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56 4 Methods for Flight Technique Optimization of Hybrid-Electric Aircraft costs and time dependent costs need to be also taken into account. As the fixed costs are independent of the speed-altitude characteristic, they are irrelevant for optimization purposes. However, the time-related cost needs to be considered to determine the economical Mach number for which the total cost is minimized. To operate their aircraft fleet for minimum overall cost, the airlines base their operation on so-called cost index (CI) [114] which relates the cost of time to the cost of fuel as highlighted in Equation 4.19. πΆπΌ = πππππ (4.2) ππΉ π’ππ with ππ πππ and ππΉ π’ππ representing the specific cost of time and the specific cost of fuel respect- ively. By computing the CI for different flight conditions and for varying aircraft gross-weight, the optimum economical Mach number can be determined for used in the aircraft perform- ance calculation. An example of the utilisation of the CI for evaluation of the optimum economical Mach number is discussed in Section 5.3.4. 4.2 Figure-of-Merits for Flight Technique Optimisation of Hybrid- Electric Aircraft The mathematical construct of SAR is based on a mass-flow due to the term πππΉπΆ in Equa- tion 4.1. Its utilization is consequently limited to aircraft whose operations are based on a fuel energy only (e.g. kerosene, diesel or hydrogen). With the consideration of electric energy, the metric SAR becomes inadequate for the determination of optimum flight technique for hybrid-electric aircraft. New figure-of-merits reflecting the specific characteristics of hybrid- electric propulsion system need to be developed. The definition of optimum speeds needs to be revisited according to the newly introduced metrics. Similarly, only the cost of fuel is con- sidered in the mathematical expression of the CI described in Equation 4.19. Consequently, the derivation of CI for hybrid-electric aircraft is necessary to cover the identification of op- timum economical flight profile. The methods developed for optimum flight techniques of hybrid-electric aircraft presented in this chapter were published by Pornet et al. [115]. A generalization of the SAR metric based on the energy consumed was proposed by Seitz et al. [104]. The energy specific air range (ESAR) metric expressed in Equation 4.3 character- izes the energetic vehicular efficiency. In concrete terms, it represents the distance travelled for a given amount of energy. ESAR = π Β· π Β· πΏ/π· (4.3) ππππΆ Β· π with the term thrust specific power consumption (ππππΆ) which relates the power of the energy supplied to the thrust requirement [104]. For speed sensitivity analysis, the speed at which maximum ESAR occurs was characterized as the maximum ESAR range cruise (MERC) by Pornet et al. [115]. The long ESAR range cruise (LERC) was defined as the speed at which 99% of the maximum ESAR occurs mirroring the definition of the LRC speed [115]. Using ESAR, as a figure-of-merit for flight technique optimization results in minimumPDF Image | Conceptual Design Methods Hybrid-Electric Transport Aircraft
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