> On Apr 28, at a TED conference, Musk explained his proposal to deploy continuous tunnel-boring machines that link cities through a network of deep underground tunnels. [...] To illustrate his idea, Musk did some back-of-the-envelope calculations outlining “a straightforward series of steps:”dig narrower tunnels with faster machines that drill continuously rather than the slow, manual and often inefficient methods used today. His full description of the math is summarized below:

> First, dig a smaller tunnel. Replacing a typical subway tunnel (about 28 feet across) with one half that size (14 feet across) reduces the area by a factor of four (since area = π x radius^2). Since tunnel costs are correlated with area, a $1 billion tunnel could now cost roughly $250 million.

> Second, speed it up. Tunneling machines today work half the time and then stop for reinforcement of tunnel walls. Musk proposes continuous tunneling and reinforcing (which is not yet possible), cutting costs in half again. A hypothetical tunnel would then cost about $125 million.

> Finally, drill faster. Today’s boring machines are nowhere near their “power or thermal limits.” That, he estimates, would cut costs by as much as five-fold. Now a $1 billion tunnel costs something more like $60 million (or even $25 million in an optimistic scenario). [...]

> It’s a trick Musk has repeated at each of his companies. Musk described an identical strategy behind Tesla’s manufacturing technology at the company’s 2016 annual meeting: reconfigure today’s inefficient factories. [...] “I do my favorite thing which is apply physics first principles,” he said. “It’s like the best tool possible.” [...]

> ... the factory was reduced to a different equation: output = volume x density x velocity. Need to bring down the cost of batteries? Fill as much of the factory’s volume possible with equipment. Instead of using 3% of the volumetric space, Tesla plans to use at least 30% to get more production per unit of space. Need to produce 500,000 cars per year rather than the 50,000 Tesla has managed so far? Speed up the assembly line by a factor of seven from its typical 0.2 meters per second to 1.5 meters per second. Then build factories as a series of mini facilities, each one iterating on the design of the last so incremental improvements can be rolled out to Tesla’s battery, solar panel, and car plants.
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