if the PV electrical power captured exceeds the equivalent electrical power-density penalties caused by the added weight and aerodynamic drag of the PV panels. Therefore, for a solar-augmented airplane, an effective solar-electric power per unit area can be defined as

(26)   \begin{equation*} p_s^{\mathrm{eff}} = p_s - \left(\Pi_W + \Pi_D\right) \end{equation*}

where the \Pi_W and \Pi_D terms are equivalent electrical power-density penalties per unit panel area associated with the added weight and drag of the PV solar panel installation, respectively. The net solar-electric benefit for the airplane is, therefore,

(27)   \begin{equation*} P_{\mathrm{s,net}} = p_s^{\mathrm{eff}} \, A_p \end{equation*}

which must be positive and have an appropriate margin for solar augmentation to improve flight time. If p_s^{\mathrm{eff}} \leq 0, then the electrical power harvested by the PV installation is insufficient to offset the electrical power-density penalties caused by the added weight and drag, and the installation will reduce flight performance rather than improve it.

Electrifying a Turbofan?

According to some claims, an electric motor driving the same fan stage can replace a turbofan engine. This all sounds straightforward, but this claim requires deeper analysis. Remember that an electric motor would only replace the engine core, as shown in Figure 15. Therefore, one immediate issue is the loss of jet thrust from the core of a turbofan engine, which accounts for approximately 30% of the total thrust. Another issue is the accessory components, such as hydraulic and pneumatic pumps, which would still be required with an electric drive.

Replacing a turbofan with an electrically powered system will inevitably require a larger fan to recover the lost jet thrust.

Therefore, if an electric motor were to drive the fan used in any particular turbofan engine with the same torque, rotational speed, and blade section Mach numbers (which affect efficiency), the resulting thrust would be lower. This “lost” thrust could be recovered using a larger fan or other design modifications. In the case of a bigger fan, if the fan is uniformly loaded, then the new “electric” diameter, D_e, can be estimated in terms of the original diameter, D, by using

(28)   \begin{equation*} \frac{D_e}{D} = \sqrt{ \frac{T_{\rm req}}{T_{\rm req} - T_{\rm lost}}} \end{equation*}

where T_{\rm req} is the required thrust and T_{\rm lost} is the lost thrust from the engine core. For a 30% loss of thrust, the new fan diameter will be about 20% larger.

The implication is that retrofitting a turbofan with an electric drive is not a plug-and-play replacement. Instead, it necessitates a substantial redesign of the propulsion system, including potential aerodynamic and structural modifications. Furthermore, larger fans exacerbate existing constraints on ground clearance for underwing engines, which are already limiting factors in many current aircraft designs. On the other hand, an electric fan system would be significantly lighter than a conventional turbofan engine, which may partially offset the added mass of larger fans. Nevertheless, the high weight of current battery systems remains a fundamental challenge, especially for medium- and long-range flight profiles.

Assessing Costs

What does it cost to charge and operate an electrically powered aircraft? To answer this question, it is necessary to compare the cost of grid electricity with the cost of equivalent usable energy from aviation fuel. Industrial consumers of electricity in the U.S. may pay on the order of $0.075 per kWh, although electricity prices vary by region, contract, demand charges, and time of use. Jet fuel prices also fluctuate substantially. For example, if Jet A-1 costs approximately $820 per metric tonne, then because one metric tonne is 1,000 kg or 2,204.62 lb, the corresponding fuel cost is about $0.82 per kg or $0.37 per lb. Airlines may also use fuel hedging to reduce exposure to short-term fuel-price volatility.

At the system level, the usable shaft energy from Jet A-1 depends on engine efficiency. If the fuel has a specific energy of about 12 kWh kg^{-1} and the effective engine efficiency is about 40–50%, then the usable shaft energy is of the order of 5–6 kWh per kilogram of fuel. Therefore, if Jet A-1 costs about $0.82 per kilogram and provides about 5–6 kWh of usable shaft energy per kilogram, then the fuel cost is approximately $0.14–0.16 per usable shaft kWh. By comparison, if electricity costs $0.075 per kWh, then the cost of electrical energy supplied to the aircraft is about $0.075 per kWh before onboard losses. After accounting for battery, controller, motor, wiring, and other electrical losses, the cost may be about $0.08–0.09 per usable shaft kWh. Therefore, on an energy-cost basis alone, electric propulsion can have a lower operating energy cost than Jet A-powered propulsion. However, this comparison does not include battery replacement cost, battery cycle life, aircraft utilization, certification costs, charging infrastructure, or payload lost to battery weight.

