By Delft Hyperloop, February 2019
In order to allow for efficient high-speed travel, airplanes climb to a cruising altitude of 11 km where the air pressure and density are a fraction of here on earth’s surface, reducing aerodynamic drag significantly. Since a hyperloop travels at speeds comparable to that of aircraft, a similar environment of low air pressure is required. This is the reason why a hyperloop travels through a near-vacuum tube. To completely remove all aerodynamic effects, a complete vacuum would be needed. This is however totally infeasible, both technically and economically. When Elon Musk introduced the world to the hyperloop concept with his white paperback in 2013, he mentioned a tube pressure of 100 Pa, this is 0.1% of the atmospheric pressure. This number has been around ever since and not reconsidered. Delft Hyperloop analysed the tube pressure and came up with the innovative idea of Variable Tube Pressure.
Even though the pressure inside the tubes will be low, the aerodynamics inside the tube still play an important role. The upper and lower side around a hyperloop pod act as contracting-expanding nozzles. The flow around the pod accelerates as the bypass area decreases to a maximum of \( M=1 \) (flow velocity equals the local speed of sound) at the so-called throat (the location where the bypass area is minimum). The airflow will become choked if the speed of the pod increases beyond this point. This causes a large increase in pressure drag and shock waves will start to appear at the tail. This effect is known as the Kantrowitz limit. In layman's terms: the air in front of a hyperloop pod cannot move around the pod at those high velocities. Thus, a pocket of air will be pushed in front of the hyperloop causing additional aerodynamic drag. The aerodynamic drag is directly related to the tube pressure, meaning that the aerodynamic drag doubles if one would double the tube pressure.
In order to create a vacuum environment within the tube, vacuum pump installations are required. The installations consist of backing pumps and root pumps. The latter is not suited for pumping from atmospheric pressure to low pressure efficiently, therefore the backing bumps are installed in front of the root pumps. The backing pumps already reduce the pressure significantly (to about 1% of the atmospheric pressure), the root pumps do the work to reach the desired operational tube pressure of 0.1%. The functionality of the vacuum installation can be divided in twofold: 1) pumping the completely tube from atmospheric pressure to operational tube pressure, 2) maintaining the operational tube pressure. The latter is necessary because the tube experiences leaking.
The simplest way to get acquainted with the vacuum system is to do a case study. Let's assume a tube from Amsterdam to Paris, with a length of 500 km. The initial pump down (from atmospheric to desired tube pressure) should not take more than 6 hours and it should maintain the desired tube pressure for an indefinite amount of time, despite leaking.
An industry expert was consulted who gave the advice of distributing the pump installations over the whole tube length in units. One unit consists of 3 root pumps and 2 backing bumps. By considering the pumping speed of the pumps one can determine how long it takes to pump done a certain volume to the desired tube pressure. The total tube is 500 km long and 3.5 m in diameter, this means that the total volume of air inside the tube exceeds a million m3. Pumping down this volume to the desired tube pressure within 6 hours would require 200 units (each consisting of 3 root pumps and 2 backing bumps). Each installation requires housing, an access road (for maintenance), ventilation, safety measures, etc. Depending on the leakage rate, an estimation can be made for the number of units required to maintain the operating tube pressure. This resulted in 6 units that must be operating constantly to maintain the 500 km tube at the desired pressure.
The leakage is an important parameter in determining the optimal tube pressure. Gases (mainly air) leak into the tube, so-called outgassing. The vacuum pumps do the work to get these gases outside the tube. Outgassing happens through the wall, connections, welds and airlocks. The pumps must work constantly because the leakage happens at all time. The lower the tube pressure, the higher the pressure difference and this results in a higher leakage and outgassing. This results in more work for the vacuum pumps to maintain the pressure.
As stated before, even though the tubes are near vacuum, aerodynamic drag is still present. The drag slows down the pods travelling through the tube. In order to maintain the high velocity, propulsion is required, which costs energy. It is also possible to choose for a lower tube pressure, this results in less aerodynamic drag and therefore less energy required for the propulsion. However, the vacuum pumps must work harder to realise/maintain the lower tube pressure. There are two scenarios:
1) Higher tube pressure, less energy required by vacuum pumps to maintain the pressure but higher drag so more energy needed for propulsion
2) Lower tube pressure, more energy required by vacuum pumps to maintain the pressure but lower drag so less energy needed for propulsion
The optimum is heavily dependent on the numbers of pods travelling through the tube. When a lot of pods are in the tube, it is more efficient to have a low tube pressure (scenario 2). If the demand for travel is low and only a few pods are travelling through the tube, it is more efficient to let those pods spend a bit more energy on propulsion and reducing the work of the vacuum pumps (scenario 1).
All in all, Variable Tube Pressure has efficiency benefits for the hyperloop system. When the tube saturation is higher (more pods in the tube), the tube pressure should be lower. It cost more energy for the vacuum pumps but saves much more energy of the propulsion of the pods. The calculated pressure should be between 30 Pa (for very high tube saturation) and 200 Pa (for low tube saturation). This corresponds to 0.03% to 0.2% of the atmospheric pressure.