*4.2. Simulation*

In this section, a Monte Carlo simulation model is set up and the SimDec method is employed on it to analyze the sensitivity of the output to the selected input factors, as well as for assessing the impact from any underlying interactions [24]. The SimDec approach falls under the general auspices of variance-based sensitivity analyses techniques [33] commonly used in engineering evaluation [34]. However, instead of relying solely on calculated numerical indices, SimDec provides powerful visualization analytics that can uncover previously hidden interactions in a much more intuitive format for most decisionmakers [24].

Firstly, the key input factors, specific energy of batteries and specific power of electric motor, are modeled as random values generated from a uniform distribution. The model is recalculated 10,000 times and the resulting values of the output, flying range, as well as the corresponding input factor values are recorded. Secondly, the key input factors are broken down into meaningful ranges based on their ongoing technological progress. The specific energy of the batteries is segmented into three states, the existing level [0.1, 0.25] kWh/kg, the near-term possible level (0.25, 0.5] kWh/kg, and the "on the horizon" level (0.5, 0.8] kWh/kg. The existing level simply reflects the real specific energy of existing batteries [16]. Some prototypes of lithium-sulfur batteries already achieved 0.4 kWh/kg specific energy, and more are expected in the near future [35]. Therefore, we chose 0.5 kWh/kg as the upper threshold for the near-term possible level. Finally, 0.8 kWh/kg specific energy is deemed achievable by the mid-century by some experts [17], and, thus, chosen as an upper limit for the on the horizon level.

The ranges of the specific power of the electric motor are comprised of the existing level [1.5, 4.0] kW/kg, an under-development level (4.0, 8.0] kW/kg, and a futuristic level (8.0, 20.0] kW/kg. The upper boundaries of the existing and under-development levels reflect the development of Siemens electric motors and correspond to the data presented in Table 3. The upper limit for the futuristic level reflects existing targets in state-of-the-art R&D projects [36].

Taken together, all the states generate nine scenarios, found in Table 5. It is important to note that the correctness of the numerical thresholds between states is not critical, since we are not interested in the precise boundaries of the resulting scenarios (which will be different for different aircrafts, anyway), but in the behavior of causalities between input and output factors, for which the precise position of the thresholds is not relevant.

Having recorded the simulation output data and the attributions of the input variables to their identified scenario partitions, each individual output value can be mapped onto its scenario index. Furthermore, a color-coding of this mapping is then applied onto the overall frequency histogram of the simulation (namely, the probability distribution of the flying range). Consequently, the resulting distribution of flying ranges, combined with the descriptive statistics of each scenario, enable a direct visualization of the individual effects of the input factors together with their interactions on the flying range output.


**Table 5.** Three states of the key input variables each form nine scenarios for decomposition.

The computation logic described in Section 4.1 is transformed into a model. The actual Monte Carlo simulation and SimDec analysis are performed using already existing macros previously implemented as an Excel tool introduced in [24] (where it can be downloaded for free).
