**4.1. Algebraic descriptors and figure-of-merits**

**Figure 3.** Compendium of advanced hybrid- and universally-electric aircraft. Adapted from [23]

124 New Applications of Electric Drives

holistically integrated electric propulsion system are expected to emerge.

an electric drive relying on battery technology is the achievable design range as indicated by the low range end on the left corner of the chart which reflects more of the regional market segment. With regards to morphology, besides the BWB configuration, no large departure from the traditional "tube and wing" were foreseen due to the implementation of hybrid-electric propulsion system. Outcome of pre-design studies investigated by Isikveren et al. [63] indicated that unless significant departure in the propulsion system integration is entertained, considering for instance distributed propulsion technology, the contemporary tube-and-wing morphology was still considered to be appropriate. Distributed propulsion technology could considerably disrupt contemporary aircraft design paradigm. This was exemplified by the LeapTech concept through distribution of multiple propellers on the wing leading-edge (see Section 2.2.3) and the Propulsive Fuselage configuration selected for the Voltair concept (see Section 2.2.3). The aviation community is in the midst of a pioneering era with regards to electro-mobility and faces an explosion of combinatorial possibilities at system level and aircraft level. Innovative approaches to electrically driven propulsion system needs to be further analyzed and thoughtfully integrated at aircraft level to determine the full potentials. With growing understanding of the technology and its implication at aircraft level, innovative advanced aircraft configurations designed through more ambitious The algebraic description of a hybrid-electric propulsion requires the establishment of two parametric descriptors [63, 64]: the Degree of Hybridization for Power (Hp) and the Degree of Hybridization for Energy (He). The parameter Hp describes the amount of electrical power relative to the overall total power. Commonly, the installed power or the useful power (power measured at the propulsor) is quoted. In the analyzes provided in the following, Hp referring to the useful power is denoted with Hp*use*. The parameter He is the ratio of electric energy consumed over the total energy and it characterizes the so-called energy split. The quantity He is evaluated along a specified segment or mission. The parameter He*block* refers, for instance, to the block mission. The need for the dual set of parametric descriptors is elucidated by Isikveren et al. [63] considering the following examples:


In addition to the algebraic descriptors characterizing the type of propulsion system, the establishment of figure-of-merits for the assessment of the vehicular efficiency is essential. Related to their instantaneous form, they are used for flight technique optimization to determine optimum altitude-speed technique as a function of the aircraft gross-weight, the aerodynamic efficiency and the overall propulsion system efficiency. The integrated form of the metrics along a given mission enables comparing the efficiency of different vehicles to complete an identical transport task. The traditional figure-of-merit used for vehicular efficiency assessment of fuel-based aircraft is the Specific Air Range (SAR). It characterizes the distance traveled per unit of fuel consumed. Optimizing an aircraft for maximum SAR results in minimizing its fuel consumption. This metric is however limited to aircraft using an energy type characterized by a mass flow. A generalization of the SAR was introduced by Seitz et al. [65] with the Energy Specific Air Range (ESAR) which determines the distance traveled per energy consumed. Maximizing ESAR results in minimizing the energy consumption of the aircraft. Optimizing for instance a universally-electric aircraft with respect to ESAR results in minimizing its electrical energy consumption. To enable the optimization of hybrid-energy transport aircraft for minimum energy cost, the COst Specific Air Range (COSAR) was published by Pornet et al. [66]. The cost of the energy is not the only factor contributing to the total operating cost of an aircraft. Fixed costs and time dependent costs need to be also taken into account. Interested in minimizing the overall cost, airlines base their aircraft fleet operation on so-called Cost-Index which relates basically the cost of time to the cost of energy. A review of the Cost-Index traditionally used for fuel-based aircraft and the establishment of Cost-Index metric for hybrid-energy aircraft are found in [66].
