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62 β’ β’ β’ 4 Methods for Flight Technique Optimization of Hybrid-Electric Aircraft Values of πππ’ππππ¦,πΈπππ less than the ratio πππππ/ππΉπ’ππ result in a πΆπΌππΈππππ‘πππ,ππππ 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 πππ’ππππ¦,πΈπππ which equal the ratio πππππ/ππΉπ’ππ nullify Equation 4.27. Under this condition the optimum economical Mach number is equal to MRC. Values of πππ’ππππ¦,πΈπππ larger than the conventional CI provide a negative πΆπΌππΈππππ‘πππ,ππππ π‘ . In this case, MRC is chosen as economical Mach number. Similarly, if the fuel price ππΉπ’ππ is very large compared to πππππ and ππΈπππ, a negative πΆπΌππΈππππ‘πππ,ππππ π‘ will be obtained as formulated in Equation 4.28. In this scenario, the eco- nomical speed corresponds to MRC. lim πΆπΌππΈππππ‘πππ,ππππ π‘ = βπππ’ππππ¦,πΈπππ (4.28) ππΉ π’ππ ββ Another case to highlight is when ππΈπππ equals ππΉπ’ππ. 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. πΆπΌππΈππππ‘πππ,ππππ π‘ = πππππ = βdπΈππ’ππππ¦,πππ‘ππ (4.29) (ππΈπππ=ππΉ π’ππ) ππΉ π’ππ dπ‘ 4.4.3 Constant Amount of Electrical Energy Consumption For this third hybrid-electric application, the amount of πΈππ’ππππ¦πΈπππ 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: dπΈππ’ππππ¦,πΈπππ = 0 dπ‘ which leads to: dπΈππ’ππππ¦,πΉπ’ππ = dπΈππ’ππππ¦,πππ‘ππ β dπΈππ’ππππ¦,πΈπππ = dπΈππ’ππππ¦,πππ‘ππ dπ‘ dπ‘ dπ‘ dπ‘ Consequently, Equation 4.17 yields: dπΆ = πππππ + ππΉπ’ππ Β· dπΈππ’ππππ¦,πΉπ’ππ = πππππ + ππΉπ’ππ Β· dπΈππ’ππππ¦,πππ‘ππ = 0 dπ‘ dπ‘ dπ‘ (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 likePDF Image | Conceptual Design Methods Hybrid-Electric Transport Aircraft
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