Another significant cost consideration is the maintenance cost of engines versus the replacement cost of batteries. Turboprops and turbofans are mature, reliable machines, but their maintenance and overhaul costs are substantial. A representative maintenance cost may be of the order of $200 per flight cycle for a turboprop and $500 per flight cycle for a turbofan, depending on engine size, utilization, contract structure, and overhaul interval. For example, for a turboprop engine rated at 820 kW, or about 1,100 shp, a maintenance cost of $200 for a one-hour flight corresponds to approximately (200/820) \approx 0.24 US dollars per shaft kWh. This value is an approximate engine maintenance cost expressed per unit of shaft energy delivered during the flight.

For an electrically powered aircraft, the analogous recurring cost is battery replacement. If an installed aviation battery pack costs about $500 per kWh of capacity and is limited to 1,500 full-use flight cycles, then the amortized battery replacement cost is approximately (500/1500) \approx 0.33 US dollars per kWh of installed battery capacity per cycle. The effective cost per usable shaft kWh will be higher if only part of the nominal battery capacity is usable, or lower if the battery achieves more cycles before replacement. Li-ion batteries may be capable of several thousand cycles under favorable conditions, but aviation certification, reserve requirements, thermal limits, battery aging, and conservative depth-of-discharge limits may reduce the allowable operational cycle life. Therefore, while the electrical energy cost per usable shaft kWh may be lower than the fuel energy cost, this advantage can be offset by the high cost of battery replacement.

Based on this cost argument, the economic case for electric propulsion depends on more than the price of electricity. It depends on battery pack cost, battery cycle life, usable depth of discharge, charging infrastructure, aircraft utilization, maintenance savings, lost payload capacity, reserve-energy requirements, and the value of reduced noise and local emissions. Electric aircraft may therefore be economically attractive for some short-duration, high-utilization missions, especially if battery costs decline and cycle life improves. However, for larger aircraft or longer missions, the cost and weight of batteries remain major obstacles.

Electrical Infrastructure

Developing an electric charging infrastructure is crucial to enabling the adoption of electric aircraft, particularly for commercial purposes. In particular, eVTOL aircraft will require numerous charging stations, and in large cities, one immediate question is where to locate them. The answer may be on building rooftops or in parking lots. All airports, including smaller regional airports, would also need to invest in charging infrastructure to provide the necessary power and enable rapid turnaround times for various electric aircraft. To make economic sense, this aircraft charging infrastructure would need to accommodate the charging needs of aircraft of various sizes and types, ranging from general aviation to commercial airliners to eVTOLs. It would be chaos if too many aircraft arrived at the same airport at the same time for a battery top-off!

Another consideration is that charging electric aircraft requires more powerful and specialized charging solutions than those for electric road vehicles. The power and electrical current demands of aircraft charging are significantly higher than those of road vehicles, and the infrastructure must also support rapid battery charging to minimize turnaround times. In the meantime, efforts to electrify airport ground operations, such as ground support equipment, tugs, baggage carts and loaders, and maintenance vehicles, can provide a starting point for developing the significantly upgraded electrical charging infrastructure needed to supply the power levels required to recharge electric aircraft.

Quantifying the load on the electrical grid, determining costs, and identifying the specific types and locations of charging stations required for electric aircraft will be critical to the success of eVTOL and other electric aircraft. Merely extending existing automotive fast-charging infrastructure will be inadequate for both power delivery and thermal management; therefore, aviation charging systems also require standardized protocols and integrated energy-management controls to ensure safety, interoperability, and reliability. Understanding the technical specifications, power requirements, and cost implications of different charging solutions will also be crucial for airport operators and aircraft manufacturers. Ultimately, addressing infrastructure challenges, including electrical charging, will be essential to a holistic approach to the electrification of all types of aviation.

Regulation & Certification Issues

The FAA and EASA are the two principal regulatory authorities responsible for ensuring aviation safety and regulating the aviation sector. These authorities are crucial in establishing and enforcing standards for aircraft design, production, pilot licensing, and maintenance and operating requirements. Their primary goal is to ensure that all aircraft designs comply with accepted aeronautical standards and that the aircraft are safe to fly.

With the emergence of electric aviation and related technical advancements, such as specialized electric motors, new battery types, fly-by-wire flight control systems, and autonomous flight, unique challenges must be addressed within the existing regulatory framework, including the Federal Aviation Regulations (FARs). The innovative technologies and components used in eVTOL and other electrically powered aircraft generally differ from those required by conventional aircraft certification standards. Therefore, adapting existing regulations or creating new ones becomes necessary.

The FAA and EASA are well aware of the need to continually evolve their airworthiness and operational regulations to keep pace with emerging technologies. They have engaged with industry leaders, research organizations, and manufacturers to understand the implications of electric aviation and autonomous flight. However, updating aviation regulations remains a complex and lengthy process, and certifying an eVTOL aircraft is likely to take many years. Nevertheless, the authorities recognize that, to advance aviation, they must continue to strike a balance between ensuring safety and fostering innovation, including formal certification and the eventual issuance of a certificate of airworthiness for all types of electrically powered aircraft.

