Perhaps more of an engineering question, but with the subject recently in the news about hyperspeed maglev tunnels I'll chance it here. Say you set up a network of line of sight underground tunnels for your maglev transportation system operating roughly 50' above sea level through the American continent. These tunnels would not contour to the curvature of the earth, rather be more akin to a knitting needle piercing the tangent of an orange, shortening travel distance by transecting the arc. My question is, given real world conditions, material strengths and costs, geothermal, fault and groundwater issues, what is the maximum depth a reinforced tunnel could exist under earth's gravity? Since both ends of the tunnel segment are at equal elevations (disregarding surface features) the effect would be a gravitational "rope swing". Couple that with evacuating the tube of air to vacuum or near vacuum levels and you have a very energy efficient delivery system. How a vacuum would increase stress loads on the tube I'm not really sure. Some very crude calculations of my own put a surface distance of 180 miles requiring a center tunnel depth of about 1.1 miles, which would be a very workable distance between stations.
closed as off-topic by Waffle's Crazy Peanut, tpg2114♦, user10851, Abhimanyu Pallavi Sudhir, Emilio Pisanty Nov 5 '13 at 12:17
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The free fall transit time through such a tunnel, is 42 minutes, from one end to the other, gravity driven. That's half the period of the circular earth orbit, at the surface. (sans air)