Not really. Electrical engines and generators are incredibly efficient. It's not the transition there that is the problem. In fact, if it was only for that loss the efficiency would be more like 97%. The problem is the friction in the mechanical parts; the wires, gears and so on.
Think about how little cooling is needed on a big electric motor. Even motors made 100 years ago are very efficient.
By contrast anything that qualifies as a "heat engine" (including internal combustion) is limited by Carnot's law to be low-efficiency. If it weren't for the extraordinary energy density of combustible fuels they wouldn't be competitive.
Amtrak still uses motor-generators on some parts of the Northeast Corridor to convert 60 Hz AC grid power to 25 Hz AC traction power.
It's exactly what it sounds like: a motor that is mechanically coupled to a generator. The motor runs on 60 Hz AC and turns the generator at the correct speed to produce 25 Hz AC.
Today, the majority of grid energy storage is done using pumped-storage hydroelectricity (PSH). "PSH reported energy efficiency varies in practice between 70% and 80%, with some claiming up to 87%." [1]
This is just a pun, but of course his proposal for energy storage already exists, and (surprise surprise) its lithium ion batteries. Significant parts of the projected gigafactory capacity are reserved producing cells for SolarCity home energy storage appliances and other storage systems.
In fact, right now the Tesla factory has 4GWh of lithium ion batteries installed for smoothing energy demands and they are actively building 400kWh storage units:
Yep, and as the maker of the most efficient of those batteries, he can make a nice clean profit. Good on him though, he (and the whole Telsa team really) did put in a lot of effort to get there.
I mean, since E = mgh, you can get the same energy storage capacity with a less deep hole if you use a heavier weight. And you can get a heavier weight either by using more expensive material (why use a cheap one? it's not like it's going to wear or anything), or a larger hole.
I'm not sure what determines the cost of digging a whole, but I suspect depth matters more than area.
Also, does the shaft has to be vertical? You could dig it with a sharp slope, and put your weight on rails. That would make the shaft longer for the same depth, but it would probably be easier to build and maintain.
I suspect they plan on recovering the power with a generator. So the input shaft to the generator has to rotate. With a deeper hole, you get more 'clicks' on the generator so you can produce power for a longer period of time before having to pull the weight back up.
I suppose they plan on using a transmission mechanism that will turn one meter down to as many turns as you want anyway, so I guess the depth of the hole is at least partially determined by how good a transmission mechanism you can afford. But since they explicitly say the hole will be the most expensive part, I'm not so sure.
You're losing torque with every gear reduction, and I believe that current out of a generator is a function of torque. So there's some happy medium between hole depth & transmission ratio for the amount of power they want to generate.
You're certainly losing torque with the gearing but that's not a problem. The problem is losing energy. Energy loss can be made arbitrarily small at increasing cost to build the transmission.
I still not sure about the details, and I don't like how they use the word "cheap" there.
Nevertheless, the density of Lead is 11.35 g/cm3 (the density of water is 1 g/cm3). The densest element in this table is Osmium with 22.6. So replacing if you replace a Lead weight with a more expensive weight you only gain x2.
Tungsten is near 20g/cm3 and is much more reasonable as far as price is concerned (Osmium is basically a precious metal). I'm not sure sparing a few hundred meters of hole digging is worth gathering tons of tungsten, but I would not be surprised if it was.
Gold is about 20g/cm^3, and although it sounds expensive, there's a lot of gold just sitting in storage. Why not store it underground here instead? This is in contrast to tungsten which has direct commercial value and would be wasted just being stored.
Well, yes. To be fair, if there was like a farm of these devices, it might makes sense to swallow that expense.
I wish gold wasn't so rare! Its such an amazing material, and our economy is not based on precious materials anymore (except the commodity markets or course), so it seems like a really sad thing that we can't have more abundant gold just yet
I mean, technically I can get a super cap the size of jam jar to kick out 1 kw, just not for very long.
A watt is a unit of how much energy is expended in a second, not how much energy is stored. There is a reason why hydrostations in wales use lakes to store energy, because you need a lot of mass at great height to be of any use.
Your units got messed up there -- it's just mgh. There's no reason to square the distance.
$ units
Currency exchange rates from 2013-07-11
2562 units, 85 prefixes, 66 nonlinear units
You have: 1000 kg gravity 1 km
You want: J
* 9806650
/ 1.0197162e-07
This came up a long time ago. It doesn't work well, the amount energy it stores is simply too low. I've seen a calculation somewhere, but it's too late here so can't reproduce - does anyone remember?
The energy density for gravity is just immensely small, that's why you need dams holding back rivers to use them to generate electricity. For a 1km hole (that's in the middle of their 500m - 1500m range) you have an energy density of 10kJ/kg of the weight that stores the energy. The energy stored in a Tesla roadster battery pack is around 50kWh which is 180MJ. This means that you need a 18,000kg weight in a 1km deep (immovable) hole to have the equivalent of a Roadster battery pack. I'd go with the battery pack.
That table uses a mass-based unit, so wouldn't that tend to create the misleading impression that lighter elements are more scarce? Energy storage capacity depends on the number of atoms, not mass (as you can intuit by comparing lithium batteries to lead or nickel-cadmium batteries -- heavier doesn't mean more powerful).
In 2011, we mined 0.2% of known lithium reserves.. This would provide over 350 years worth of lithium at current rates. Obviously usage is dramatically increasing but so will our known reserves as the overall level of demand increases. This is also without developing a method to pull the relatively abundant lithium from sea water and without recycling any lithium we're currently disposing of.
Ambri is interesting from a lifecycle and cost perspective but I don't think a lithium shortage is going to have any real impact on prices.
That's a fine saying but even at 20% YoY increases in lithium usage, we'd still have 35 years or known reserves -- without any increase in exploration or recycling.
As oil & gas have shown, if there's exponential demand for a naturally occurring element, we'll definitely find ways to pull more of it out of the ground.
Except all those dire predictions turned out be wrong. We didn't run out of food or resources, and birth rates have now declined in almost every country in the world. Population growth is basically now a complete non-issue. In retrospect, ignoring the Paul Ehrlichs of the world turned out to be the right move - a far cry from mankind's greatest shortcoming.
If we run out of lithium we'll figure something else out, just like we would for any other resource.
Except that then we have run out of available lithium, which means that solutions that require lithium will be inaccessible. Running out of chemical elements is a problem. The helium shortage is a serious problem. High-energy physics is made from helium.