Hydrogen Fuel Cells

Advancements in battery technology continue, with ongoing research into battery chemistries that could improve energy density while reducing weight, maintaining safety, and ensuring durability. In the meantime, hydrogen-powered fuel cells offer another path for using the efficiency advantages of electric propulsion. In a fuel-cell aircraft, hydrogen is supplied to a fuel cell, where it reacts electrochemically with oxygen from the air to produce electricity, water, and heat. The electricity then drives electric motors, much as it does in a battery-powered aircraft. Therefore, the airplane still uses an electric propulsion system, but the onboard energy is stored primarily as hydrogen rather than in batteries.

Hydrogen has a much higher specific energy than batteries on a mass basis so that it can reduce the mass of the stored energy required for longer flight endurance or range. However, hydrogen has a very low density, so it requires high-pressure tanks, cryogenic liquid storage, or other storage methods, all of which add weight, volume, complexity, and cost. Hydrogen is also highly flammable, so leaks, ventilation, ignition prevention, crashworthiness, and ground-handling procedures become important safety considerations. The fuel cell itself also adds weight and must reject heat, manage water, and provide reliable power over the full operating envelope.

The environmental benefit of hydrogen depends strongly on how the hydrogen is produced. Hydrogen made from fossil fuels can still have significant lifecycle greenhouse gas emissions, whereas hydrogen produced by electrolysis using low-carbon electricity can offer much greater emissions reductions. Therefore, hydrogen-electric aircraft may help address some of the limitations of battery-electric aircraft, but they introduce new challenges in fuel production, storage, distribution, airport infrastructure, certification, and operational safety. Investigating the performance and emissions potential of fuel-cell-powered aircraft remains an important area for future research.

Small-Scale Electric Propulsion for UAVs

At the scale of small UAVs, electric propulsion offers several advantages. Electric motors are lightweight, highly efficient, mechanically simple, and require minimal maintenance compared to small internal combustion engines. Because these aircraft are relatively light and typically fly short missions, the limited specific energy of batteries is less of a constraint. Consequently, electric propulsion has become the dominant solution for many small UAV applications, including research platforms, mapping, surveillance, and student design competitions. As aircraft size and mission range increase, however, the limitations imposed by battery energy density become progressively more significant. These constraints help explain why electric propulsion is highly successful for small UAVs but remains more challenging to apply to larger aircraft and vertical-takeoff vehicles.

At this scale, the primary components include the battery, brushless DC motor (BLDC), and electronic speed controller (ESC). Lithium polymer (LiPo) or lithium-ion batteries are typically used for their high energy density and rapid discharge capability. The battery’s voltage, capacity, and discharge capability help determine the available electrical power and flight endurance, while the motor and propeller determine how that power is converted into thrust. The BLDC motor, favored for its high efficiency and precise electronic commutation, delivers mechanical shaft power to the propeller.

Commutation and motor control are handled by the ESC, which interprets throttle commands, typically in the form of pulse-width modulated (PWM) signals, and regulates the voltage and current supplied to the motor. The ESC converts PWM input signals, typically ranging from 1.0 ms (idle) to 2.0 ms (full throttle) at 50 Hz, into a three-phase power output. Internally, ESCs employ high-frequency switching of power transistors to regulate the output voltage and timing. Most ESCs include startup sequencing and thermal protection and may provide telemetry of voltage, current, temperature, and rotational speed (rpm).

The electrical power delivered from the battery is given by

(29)   \begin{equation*} P_{\text{bat}} = V \, I \end{equation*}

where V is the voltage and I is the current draw. The mechanical power output at the motor shaft, assuming motor efficiency \eta_m, is

(30)   \begin{equation*} P_{\text{shaft}} = \eta_m \, P_{\text{bat}} = Q \, \Omega \end{equation*}

where Q is the torque and \Omega is the angular velocity. The battery’s nominal energy capacity, expressed in Watt-hours, can be estimated as

(31)   \begin{equation*} E_{\text{bat}} \approx C \, V_{\rm nom} \end{equation*}

where C is the battery capacity in ampere-hours (Ah) and V_{\rm nom} is the nominal battery voltage. The corresponding flight endurance can be estimated by

(32)   \begin{equation*} t_{\text{flight}} = \frac{E_{\text{bat}} \, \eta_{\text{total}}}{\overline{P}_{\text{load}}} \end{equation*}

where \overline{P}_{\text{load}} must be interpreted consistently. If it is the average electrical power drawn from the battery, no propulsion efficiency factor should be applied. If it is the average shaft power required by the propeller, then the electrical energy available from the battery must be multiplied by the appropriate motor and drivetrain efficiencies.

