Sisyphus’s train set
economist.com
economist.com
Linked article is short on details, but the link wiredfool gave has more details including a video with numbers (2nd video 02:00). They claim >93% (Combined M&E) one-way efficiency. I don't know what one-way is, but 0.93^2 = 86%, which would make the loss noticeable, but I would still consider it good enough for storing solar/wind.
For comparison, that's the power consumption equivalent of running 40 household washing machines, a ceiling fan, a router, printer, bright LED lighting, a fridge+freezer, a large color TV, ten smartphones, a laptop, an electric heating blanket, two table fans, two smaller TVs, an electric shaver, a scanner, twenty more smartphones, three more table fans to keep them cool, two fountains or other water features, a small vacuum cleaner and a partridge [0] in a pear tree.
[0] Potts, G. R. 1986. The partridge: pesticides, predation, and conservation. (Daily food consumption of a partridge ranges from 71 kcal/day at 15C to 155 kcal/day at -15°C, which works out to be roughly 3.5-7.5 watts, or roughly the power consumed by a few smartphones.)
Secondly, the power that the human body can store in just a few minutes is pretty cool. You can think of a person who eats 2300 calories a day as a 2700 watt-hour battery. Such a battery would be pretty powerful: it holds the equivalent of roughly 300 smartphone charges. You can "charge" the human body in just a few minutes of eating calorie-dense food like nuts or peanut butter or fatty food. But to charge a 2700 watt-hour battery, comparable to the human body, you'd need to draw the maximum power you could (from a wall in a house with standard wiring) - for about two hours.
Sure, I agree that the human body isn't really consuming the power until it gets fully digested. But the reality is that if I'm in a rush, I can wolf down an apple+190g peanut butter and be done 4 minutes later with 1200 calories in my body. Which is pretty useful in real life, at least for me. If my body instead "charged" from a wall outlet (which can usually deliver a lot of power, 1440W or so continuously) it would take an hour to provide me with 1200 calories. Sure, people often do eat slowly. But there have been many times in my life when there's not enough time for whatever reason, and taking an hour to eat a meal would be unacceptable. And it's times like that when I really appreciate that I can eat something fast, and "charge" my body at the rate of tens of kilowatts.
[0] http://www.pcworld.com/article/3096292/storage/seagates-10tb...
[1] http://www.cisco.com/c/m/en_us/solutions/service-provider/vn...
That hasn't been built yet (it seems more or less at the 'back of an envelope' stage to me) and would be more expensive to build, but it promises to store quite a bit more energy (20 GWh vs 12.5 MWh), so it might be cheaper per kWh.
I also think it can be built using existing technology and will be safe enough if the tunnel is built underground (derailments would be catastrophic)
One problem is that this only works at scale. Halve the diameter of the ring, and you likely have to halve the top speed of the train, decreasing capacity by 75%.
They got rid of the forces acting on the center of a flywheel that tear apart large fast flywheels by getting rid of the axle and using a rail on the outside of the wheel to counteract the centrifugal forces.
I would guess they want to use maglev as a rail system, as a conventional track may break down too soon at 2000 km/h. On the other hand, it is 'only' 15 km of rails in a controlled environment, and they can use enormous wheels, so it may be possible to lay conventional track a lot smoother than outside.
If you've got a large Hyperloop network with hundreds or thousands of ~40,000 kg vehicles shooting through it at 700 mph, each of those is 400 kWh of stored energy.
Of course, it'd be crazy hard to actually use because demand for travel on the network isn't gonna be constant, but it's an entertaining thought.