## 3 Discussion of Results from Sensitivity Analyses
### Studies Concerning Tank Materials and Technologies
#### 3.1.2 Sensitivity to Insulation Materials  
As completed for the structural materials, the present section shows the effects of varying the material selected for the insulation layer and \(t_{ins}\), considering a tank made of AA2219 with \(L/D_{str}\) = 1.5, \(d_{supp}/L\) = 0.8, and \(f_{end}\) = 0.6. Since insulant density influences the structural sizing, the figure of merit considered here is the empty mass fractions \(\mu_{tank}\), defined according to Equation (49), which is the sum of structural and insulant mass fractions. As can be recognised, lower \(\mu_{tank}\) values are expected to provide better aircraft performance. \[\mu_{tank}=\frac{M_{str}+M_{ins}}{V_{int}\,\rho_{LH}} \tag{49}\]  
A range comparison is provided to evaluate the possible effects on aircraft performance; hence, the external tank radius is adapted as \(t_{ins}\) varies to keep the same \(V_{int}\) value. Results depicted in Figure 17a show that polystyrene foam (PS), given its lower density, performs better in terms of \(\mu_{tank}\). Less obvious are the results in terms of flight range given by Figure 17b, which underlines that different insulation foams provide similar range performance, and that this latter improves significantly only up to \(t_{ins}\) values around 100 mm. This indicates that, increasing \(t_{ins}\) above this value, a balance is reached between the reduction in vented LH\({}_{2}\) and the increase in LH\({}_{2}\) consumption due to the overall weight increase. The constant volume assumption has no practical applications, since if \(t_{ins}\) is increased, the internal radius (hence \(V_{int}\)) has to be reduced to keep the compatibility with the section dimensions. Therefore, the following results refer to the same tank considered in the previous analysis, described in Table 8, in which the maximum available radius refers to the PARSIFAL case (Table 1) and insulant material is the polystyrene foam. Figure 17: Influence of insulant material selection and layer thickness (\(t_{ins}\)) on empty mass fraction \(\mu_{tank}\) (**a**) and range flown (**b**), assuming the same internal volume available for LH\({}_{2}\). The iso-range curves shown in the charts of Figure 18 show that for any value of \(L/D_{str}\), longer ranges are achievable if \(t_{ins}\) is close to 50 mm. A possible explanation is that moving from any point of the charts to lower \(t_{ins}\) values, the inertial loads due to the insulant are smaller and lead to thinner tank structures. The lower the thickness of these two layers, the larger the internal radius, which allows to embark the same amount of LH\({}_{2}\) with a shorter tank. At the same time, reducing \(t_{ins}\) increases the heat exchange, hence a larger fraction of LH\({}_{2}\) is vented-out and a longer tank is needed to compensate this loss. These two opposite effects drive the shape of the iso-range curves shown in the following charts, determining an optimal value of \(t_{ins}\), that, for the materials' properties considered here, is around 50 mm. Moreover, this optimality condition is more evident as \(L/D_{str}\) increases. Figure 18a indicates that, for an assigned value of \(t_{ins}\), \(\mu_{tank}\) reaches the lowest values as \(L/D_{str}\) approaches 1.5, which confirms the choices described at the end of Section 3.1.1. From Figure 18b, it is possible to observe that the gradient of iso-LH\({}_{2}\) curves is well-aligned with the gradient of the iso-range curve only for high values of \(t_{ins}\), meaning that as this latter decreases the mass of LH\({}_{2}\) is not useful to extend the flight range, i.e., the vented fraction increases. As already observed in Figure 17b, for \(L/D_{str}\) = 1.5 this alignment is reached when \(t_{ins}\) approaches 100 mm.