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Why Ultra-Efficient 4,000 mph Vacuum-Tube Trains Aren't Being Built
cylonlover writes "In the 1800s, when pneumatic tubes shot telegrams and small items all around buildings and sometimes small cities, the future of mass transit seemed clear: we'd be firing people around through these sealed tubes at high speeds. And it turns out we've got the technology to do that today – mag-lev rail lines remove all rolling friction from the energy equation for a train, and accelerating them through a vacuum tunnel can eliminate wind resistance to the point where it's theoretically possible to reach blistering speeds over 4,000 mph (6,437 km/h) using a fraction of the energy an airliner uses – and recapturing a lot of that energy upon deceleration. Ultra-fast, high efficiency ground transport is technologically within reach – so why isn't anybody building it? This article looks into some of the problems."
Kinetic energy (KE) = 1/2 * mass * velocity^2
Change in KE from one speed to another (Delta KE) = 1/2 * mass * (V_end^2 - V_start^2)
X = (Delta KE) / (1/2 mass) = (V_end^2 - V_start^2)
To go from 50 to 100, X = 7500
To go from 3000 to 3050, X = 302500
so the author's statement of
it takes more or less the same amount of energy to accelerate from 3,000 to 3,050 mph (4,828 to 4,908 km/h) as it takes to get from 50 to 100 mph (80 to 161 km/h)
is incorrect. That 50 mph change in velocity takes over 40 times the energy when starting at 3000 mph as it does when starting at 50 mph.
If the energy required to accelerate from 3000 mph to 3050 mph were applied to the vehicle from a standstill, the vehicle would accelerate to 550 mph.