Why is helium found underground with natural gas? My theory is that the helium underground comes from radioactive decay and gets trapped along with methane.
We will never "run out" of anything, including oil or lithium. We'll stop wasting these resources the minute their prices rise to a level where something else becomes more economical. Regardless of when that happens, there will be plenty of lithium left for any potential fusion sources that might be developed later.
For peak storage, vanadium accumulators are well established. Lithium cells give you an advantage in density, but for peak storage you are looking at capacity first, and then you consider the footprint. With vanadium you are only limited by the size of your electrolyte tank. The additional advantage is that vanadium reserves are much greater than lithium reserves.
I think it's more likely we'll see an asteroid mining economy bringing lithium for batteries on Earth than millions of 1km holes with 20 ton weights storing energy for single charges of electric vehicles.
Whatever local (i.e. small scale) energy storage we have in the future you can probably bet (from first principles) with 99% certainty it will be based on the electromagnetic force. Gravity is too weak to be practical for smaller scale storage and cannot give mobile storage units since you have to deal with huge weights. For large scale see the "pumped storage" system already mentioned in this thread. Just for illustration, the "Taum Sauk Hydroelectric Power Station" can produce 175MW of continuous power. If you dropped the 18T weight in the 1km shaft you'd get about 13MW averaged over the 14s fall. Then you have to lift it up again if there are still enough pieces left.
Even if you found a way to store energy in nuclear interactions (i.e. "charge a nuclear battery") you don't want to have a bunch of containers full of radioactive material all over the place. If one thought it through, I wouldn't be surprised if there are in-principle issues for the charging part similar to the ones with gravity.
Since we don't know of any others, this leaves only the electromagnetic force to store energy with sufficient mass (or volume) density in practical ways. Whatever it ends up being (chemical batteries, supercapacitors or something else) the future local energy storage unit will separate and hold charges apart.
Also lifting 500 tons is a lot easier when you don't have to move it horizontally. 1.2MW isn't as much as a wind turbine though which is a pity because they conceivably could be a good pairing.
Okay, so what if you built a huge artificial dam way above sea level? To store energy you would pump water uphill. Usable work could then be extracted when the water is allowed to travel back downhill.
This doesn't make sense. Gravity doesn't have an energy density. The energy density of this system is going to be directly related to the density of the material being raised/lowered.
That's a devastating critique. The idea seemed a bit too good to be true, but I couldn't quite put my finger on why. Thanks for posting that.
I did a little more research, and I'm not sure anymore that it's a complete deal-breaker. But it's definitely going to put limits on how far this can scale.
The idea is to cut a 1km diameter cylinder into the ground (solid rock), and then lift it up up to 500m by pumping water underneath it. The power stored can power a country for a day.
I am somewhat sceptical, but this guy is totally serious about it.
But presumably you'd need more than a day's worth of power to lift the damn thing? That's probably doable, but still, I suspect that'd be the main problem.
The efficency is said the be 80%, just like any other pumped storage system. It just uses considerably less space than a water reservoir (actually close to none, as the top of the cylinder remains untouched) and is scalable by adjusting the radius.
I guess the main problem is to keep the water confined (200bar of pressure) while keeping the mass movable. Maybe someday they build a small testing facility, so we know for sure.
OK, a typical mine hoist is about 10 metric tons. 10 metric tons descending at 1m/sec is very close to 100KW. So a 1000 meter deep hole can deliver 100KW for 1000 seconds, or 27 KWH. That's about $3 worth of electricity, and about 1/3 of the battery capacity of a Tesla Model S with the large batter option.
Depends on the spot price of power. Power on the open market (where utilities have to buy it to provide to customers) changes every minute. Its usually cheap at night until the early morning, starts to increase, and then spikes around 3-4pm (+_30-60 minutes, depending on the country).
If you delivered power when it was most expensive (ie high demand) and consumed it in the middle of the night, the arbitrage may work out.
Is a 500m-1500m shaft is pretty much going to fill with water? I could see a well designed weight being able to work in water (although water turbulence would erode the shaft walls. I don't see how air compression would solve this.
The principle however of storing energy by raising a weight could also be used anywhere with a steep enough hill/cliff/montain and the weight could in theory be on a rail not just suspended.
Efficiency would potentially not be on par, however linked into solar/wind systems this is less about efficiency and more about creating a 1MW long term battery with a lifetime of 50+ years.
Guessing cost of digging and maintaining a hole compared to installing a guide rail is significantly higher.
Although I think the idea isn't workable (energy density is too low, cost of boring the hole is tremendous), most of the other commenters here seem to think they'd just have one weight, whether it is 1000 KG or 50,000 KG.
Any sane plan would be to have more than one weight. When the first weight hits the bottom, it would release from the cable and another weight up top would grab the cable and start dropping. To store energy, the top weight would get winched up, and when it hit the top it would lock into place somehow and the next weight at the bottom of the shaft would engage the lifting cable, etc. The cable would have to follow a circular track, rather than having 1KM of cable for each weight.
What advantage does this provide over combining all your weights together into one big one? If you want to limit the tension on the cable, just use more cables.
You shouldn't be so confident that you know the only "sane" way to design such a thing. It's not a field anyone has experience in. These are only guesses.
Well, it does mean your cables and dynamo can be smaller. But then you've got a new problem of coupling the cables to the load at the bottom and somehow storing loads at the top that the cables must reach past/through.
You have a shaft 1km or 1.5km deep. You can afford to stack a lot of weights vertically. Imagine each has a hole running through the middle, where the cable runs, and a mechanism whereby the weight can engage/disengage from the cable. The cable forms a circular loop that passes through all the weights from the top of the shaft to the bottom, then circles around past a large pulley and back to the top, completing the loop.
At the top of the shaft there would be hefty prongs that retract when the weight needs to start dropping, and when the weight returns during a recharge cycle, the prongs reinsert themselves in to the shaft when the weight is lifted back into position.
Most likely each weight would have a "C" cross section with a nearly closed mouth -- just a slot from the edge of the weight to the larger central opening so that the weight can be removed/replaced from the cable if needed.
That's a good point. Say you fill half the hole with containers of water. Let's assume it's 1km deep. Say we have a circular hole that's 2m across, that should get you W = m * g * d = (3.14 * 1m^2 * 500m * 1000kg/m^3) * 9.8m/s^2 * 500m = 7.7 * 10^9 J or 7,700 MJ? That's a lot higher than the numbers being thrown around here.
