## 4 Experimental Validation
### Comparison of Pressure Drop in Conformity with Impact Energy under Off-State  
In this section, the drop test is performed by mounting the aircraft landing gear with the MR shock absorber onto the drop device to analyze the internal pressure response in conformity with impact energy under off-state conditions. The impact energy is applied and tested at 456.7, 937.5 J, and 1538 J. Figure 7 presents the inside pressure drop and estimated damping force of the MR shock absorber for, respectively, stroke displacement and velocity when the landing gear system is freely dropped. \(\Delta P_{total}\) and \(\Delta P_{maj}\) on the legend are the pressure drop models calculated using Equations (31) and (33) via the stroke velocity estimated through their respective experiments. Experimental data on the legend refers to the pressure drop measured by the actual measured upper and lower chamber pressures. The initial stroke displacement and velocity start from the origin of the coordinates, as shown in Figure 7. As the compression process progresses, the stroke displacement and velocity, pressure drop, and estimated damping force increase simultaneously. In Figure 7a,c,e, the response of the \(\Delta P_{maj}\) model increases in error compared with the \(\Delta P_{total}\) model as the impact energy increases. To compare the differences, the results of the dissipated energy for the pressure drop models are presented in Table 2. The difference between the impact energy and the dissipated energy comes from the elastic potential energy conserved through the pneumatic chamber and the tire. In Table 2, as the impact energy increases, the relative error of the dissipated energy is within 15% for the \(\Delta P_{total}\) model. However, in the \(\Delta P_{maj}\) model, the relative error gradually increases up to 54%. InFigure 7b,d,f, as the stroke velocity increases, the difference between the \(\Delta P_{total}\) model and the experiment does not increase, whereas the error from the experimental result increases compared to the \(\Delta P_{maj}\) model; the difference in the slope due to the quadratic term of the flow rate increases as the stroke velocity increases. Table 2 also shows the error results numerically. In addition, Figure 7e,f is suitable for comparing the error of the pressure drop models with a maximum rebound speed of about 0.6 m/s after the first compression; the root mean square (RMS) of errors and relative errors for the experiment and pressure drop models are compared using data with a stroke velocity range of \(-\)0.1 m/s or less. For the \(\Delta P_{total}\) model, the RMS values for the error and relative error with the experimental data are 35.69 kPa and 37.95%, respectively; for the \(\Delta P_{maj}\) model, they are 16.22 kPa and 28.92%, respectively. The characteristics of the minor loss are not well displayed during rebound, which resulted in small RMS values of the \(\Delta P_{maj}\) model. In other words, the pressure drop model can be simplified as Equations (28) and (29) by considering only the major loss at the time of rebound. In Figure 7e,f, the maximum stroke velocity during the second compression is about 0.5 m/s, which is suitable for comparing the error for the pressure drop model with low-speed compression. The RMS values of the error and relative error for the experiment and pressure drop models are compared using data within the stroke velocity range from 0.1 to 0.5 m/s. For the \(\Delta P_{total}\) model, the RMS values for the error and relative error with the experimental data are 10.94 kPa and 4.507%, respectively; for the \(\Delta P_{maj}\) model, they are 45.07 kPa and 15.02%, respectively. Furthermore, the dynamic viscosity and initial yield stress are estimated to be 0.2882 Pa-s and 230.3 Pa as a result of performing nonlinear least square parameter estimation based on Equation (15) using the experimental data, where the estimated values are similar to those measured with the MR viscometer.