## 4 Conclusions  
A comprehensive structural analysis was conducted on three different hydrogen vessel materials. It has been found that a Grade 5 (Ti-6 Al-4V) titanium storage vessel can perform well with hydrogen compressed at different pressures (35 MPa-70 MPa) with minimal deformation and greater-than-unity safety factors for both lower- and higher-pressure conditions. Titanium with a minimal thickness of 25 mm has shown good structural performance for 35, 50, 60, and 70 MPa. The main drawback of using titanium is the cost, as titanium is expensive (GBP 61,640) and weighs more than the equivalent (854.34 kg) 6061-T6 aluminium vessel. Aluminium, on the other hand, showed good structural performance, along with having a safety factor above unity at 35 MPa; however, when the pressure increased, aluminium could not cope with higher pressures. The aluminium vessel's weight is lower (512.24 kg), and its cost is cheaper (GBP 717), than titanium and stainless steel. The 304 stainless steel failed to perform well at both lower and higher pressures. Moreover, instead of 35 MPa of compressed hydrogen, using 70 MPa pressure of compressed will require a lower volume of hydrogen to generate required power--this will positively impact the design of the vessel by reducing the size compared to the 35 MPa design. It is possible to gain a 39.2% reduction in weight with 70 MPa compressed hydrogen. CO\({}_{2}\) emissions, using a fuel cell instead of conventional gas turbine for APU, are reduced by 45.6%, which makes the fuel cells in aviation for APU application very attractive: fuel cells act as a key player to reduce CO\({}_{2}\) emissions in the aviation industry. Titanium's exceptional properties make it an ideal choice for storing hydrogen when safety is the highest priority. We recommend titanium vessels for higher-pressure (70 MPa) applications and aluminium for lower-pressure (35 MPa) applications. We suggest that this ultimately could lead to secure and safe electric aircraft, helping aviation and aerospace to promote an emission-free sector. We show that aluminium exhibits less deformation in the hemispherical end caps. So, we recommend a further future investigation into a vessel design using two materials, aluminium for hemispherical end caps and titanium for the middle part of the vessel. We expect this approach to reduce capital and running costs. In addition, we note that carbon composites have a yield strength of 1900 MPa and may be used for storing hydrogen with the benefits of low cost and weight. The cost of the carbon-reinforced composite is lower than that of titanium. Furthermore, to reduce the size of the hydrogen vessel, we recommend the use of a hybrid system of fuel cells and the  
Figure 10: Cost of each vessel for 35 MPa and 75 MPa design. conventional gas turbine APU, which will reduce the amount of hydrogen needed and, hence, the size and weight of the vessel. Finally, model limitations and operational factors such as electrochemical behaviour, thermal effects, fluid dynamics, vibration, thermal effects, and hydrogen embrittlement were not addressed in this study and are strongly recommended as future work. [PERSON] developed the model and investigated the available models in the literature; [PERSON] and [PERSON] were involved in revising the paper and introducing technical suggestions; [PERSON] was involved in directing the research, developing the methodologies, and analysing the results with the first author. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Any data required can be requested from the corresponding author via email: [EMAIL_ADDRESS]. The Authors would like to thank School of Engineering and Physical Sciences at the University of Lincoln for their support. The authors declare no conflict of interest. The following abbreviations are used in this manuscript:  
H.  
Height of the vessel (in m)  
LHV.