Edit: just noticed the comment about 500,000 kg -> 1.2MWh. Read that as MJ at first... d'oh.
My understanding is that peak power availability is at least as important as total energy storage. (The main use of grid storage is to handle spikes in usage, or similarly to fill in for dips in generation - like from wind turbines. Either way, peak power available is important.) One big weight would give you significantly more peak power than several smaller ones. Yes it would require more or stronger cables, motors, and other infrastructure, but the cost of all those is small compared to the shaft, so I imagine a single weight would maximize peak power / cost.
So basically clock-type counterweights. PSH seems like it would be far more efficient - there's surely a lot of mechanical losses in the sort of system in the OP?
If the hole could be used for some sort of heatpump too then maybe that would weigh off [no pun intended!] some of the problems.
This is neat, but not novel. I used to live in a house (UK, middle of nowhere) that had a deep borehole that was used for this purpose 130 years ago. The weight and winding were long gone, but the dynamo was still sat there. Oh, and it wasn't raised by water, rather, servants, back in the day.
No, the additional load is not worth it. It would be one of the least sustainable things you could do due to all of the heavier columns you'd have to use.
Good thing HN wasn't around durning the development of most of humanity's great inventions. "So your telling me I'm going to have to hold my food over this fire for 15 minutes before I eat it? No thank you, I'd stick with my raw meat."
The majority of humanity's great inventions didn't have basic physics saying "this isn't brilliant" long before a prototype got built. Most of humanity's great inventions were things that were difficult because human beings thought they were difficult, or complicated or intricate or whatever.
On their webpage they say " The biggest single cost is the hole, but it is expected that firstly this will have a very long life and secondly, as the technology rolls out, the costs of drilling will reduce significantly. So the economics will improve in time."
Drilling will not get cheaper without a serious reform of the law, and that's unlikely to happen. There are two primary kinds of drillers; water and energy. Folks involved in water have VERY protective rules in all states. The reasons are 1. good lobbying and 2. if you screw up you destroy the water supply.
Energy drilling is no cheaper. Drilling rigs are huge machines that aren't moved easily and cost at least $50k a day on land and $500k a day for seagoing. That's before you pay another $20k per day in staff and god knows how much for fuel for everything; a rig will produce at least 5MW of power.
Could they custom build a rig just for drilling for their idea and would that work? Sure. But they'd probably spend several million and then you've got to have it running 24/7 for it to pay off.
The regulatory hurdle is going to be non-trivial as well. They're going to case it which helps. But the casing would probably need to be cemented in place which is a non-trivial cost as well. And convincing lawmakers that this doesn't quack like some other kind of well is going to be no easy feat.
The hole for this has different requirements than holes for water and petroleum: you'd not want to drill one of these holes into an aquifer, because then it would fill up with water. Oil and gas wells have to be drilled in specific places where the oil and gas are, naturally. In this case, you'd want nothing but a dry, empty hole. A dry, empty hole would be the kind of hole least likely to interact with anything underground.
I'm not sure this has much to do at all with water and energy drilling. They're talking about using abandoned mine-shafts. Those are much wider and shallower than the kind of holes used to reach petroleum.
Sadly what you say is true. Despite the fact that humanity has been drilling holes into various types of soil for over 8000 years, we don't really have a good way to do it. The situation is not quite as bad as you're describing though. It is not $50k per day, more like $5k. That is for machines that can only do soil, not rock, and aren't as much drilling as they're making a hole. But in places where you can do agriculture, you'd have at least 5m of soil above rock, and more usually 50+ meters. I wonder how much power this system would have with a 10 meter deep hole (like is regularly installed for heating water in homes these days).
These guys may be on to something. Scaling down seems to me to be the key. Full gridless operation with solar panels (at least in earthquake-free zones).
If you want to go deep enough for the system scale to be reasonable, you have to get a big drilling rig. You'll hit rock within a couple hundred feet or perhaps a thousand, but I'm not sure of anywhere in the world with 5,000-10,000 feet of dirt.
The problem with going shallower is that the system capacity is directly proportional to depth and weight. Too shallow and you have to have huge weight and that means a large diameter hole and really big cables and such.
But going deeper requires drilling through rock, and aquifers which are located within the rock. That means big regulatory hurdles because nobody wants to poison the aquifer on accident. Plus the large costs of drilling through rock.
I really like the idea from a theoretical standpoint. It's very elegant. But it doesn't seem practical from an economic or regulatory standpoint. If there are places where you can get the diameter and depth for free, it's clearly genius. But I don't think purpose-drilled holes for this will become a thing -- at least barring some kind of immense breakthrough that I can't even imagine.
It is quite easy to calculate how much energy can be stored and how much power can be generated for how long.
The potential energy of a mass in joule is simply
m * g * h
where m is in kilogram, g is 9.8 m/s^2, h is the height in metre.
So, for example, 100 ton lifted 100 metre gives 98MJ.
That's 1MW for 98 seconds.
To make this very concrete my house uses, in the summer, about 40kW-hr per day for water heating, cooking, and the rather large amount of computer equipment we have.
That is 40000 * 3600 = 144MJ. So assuming that your solar power system can supply that over a 12 hour period we need to store half of it, 72MJ, to keep
us going after dark. Your ten metre deep hole would need a 734 ton weight: 735000 kg * 9.8 m/s^2 * 10 m = 72MJ
Average energy use in the Netherlands is 3340 kW-hr per household per year, which amounts to about 9.15kW-hr per day (and seeing that these are averages, I gather that the type of household to pioneer this sort of tech will be sufficiently energy-conscious to use quite a bit less than that).
Either way, I think you'd have to round your estimate to order-of-magnitude anyway, because of the rather big assumption "that your solar power system can supply that over a 12 hour period we need to store half of it, 72MJ, to keep us going after dark", because getting max solar power for half the day and no solar power for the rest is not exactly how it works, nor does one use the same amount of energy during day and night (which is why I can opt in to an energy plan that gives you discount on electricity at night, because there's a surplus then).
3340 kW-hr is a remarkably low figure.
Anyway the point was not to be accurate but to show the kind of working that gives the answers.
Even if we accept your figure the peak daily use is probably at least double your 9kW-hr/day (winter for example) and even if you use less at night you still need probably about 12MJ storage to allow solar to work per household, etc., etc. So, yes, in the Netherlands you need a smaller mass but it is still in the order of 100 ton.
The point of my reply was to show the person I was replying to how easy it is to find out how much mass and height is needed, you just have to plug in your own energy consumption and generation figures.
