## 4 Simulation and Experiment
### Span of 200 m PTL Case
Instead, the FPTLIR may descend at other points along the PTL. It was therefore essential to carry out a detailed study and comparison of the dynamic characteristics of the FPTLIR's descent at different points along the PTL during the inspection process. To facilitate a comparative analysis of the dynamic behavior of the system as the FPTLIR descended at different points, several descent points were established to evaluate the dynamic performance of the system. As the PTL was positioned horizontally at a constant height and its sides were symmetrical, only the descent behavior at different points along one side of the PTL was examined. In a 200-metre long PTL, simulation experiments were carried out by placing a descent point at 10-metre intervals along one side over a length of 100 m.  
To enable a comparative analysis of the FPTLIR's Z-displacement at different landing sites, the relative change in displacement was calculated by subtracting the pre-landing steady-state displacement from the post-landing dynamic displacement. Figure 13a shows that the Z-displacement of the FPTLIR reached a peak value at each landing point, followed by oscillatory behavior. As the landing point approached the tower, the peak displacement and the time to reach stability decreases. This phenomenon is due to the increased tension in the PTL as the landing point approaches the tower, which reduced the deformation caused by external disturbances and accelerated the stabilization process. When the FPTLIR landed at different points, the variation patterns of each attitude angle remained unchanged compared to those at point 9. To clearly see the attitude change of different points, the initial 20 s of data are shown in Figure 13b-d. The frequency of the pitch angles remained relatively constant across the different contact locations and its value fluctuated within the range of \(-0.04^{\circ}\) to \(0.06^{\circ}\) across the different contact points. The pitch angle had the highest frequency, followed by the roll angle. The roll angle decreased over time and increased as the FPTLIR approached the tower. To clarify the factors contributing to the variations in the FPTLIR's Z-displacement and attitude angles at different landing points, the landing point was set at the midpoint. The horizontal stress variations of the PTL at different points along the line were then recorded, as shown in Figure 14.  
The minimum stress was located in the central region of the PTL, while the maximum stress can be observed near the tower within the static condition at time 0 s. The stress distribution generally showed a progressive escalation from the center towards the tower. The static analysis shows a rapid increase in stress from point 0 to point 3, followed by a more gradual increase, culminating in a pronounced escalation after point 10. As seen in the dynamic results, the stress at point 0 first increased to a peak, then underwent fluctuations before reaching stability at 7.1 s. At the same time, as the landing site approached the tower, the stress magnitude increased, the fluctuation amplitude decreased and the attainment of stability was accelerated. After the FPTLIR's landing stabilization, the total stress across the PTL increased to an elevated state. To investigate the dynamic behavior of the FPTLIR during descent over different masses, the study considered FPTLIRs ranging from 15 kg to 100 kg, as referred to in [11; 34]. The mass of the FPTLIR was systematically varied from 10 kg to 100 kg, specifically set at 10 kg, 55 kg, and 100 kg for different simulation experiments. The FPTLIRs were consistently programmed to land at point 9. This analysis compared the dynamic performance of FPTLIRs with different masses during their descent. It was hypothesized that variations in mass would be due to changes in FPTLIR density, and consequently have a linear effect on the rotational dynamics of the FPTLIR. Figure 14: Tension variation in the PTL at different locations when the FPTLIR lands at the midpoint.