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Comment by syllable_studio | Hacker News Reader

It is worth it to dig a hole! Because building one tall tower is ~exponentially~ (edit: quadratically) better than building multiple shorter ones side by side with the same combined height. You can dig a mile deep which is about 10 times taller than the practical height of a tower. My startup, Terrament, is working on a similar technology, and there is a slide in our deck that illustrates this. https://docs.google.com/presentation/d/17FI-jrI9RWS3q7Ng44Yh...

Reusing abandoned mine shafts could have an advantage. But there is also ample researching showing that the cost of digging from scratch is still worth it. The US Dept of energy even studied it back in the 1980s when they were evaluating underground pumped hydro energy storage. I wrote a white paper on it that's linked from here. see here https://www.terramenthq.com/uphs/

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It is not exponentially better. Energy stored in a stacked mass scales as n^2 whereas horizontal stacks scales as n. That’s quadratic scaling, not exponential.

Damn, you're right - thanks spot5010. I thought that I could use "exponential" colloquially and it would still be accurate enough (because quadratic scaling is even more esoteric to most people). But thanks for the callout, you're right that saying exponential is technically just wrong. I'll figure out how to re-word.

Could you explain how it is quadratic? I would have thought it to be linear, by the formula for potential energy

Take a look at Terrament slides. They are driving a train vertically into the ground. With increased depth more cars can be added, increasing total weight, so m = Ch and ep =~ Ch*h/2

Yeah, I clearly need to change the wording here as it's just adding confusion.

The key thing here is that adding 10x height gives you 10x more PE per weight without extra digging costs (or tower costs assuming the cost per unit of height is constant)

Here's how to think of it: by digging one deep hole instead of many shallow holes (with the same amount of digging) you get (n^2 / 2) instead of (n/2) Potential energy. The average height of all the modules is half the height of the shaft. With one deep shaft, the modules pass through the same excavated volume so they can all go deeper on average.

There is no stacked mass however. Just a single piece of mass moving up/down that results in linear scaling from height.

Edit: reviewed the Terraent slides they indeed plan to literally drive a mile long train vertically into the ground. In which case the quadratic argument stands.

At the cost of significant added complexity. It comes down to drilling cost vs installation/ maintenance cost.

Bro, your pitch deck is 100 slides!

But also, getting your quadratic gain on a mile deep hole requires a mile of weights to lower into it. That's a lot more above ground infrastructure than just the single shaft!

Haha well, 70 of those slides are appendix slides.

The way our design works, the modular weights are autonomous on a track. So we don't have huge cranes above ground. We just have a track above ground that also runs a mile. That track can be partly or fully buried if desired. It will be enclosed protecting it from weather, and solar can be installed on top to save real-estate.

But yes, these installations are enormous. They might cost around $150M and could provide about 200MW.

You're not making any sense. mgh is mgh. If you lift the blocks above or below the ground makes no difference. But you absolutely save a ton of money by not digging the expensive hole that will fill up with water.

- You can't build a mile tall tower though.

- Keeping water out of a hole is a solved problem.

- as discussed in other comments here, adding more height gives you more PE for the same amount of weight so it's a very valuable investment that pays profits over 20-100 years for your one time investment.

https://docs.google.com/presentation/d/17FI-jrI9RWS3q7Ng44Yh...

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