It wouldn't surprise me at all if the cost structure does work out but the complete picture can't be disclosed for competitive reasons. There are a lot of "obvious ideas" that have only come to fruition recently where the technology was already basically proven, but only entered productive use after several generations of systemic improvements made it a competitive choice. For example: LED lighting was around for several decades but only had niche application until gradual cost/quality improvements pushed it ahead of older lighting tech - and now every major city is rushing to replace all their old street lights. With the Gravitricity tech there are factors like the cost of drilling, the strength, cost and density of the materials used, and lifetime maintenance costs relative to other solutions. There's lots of room for expertise to know for sure what the issues and bottlenecks are.
I'm looking through all the dismissive comments to see if any of them are pinpointing it as a scam - because this is, after all, the kind of idea that is simple enough to captivate laypeople and lift dollars out of their pockets. But judging from this kind of response, it seems like it's also the kind of idea that is simple enough to be dismissed as a "they would have done it already if it worked," rationalized via fuzzy back-of-the-envelope math.
Ultimately, since I have no stake in this one, I'll just wish them luck.
There are a many places in the world where this approach would work and where regulation is not so onerous. Not everyone lives in the United States. And, as your comment seems to indicate, that is a good thing :)
A lot of bad ideas happen in between humanity's greatest inventions. When you look at the past, you are only looking to the successful stories. Maybe a lot of people with unrealistic or bad ideas would have benefited from HN.
That's the hard part though, isn't it? Telling the difference between bad ideas and good ones. Even professionals at it (AKA venture capitalists) get it wrong all the time. So the questions is- knowing that you don't know whether you're looking at a bad idea or a good one, how should you behave?
Even if it's a bad idea, I still prefer a community that encourages people to try anyway and make things for its own sake. HN culture felt much more positive and constructive when I joined a few years ago. While that ethos is still present, there's an unfortunate tendency for the snark to rise to the top.
The responses in that Dropbox thread were pretty solid though. To all the naysayers, I mean. It's sort of a ritual format to test any new idea with the back and forth. That in and of itself isn't a problem.
Real problems: Dismissive people who don't/can't/wont listen to good responses. Good founders/ideas but just really bad at communicating. Those are basically the type i and type ii errors of this format.[1]
_____
[1] A grey area exists in some other areas too (some people just get 'lucky'; others for good reason can't disclose everything the key answers/insights for competitive reasons)
I thought Dropbox was a good idea until all the files I put there mysteriously disappeared. (I think what may have happened is that they started cleaning up the machine I used at a former company and it was still connected.)
Online syncing is not backup, just like RAID mirroring is not backup, but that doesn't make either bad ideas. Dropbox does however archive deleted files for 30 days, and you can pay extra to extend it to a year: https://www.dropbox.com/help/296
A subway tunnel might have a diameter of about 6 meters, so cross section = 3 * 3 * pi = 28 square meters. Digging subway tunnel through rock costs about $100M per kilometer. On the one hand, these holes would be vertical, which is harder than horizontal; on the other hand, they wouldn't need ventilation and train tracks and stuff. Let's handwave and say it's $100M for a 1 km deep hole.
Now, you can't fill the whole tunnel perfectly or the air can't escape, so our total volume of mass will be about 25 m^2 * 1000 m = 25,000 cubic meters. If the weights are made from lead, that's a total mass of ~280,000 tons or 2.8 * 10^8 kg, at a mean depth of 500 meters, so our total potential energy is 2.8 * 10^8 * 500 * 9.8 = 1.4 TJ, or 1.3 TJ net assuming you get the efficiency they claim. 1 kWh is 3.6 MJ, so you can store ~400,000 kWh at $100M capital cost (ignoring for the moment the cost of weights, generators, etc.), which is $250 per kWh installed capacity.
That's pretty good... but you also have to pay for weights and a bunch of other stuff. Bulk lead costs about $2,000 per ton on the current market, so that's $560M for the weights, which puts you back in the $2,000 per kWh range which doesn't beat lithium batteries. So you have to use iron or some cheaper material... but then you don't have as much storage capacity because the density is lower, and even with iron you're paying $400 per metric ton or $80M for all your weights. So this isn't obviously impossible like Solar Roadways, but even in the best case it won't make storage dramatically cheaper.
One major advantage this would have over chemical batteries (Lithium-Ion or otherwise) is that it should allow for many, many more cycles. You would have to replace cables and motors and such at some point, but the expensive components - the hole and the weight - should last near-indefinitely.
It certainly appears more expensive than pumped storage, but as they say, it doesn't require a convenient mountain and lake. That makes for much more flexibility in placement, and the closer you can place the storage to the demand, the less is wasted in transmission, and the less storage you ultimately need. That said, the pumped heat storage design[1] that hit the homepage yesterday would have all those same advantages, and although the efficiency would be slightly lower, it looks much cheaper to build.
For the gravity-based design, you need to lower a weight directly up and down in a controlled manner (ie without swinging etc.) That basically requires a shaft in the ground. If you have a mountain and a lake handy, pumped storage would be more economical, but the advantage of this design - as I understand it - is it can be deployed in places that don't have those things.
Actually an inclined plane and a hole in the ground are identical in terms of their energy storage, both are a function of their highest and lowest points. Which suggests a very simple implementation which is to run a pair of rails up the side of a mountain and but the winder/generator at the top and tie it off to the end of a rail car filled with rocks. Sure you would give up some efficiency with the friction of rail on steel but it would be pretty cheap to implement. On some of the alluvial fans in the Mohave it would make for an interested 'excess energy' storage mechanism for solar.
That said, how are those gravity fed porch lights doing? That seems like it would be an interesting proxy here.
I think the important factor here is the possibility of placing these things anywhere one wants. If mountains are available, I don't see why not (except maybe they would ruin the natural beauty and hence tourism...but I don't know how much impact that has). But if they are not, you can always just dig a big hole.
External rails on a mountain don't allow for the optional compressed air part of the system that (according to the page) can double the efficiency of the system at less than double the cost.
I have seen the 1830s-sh remains of such a system in Tasmania. They sent coal in buggies down a ~200m inclined railway to the dock below, using it as counterweight to haul goods up the hill. Win-win!
Suppose you have standard rail tracks and use a surplus freight train. Congratulations, you can now store the amount of energy needed to push a single train up a single mountain. That's not nothing, but it probably isn't enough to be useful on a utility scale.
