# Model-Based Design of Aircraft Landing Gear System
## 4 Simulation Results
### Landing Gear  
The last relevant results are regarding the behavior of the modeled components of the landing gear, more specifically the wheels and the brakes.  
For what concerns the wheels, in Figure 12, the wheels' rotational speeds are reported.  
We can see that, as soon as the aircraft touched the ground, the wheels accelerated to a rotational speed that matches the longitudinal speed of the aircraft. At 5 s of simulation, the brakes were engaged, which caused a sudden reduction of the wheels' speed. A few instants later, the slip coefficient reached a value of \(-0.3\), which triggered the disengagement of the brakes, as explained earlier. It must be noted that in this phase, the aircraft is still in a transitional phase in terms of vertical displacement: therefore, the vertical reaction force is not sufficient to avoid wheel lock when the braking system is engaged. When the vertical force on the tires is sufficiently high, the wheels reach a sort of equilibrium, where their speeds match the aircraft speed, thus coming to a stop at the same time as the aircraft. A similar trend can be seen in other works found in the literature, including experimental tests showing a decrease in the wheel rotational speed with respect to the longitudinal aircraft speed when excessive braking force was applied [29, 30, 31]. It is noticeable that such phenomenon did not occur for the 737-800, since, as explained earlier, the mass of this aircraft made it possible to avoid the risk of wheel lock, thus not requiring the intervention of the antiskid system.  
Figure 11: Vertical motion of the aircraft during landing. Similar trends can be seen in [27,28].  
The other component considered in the landing gear are the brakes. In Figure 13, some relevant quantities are included.  
First of all, the temperature reached by the brake is shown. As we can see, as the brakes were engaged at 5 s from landing, the temperatures started to increase. Such increases were slightly slower initially, due to the braking system control that, in the first braking phase, disengages the brakes a couple of times. When the brakes were fully engaged, the temperatures rose with a higher intensity until the braking action was stopped, as can also be seen in the literature [30]. It can be noticed that the Boeing 737-800 brakes reached  
Figure 12: Main landing gear wheels behavior during landing. Similar trends can be seen in [29; 30; 31].  
Figure 13: Brakes characteristics during landing. Similar trends can be seen in [30; 32].  
temperatures that were much higher than the other two cases: this is most likely due to the much higher mass of this aircraft, thus requiring a larger amount of kinetic energy to be converted into thermal energy. The temperature curves behavior can be further confirmed from the curve of braking energy, which represents the mechanical energy converted into thermal energy by the brakes. It was obtained by integrating the braking power curve, reported in the same plot, and it clearly shows a similar trend to the temperature curve. This is to be expected, since there is a direct proportionality between the energy absorbed by a mass and its temperature, as was demonstrated by the experimental test performed by [PERSON] et al. [32].