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Let’s Speculate What Musk’s Hyperloop Will Be

It’s the weekend, and before I take off, I decided to spend an hour taking a stab at Elon’s immortality amongst the faithful.

He’s set to announce his superbly hyped, probably unrealistic hyperloop design next month. I intend to release his idea first, for the purpose of killing a god.

My suspicion is that people chiming in so far aren’t even on in the right parking lot. Musk is the guy who built a spaceship company and is currently trying to blanket the US in state of the art charging stations in under two years.

Reality isn’t exactly a factor here.

My guess is that he’s going to propose taking advantage of inefficiencies in geodesics to construct a path that’s shorter than the “shortest” Great Circle path over the Earth’s surface, while setting it up in a way that reduces energy consumption along the way.

A.k.a. bury a big damn tunnel that loops radially towards the Earth’s core.

Something like this:

HLT 1

The shortest integral path along a geodesic surface is along the path of a Great Circle – that’s one of the key findings of Riemann. However, the shortest path between two points, at least in Euclidean space (of which the Earth’s relative size is still small enough to talk about multivariate calculus) remains a “straight line” in the Euclidean sense.

Since the Earth’s a sphere, there exist lots of paths through the surface which are shorter than simply walking along the circle perimeter. This is sort of complimentary thinking of how airplane flight paths are calculated.

HLT 2

If you choose a path that offsets with its lowest point not in the middle of the distribution, then you could potentially construct a tunnel that rolls “downhill” most of the way and takes less distance to travel than any possible path over the surface by a bus or a plane. You don’t need to travel 800 miles per hour, or whatever the estimates are, because you’re utilizing geometry to shorten the distance – basically you’re just moving smart, rather than fast.

If you construct two similar paths mirroring each other, then you have one directional and one return path, both of which roll downhill most of the way, and only require minimal energy to lift you back to the surface.

HLT 3

Interestingly, this approach only works over very large surface areas, because small regions on a globe approximate flat space. Of course, finding some paths that will actually work will be calculation intensive, because at some point the roll straightens out relative to the core and you stop rolling “downhill”. I’m guessing if this is sort of his idea, then his calculations have found a family of paths that will pull it off.

Since any curved path with one leg shorter than another resembles a saddle point, it evokes imagery of hyperbolic geometry…hence, Hyperloop.

Just a guess here. Naturally if I’m right, I demand full credit for early publication (no I’m not that stupid it will never happen).

I like my odds though, because this approach is:

1) Imaginative
2) Physics intensive/clever
3) Totally unrealistic

Hence, it just sort of screams “Classic Musk”.

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