That implies that you want a weight orders of magnitude more than a train (or many trains per charge "cycle" with a stockyard at each and of the mountain to store them) You're now going to need a very tough track and wheelset. They're also going to wear quickly. Probably enough to make it impractical to build and operate.
Maybe? But what if it cost way, way more? You actually have to look at the time value of money for anything that takes more than a year or two to pay off to be sure that there isn't some kind of false economy.
If you assume that the thing lasts forever, well, you divide $x/infinity so it's free. EXCEPT that you've got $x tied up that could be earning interest instead. So it's not $x/infinity, it's the opportunity cost on $x versus anything else out there like batteries, the grid, etc.
If the capacity is proportional to the depth of the tunnel and the mass of the weights, and the maximal mass of the weights is proportional to the depth of the tunnel, then wouldn't the capacity grow quadratically with the invested money?
Edit: You assumed that they can both fill most of the tunnel up with lead and move that up or down 500 meters. The volume that they can fill with that is thus only half of what you say.
Why is the maximal mass of weights proportional to depth? It's more proportional to diameter than anything else. There's a practical limit to how much weight you can hang. Sure if you make a 10km deep hole and a 3km deep weight you could store a lot of energy. But a 3km deep weight might not hold itself together.
If we have enough volume that we can't use the most dense possible weight for all of it, we can find cheaper weight materials by dropping the density constraint.
Couldn't you have the weight grip the sides of the tunnel with gears attached to a generator/motor (inside the weight) so the weight wouldn't rip itself apart? It would be the same machinery that ordinarily would operate the pulley at the top, just moved down into the weights (cause with this, you would need no more pulley). (To illustrate why it wouldn't rip itself apart, imagine gaps on the weight every 100 meters.)
Technically that would work fine. Economically, it's a disaster. McMaster prices are at least 2x what's available if you buy direct from a source, and if you were buying in bulk it'd probably get cheaper still. But this is cheap, cheap stuff for not that much weight. You'd need something I dunno, 100x-10000x stronger to do what you're talking about: http://www.mcmaster.com/#racks-and-pinions/=upn9xl
The appeal of the cables is that they're cheap. And they're cheap because they're easy to make (all things considered). Once you start applying sophistication to the design the price gets higher, and it's already too high from having to drill the hole.
Digging subway tunnel through rock costs about $100M per kilometer. On the one hand, these holes would be vertical, which is harder than horizontal
I would have thought that a better comparison would be oil wells, which cost about $500 per ft of depth, or $1.5M per km.
our total volume of mass will be about 25 m^2 1000 m = 25,000 cubic meters. If the weights are made from lead, that's a total mass of ~280,000 tons*
You seem to be assuming that the entire depth of the shaft is filled by weights. My impression was that the weight was much smaller than the shaft it fell down.
Actually 1/2 the shaft filled by weights is optimal independently of material, considering only raw energy. (E=p A h(H-h), respectively density, area, payload height and shaft height, Eopt=p A H^2/2 ). Pretty surprising to me that the energy increases quadratically with depth.
Yes, if you're considering only energy. But in practice there are other considerations, such as the cost of the weight, the strength (and thus cost) of the cables, the amount of torque which can be produced for lifting the weight, etc.
I feel this idea would mesh well with the mining industry. Dig straight down, reinforce the walls on the way, separate out the desired minerals, pull up the drill, put in a pendulum and move the rig over and start again. You already need to setup giant motors to move the pendulum, so getting the ore up would be easy. An ideal site would have an abundance of lead, which would cut down on the pendulum cost. Unused rock could be mixed into cement for the walls. The small footprint combined with the benefits of being able to store solar or wind energy for long periods of time could make it the first form of mining that environmentalists approve of.
What's the math look like for the side of a mountain or hill, where you pour a concrete channel and put wheels on the weight so it can be rolled up and down the hill. I'm just wondering if there are places like in the Rockies where this idea would be viable.
The depth requirement is 500m to 1500m. Though cliffs can be much taller than this, they usually are not totally vertical and cannot accomodate this much depth.
It's not a key component, but it is a significant benefit of their system. The main reason though is that the primary benefit of this system is flexibility of placement. By locating grid storage close to where it's used most, you save significantly on transmission losses (and infrastructure). Finding sufficient vertical cliffs would be even more difficult than finding suitable locations for pumped hydro.
Also if you expose the weight to open air and wind the whole system would be much trickier than using an enclosed shaft.
Or what about the ocean? It's 4km deep on average, so why not just drop the weights there? No need for setting up tracks or carrying the weight up a mountain.
Can we get a source for the $100M per kilometer figure? The NYC subway system has 373 km of tunnels, 60% of which is underground, which would translate to roughly 22 billion dollars just for the digging... that just seems way too high to me.
2nd Avenue subway [0] requires about 8.5 miles worth of tunnels (several hundred feet of which were already dug back in the 70's) and it's budget is $17 billion. Of course that whole cost isn't just for digging tunnels, but it's a clear indication that digging tunnels (especially in dense urban areas) can be extremely expensive.
There is a very large difference between building complex tunnels and a simple hole in the ground. The cost for drilling a straight exploratory/mining hole was 10 Million/km in the 70's and 80's[0]. I can easily imagine this being cheaper by a factor of 2-5 with current advances. Not to mention this concept has a lot of synergy with mining companies.
There is a difference, but it's not necessarily large for deep drilling. Once you start drilling large diameter holes deep into the ground, you have to shore up that hole to prevent it from collapsing in on itself. For wells or expiatory holes, water or slurry is used, but that's not an option in this case, so there will need to be a casing involve. Installing that casing so that the pieces line line up perfectly is a complex endeavor (not impossible, it's been done, just not straight forward as "drill a hole")
> Now, you can't fill the whole tunnel perfectly or the air can't escape, so our total volume of mass will be about 25 m^2 1000 m = 25,000 cubic meters.*
You seem to have accidentally assumed that the weight will stretch the full height of the hole. Obviously this would leave it unable to move vertically.
What about depleted Uranium? 19G / cm^3, 1.7 the density of lead. No idea what the cost is, but I can't imagine that waste material would be that costly.
1. Digging mine shafts is dramatically cheaper than structal tunnels. They dig exploratory shafts frequently to roughly these depths for well under $1m
2. Using a disused mineshaft would have a negative cost associated with it because the security associated with keeping it safe is non zero.
Actually, the majority of the weight would be in steel rope.
