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we can write L ef 1 Rf = Dηpηintηeng g ln 1−m /m . (3) fTO where L/D is the lift-to-drag ratio, ηp is the propulsive efficiency, ηint is the efficiency due to propulsion integration losses, ηeng is the engine thermal efficiency, ef is the fuel specific energy, and mf /mT O is the ratio of fuel weight to takeoff gross weight. For battery-powered aircraft, a different version of the Breguet range equation can be derived as [8, 22] R = Lη η η eb mb . (4) b D p int e g mTO where ηe is the total efficiency stackup of the electric propulsion system, eb is the battery specific energy, and mb/mTO is the ratio of battery weight to takeoff gross weight. These equations differ due to the decrease in fuel mass (and therefore, induced drag) during a mission for fuel-powered aircraft. We can see that for both fuel-burning and battery-powered configurations, range is directly proportional to specific energy (eb, ef). At state of the art (SOA) specific energies, concepts with significant HE will have very small useful ranges or very poor payload fractions. For a realistic set of mission requirements (including a given de- sign range), low eb leads to dramatically heavier takeoff gross weight (TOGW) and higher total energy consumption. The effect of specific energy is mission-, scale-, and platform-dependent, but sensitivities obtained for particular concepts can be found in the literature [23, 24, 25, 26]. Since eb is important to other industries (such as automotive and consumer elec- tronics), academic and industrial research in higher-specific-energy batteries is ongoing. For aviation, advanced concept studies require an estimate of battery technology avail- able near the first-flight date. Projecting future battery technology is outside the scope of this article, but study authors are assuming eb on the order of 400–1000 Whr/kg for advanced concepts, depending on the time frame [21, 27]. Individual eb assumptions for specific studies are tabulated in 4. The SOA of energy storage technologies, including alternative battery chemistries, is discussed by Rheaume and Lents [21]. The NAE committee report projected that eb will reach 400–600 Whr/kg by 2035 [10]. Volumetric energy density is a related consideration for energy storage devices. Jet fuel is Pareto optimal in ef and volumetric energy density. While compressed hydrogen has very high ef , its volumetric density is extremely low. Lithium-ion batteries have much lower volumetric energy density than jet fuel, but the performance gap is narrower than for eb [8]. Specific power of electrical devices (pe), including motors/generators and power conversion, is another key technological parameter in the design problem [27]. Since no single number captures the full operational envelope of an electrical device, the power considered in this metric could be rated power, maximum power, or design power. Electric motors are often rated for short-term burst power, which is usually substantially higher than the maximum continuous power; the analogous rating for a turbofan is takeoff thrust and maximum continuous thrust, respectively. Unless otherwise specified, motor specific power (pm) values listed in this article refer to short- term burst power. 7PDF Image | Electric, hybrid, and turboelectric fixed-wing aircraft
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