From Red Cells to Snowboarding: A New Concept for a Train Track

Feng and Weinbaum [J. Fluid Mech. 422, 282 (2000)] have shown that there is a remarkable dynamic similarity between a red cell gliding on the endothelial surface glycocalyx and a human snowboarding on fresh powder although they differ in mass by ${10}^{15}$. The lift forces in each case are 4 orders of magnitude greater than classical lubrication theory. Herein we report the first measurements of the pore pressures generated on the time scale of snowboarding and show a feasibility of designing a train that can glide on a track whose permeability and elastic properties are similar to goose down.

Figure 1

Schematic of dynamic snow compression apparatus.

Figure 2

Time-dependent pressure at the center of the piston and its comparison with the predictions of Eq. (5) during dynamic compression experiments in the porous cylinder-piston apparatus. (a) For snow, $m=5.9\mathrm{k}\mathrm{g}$, $h_0=11.43\mathrm{c}\mathrm{m}$, $\Delta h_{\max }/h_0=0.22$, and $P_{\max }=788\mathrm{P}\mathrm{a}$. (b) For goose down, $m=6.4\mathrm{k}\mathrm{g}$, $h_0=12.77\mathrm{c}\mathrm{m}$, $\Delta h_{\max }/h_0=0.35$, and $P_{\max }=400\mathrm{P}\mathrm{a}$.

Figure 3

Sketch of the new train model in the transverse plane (not to scale).

Figure 4

The velocity $U$ required to support a train car of 50 metric tons gliding on a porous track as a function of $h_2/h_1$ for various $K$. Note that for $U>35\mathrm{m}/\mathrm{s}$, $h_2/h_1<1.1$. $L=25\mathrm{m}$, $W=2\mathrm{m}$, and $h_2=0.10\mathrm{m}$.

Figure 5

Forces on the train car. Here $U$ is its velocity, $N_a$ and $N_s$ are the normal forces due to air and goose down, respectively, $T$ is the force due to solid sliding friction, and $D$ is the aerodynamic drag.