## 3 Discussion of Results from Sensitivity Analyses
### Studies Concerning Tank Materials and Technologies  
#### 3.1.1 Sensitivity to Structural Materials  
The effects of the several design parameters on the structural design of non-integral tanks made of unstiffened shells LH\({}_{2}\) as the one depicted in Figure 2, were investigated through the sizing procedure described in the previous section considering the different materials reported in Table 4. The figure of merit considered here is the structural mass fraction (\(\mu_{str}\)) defined in Equation (48), where \(M_{str}\) is the total mass of the tank's walls, \(V_{int}\) is the gross internal volume of the tank, and \(\rho_{LH}\) is the density of the LH\({}_{2}\). \[\mu_{str}=\frac{M_{str}}{V_{int}\cdot\rho_{LH}} \tag{48}\]  
Figure 16 shows the results of the sensitivity analysis for assigned values of external diameter of the tube, \(D_{str}\) = 3 m, and thickness of the insulation layer, \(t_{ins}\) = 0.1 m, which contributes to the inertial loads acting on the structure. The parameters considered are:  
Figure 16: _Cont._  
* \(f_{endt}\), the aspect ratio of endcaps (Figure 16a);
* \(L/D_{str}\), the aspect ratio of the cylindrical tube (Figure 16b);
* \(d_{supp}/L\), the ratio of distance between supports and tube length (Figure 16c);
* \(p_{int}/p_{ref}\), the ratio between the internal pressure and the reference value of 144.8 kPa (Figure 16d);
* In each chart, the points highlighted in black indicate the values assigned to the parameters when they are not the object of sensitivity analyses. As a first general comment. Figure 16 highlights how, in most of the cases, the lower density of the aluminium alloy makes this latter a better compromise than steel or titanium alloy. More in detail, the following remarks can be pointed out:  
* Concerning \(f_{endt}\), for each selected material it is possible to prescribe a minimum value that avoid the increase in \(\mu_{str}\). In fact, at low values the endcaps get thicker (see the \(f_{endt}\) effect in Equation (20)) and a snowball effect is produced on the structural mass, as the increase in associated inertial loads pushes towards greater tube thickness to avoid buckling conditions. If, instead, higher \(f_{endt}\) values are considered, endcaps walls do not grow in thickness, but the contained LH\({}_{2}\) mass grows linearly with \(f_{endt}\), which determines higher inertial loads and eventually produces a slight but constant increase in tube thickness;
* For \(L/D_{str}\), values close to 1 minimise \(\mu_{str}\), whereas higher values amplify the inertial loads, causing the increase in tube thickness as previously explained. For lower values, the slight increase in \(\mu_{str}\) is only due the reduction in internal volume available for LH\({}_{2}\) mass. * The effect of increasing \(d_{supp}/L\), visible only for aluminium and titanium alloys, is a higher peak value of the compressive axial load (\(N_{max}\)), which is one of the inputs of the buckling verification in Equation (22). Values of \(d_{supp}/L\) larger than 1 are possible, meaning that the supporting frames are connected to the endcaps. Considering \(p_{int}/p_{ref}\), for any of the structural material there are no benefits in increasing the internal pressure, since the main effect would be a reduction in LH\({}_{2}\) density (see Figure 3), hence an increase in \(\mu_{str}\). The dashed vertical line in Figure 16d indicates the constraint resulting from setting the minimum value of \(\Delta p\) to 20% of external atmospheric pressure. Therefore, the present analysis allows to draw some design guidelines:  
* It is suggested to prefer the aluminium alloy AA2219 as structural material;
* A \(f_{endt}\) value greater than 0.4 should be chosen. In this study, the value 0.6 was selected in accordance with [26], where a value of 1/1.6 is suggested to minimise Direct Operating Costs;  
Figure 16: Structural mass fraction (\(\mu_{str}\)) for different materials and design parameters: (**a**) \(f_{endt}\), (**b**) \(L/D_{str}\), (**c**) \(d_{supp}/L\), and (**d**) \(p_{int}/p_{ref}\).