[usrusr]

Part of me certainly hated myself for not stopping to read right there.

But it's an interesting approach despite the bad writing: if you fill a 1400m shaft with a dense chain of buckets (my term, they seem to call them vessels) you'll need a surprising low amount of mass throughput for a given amount of power flowing in/out. Because there is just so much in transit at any given point in time.

A naive implementation would quickly run into limits in rope strength and the like, but the schematic drawing suggests that the system they suggest consists of a chain of shorter loops, each just carrying whatever low number of vessels is easiest to engineer, and handing them over bucket-brigade style. This sounds complicated, but a similar thing is routinely done by gondola lifts with intermediate stations between separate wire loops (but here, handover could presumably be done simpler and in less maintenance-demanding ways because latency is no goal at all). So you'd design a system that works for three loops in a shaft not much deeper than a deep cellar and then scale it out to a very deep mine.

The power in/out is simply the throughput of a single stage times how many of those stages can be stacked in the shaft (or rather: hung to the sides of the shaft on top of each other, they'd certainly not be stacked in the statical sense). And if your battery is ever considered full but you still have extra energy to store, you could always decide to dig more horizontal tunnel, like when the mine was still serving it's original purpose. All you need is room (and transportation) for a larger spoil heap in the sun.

Digression: it's hot down there. Could you, with sufficiently insulated pipes, spin up a geothermally powered loop of air where the hot air carries moisture up skyside? If the sand is drier on the way up than it was on the way down while discharging you could theoretically end up with efficiency > 100. (in reality, more energy will certainly be lost to uninvited water finding it's way down, but perhaps this geothermal harvest could help battle the losses to water ingress)

[usrusr]

PS: what was up with my mind when I wrote this? (second paragraph) Some serious confusion about throughput and power: power and mass throughput are obviously the same at a given shaft height, the advantage of a chain with less gaps/more vessels in transit at the same time is that you don't need much speed to achieve throughput.

Still, the approach of stacking many copies of the same loop design, with a well designed handover mechanism remains the way to go, instead of one big elevator trying to achieve throughput by faster travel. The key core idea is that the structure that carries the upper parts of the whole thing is already there (all the ground that hasn't been dug into)