# Model-Based Design of Aircraft Landing Gear System
## 2 Preliminary Sizing Model
### Wheels and Tires Sizing  
First of all, the wheels and tires of the aircraft must be dimensioned in order to provide the correct behavior of the aircraft during the ground maneuvers. More specifically, the tires and wheels of the main landing gear absorb most of the impact during landing and support the majority of the weight of the aircraft on the ground [12]. Therefore, it is fundamental to estimate the actual weight that the landing gear must carry. Based on the mass of the aircraft, it is possible to obtain the static load on each of the main wheels through the moments equilibrium, as the following equation from [PERSON] [5] illustrates:  
\[F_{main,pert}=\frac{M_{land}\cdot g}{N_{turbed}}\frac{d_{nose,CG}}{d_{turbed \text{ }base}} \tag{1}\]  
Based on this value, the main dimensions of the tires and wheels can be evaluated: in fact, each tire is characterized by an index called the rated load, which indicates the max \begin{table}
\begin{tabular}{c c c} \hline \hline
**System** & **Parameter** & **Description** \\ \hline \multirow{4}{*}{Environment} & \(g=9.81\) m/s\({}^{2}\) & Gravity constant \\  & \(\rho_{air}=1.293\) kg/m\({}^{3}\) & Air density \\  & \(T_{amb}=25\)\({}^{\circ}\)C & Ambient temperature \\  & \(H_{air}=10\) W/(m\({}^{2}\)-K) & Air convection coefficient \\ \hline \multirow{4}{*}{Aircraft} & \(M_{land}\) [kg] & Aircraft landing mass \\  & \(V_{long}\) [m/s] & Longitudinal landing speed \\  & \(V_{vert}\) [m/s] & Vertical landing speed \\  & \(a_{land,m}\) [m/s\({}^{2}\)] & Mean landing deceleration \\  & \(C_{lift}\) & Lift coefficient \\  & \(C_{drag}\) & Drag coefficient \\  & \(S_{wing}\) [m\({}^{2}\)] & Wing reference surface \\  & \(d_{turbeduse}\) [m] & Landing gear wheelbase \\  & \(d_{nos,CG}\) [m] & Nose-gear-to-CG distance \\  & \(LF_{it}\) & Aircraft load factor (lift-to-weight ratio) \\ \hline \multirow{4}{*}{Wheels and Tires} & \(N_{turbed}\) & Number of main wheels \\  & \(f_{full}\) & Rolling resistance coefficient \\  & \(B_{dry}\), \(C_{dry}\), \(D_{dry}\), \(E_{dry}\) & Pacejka coefficients \\  & \(\eta_{fire}\) & Tire efficiency \\ \hline \multirow{4}{*}{Brakes} & \(\rho_{b,r}\) [kg/m\({}^{3}\)] & Brake rotors density \\  & \(\rho_{bs}\) [kg/m\({}^{3}\)] & Brake stators density \\  & \(C_{b}\) [J/(kg\(\cdot\)K)] & Brake discs specific heat \\  & \(k_{b}\) [W/(m\(\cdot\)K)] & Brake discs thermal conductivity \\  & \(N_{b,r}\) & Number of brake rotors \\  & \(f_{brake}\) & Brake discs friction coefficient \\ \hline \multirow{4}{*}{Shock strut} & \(LS_{gear}\) & Landing gear load factor \\  & \(\rho_{oil}\) [kg/m\({}^{3}\)] & Shock oil density \\ \cline{1-1}  & \(C_{dis}\) & Orifice discharge coefficient \\ \cline{1-1}  & \(\eta_{shock}\) & Shock absorber efficiency \\ \cline{1-1}  & \(P_{static}\) [Pa] & Shock static pressure \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initialization aircraft parameters for the landing gear components sizing. vertical load applicable on the tire [15]. Therefore, a higher tire rated load will be able to cope with a higher aircraft mass. However, as can be seen in Figure 1, there are multiple dimensions that characterize wheels and tires, where each combination corresponds to a different rated load. Additionally, tire manufacturers employ the tire ply index \(N_{ply}\) to characterize their products, which represents the strength of the tire. Since there is no actual empirical formulation which makes it possible to find all the necessary values, it is more suitable to resort to the largely available catalogs from the tire manufacturers.