For one type [0], the safe limit is a tensile load of about 134-150 MN/m^2 (= MPa) [1]. At a density of 8 g/cm^3, the limiting length of a uniform cable is ~1.7 - 1.9 kilometers. If you have a stationary, suspended cable of this length, its own weight puts it at its maximum load; it can't lift anything else.
Steel rope on McMaster is around $10,000/ton [of rope]. So, these assumptions are a dead end.
You can't solve this by using shorter cables, because that decreases your energy capacity at the same rate. If you use cables of 1/10th the length (~100 m), you get only 1/10th the potential energy storage per ton. The cable thickness per lifted ton is constant.
[1] The breaking limit of rope is far higher (~700 MPa), and the breaking limit of a single wire strand -- the tensile strength -- is higher still (1,770 MPa according to [2])
For the cross section area, I'm assuming a circular rope (not accurate).
"You can't solve this by using shorter cables, because that decreases your energy capacity at the same rate. If you use cables of 1/10th the length (~100 m), you get only 1/10th the potential energy storage per ton. The cable thickness per lifted ton is constant."
This is a simple "figure of merit" for cable in this problem,
cost / (length * load capacity (N))
The is the same as the cost / energy stored. The denominator is simply the work equation (distance * force) -- the mechanical work the cable can do before it runs out of length.
= cost / energy
This is actually sort-of constant, since the denominator is ~proportional to the cable volume. (The load capacity is ~ the cross sectional area d^2).
For steel rope from [0], it looks like a lower bound of about $1,200/kWh.
Here's a related idea: take a piece of land made of granite. Cut a 1km diameter plug of granite, one km deep. Store power by pumping water under the plug, raising the whole thing half a kilometer in the air. It would store enough energy to power Germany for a day.
I think the coolest thing about this concept (for me) is viewing it as a "whole-system" energy storage procedure.
It is effectively 100% renewable, 100% distributable, using 100% commodities (ie: rocks in a hole).
As a thought experiment: if on average you can meet 110%+ daily power expenditure captured from renewables (solar, wind, whatever), and store it by lifting up these weights, then you've broken into the "free energy" loop.
More specifically, don't look at the power input or storage, look at the power output / usage. If your input + storage capacity is greater than your output rate then energy effectively becomes "free forever".
Simulate it on a small scale. Get a pinwheel to run a small motor that winds something up. Attach a small LED to it that you only run occasionally. Basically, just so long as you have a really small output draw compared to your input rate and storage capacity, this "battery" will give you energy when you want it with minimal maintenance costs and minimal consumables.
I'm far from being even slightly knowledgeable in this topic, but would it be possible to build this in very deep waters? Like a massive column containing a tunnel? Seems cheaper than digging a 1km hole.
At the base of a 1000m shaft you'd have approximately 100 atmospheres of pressure. Not saying it cannot be done, but construction and materials cost would still be very high. Maintenance too. Plus you've lost the advantage of locating it anywhere.
The key figure of merit for comparing energy storage is not $/KWh, but rather $/KWh*Number of cycles. Li-ion only has about a 1000 cycles. Assuming one cycle per day (solar charge during day+discharge during night) in 50 years there are 18000 cycles.
The figure of merit for Li-ion is 250x1000=2.5e5. My estimate (and those of others) is that this costs up to about $2000/KWh. So the figure of merit for this is 1000x18000=0.9e7. Two orders of magnitude better than Li-ion.
Edit: I am ignoring the cost of capital, interest rates etc. Somebody should do this analysis.
I did some quick analysis comparing the proposed project against Li-ion, adjusting for storage and lifespan, and the result is very hopeful. I used values for $/KWh and lifespan from abdullahkhalids' comment. The analysis shows that if you can get more than one cycle per day out, the proposal offers fantastic value.
Finance uses something called 'equivalent annual cash flows' (EACFs) to compare projects of different lifespans. Using EACFs makes this analysis very simple.
Using abdullahkhalids' figures and assuming a single cycle per day, the equivalent annual cash flows per KWh are equal when the cost of capital is about 4.35%.
Something magical happens when you assume can get more than one cycle per day. At two cycles per day, your funding costs could be 10% and the project still feasible! At four cycles per day and with a 5% cost of capital, Li-ion costs almost four times as much as the proposed project.
Could someone shine some light on how many cycles per day is realistic for both Li-ion & the proposal?
PS if you find this sort of analysis interesting and want to hit me up to talk about such things, feel free to send me an email (available in my profile).
This is just rampant speculation - but what if they used depleted uranium as the weight? They could get paid to take the material off others hands (instead of buying lead) and it's almost 70% more dense.
Probably... but it's still an intriguing idea! Especially since their pressurized gas proposal already calls for a sealed cavity; maybe there actually is potential there. (Of course, there would probably be a significant PR cost too.)
That said, they can already get more weight by making the weight taller, so density likely isn't a huge benefit. Whatever's the cheapest cost/kg (and without the other issues of Uranium) would probably be best.
I really hope these guys succeed, even if they don't replace conventional batteries everywhere. One thing I've been thinking for a long while is that: the future of humanity is in how advanced drilling equipment we can make. Think about it: asteroid mining, colonizing planets or even just conventional mining...all require drilling. If this technology catches on, there will be so much research done in finding better drilling techniques. In fact there is so much resources to be found in our Earth itself, if we drill deep enough.
Also, imagine if we have a base on the moon powered by solar cells: having the technology to drill quickly and cheaply would be indispensable in storing energy captured during lunar "days". Although I imagine you would need deeper holes because of the smaller g.
216 comments
[ 3.2 ms ] story [ 251 ms ] threadBy contrast anything that qualifies as a "heat engine" (including internal combustion) is limited by Carnot's law to be low-efficiency. If it weren't for the extraordinary energy density of combustible fuels they wouldn't be competitive.
It's exactly what it sounds like: a motor that is mechanically coupled to a generator. The motor runs on 60 Hz AC and turns the generator at the correct speed to produce 25 Hz AC.
[1] https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricit...
In fact, right now the Tesla factory has 4GWh of lithium ion batteries installed for smoothing energy demands and they are actively building 400kWh storage units:
http://www.greentechmedia.com/content/images/articles/straub...
I'm sure that the end game idea in his mind is using the 85kWh+ batteries of Teslas everywhere for distributed energy storage.
I mean, since E = mgh, you can get the same energy storage capacity with a less deep hole if you use a heavier weight. And you can get a heavier weight either by using more expensive material (why use a cheap one? it's not like it's going to wear or anything), or a larger hole.
