## 5 Nominal Simulation and Monte Carlo Shooting Simulation
### Quality Comparison of Mode Switching  
The normal overload of an aircraft is the overload in the pitch direction perpendicular to the flight speed, which is the ratio of the centripetal acceleration to the gravitational acceleration. The aircraft will generate normal overload when performing pitch maneuvering flight. Normal overload will affect the equipment safety of the aircraft and the physiological condition of the pilot and passengers, such as excessive normal overload will also cause passenger comfort reduction and energy loss of the aircraft, and in serious cases even cause pilot loss of consciousness or black eye phenomenon and structural and airborne equipment damage of the aircraft.  
Therefore, normal overload can be used as an important indicator to reflect the smoothness of mode switching. In UAV VtoIA7, we believe that the limit normal overload within \(-\)1.5-3.8 can ensure the safety of the UAV and airborne equipment; considering the future manned scenario of air cars, a normal overload outside the range of \(-\)1-2.5 is considered unacceptable.  
Figure 21 draws the normal acceleration diagram under three modes of switching in nominal simulation, which can intuitively and clearly outline the contrast between them, and also reflect the significance of normal overload as a soft switching indicator. The ranges of normal acceleration for the three modes are \(-\)0.29-0.23, \(-\)0.04-0.04, and \(-\)0.04-0.02, respectively, which imply ranges of normal overload of 0.71-1.23, 0.96-1.04, and 0.96-1.02, respectively. Therefore, in the nominal simulation, the soft switching design can decrease the maximum normal acceleration by about 86%, and the maximum normal load by about 17%.  
Figure 21: Schematic diagram of normal acceleration under nominal simulation trajectory.  
Figure 20: Comparison between three designs for the transition phase.  
As shown in Figure 22, the design of the transition segment can significantly reduce the overload limit caused by mode switching, which is manifested in:  
1. In the case of model uncertainty, there is a greater risk without a transition segment. Although the limit normal overload in 70% of cases is distributed between 0 and 2, it can reach \(-6\) and 10 in extreme cases. Considering the future requirements of UAM vehicles for passenger comfort and equipment safety, direct switching is obviously a dangerous and fatal practice.
2. Under the soft switching design, the 5 s switching mode design can control the limits of the normal overload between 0.45 and 2, and about 90% of them are distributed between 0.9 and 1.1; in other words, the limit of the normal acceleration is within 0.1 to 1 times the gravitational acceleration. Therefore, the soft switching design of the 5 s switching mode can reduce the normal overload by about 80% and the limit of the normal acceleration by about 90% under the condition of 20% model uncertainty.
3. The 10 s switching mode design can control the limits of the normal overload between 0.92 and 1.08, and about 90% of them are distributed between 0.93 and 1.06, that is, the limit of the normal acceleration is within 0.06 to 0.08 times the gravitational acceleration. Therefore, under the condition of 20% model uncertainty, the soft switching design of the 10 s switching mode can reduce the normal overload by about 55% and the limit of the normal acceleration by about 90% compared with the 5 s switching mode design.  
The soft switching design adopted in this paper can reduce the limit of the normal overload by about 17% under the condition of accurate model, and by about 89% under the condition of 20% model uncertainty. Therefore, especially for eVTOL aircraft with inaccurate modeling, there is a higher demand for soft switching, and a smooth switching design is needed to improve passenger comfort and solve the safety hazards caused by mode switching.