## 2 Overall Analysis Approach and Implemented Methods
### Overview of the Analysis Method  
The analysis method adopted here aims at defining the relevant parameters for the integration of hydrogen tanks into the fuselage of an SMR aircraft with assigned shape and aerodynamic characteristics, previously determined considering turbofan engines propelled with kerosene. Therefore, the present method is based on the main assumption that, at a conceptual level, a LH2 transport aircraft sharing the same external shape of a conventional Jet A fuel aircraft, can be studied modifying the characteristic of this latter, once the volume, structural mass, and insulation foam mass needed for tanks is estimated. Moreover, it is assumed that each tank is a non-integral vessel with a circular cross-section, composed of a cylindrical central tube and semi-ellipsoidal endcaps, with a structure made of unstiffened shells covered by a uniform layer of insulation foam (see Figure 7 Section 2.3). For a better understanding, an artificial representation of tank-fuselage integration layouts is given in Figure 5, which shows both solutions aiming at maximising the available internal volume while keeping continuity between fore and aft fuselage through a \"catwalk\" (Figure 5a,c), and solutions which limit the tanks' impact on the fuselage design as in Figure 5b. The parametric description of all these geometries is provided in Section 2.3. The analysis method is represented in Figure 6 and implemented as follows:  
* The available fuselage section is approximated as an elliptic area, hence the tanks' layout and the external radius of each of them are parameterised as functions of a single variable; \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Treatments**} & \multicolumn{2}{c}{\(\sigma_{y}\)**, Yielding Strength at T = 20 K at T = 20 K at T = 20 K at T = 20 K [MPa (10\({}^{3}\) psi)]**} & \multicolumn{2}{c}{\(\sigma_{ur}\)**, Ultimate at T = 20 K [MPa (10\({}^{3}\) psi)]**} & \multicolumn{2}{c}{\(E\)**, Modulus of Elasticity at T = 20 K [GPa (10\({}^{6}\) psi)]**} & \multicolumn{2}{c}{\(\rho_{sr}\)**Density**} \\ \hline Stainless steel grade (SS301) & Tempered (3/4 hardened) & 1585 (230) & 2000 (290) & 207 (30) & 7890 \\ \hline Aluminium alloy (AA2219) & Heat-treated, cold worked, then artificially aged (T8) & 448 (65) & 655 (95) & 76 (11) & 2825 \\ \hline Titanium alloy Ti-5 Al-2.5 Sn & Extra-low interstitial grade, annealed & 1344 (195) & 1655 (240) & 124 (18) & 4480 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Properties of structural metallic materials at cryogenic conditions (T = 20 K), for 1.6-mm-thick sheets ([37]). Figure 5: Illustration of possible tanks–fuselage integration layouts: (**a**) full-section with “catwalk”, (**b**) part-section with cargo deck occupation, (**c**) multiple groups of tanks (full-section case). It is assumed the insulation foam is the outermost layer of the tank, hence once its thickness is given, the external radius of each tank structure can be calculated;
* The ASME Boiler and Pressure Vessel Code ([38,39]) are then adopted to the define the structural thickness of each tank, considering the load conditions defined in [26].