# A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear
## 3 Drop Test Simulation and Results
The acceleration of the effective mass was one of the two parameters measured during the drop test, using a monoaxial accelerometer placed at the top of the effective mass (Figure 11). The nominal acquisition range of the accelerometer was equal to 3 Hz to 5 KHz; during the test, the vertical acceleration was acquired with a sampling frequency of 100 Hz. The most significant measurement points are reported in Figure 9, and they show excellent agreement between numerical expectations and experimental findings (to enhance the quality of the figure, the experimental data were plotted with a marker every 0.05 s). The ground reaction force (\(F_{z}\)) was the other parameter measured during the drop test; experimental data were obtained by placing four load cells under the tire's impact area (Figure 11). Each load cell measured along the normal to the plane of impact (z-axis) and was characterized by a nominal acquisition range of 0.08 Hz to 2  
Figure 11: Drop test arrangement (sketch). Figure 10: Time history of shock absorber total force (\(F_{a}+F_{d}\)). compressive load of 5000 lb; for the acquisition of vertical load, a sampling frequency of 100 Hz was set. The four outputs of the cells were summed to get the experimental trend of \(F_{Z}\); with the experimental error of each measurement equal to \(\pm 10\) lb, the overall experimental uncertainty of \(F_{Z}\) values was equal to \(\pm 40\) lb (\(\pm 18.14\) kg). By working on simulation output, \(F_{z}\) was numerically evaluated as \(-F_{PN}(t)\), and its trend satisfactorily followed the experimental measurements (Figure 12); to enhance the quality of the graph, the experimental data were plotted with a marker every 0.05 s.  
The theoretical time history of the horizontal force acting on the wheel hub is reported in Figure 12 to facilitate a discussion on its consistency with \(F_{z}(t)\). Before the impact, the tire has relative horizontal speed with respect to the ground, which is equal to the aircraft's landing speed. At touchdown, the horizontal friction force between the tire and the ground induces elastic displacement of the wheel hub along the \(x\)-axis (\(x_{1}\)). A recovery force due to the elasticity of the landing gear leg then arises (\(Kx_{1}\)), and the damped oscillatory motion of the wheel hub begins. The maximum and minimum values of the elastic recovery force are referred to as spin-up and spring back, respectively; as shown in Figure 12, they occur at \(t_{su}\) = 0.33 s and \(t_{sb}\) = 0.37 s.  
When \(t_{su}<t<t_{sb}\), vertical force \(F_{z}\) abruptly decreases; this is in full agreement with the physics of the phenomenon, as the ground impact force is alleviated by the forward bending of the landing gear leg. As also confirmed by the experimental data, after \(t_{sb}\)\(F_{z}\) increases because of the amplification induced by the rearward bending of the landing gear leg, and then its trend becomes prevalently influenced by the shock absorber dynamics rather than by the horizontal (elastic) deflections of the leg. The initial oscillation of \(F_{z}\) vs. time is essentially due to the elastic response of the landing gear along the \(x\)-axis; a first peak arises when the horizontal force reaches the spin-up value (\(t=t_{su}\)), then the vertical load decreases up to a local minimum occurring at \(t=t_{sb}\), that is, when the horizontal load reaches the spring-back value. Since the numerical trend of \(F_{z}\) follows the same initial oscillation resulting from the experiment, it is indirectly proven that the landing gear motion along the \(x\)-axis is coherently reproduced in terms of instants of time when spin-up and spring-back occur. Moreover, during this oscillation, the amplitude of \(F_{z}(t)\) is deeply influenced by the elastic bending of the landing gear leg, which is in turn driven by the horizontal load at  
Figure 12: Time history of vertical and horizontal forces at the hub.