## 4 Discussion  
The discussion section is based on comparing the performance of the _base_ and _compressor_ cases. For this purpose, the drag cannot be used and a new variable needs to be employed, which is the input power. When the compressor is not installed and the train is a completely closed body, the aerodynamic resistance is a variable representative of the performance of the vehicle. However, in the _compressor_ case, the capsule is not a closed body, and part of the flow is allowed to go through it, increasing its energy internally thanks to the turbomachinery. In this scenario, the drag and the thrust have no physical meaning if computed separately, and only the net thrust can be obtained. The net thrust is not a variable comparable to the drag of the first case. Note that the former has to be equal to zero for the comparison, as discussed in Section 2.6. The definition of the power takes into account the required energy per time unit that maintains the vehicle speed; on the _base_ case to overcome the drag, and in the _compressor_ case to reach a zero net thrust level. Thus, the power is computed differently depending on the case:  
* _Base_ case: the mechanical power transmitted to the vehicle: \(P_{base}=DragV_{ref}\). * _Compressor_ case: the aerodynamic power the compressor transmits to the fluid: \(P_{comp}=m_{c}c_{p}(T_{t,n}-T_{t,c})\). Note that none of the cases consider the efficiency, which means that the electric machine that drives the system must have higher power. This is a strong simplification, as the _base_ case is typically driven by a linear motor, whose electromechanical efficiency is considerably lower than the one of a rotatory motor driving the compressor. Once it is clear how the power has been defined, in Figure 10, the required power for the _base_ and _compressor_ cases is compared. The main conclusion is that, while for low blockage ratios the difference is not important, for higher ones, it is beneficial to use a compressor to minimize the required energy for both 500 km/h and 700 km/h. From the same figure note that, for the _base_ case, the slope of the curve at 700 km/h increases exponentially for all the BR, as the Kantrowitz limit has been surpassed from \(\beta=0.18\). When the reference speed is decreased to 500 km/h, this exponential growth also starts to occur from the same limit, set at \(\beta=0.36\). In the case of installing the compressor, the slope of both curves is considerably lower, especially at 500 km/h, when the Kantrowitz limit is never reached. The actual percentage at which the _compressor_ case improves is represented in Figure 11. Note that for low blockage ratios, the compressor does not work properly (even worse for 500 km/h), but for high blockage ratios, the power consumption is around 70 % lower than for the _base_ case. Both curves decrease asymptotically to a certain value, from which the relative improvement of the compressor is constant. The compressor bases its improvement on delaying the transonic effects. Thus, the shock waves present in Figure 9 occur at higher speeds, as shown in Figure 12, and the induced pressure and speed upstream the capsule are mitigated, as shown in Figure 13. These effects, as they appear at high blockage ratios, explain why the improvement of the compressor is more significant in this region. Thus, the power reduction can be better explained by analyzing the flow patterns. This is why in Figure 12, the Mach contours for the _base_ and _compressor_ cases are compared for different blockage ratios at the largest simulated speed, 700 km/h. For \(\beta=0.20\), Figure 12a shows no shock waves in any of the cases. However, the acceleration of the flow on the passage is more significant for the _base_ case. Here, the improvement in the case is not due to the avoidance of transonic effects, but regarding the mitigation of the downstream subsonic separation. For \(\beta=0.50\) and \(\beta=0.75\) in Figure 12b,c respectively, the flow behavior is equivalent.