An analytical investigation is made of the compression wave generated when a high-speed train enters a long tunnel with distributed venting. The compression wave amplitude is determined by train speed and the area ratio of the train and tunnel, but its rise time depends principally on the geometry of the tunnel entrance. Vented tunnel entrance “hoods” are frequently used to increase the rise time, in order to reduce the impact of the micro-pressure pulse radiated from the tunnel exit when the compression wave arrives at the far end of the tunnel. Approximate calculations are performed to determine the initial rise time for a tunnel of rectangular cross section with a continuously variable vented roof near the entrance, for train Mach numbers less than about 0.2 (∼150 mph). The distribution of venting apertures can be optimized to maximize rise time, and a sixfold increase is shown to be possible when the aperture distribution decreases exponentially with distance into the tunnel. The method of this paper is applicable also to more general tunnel entrance geometries, and for higher train Mach numbers.
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