4 ms·

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.

syllable_studio 6y ago
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.
tboerstad 6y ago
Could you explain how it is quadratic? I would have thought it to be linear, by the formula for potential energy
- extropy 6y ago
  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
- syllable_studio 6y ago
  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.
extropy 6y ago
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.

syllable_studio 6y ago

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.

tboerstad 6y ago

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

extropy 6y ago
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
syllable_studio 6y ago
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.

extropy 6y ago

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.