Turning high-rise buildings into batteries

Having run the numbers on various tower-of-blocks storage systems, I came in prepared to be very unimpressed. I'm still fairly skeptical on a lot of levels, but I'm at least not going to laugh at the idea this time.

Reminder that a kWh is 2,655,220 ft-lbs, with a foot-lb being a pound raised 1 foot. Or 367097 kg-m.

Let's say we want to store a megawatt-hour in the Burj Khalifa, 828m tall. We can quickly calculate how much weight we need: 443kg, assuming perfect work<->energy conversions.

Let's compare that versus a more regular scenario though. Let's take a 60 story residential building. This is ~206m tall. Now to store 1MWh we need 1782kg, or ~2 tons. This is still quite doable, but this is still a pretty tall building.

Storage (per weight) keeps going down linearly with building height. But also up with weight. Even in New York, the number of buildings over 40 stories is probably under 100, it looks like in the paper. Making 100MWh of storage would be nice, but also for scale, Moss Landing plant in San Jose has 1.2GWh of storage attached to it (California requires new capacity to have grid batteries!). That's a grid battery for a 1GW natural gas plant, so it's going to be big, but it puts into scale how hard it would be to turn NYC into an effective height-battery.