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4.4 Operational Economics Optimization 59 4.4 Operational Economics Optimization The interest of airlines lies in minimizing their cash operating cost. In addition to the energy cost, fixed cost and time-related cost are relevant for operating cost optimization purposes. The utilization of COSAR as objective function leads to minimize the cost of energy for a given stage length. Thereafter, the time-related cost needs to be considered to determine the optimum economical Mach number for which the total cost is minimized. The derivation of the CI for hybrid-electric concepts is established in this paragraph. A generalized cost function, C, can be expressed as in Equation 4.13. 饾惗 = 饾惗0 + 饾憪饾憞 饾憱饾憵饾憭 路 饾憽 + 饾憪饾惛饾憶饾憭饾憻饾憯饾懄 路 饾惛饾憜饾憿饾憹饾憹饾憴饾懄,饾憞 饾憸饾憽饾憥饾憴 (4.13) 饾惗0 denotes the fixed cost of the airlines which represents the cost independent of the trip time. As a result, 饾惗0 does not play any role in the speed-altitude optimization problem. 饾憪饾憞 饾憱饾憵饾憭 includes flight crew, cabin crew and time-dependant maintenance. The time of the mission is represented by the variable t. The specific cost of energy 饾憪饾惛饾憶饾憭饾憻饾憯饾懄 was established in Equation 4.11. 饾惛饾憜饾憿饾憹饾憹饾憴饾懄,饾憞饾憸饾憽饾憥饾憴 is the total energy consumed. The possible influence on 饾憪饾憞饾憱饾憵饾憭 due to the utilisation of unconventional propulsion system such as hybrid-electric is not considered in the following formulations. For the particular application of a hybrid-electric aircraft, the function is formulated in Equation 4.14. 饾惗 = 饾惗0 + 饾憪饾憞 饾憱饾憵饾憭 路 饾憽 + 饾憪饾惞 饾憿饾憭饾憴 路 饾惛饾憜饾憿饾憹饾憹饾憴饾懄,饾惞 饾憿饾憭饾憴 + 饾憪饾惛饾憴饾憭饾憪 路 饾惛饾憜饾憿饾憹饾憹饾憴饾懄,饾惛饾憴饾憭饾憪 (4.14) In order to establish the cost per stage length, the cost function can be formulated as in Equation 4.15 considering a given stage length, R, and a block speed, V. 饾惗 = 饾惗0 + 饾憪饾憞 饾憱饾憵饾憭 + 饾憪饾惞 饾憿饾憭饾憴 路 饾憙饾憜饾憿饾憹饾憹饾憴饾懄,饾惞 饾憿饾憭饾憴 + 饾憪饾惛饾憴饾憭饾憪 路 饾憙饾憜饾憿饾憹饾憹饾憴饾懄,饾惛饾憴饾憭饾憪 (4.15) 饾憛饾憛饾憠饾憠饾憠 Finally, according to the COSAR metric established in Equation 4.8, the cost function of a hybrid-electric aircraft is defined as: 饾惗 = 饾惗0 + 饾憪饾憞饾憱饾憵饾憭 + 1 (4.16) 饾憛 饾憛 饾憠 饾惗饾憘饾憜饾惔饾憛 The influence of the time-related cost on the optimum speed of a hybrid-electric aircraft can be evaluated by analysing Equation 4.16. On one hand with increasing Mach number the cost of time decreases for a given stage length. This leads to a cost economical Mach number which tends to be higher than MCRC. However, this increase in optimum speed is counteracted by the rise of COSAR at higher Mach number. On the other hand if the specific cost of time is negligible against the specific cost of energy, the economical Mach number coincides with MCRC. In view of optimizing the flight profile of hybrid-electric aircraft with respect to the time- related cost and the cost of energy, a cost-index metric is derived in the following. Differen-PDF Image | Conceptual Design Methods Hybrid-Electric Transport Aircraft
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