## 2 Overall Analysis Approach and Implemented Methods
### Mission Analyses
#### 2.6.2 Mission Description and Simulation  
This reference mission used to assess the performance of the box-wing aircraft was divided into segments with their own characteristics, as described in the following and schematically shown in Figure 15:  
* Ground holding: is a 30 min standby phase carried out with the engines switched off, which is necessary for fuelling and for other aircraft preparation operations ([24]). * Taxi-out: it is conducted according to the Landing and Take-off (LTO) cycle specifications defined by ICAO ([48]); its duration is equal to 13 min, half of the total taxi in and out duration, in which the engine power setting is set to 7% of maximum thrust, corresponding to the idle condition. * Take-off: as for the taxi-out phase, the take-off was also computed by using the ICAO engine emissions database specifications; specifically, the duration of the manoeuvre is set to 0.7 min in which the engine power setting is 100%. * Take-off path: this segment of the mission acts as a link between the on and off ground mission stages; the take-off flight path starts 35 ft above the ground and ends when the height of 1500 ft is reached. In this stage, the aircraft is configurated for starting the climb ([43]). * Climb: this stage is divided into three main phases in which the aircraft accelerates and gains altitude, as suggested by the flight programme described in [49]; the climb ends as the altitude of the cruise condition is reached. * Cruise: this segment is performed with a constant speed-constant altitude flight programme; the reference cruise condition is \(h_{cr}\) = 11,000 m and \(M_{cr}\) = 0.79. * Descent: the descent is performed with an imposed speed profile and a constant rate of descent, as described in [43]. The phases outlined above represent what is known as standard mission. In this study, the standard mission was simulated by time-integrating the equations of motion of the aircraft by means of the Euler algorithm, as reported in [45]. In addition to the standard mission, there is a further part of the mission that must be considered when designing an aircraft; this additional phase, called diversion, takes off-design situations, such as weather or technical emergencies, into account. Therefore, diversion is supposed to start after an emergency occurring close to the planned landing and it is meant to divert the aircraft to a new airport, defined as the alternate. Thus, the diversion phase consists of a climb, a cruise at diversion altitude, a descent, a holding phase of 40 min and a landing. An amount of reserve fuel, equal to 5% of the calculated total fuel, is then added at the end of the mission analysis. In this study, the diversion is not simulated as done for the standard mission phases, and the fuel consumption during the diversion phase is estimated on the basis of the performance data available for the baseline box-wing aircraft ([43]). This simplification was introduced to reduce the simulation time, which for a LH\({}_{2}\)-propelled aircraft is longer than that for a conventional propulsion aircraft, since at each time step both the fuel flow and the state dynamics of the hydrogen inside the tanks vary. More in detail, the amount of fuel required to perform the descent and diversion, as well as for reserve, is calculated a priori by interpolating the available data of the reference box-wing ([43]) on input values related to the LH\({}_{2}\) aircraft under investigation. Such amount of fuel sets a minimum threshold for the LH\({}_{2}\) to be contained in the tanks at the end of cruise phase. Therefore, the standard mission is simulated until the total fuel in the tanks reaches such threshold value, then the simulation stops and the aircraft performance, such as the flight distance, is obtained in output without the need to iterate. It is worth remembering that the LH\({}_{2}\) consumption during flight takes both the consumption needed to feed the engines and the amount of H\({}_{2}\) expelled by venting into account, as described in detail in Section 2.4.1.