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The issue with using natural landscapes is that it limits your height. And adding more height is ~exponentially~ (edit: quadratically) better than just adding m

The issue with using natural landscapes is that it limits your height. And adding more height is ~exponentially~ (edit: quadratically) better than just adding more installations with an equivalent total height. (You can dig about a mile deep). You can see more details in my comments below - search for the text "It is worth it to dig a hole!"

dragontamer 6y ago
I was thinking of combining techniques. Best case scenario in USA is something like Owens Valley: 14,000 at its peak, but 4000 feet at the bottom of the valley. Leading to ~10,000 feet (or nearly 2-miles) of elevation change. From there, you can dig another mile underground, leading to 1-mile (under ground), or -1000 feet elevation, to a peak elevation of 14,000. If a tower were built on the top of the mountain: you could gain another 2000 feet or so on top: so maybe 16,000 (a 2000 foot tower on top of the mountain peak) to -1000ft (1-mile deep from the bottom of the 4000-ft elevation valley), for a total differential of 17,000 feet. Ignoring earthquakes and other issues, of course. :-) Just purely from a hypothetical perspective: working with nature and the natural landscape seems like it'd be better than "just" digging a hole. EDIT: Repurposing abandoned mine shafts might be worthwhile, depending how deep they are.
andbberger 6y ago
Wrong, wrong, wrong, so wrong! Gravitational potential energy is (approximately) linear in height. I say approximately because this assumes constant g (which is a good assumption when h is small compared to the radius of the earth, which it is). And in fact, a consequence of gravity's 1/r^2 nature is that one is only subject to gravitational acceleration from what is beneath them (shells above cancel out), so mine shafts are less efficient than towers (the effect size is small to the depths we can mine). So adding more height doesn't help, and if that height is underground it could actually hurt net efficiency. Efficiency in this context refers potential energy stored per unit height. The field is conservative no matter what you build.
- syllable_studio 6y ago
  Hey andbberger, Yeah, we're _definitely_ assuming that g is constant for all elevations :) There's another thread on this comment page talking about why height is important. Please see this slide in our presentation illustrating it. https://docs.google.com/presentation/d/17FI-jrI9RWS3q7Ng44YhiHs7il8JvnxK-cV6_g_-cGo/edit#slide=id.g844fb8814b_1_136 https://docs.google.com/presentation/d/17FI-jrI9RWS3q7Ng44Yh...
  - Xylakant 6y ago
    I don't think it's fair to call that "scales quadratic". Certainly the energy stored in the total number of blocks is growing quadratic by digging deeper, but it also ignores that costs and effort grow when digging deeper. In effect, adding a block at the bottom comes with substantially higher effort than adding a block right next to it on the same level.
- reitzensteinm 6y ago
  I'm assuming that the quadratic parent refers to comes from the increased potential energy per kg of material multiplied by the ability to store more material due to the additional volume. If you picture a dense weight like a cannon ball on the end of a string you're right, but if you're digging down n meters, encasing n/2 meters worth of dirt and moving it up and down the free n/2 meters of shaft, the energy storage would indeed be proportional to n^2. I don't know anything about the field and had the same reaction you did, but considering parent is running a startup in it they're either a lunatic that doesn't know the equivalent of FizzBuzz or there's something we missed on first inspection, and we should charitably assume the latter...
  - syllable_studio 6y ago
    Haha, thanks. It's a little of both of course. You have to be a bit of a lunatic to think you can do these things. But someone's got to get it done.
    - reitzensteinm 6y ago

dragontamer 6y ago

I was thinking of combining techniques. Best case scenario in USA is something like Owens Valley: 14,000 at its peak, but 4000 feet at the bottom of the valley. Leading to ~10,000 feet (or nearly 2-miles) of elevation change. From there, you can dig another mile underground, leading to 1-mile (under ground), or -1000 feet elevation, to a peak elevation of 14,000. If a tower were built on the top of the mountain: you could gain another 2000 feet or so on top: so maybe 16,000 (a 2000 foot tower on top of the mountain peak) to -1000ft (1-mile deep from the bottom of the 4000-ft elevation valley), for a total differential of 17,000 feet. Ignoring earthquakes and other issues, of course. :-) Just purely from a hypothetical perspective: working with nature and the natural landscape seems like it'd be better than "just" digging a hole. EDIT: Repurposing abandoned mine shafts might be worthwhile, depending how deep they are.

andbberger 6y ago

Wrong, wrong, wrong, so wrong! Gravitational potential energy is (approximately) linear in height. I say approximately because this assumes constant g (which is a good assumption when h is small compared to the radius of the earth, which it is). And in fact, a consequence of gravity's 1/r^2 nature is that one is only subject to gravitational acceleration from what is beneath them (shells above cancel out), so mine shafts are less efficient than towers (the effect size is small to the depths we can mine). So adding more height doesn't help, and if that height is underground it could actually hurt net efficiency. Efficiency in this context refers potential energy stored per unit height. The field is conservative no matter what you build.

syllable_studio 6y ago
Hey andbberger, Yeah, we're _definitely_ assuming that g is constant for all elevations :) There's another thread on this comment page talking about why height is important. Please see this slide in our presentation illustrating it. https://docs.google.com/presentation/d/17FI-jrI9RWS3q7Ng44YhiHs7il8JvnxK-cV6_g_-cGo/edit#slide=id.g844fb8814b_1_136 https://docs.google.com/presentation/d/17FI-jrI9RWS3q7Ng44Yh...
- Xylakant 6y ago
  I don't think it's fair to call that "scales quadratic". Certainly the energy stored in the total number of blocks is growing quadratic by digging deeper, but it also ignores that costs and effort grow when digging deeper. In effect, adding a block at the bottom comes with substantially higher effort than adding a block right next to it on the same level.
reitzensteinm 6y ago
I'm assuming that the quadratic parent refers to comes from the increased potential energy per kg of material multiplied by the ability to store more material due to the additional volume. If you picture a dense weight like a cannon ball on the end of a string you're right, but if you're digging down n meters, encasing n/2 meters worth of dirt and moving it up and down the free n/2 meters of shaft, the energy storage would indeed be proportional to n^2. I don't know anything about the field and had the same reaction you did, but considering parent is running a startup in it they're either a lunatic that doesn't know the equivalent of FizzBuzz or there's something we missed on first inspection, and we should charitably assume the latter...
- syllable_studio 6y ago
  Haha, thanks. It's a little of both of course. You have to be a bit of a lunatic to think you can do these things. But someone's got to get it done.
  - reitzensteinm 6y ago