Worked Example #2 – Endurance of a small UAV

A fixed-wing UAV with a single motor driving a propeller is powered by a 14.8 V battery with a 6,600 mAh capacity. During the cruise, it draws 9 A. Assuming 90% usable battery capacity, estimate its flight endurance. If the motor efficiency is 80%, determine the corresponding shaft power.
Show solution/hide solution.

The battery capacity is

    \[ C = 6{,}600~\text{mAh} = 6.6~\text{A\,hr} \]

so the usable battery capacity is

    \[ C_{\text{usable}} = 0.90 \times 6.6 = 5.94~\text{A\,hr} \]

Hence, the flight endurance is

    \[ t_{\text{flight}} = \frac{5.94}{9} = 0.66~\text{hr} \approx 39.6~\text{min} \]

The corresponding electrical power draw is

    \[ P_{\text{elect}} = VI = 14.8 \times 9 = 133.2~\text{W} \]

If the motor efficiency is 80%, then the shaft power is

    \[ P_{\text{shaft}} = 0.80 \times 133.2 = 106.6~\text{W} \]

Therefore, the UAV endurance is about 39.6 minutes, and the corresponding shaft power is about 107 W.

Summary & Closure

Electrically powered aircraft offer several potential benefits for modern aviation, including higher energy efficiency and lower carbon emissions compared with conventional fossil-fuel-powered aircraft. However, even in the long term, passengers will likely fly on electric aircraft primarily over relatively short distances. Battery technology remains one of the principal factors limiting the feasibility of electric aviation. Other considerations include infrastructure development, charging systems, certification requirements, operational economics, and public acceptance.

A combination of technical approaches will likely be employed in the coming decades to address the challenges associated with “pure” electrically powered aircraft. This more diversified strategy may include improvements in aircraft design, greater use of sustainable aviation fuels (SAFs), and the development of hybrid-electric or hydrogen-electric propulsion systems. When applied collectively, these technologies could help reduce emissions from the aviation sector while maintaining the performance and operational flexibility required for commercial flight. In the meantime, engineers must continue to develop solutions that meet the unique requirements of electric propulsion while addressing broader concerns about energy use and environmental impact.

At smaller scales, however, electric propulsion has already proven highly effective. Small UAVs provide an excellent platform for understanding the principles of electrical power generation, motor efficiency, energy storage, and propulsion system integration. A solid understanding of electrical and mechanical power conversion, control signaling, and energy budgeting enables students to analyze and optimize UAV propulsion systems with confidence. As UAV applications continue to expand in both civil and military domains, this knowledge provides a practical foundation for further coursework, design activities, and professional practice.

5-Question Self-Assessment Quickquiz

For Further Thought or Discussion

  • Why does the goal of decarbonizing terrestrial transport and electrifying aviation also pose an educational challenge?
  • Electric car manufacturers have been experiencing problems with vehicles catching fire. How can the flying public be confident in electrically powered aircraft, given that an in-flight fire is likely to be catastrophic?
  • List critical factors that influence the performance of electrically powered airplanes compared to traditional internal combustion engine aircraft.
  • Given that air transport of lithium-ion batteries as cargo is banned or strictly controlled, how can their use as the primary propulsive energy source be considered for propelling an airplane?
  • Turboprops and turbofan engines are well-proven, refined, efficient, and reliable. Why would the aviation industry ever want to stop using them?
  • Are hybrid-electric systems more environmentally friendly than traditional ones? Discuss.
  • Battery technology has not yet reached sufficient maturity to make commercial electric air transport viable. Discuss this statement.
  • Advances in battery and electric motor technology, combined with more efficient aerodynamic designs, will characterize the future of electric aviation. Discuss.
  • Beyond the low energy density of batteries, infrastructure and regulatory hurdles are likely more severe than technical challenges. Discuss this viewpoint.
  • Regulators often need to develop standards, safety rules, and certification guidelines to keep pace with technological advancements and the introduction of new products. Why?

Other Useful Online Resources

Take a deeper dive into the field of electrically powered aircraft by following up with some of these online resources:

  • Chat with ChatGPT about its thoughts on electric aviation.
  • A great webpage by Airbus about hybrid and electric flight.
  • This is a good video on hydrogen-powered versus electric-powered aircraft.
  • Take a flight on the world’s first certified electric airplane.
  • Find out about the world’s fastest 345 mph electric airplane!
  • A video reviewing the progress of eVTOL and electric aviation.
  • The False Promise of Green Energy – lecture by Prof. Andrew Morriss.

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Introduction to Aerospace Flight Vehicles Copyright © 2022–2026 by J. Gordon Leishman is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, except where otherwise noted.

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