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76 5 Integrated Performance of Hybrid-Electric Propulsion Systems 5.6 and Figure 5.7 respectively. COSAR depends on the specific market price of the energy sources. The relative value of COSAR is evaluated assuming a fuel price of 6 USD/USG, an electricity price of 0.07 USD/kWh in Figure 5.8 and an electricity price of 0.16 USD/kWh in Figure 5.9. The aircraft weight condition of 98% of MTOW represents a typical aircraft weight at TOC. The analysis of Figure 5.6 indicates that maximum SAR occurs at a Mach number close to 0.7 and a FL of 350. The evaluation of maximum ESAR in Figure 5.7 shows that it evolves towards higher Mach number value. Recalling Section 4.2, ESAR takes into account the overall energy consumption of the aircraft. In addition to the fuel energy, which is exclusively considered in SAR, the electric energy consumption is comprised in the ESAR metric. The increase in Mach number is rooted in the operational characteristics of the hybrid-electric propulsion system and especially the management of the electrical energy. As the electric motor runs continuously at its maximal power during cruise, the operation of the electric motor is independent of the flight conditions. However, the flight speed influences the flight time and as a result the amount of electrical energy consumed during cruise. For a given mission, increasing the Mach number reduces the electric energy requirement. As a result, the Mach number value for maximum ESAR increases. However, this change is counteracted by the higher fuel consumption occurring at higher flight speed. With a Mach number of 0.71, the speed for optimum ESAR is consequently slightly higher than the Mach number of 0.7 for optimum SAR. This operational characteristic explains also the optimum SAR trend. Lowering the operating Mach number increases the flight time and as a result leads to higher electric energy consumption. This effect amplifies the influence of decreasing Mach number on fuel consumption. Consequently, optimum fuel consumption occurs at rather low Mach numbers. When analysing the optimum COSAR trend, the specific cost of each energy sources needs to be taken into account. Recalling Equation 4.11, 𝐻𝐸 weights the specific cost of each energy involved in the hybrid-energy propulsion system. For an instantaneous point performance computation, 𝐻𝐸 is a constant value. However, it is interesting to note that during cruise, the instantaneous value of 𝐻𝐸 tends to increase. Assuming that the efficiency of the conventional and electrical system remains about constant during cruise, this evolution of 𝐻𝐸 is explained by the operation of the electric motor during cruise at its maximal power while the power requirement of the turbofans diminishes as a result of the aircraft weight reduction during cruise. In Figure 5.8, the specific price of the electric energy represents roughly 40% of the specific price of the fuel. The cost of fuel dominates consequently the energy cost relation leading to a flight schedule tending to minimize the fuel energy consumption. It results in an COSAR speed optimum which lays between the SAR and ESAR speed optimum while being closer to the SAR optimum. For a specific electricity price of 0.16 USD/kWh, the electric price equals about the fuel specific price. As demonstrated by Equation 4.12, COSAR is equivalent to the ESAR metric under this price condition. As the result the optimum flight technique for maximum ESAR and maximum COSAR in terms of speed and altitude are identical and the contour of Figure 5.9 coincides with the one of Figure 5.7. In the modelling of the hybrid-electric propulsion system, the influence of altitude on the efficiency of the electric motor was neglected in first instance assuming an appropriate thermalPDF Image | Conceptual Design Methods Hybrid-Electric Transport Aircraft
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