[chrisb]

The energy density really is abysmal, which is why the "lifting heavy things up" techinique of energy storage is essentially never discussed outside of pumped-storage.

The problem is the linear relationship between the mass, the height, and the stored energy: energy = mass * height * gravitational-acceleration.

gravitational-acceleration is fixed at the earth's surface to ~10m/s2

So taking an example of 1,000,000 tons lifted up 100 meters:

energy = 1,000,000,000 (mass) * 100 (height) * 10 (gravity) = 1,000,000,000,000 Joules

This looks like a lot, but really isn't. It's equal to ~278 MWh (megawatt hours), which means it can supply 278 MWs for one hour. 278 MWs is equivalent to one small power station.

Note that the largest pumped-storage power station in the UK, which is of course constrained by exactly the same E = mgh formula, Dinorwig (https://en.wikipedia.org/wiki/Dinorwig_Power_Station) stores ~9,000 MWh.

Another way to consider this is to calculate how much mass needs lifting 100m to supply the whole of a country for a day.

As a very crude estimate the UK requires an average of about 30,000MW of electrical energy. Over a day this equals 30,000,000,000 * 24 3,600,000 Joules = 2.510^18 Joules per day.

The mass required to be lifted up 100m to store this is 2.510^18 / (100 10) = 2.510^15 Kg = 2.510^12 tons = 2,500,000,000,000 tons.

Which is many times more than the current global annual concrete production of 10,000,000,000 tons (ref: http://www.columbia.edu/cu/civileng/meyer/publications/publi...)

[thechao]

I live in an extremely hilly area, made of soft rock (limestone), but very little water. Carving out a hill to 100m down, with a 100x100m cross section is totally doable—we have larger projects just to make flat land to build houses on. If the weight was only 10m high, it’d be ~200k tons. By your calculation that’s ~54MWh/day, or enough energy to power ~1500 homes. There’s a hill the right size next to my village of ~1200 homes. We have excess wind & solar power.

So... where do I sign up?

[seren]

But what kind of machine do you need to raise a hill up and down by a few meters ? Even if breaking the load in small bits, the cost and maintenance of equipment would likely be a few magnitude higher that the energy stored or saved.

[thechao]

An electric motor moves it up. An electric regenerating break (an electric generator) keeps it from going down too quickly and/or not at the right time. The particulars of maintenance and long term robustness are pretty straightforward engineering efforts. The largest steam hammers are 125 short tons, and they can operate for decades.

Why would the stresses be any greater than burying a turbine electric generator at the bottom of a hydroelectric dam? The forces would be similar, right? That's the whole point: it's just a crap load of "pressure" due to a bunch of stuff piled up on top.

[pjc50]

I'd do it with hydraulics. Turn the rock into a giant piston: https://heindl-energy.com/