I'm not sure what determines the cost of digging a whole, but I suspect depth matters more than area.
Also, does the shaft has to be vertical? You could dig it with a sharp slope, and put your weight on rails. That would make the shaft longer for the same depth, but it would probably be easier to build and maintain.
You should be able to get millions of rotations from a single centimetre hole, given that the mass is large enough and you have a good gear ratio..
Nevertheless, the density of Lead is 11.35 g/cm3 (the density of water is 1 g/cm3). The densest element in this table is Osmium with 22.6. So replacing if you replace a Lead weight with a more expensive weight you only gain x2.
http://www.lenntech.com/periodic-chart-elements/density.htm
I wish gold wasn't so rare! Its such an amazing material, and our economy is not based on precious materials anymore (except the commodity markets or course), so it seems like a really sad thing that we can't have more abundant gold just yet
I mean, technically I can get a super cap the size of jam jar to kick out 1 kw, just not for very long.
A watt is a unit of how much energy is expended in a second, not how much energy is stored. There is a reason why hydrostations in wales use lakes to store energy, because you need a lot of mass at great height to be of any use.
Edit:
here it is. https://news.ycombinator.com/item?id=6739349
That's why companies like Ambri are looking at using other materials in the batteries they're developing for grid energy storage.
http://en.wikipedia.org/wiki/Abundance_of_elements_in_Earth%...
If Ambri's technology does pan out, it will be due to a cheaper manufacturing process, not because they're avoiding lithium.
Ambri is interesting from a lifecycle and cost perspective but I don't think a lithium shortage is going to have any real impact on prices.
As oil & gas have shown, if there's exponential demand for a naturally occurring element, we'll definitely find ways to pull more of it out of the ground.
If we run out of lithium we'll figure something else out, just like we would for any other resource.
-- I guess there's no need to speculate when you have Google: https://www.google.com/search?q=where%20does%20helium%20come...
Whatever local (i.e. small scale) energy storage we have in the future you can probably bet (from first principles) with 99% certainty it will be based on the electromagnetic force. Gravity is too weak to be practical for smaller scale storage and cannot give mobile storage units since you have to deal with huge weights. For large scale see the "pumped storage" system already mentioned in this thread. Just for illustration, the "Taum Sauk Hydroelectric Power Station" can produce 175MW of continuous power. If you dropped the 18T weight in the 1km shaft you'd get about 13MW averaged over the 14s fall. Then you have to lift it up again if there are still enough pieces left.
Even if you found a way to store energy in nuclear interactions (i.e. "charge a nuclear battery") you don't want to have a bunch of containers full of radioactive material all over the place. If one thought it through, I wouldn't be surprised if there are in-principle issues for the charging part similar to the ones with gravity.
Since we don't know of any others, this leaves only the electromagnetic force to store energy with sufficient mass (or volume) density in practical ways. Whatever it ends up being (chemical batteries, supercapacitors or something else) the future local energy storage unit will separate and hold charges apart.
This is not unachievable with some lifting systems currently exceeding this lifting weight.
http://en.wikipedia.org/wiki/Pumped-storage_hydroelectricity
At least if this contraption breaks, there's nothing important below it.
Every night the lights dim for a bit when the grid starts being used to pump water back up.
http://en.wikipedia.org/wiki/Smith_Mountain_Dam
You can have a much much heavier weight.
I did a little more research, and I'm not sure anymore that it's a complete deal-breaker. But it's definitely going to put limits on how far this can scale.
The idea is to cut a 1km diameter cylinder into the ground (solid rock), and then lift it up up to 500m by pumping water underneath it. The power stored can power a country for a day.
I am somewhat sceptical, but this guy is totally serious about it.
I guess the main problem is to keep the water confined (200bar of pressure) while keeping the mass movable. Maybe someday they build a small testing facility, so we know for sure.
Numbers not looking reasonable for this concept.
If you delivered power when it was most expensive (ie high demand) and consumed it in the middle of the night, the arbitrage may work out.
The principle however of storing energy by raising a weight could also be used anywhere with a steep enough hill/cliff/montain and the weight could in theory be on a rail not just suspended.
Efficiency would potentially not be on par, however linked into solar/wind systems this is less about efficiency and more about creating a 1MW long term battery with a lifetime of 50+ years.
Guessing cost of digging and maintaining a hole compared to installing a guide rail is significantly higher.
So you're saying you get a free well as part of the deal?
If you can build one of these cheaply, and the running costs are trivial, then it's worth doing.
How many of them would you need to smooth out the energy of a wind farm, for instance?
Any sane plan would be to have more than one weight. When the first weight hits the bottom, it would release from the cable and another weight up top would grab the cable and start dropping. To store energy, the top weight would get winched up, and when it hit the top it would lock into place somehow and the next weight at the bottom of the shaft would engage the lifting cable, etc. The cable would have to follow a circular track, rather than having 1KM of cable for each weight.
You shouldn't be so confident that you know the only "sane" way to design such a thing. It's not a field anyone has experience in. These are only guesses.
At the top of the shaft there would be hefty prongs that retract when the weight needs to start dropping, and when the weight returns during a recharge cycle, the prongs reinsert themselves in to the shaft when the weight is lifted back into position.
Most likely each weight would have a "C" cross section with a nearly closed mouth -- just a slot from the edge of the weight to the larger central opening so that the weight can be removed/replaced from the cable if needed.
Edit: just noticed the comment about 500,000 kg -> 1.2MWh. Read that as MJ at first... d'oh.
If the hole could be used for some sort of heatpump too then maybe that would weigh off [no pun intended!] some of the problems.
Well well well, I must buy a well.
On their webpage they say " The biggest single cost is the hole, but it is expected that firstly this will have a very long life and secondly, as the technology rolls out, the costs of drilling will reduce significantly. So the economics will improve in time."
Drilling will not get cheaper without a serious reform of the law, and that's unlikely to happen. There are two primary kinds of drillers; water and energy. Folks involved in water have VERY protective rules in all states. The reasons are 1. good lobbying and 2. if you screw up you destroy the water supply.
Energy drilling is no cheaper. Drilling rigs are huge machines that aren't moved easily and cost at least $50k a day on land and $500k a day for seagoing. That's before you pay another $20k per day in staff and god knows how much for fuel for everything; a rig will produce at least 5MW of power.
Could they custom build a rig just for drilling for their idea and would that work? Sure. But they'd probably spend several million and then you've got to have it running 24/7 for it to pay off.
