# Model-Based Design of Aircraft Landing Gear System
## 4 Simulation Results  
Once the model has been set up, it is possible to run the simulation to capture the behavior of the aircraft during landing. Regarding this purpose, once the main aircraft data has been defined, the sizing script is run, which will then automatically populate the dynamic model with the necessary computed parameters, thus allowing for the execution of the dynamic simulation of the landing phase. Since the model uses multiple integrators, it is required to define the integration settings. It was decided to employ an \"ode1 (Euler)\" fixed-step solver. Regarding the integration step, a value of \(T_{step}=0.0001\) s was set. Such a value makes it possible to maintain a good quality of the simulation and a low simulation time (a couple of seconds). From the simulation, it was then possible to extract some relevant curves that show the behavior of the aircraft. To demonstrate the flexibility of the models, three test cases have been employed with very different sizes and missions: an ATR 42-600 (manufactured by ATR, Blagnac, France), which is a regional twin turboprop transport; a Boeing 737-600 (manufactured by The Boeing Company, Chicago, IL, USA), which is a twin turbofan airliner; and a McDonnell-Douglas F-15D (manufactured by McDonnell Douglas Corporation, Saint Louis, MO, USA), which is a military fighter. The relative numerical results from the preliminary sizing and from the dynamic simulations are reported in Table 2.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**ATR 42-600**} & \multicolumn{2}{c}{**F-15D**} & \multicolumn{2}{c}{**B737-800**} \\  & **Actual** & \begin{tabular}{c} **Computed** \\ **(Error *)** \\ \end{tabular}  & **Actual** & \ \begin{tabular}{c} **Computed** \\ **(Error *)** \\ \end{tabular}  & **Actual** & \begin{tabular}{c} **Computed** \\ **(Error *)** \\ \end{tabular}  \\ \hline MTOW [kg] & 16,900 & & 30,844 & & 79,002 & \\ MLW [kg] & 16,400 & & 20,185 & & 66,349 & \\ \(d_{wheelase}\) [m] & 8.78 & & 7.50 & & 15.60 & \\ \(d_{nose,CG}\) [m] & 8 & & 7 & & 15 & \\ \(x_{land}\) from TD & 661 ** & 730 (+10.4\%) & 784 ** & 1008 (+28.6\%) & 1280 ** & 1399 (+9.3\%) \\ \(x_{land}\) from & 966 & 1035 ** (+7.1\%) & 1100 & 1324 ** (+20.4\%) & 1634 & 1753 ** (+7.3\%) \\ \(V_{long}\) [m/s] & 62.0 & & 64.3 & & 72.0 & \\ \(V_{vert}\) [m/s] & 3.05 & & 3.05 & & 3.05 & \\ \hline \(N_{wheel}\) & 4 & & 2 & & 4 & \\ \(D_{rim}\) [in] & 16.00 & 13.34 (\(-16.6\%\)) & 18.00 & 16.81 (\(-6.6\%\)) & 21.00 & 19.17 (\(-8.7\%\)) \\ \(N_{ply}\) & 12 & 13 (+8.3\%) & 26 & 21 (\(-19.2\%\)) & 28 & 27 (\(-3.6\%\)) \\ \(D_{irte,out}\) [in] & 31.80 & 22.84 (\(-28.2\%\)) & 34.50 & 32.11 (\(-6.9\%\)) & 44.50 & 40.74 (\(-8.4\%\)) \\ \(W_{tire}\) [in] & 8.53 & 7.57 (\(-11.3\%\)) & 8.40 & 11.06 (+31.7\%) & 14.80 & 14.65 (\(-1.0\%\)) \\ \(RL_{Lite}\) [lbs] & 11,000 & 10,992 (\(-0.1\%\)) & 30,100 & 27,030 (\(-10.2\%\)) & 44,700 & 45,000 (+0.7\%) \\ \(W_{flanges}\) [in] & 7.00 & 5.53 (\(-21.0\%\)) & 7.50 & 7.74 (+3.2\%) & 10.50 & 10.18 (\(-3.0\%\)) \\ \(m_{tire}\) [kg] & 19.00 & 9.52 (\(-49.9\%\)) & 36.80 & 31.62 (\(-14.1\%\)) & 91.00 & 68.29 (\(-25\%\)) \\ \(u_{wheel}\) [kg] & 19.50 & 20.71 (\(+6.2\%\)) & & 36.55 & 36.30 & 53.11 (\(+46.3\%\)) \\ \(k_{hire}\) [N/m] & 99,760 & & 1,528,150 & & 1,782,600 \\ \hline \(N_{b,r}\) & 2 & & 4 & & 4 & \\ \(p_{b,r}\) [kg/m\({}^{3}\)] & \(\approx\)8000 & & \(\approx\)1800 & & \(\approx\)1800 & \\ \(p_{b,s}\) [kg/m\({}^{3}\)] & \(\approx\)8000 & & \(\approx\)1800 & & \(\approx\)1800 & \\ \(D_{r,out}\) [m] & \(<\)0.3777 & 0.3259 & \(<\)0.4255 & 0.3954 & \(<\)0.4928 This table provides a synthesis of the results obtained through the models, including a comparison of the computed data with the actual characteristics of the real aircraft. A few considerations could be made regarding the accuracy the model:  
**The landing performance:**: In terms of prediction of the landing distance from touchdown, the model tended to overestimate it.