One of the most unique aspects of the Hyperloop is its near-vacuum environment, allowing the pods to travel at extremely high speeds with minimal energy consumption. Such a unique environment requires appropriate infrastructure: the Hyperloop tube. Besides maintaining a low pressure environment, the tubes protect the system from all external conditions. Temperature differences, stresses due to differences in air pressure and other influences present a challenge to the tube. This article will examine how the geometry and material choice contribute to overcoming these challenges and what needs to done before the Hyperloop can be implemented.

#### Designing the tube

A Hyperloop tube needs to be strong to withstand the forces exerted on it and stiff enough to resist major deformations. Moreover, thousands of kilometres need to be produced for the European network requiring the tubes to be easily produced and relatively inexpensive. These criteria need to be taken into account when comparing potential tube materials. The materials examined are concrete, steel, aluminium and acrylic. Due to the high strength, high stiffness and the ability for mass production, steel is chosen as the best option. The other materials were not chosen for several reasons. Concrete has a low tensile strength and is not always airtight. Aluminium has a lower stiffness and higher costs than steel. Acrylic is significantly more expensive than steel.

Now that a material has been chosen, the different forces exerted on the tube need to be explored. Since it is quite early in the design stage, not all forces in and around the tube are known. Designing the tube for allowed deformation (maximum deflection) is therefore not possible. However, designing for another important aspect is possible: the air pressure due to the near-vacuum environment. The difference in air pressure exerts a radial force which can cause buckling. This phenomenon is called vacuum buckling and is especially dangerous for thin-walled containers, such as the Hyperloop tube. The equation below describes the relation between the wall thickness, tube radius and pressure difference (Hauviller, 2007).

$p_{cr}= \frac{E}{4(1-\nu^2)}\cdot(\frac{t}{R})^3$

Where p𝑐𝑟 is the critical pressure difference, E the Young’s modulus, 𝜈 the Poisson’s ratio and t divided by R the ratio between the wall thickness and the radius. The air pressure inside the tube is assumed to be 3 Pa and outside atmospheric pressure. The Young’s modulus and Poisson’s ratio are both characteristics of the material used, in this case steel. Finally there is the radius of the tube, which is currently set at 1.75 m. Using all the known parameters, a minimum wall thickness of 21.4 mm is needed to prevent vacuum buckling. With a safety factor of 1.5 applied to the pressure difference (p𝑐𝑟 multiplied by 1.5), the Hyperloop tubes get a design wall thickness of 25 mm.

#### Challenges

Vacuum buckling has been accounted for but some challenges still remain. These challenges need to be overcome for the Hyperloop to become a reality and are important future research topics.

The cost of steel: As explained earlier in the post, steel has many benefits. It is strong, stiff, easy to produce and relatively inexpensive. However, creating a tube of 25 mm thick for thousands of kilometres requires enormous amounts of steel. This is not only expensive but also harmful to the environment. Different tube design could potentially reduce the material needed while still retaining the required strength and stiffness. The invention of new materials could also result in a higher strength-to-weight ratio. Moreover, research into cleaner production processes could help reduce emission.

Damage to the tube: The Hyperloop is not influenced by weather and other external factors due to the steel tube. To make sure external factors remain inconsequential, the tube must be able to withstand these external factors without being damaged. Furthermore, it is important to know what happens if the tube does get damaged. An assessment of the effect of corrosion, wind loads and other external influences on the tubes, in the form of structural health monitoring, could be used to create a robust and sustainable design.

Thermal expansion: Steel experiences thermal expansion when exposed to temperature changes. Due the tubes being ‘clamped’ between two stations, compressive forces in the tube may occur. To prevent buckling of the tubes, these compressive forces need to be minimised. Solutions to this problem consist of using mechanical/thermal prestressing to reduce the compressive stresses in the tubes. Moreover, connections between tube sections can be created into expansion joints or filled with elastic material which allows the sections to elongate.

Hauviller, C. (2007). Design rules for vacuum chambers.