# High-Speed Vehicles in Low-Pressure Tunnels--Influence of Choked Flows
## 3 Sensitivity to Key Parameters
### Operational Considerations
#### 3.3.3 Number of Vehicles  
In tunnels of sufficient length, it will be common for more than one vehicle to be travelling at any given time. The actual number and the intervals between vehicles will vary according to demand, and many combinations will need to be assessed during practical design studies. Herein, just one case is considered. At time zero, there are three stationary vehicles, separated by gaps of 25 m. Their noses are, respectively, 250, 175 and 100 m from one end of the tunnel. The second and third vehicles begin their journeys 10 s and 20 s after the first. Although a detailed investigation of the interactions between each vehicle would not be practicable, useful information can be deduced from comparisons of the pressures and velocities along the individual vehicles. In Figure 11, the upper, middle and lower rows relate to the first, second and third vehicles, respectively. The equivalent histories for a single vehicle are in Figures 2b and 4b. These Figures can be used to assess the significance of a vehicle's location within a group. Interactions between the three vehicles are especially pronounced in the velocity histories. In common with the single-vehicle case, the velocity behind the tail (T\({}_{\text{ann}}\)) of the third vehicle shows strongly increasing backflow during, and after, the period of choking. This contrasts sharply with the histories behind the first two vehicles. It is a consequence of the fact that the first two vehicles are helped by following vehicles during the later stages of their journeys whereas the third is not. The influence of mutual help is also seen in the  
Figure 10: Influence of vehicle speed history on pressures along it, (**a**) acceleration = 5 m/s\({}^{2}\), (**b**) maximum speed = 240 m/s, (**c**) speed history, (**d**) speed history. (_N\({}_{tun}\), T\({}_{tun}\)_ = small distances ahead of the nose and behind the tail. _N\({}_{ann}\), T\({}_{ann}\)_ = in the annulus, small distances from the nose and tail). much-reduced durations of periods of choked flow along the first and second vehicles in comparison with the third. The different consequences of mutual help are also seen in the pressure histories. Alongside the first vehicle, for instance, the pressures are initially similar to those for a single vehicle, whereas, in later stages of the journey, they are very different--because this vehicle is in the region of high pressure induced ahead of the following vehicles. In contrast, for the third vehicle, strong differences exist in the early stages, whereas those in the later stages are much less pronounced. Informative comparisons can be made between the aerodynamic drag forces on the three vehicles with the corresponding force for a single vehicle with the same overall length of 150 m (pressures for the latter are presented in Figure 8d above). Table 3 shows the peak values of drag force and power demand for each vehicle together with the total energy  
Figure 11: Influence of position in convoy on flow conditions (single tunnel), (**a**) pressures along leading vehicle, (**b**) velocities along leading vehicle, (**c**) pressures along middle vehicle, (**d**) velocities along middle vehicle, (**e**) pressures along trailing vehicle, (**f**) velocities along trailing vehicle. (\(N_{tun}\), \(T_{tun}\) = small distances ahead of the nose and behind the tail. \(N_{ann}\), \(T_{ann}\) = in the annulus, small distances from the nose and tail). consumption during the simulated period. Perhaps the most striking single result is the fact that the maximum drag force on the trailing 50 m vehicle exceeds that on the single 150 m vehicle. However, this has a simple explanation. The leading two vehicles cause a strong accumulation of mass ahead of them whilst their tails are choked. The release of this mass when the second vehicle unchokes exposes the trailing vehicle to a strong headwind. This exists only during the later stages of the journey after the trailing vehicle has begun to decelerate and after the time of maximum power demand.