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58 4 Methods for Flight Technique Optimization of Hybrid-Electric Aircraft with the electrical power supply (𝑃𝑆𝑢𝑝𝑝𝑙𝑦,𝐸𝑙𝑒𝑐) and (𝑃𝑆𝑢𝑝𝑝𝑙𝑦,𝐹𝑢𝑒𝑙), the fuel power supplied. The fuel power provided by the combustion engine is equal to the 𝐹𝐹 multiplied by the fuel heating value 𝐹𝐻𝑉. 𝑃𝑆𝑢𝑝𝑝𝑙𝑦,𝐹𝑢𝑒𝑙 =𝐹𝐹·𝐹𝐻𝑉 (4.7) COSAR = 𝑀 · 𝑎 · 𝐿/𝐷 (4.8) (𝑇 𝑆𝑃 𝐶𝑆𝑢𝑝𝑝𝑙𝑦,𝐹 𝑢𝑒𝑙 · 𝑐𝐹 𝑢𝑒𝑙 + 𝑇 𝑆𝑃 𝐶𝑆𝑢𝑝𝑝𝑙𝑦,𝐸𝑙𝑒𝑐 · 𝑐𝐸𝑙𝑒𝑐) · 𝑊 where, 𝑐𝐸𝑙𝑒𝑐 is the specific cost of electricity. It is worthwhile highlighting the fact that if the electricity price is negligible versus the fuel price, the COSAR speed-altitude optimum will be equivalent to the one given by the SAR metric. In order to relate COSAR to the design parameters introduced in Section 3.2.1, 𝐻𝐸 can be expressed as the ratio of the instantaneous electric power supply over the total instantaneous power requirement at the energy sources as established in Equation 4.9. 𝐻𝐸 = 𝑃𝑆𝑢𝑝𝑝𝑙𝑦,𝐸𝑙𝑒𝑐 (4.9) 𝑃𝑆𝑢𝑝𝑝𝑙𝑦,𝑇 𝑜𝑡𝑎𝑙 The COSAR figure-of-merit can be formulated as a function of 𝐻𝐸 according to Equation 4.10. (4.10) (4.11) (4.12) Due to the dependency of 𝑐𝐸𝑛𝑒𝑟𝑔𝑦 on the flight condition, it is important to highlight that Equation 4.12 does not represent a proportional relation between COSAR and ESAR. Using COSAR as an objective function means optimizing the flight profile of hybrid-energy aircraft according to the current market energy price for minimum energy cost. The speed which maximizes COSAR was designated as the maximum COSAR range cruise (MCRC) while the long COSAR range cruise (LCRC) was defined as the speed which fulfils the 99% maximum COSAR condition [115] . COSAR = 𝑀 · 𝑎 · 𝐿/𝐷 𝑃𝑆𝑢𝑝𝑝𝑙𝑦,𝑇𝑜𝑡𝑎𝑙 ((1 − 𝐻𝐸) · 𝑐𝐹𝑢𝑒𝑙 + 𝐻𝐸 · 𝑐𝐸𝑙𝑒𝑐) · 𝑊 𝑇𝑇𝑜𝑡𝑎𝑙 By defining the combined cost of energy in Equation 4.11, 𝑐𝐸𝑛𝑒𝑟𝑔𝑦 = (1 − 𝐻𝐸) · 𝑐𝐹𝑢𝑒𝑙 + 𝐻𝐸 · 𝑐𝐸𝑙𝑒𝑐 COSAR can finally be formulated as a function of ESAR according to Equation 4.12. COSAR = ESAR 𝑐𝐸𝑛𝑒𝑟𝑔𝑦PDF Image | Conceptual Design Methods Hybrid-Electric Transport Aircraft
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