# A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear
## 4 Conclusions  
A numerical method was developed to simulate the impact dynamics of oleo-pneumatic landing gear characterized by trailing-link or telescopic leg arrangements.  
The method uses a rational formulation of the differential equation of motion involving only four state variables for the entire system: vertical (rigid) displacement at the cylinder head and piston base, (rigid) rotation of the wheel, and horizontal (elastic) displacement of the wheel hub.  
Despite the limited number of variables, all the relevant forces that arise during the drop were duly simulated, along with their effects on the landing gear's motion along the vertical and horizontal axes. A set of intercommunicating routines was implemented in MATLAB environment to integrate the dynamic impact equations, starting from user-defined initial conditions and general parameters related to geometric and structural landing gear layouts. This tool was then used to simulate a drop test of a reference landing gear, and the obtained results were successfully validated against available experimental data.  
Besides the good correlation level between numerical predictions and experimental measurements, the proposed approach proved extremely reliable in capturing the physics of all the complex phenomena occurring at drop-impact, including the spin-up and spring-back of the landing gear leg, commonly simulated only through FE-based methodologies. Owing to this remarkable performance and the low level of sophistication of the adopted models, the proposed numerical approach can be reasonably considered as a fast, powerful, and effective tool for supporting engineering activities that usually take place during the development of landing gear units, from the preliminary design of the shock absorber to the design optimization of its main components, and from the refinement of already consolidated layouts to the virtual testing of mature design solutions before manufacturing the test item.  
On the other hand, some improvements are necessary to increase the versatility of the proposed methodology for different possible applications. Focusing on the specific certification tasks the drop-simulation is intended to support, adjustments to the formulation are expected to be made in order to overcome current limitations in the following aspects:  
* Landing gear type: Although the single-leg oleo-pneumatic landing gear represents a very common layout, multi-shock-absorber/multi-wheel arrangements need to be included in the model to properly address drop-test simulations in the framework of certification processes for large airplanes.
* Landing gear free-fall attitude: The assumption of free fall along the normal to the ground needs to be relaxed in order to enable the simulation of drop-tests onto inclined planes, generally recommended by airworthiness regulations to account for particular or emergency landing conditions.  
Part of the research described in this paper has been carried out in the framework of TVANO Project, which was funded by the Italian Ministery of Research and Instruction, and the Italian Ministery of the Economic Development, under the National Operative Plan (PON) for research and competitiveness, years 2007-2013; research project code CTN01_00236_256622.  
Not applicable.