Conceptual Design Methods Hybrid-Electric Transport Aircraft

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Conceptual Design Methods Hybrid-Electric Transport Aircraft ( conceptual-design-methods-hybrid-electric-transport-aircraft )

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62 β€’ β€’ β€’ 4 Methods for Flight Technique Optimization of Hybrid-Electric Aircraft Values of 𝑃𝑆𝑒𝑝𝑝𝑙𝑦,𝐸𝑙𝑒𝑐 less than the ratio π‘π‘‡π‘–π‘šπ‘’/𝑐𝐹𝑒𝑒𝑙 result in a πΆπΌπ‘ƒπΈπ‘™π‘’π‘π‘‘π‘Ÿπ‘–π‘,π‘π‘œπ‘›π‘ π‘‘ lower than the CI. This condition tends to lower the optimum flight speed. However, the resulting economical Mach number is still higher than MRC. Values of 𝑃𝑆𝑒𝑝𝑝𝑙𝑦,𝐸𝑙𝑒𝑐 which equal the ratio π‘π‘‡π‘–π‘šπ‘’/𝑐𝐹𝑒𝑒𝑙 nullify Equation 4.27. Under this condition the optimum economical Mach number is equal to MRC. Values of 𝑃𝑆𝑒𝑝𝑝𝑙𝑦,𝐸𝑙𝑒𝑐 larger than the conventional CI provide a negative πΆπΌπ‘ƒπΈπ‘™π‘’π‘π‘‘π‘Ÿπ‘–π‘,π‘π‘œπ‘›π‘ π‘‘ . In this case, MRC is chosen as economical Mach number. Similarly, if the fuel price 𝑐𝐹𝑒𝑒𝑙 is very large compared to π‘π‘‡π‘–π‘šπ‘’ and 𝑐𝐸𝑙𝑒𝑐, a negative πΆπΌπ‘ƒπΈπ‘™π‘’π‘π‘‘π‘Ÿπ‘–π‘,π‘π‘œπ‘›π‘ π‘‘ will be obtained as formulated in Equation 4.28. In this scenario, the eco- nomical speed corresponds to MRC. lim πΆπΌπ‘ƒπΈπ‘™π‘’π‘π‘‘π‘Ÿπ‘–π‘,π‘π‘œπ‘›π‘ π‘‘ = βˆ’π‘ƒπ‘†π‘’π‘π‘π‘™π‘¦,𝐸𝑙𝑒𝑐 (4.28) 𝑐𝐹 𝑒𝑒𝑙 β†’βˆž Another case to highlight is when 𝑐𝐸𝑙𝑒𝑐 equals 𝑐𝐹𝑒𝑒𝑙. This condition leads to the formulation of the traditional cost index definition however in this case with the total energy supplied considered. As a result the economical Mach number may be changed compared to the conventional case if the energy consumption characteristic is different. πΆπΌπ‘ƒπΈπ‘™π‘’π‘π‘‘π‘Ÿπ‘–π‘,π‘π‘œπ‘›π‘ π‘‘ = π‘π‘‡π‘–π‘šπ‘’ = βˆ’d𝐸𝑆𝑒𝑝𝑝𝑙𝑦,π‘‡π‘œπ‘‘π‘Žπ‘™ (4.29) (𝑐𝐸𝑙𝑒𝑐=𝑐𝐹 𝑒𝑒𝑙) 𝑐𝐹 𝑒𝑒𝑙 d𝑑 4.4.3 Constant Amount of Electrical Energy Consumption For this third hybrid-electric application, the amount of 𝐸𝑆𝑒𝑝𝑝𝑙𝑦𝐸𝑙𝑒𝑐 stored is consumed irre- spective of the flight speed. It represents, for instance, the case of a number of fully charged batteries installed on board of an aircraft whose capacity is consumed independently of the flight speed until the end of the mission according to a given state-of-charge. With respect to the specificity of this hybrid-electric propulsion system, the variation of the electric energy consumed at the energy source during the total mission time, t, is zero: d𝐸𝑆𝑒𝑝𝑝𝑙𝑦,𝐸𝑙𝑒𝑐 = 0 d𝑑 which leads to: d𝐸𝑆𝑒𝑝𝑝𝑙𝑦,𝐹𝑒𝑒𝑙 = d𝐸𝑆𝑒𝑝𝑝𝑙𝑦,π‘‡π‘œπ‘‘π‘Žπ‘™ βˆ’ d𝐸𝑆𝑒𝑝𝑝𝑙𝑦,𝐸𝑙𝑒𝑐 = d𝐸𝑆𝑒𝑝𝑝𝑙𝑦,π‘‡π‘œπ‘‘π‘Žπ‘™ d𝑑 d𝑑 d𝑑 d𝑑 Consequently, Equation 4.17 yields: d𝐢 = π‘π‘‡π‘–π‘šπ‘’ + 𝑐𝐹𝑒𝑒𝑙 Β· d𝐸𝑆𝑒𝑝𝑝𝑙𝑦,𝐹𝑒𝑒𝑙 = π‘π‘‡π‘–π‘šπ‘’ + 𝑐𝐹𝑒𝑒𝑙 Β· d𝐸𝑆𝑒𝑝𝑝𝑙𝑦,π‘‡π‘œπ‘‘π‘Žπ‘™ = 0 d𝑑 d𝑑 d𝑑 (4.30) (4.31) (4.32) The CI definition obtained in Equation 4.33 is similar to the conventional CI established in Equation 4.19. As the electric energy consumption is independent of the time, it is like

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