Aerodynamic drag on trains in tunnels .2. Prediction and validation

The principal sources of aerodynamic drag on simple trains in tunnels are (a) surface skin friction and (b) stagnation pressure losses at the nose and tail. On sufficiently long trains, the first of these is dominant. On shorter trains, local losses can be more important.This paper seeks to provide a theoretical basis for predictions of the dependence of drag on the train/tunnel blockage ratio, attention being given to tunnel resistance as well as to train resistance. Hitherto, most predictions have relied on empirical formulae.It is shown that the train skin friction coefficient varies approximately linearly with the blockage ratio, beta(z). The dependence increases with increasing train roughness. The nose loss coefficient k(N) is shown to be smaller than 0.1 for reasonably streamlined noses. An approximate relationship between k(N) and beta(z) is hypothesized. The tail loss coefficient k(T) is shown to be approximately equal to beta(z)(2) for poorly streamlined tails. A tail shape coefficient is introduced for use with more streamlined tails.