The regulatory hurdle is going to be non-trivial as well. They're going to case it which helps. But the casing would probably need to be cemented in place which is a non-trivial cost as well. And convincing lawmakers that this doesn't quack like some other kind of well is going to be no easy feat.
I'm not sure this has much to do at all with water and energy drilling. They're talking about using abandoned mine-shafts. Those are much wider and shallower than the kind of holes used to reach petroleum.
http://waterdata.usgs.gov/nwis/current/?type=gw
These guys may be on to something. Scaling down seems to me to be the key. Full gridless operation with solar panels (at least in earthquake-free zones).
The problem with going shallower is that the system capacity is directly proportional to depth and weight. Too shallow and you have to have huge weight and that means a large diameter hole and really big cables and such.
But going deeper requires drilling through rock, and aquifers which are located within the rock. That means big regulatory hurdles because nobody wants to poison the aquifer on accident. Plus the large costs of drilling through rock.
I really like the idea from a theoretical standpoint. It's very elegant. But it doesn't seem practical from an economic or regulatory standpoint. If there are places where you can get the diameter and depth for free, it's clearly genius. But I don't think purpose-drilled holes for this will become a thing -- at least barring some kind of immense breakthrough that I can't even imagine.
The potential energy of a mass in joule is simply
where m is in kilogram, g is 9.8 m/s^2, h is the height in metre.So, for example, 100 ton lifted 100 metre gives 98MJ.
That's 1MW for 98 seconds.
To make this very concrete my house uses, in the summer, about 40kW-hr per day for water heating, cooking, and the rather large amount of computer equipment we have.
That is 40000 * 3600 = 144MJ. So assuming that your solar power system can supply that over a 12 hour period we need to store half of it, 72MJ, to keep us going after dark. Your ten metre deep hole would need a 734 ton weight: 735000 kg * 9.8 m/s^2 * 10 m = 72MJ
Either way, I think you'd have to round your estimate to order-of-magnitude anyway, because of the rather big assumption "that your solar power system can supply that over a 12 hour period we need to store half of it, 72MJ, to keep us going after dark", because getting max solar power for half the day and no solar power for the rest is not exactly how it works, nor does one use the same amount of energy during day and night (which is why I can opt in to an energy plan that gives you discount on electricity at night, because there's a surplus then).
Even if we accept your figure the peak daily use is probably at least double your 9kW-hr/day (winter for example) and even if you use less at night you still need probably about 12MJ storage to allow solar to work per household, etc., etc. So, yes, in the Netherlands you need a smaller mass but it is still in the order of 100 ton.
The point of my reply was to show the person I was replying to how easy it is to find out how much mass and height is needed, you just have to plug in your own energy consumption and generation figures.
I'm looking through all the dismissive comments to see if any of them are pinpointing it as a scam - because this is, after all, the kind of idea that is simple enough to captivate laypeople and lift dollars out of their pockets. But judging from this kind of response, it seems like it's also the kind of idea that is simple enough to be dismissed as a "they would have done it already if it worked," rationalized via fuzzy back-of-the-envelope math.
Ultimately, since I have no stake in this one, I'll just wish them luck.
Definitely more negative comments on HN these days (although it's always been a skeptical audience).
Real problems: Dismissive people who don't/can't/wont listen to good responses. Good founders/ideas but just really bad at communicating. Those are basically the type i and type ii errors of this format.[1]
_____
[1] A grey area exists in some other areas too (some people just get 'lucky'; others for good reason can't disclose everything the key answers/insights for competitive reasons)
A subway tunnel might have a diameter of about 6 meters, so cross section = 3 * 3 * pi = 28 square meters. Digging subway tunnel through rock costs about $100M per kilometer. On the one hand, these holes would be vertical, which is harder than horizontal; on the other hand, they wouldn't need ventilation and train tracks and stuff. Let's handwave and say it's $100M for a 1 km deep hole.
Now, you can't fill the whole tunnel perfectly or the air can't escape, so our total volume of mass will be about 25 m^2 * 1000 m = 25,000 cubic meters. If the weights are made from lead, that's a total mass of ~280,000 tons or 2.8 * 10^8 kg, at a mean depth of 500 meters, so our total potential energy is 2.8 * 10^8 * 500 * 9.8 = 1.4 TJ, or 1.3 TJ net assuming you get the efficiency they claim. 1 kWh is 3.6 MJ, so you can store ~400,000 kWh at $100M capital cost (ignoring for the moment the cost of weights, generators, etc.), which is $250 per kWh installed capacity.
That's pretty good... but you also have to pay for weights and a bunch of other stuff. Bulk lead costs about $2,000 per ton on the current market, so that's $560M for the weights, which puts you back in the $2,000 per kWh range which doesn't beat lithium batteries. So you have to use iron or some cheaper material... but then you don't have as much storage capacity because the density is lower, and even with iron you're paying $400 per metric ton or $80M for all your weights. So this isn't obviously impossible like Solar Roadways, but even in the best case it won't make storage dramatically cheaper.
It certainly appears more expensive than pumped storage, but as they say, it doesn't require a convenient mountain and lake. That makes for much more flexibility in placement, and the closer you can place the storage to the demand, the less is wasted in transmission, and the less storage you ultimately need. That said, the pumped heat storage design[1] that hit the homepage yesterday would have all those same advantages, and although the efficiency would be slightly lower, it looks much cheaper to build.
[1]: http://www.windpowerengineering.com/featured/business-news-p...
Edit: I mean that an inclined rail could be just as good as a hole, and way cheaper.
That said, how are those gravity fed porch lights doing? That seems like it would be an interesting proxy here.
That implies that you want a weight orders of magnitude more than a train (or many trains per charge "cycle" with a stockyard at each and of the mountain to store them) You're now going to need a very tough track and wheelset. They're also going to wear quickly. Probably enough to make it impractical to build and operate.
If you assume that the thing lasts forever, well, you divide $x/infinity so it's free. EXCEPT that you've got $x tied up that could be earning interest instead. So it's not $x/infinity, it's the opportunity cost on $x versus anything else out there like batteries, the grid, etc.
Edit: You assumed that they can both fill most of the tunnel up with lead and move that up or down 500 meters. The volume that they can fill with that is thus only half of what you say.
Couldn't you have the weight grip the sides of the tunnel with gears attached to a generator/motor (inside the weight) so the weight wouldn't rip itself apart? It would be the same machinery that ordinarily would operate the pulley at the top, just moved down into the weights (cause with this, you would need no more pulley). (To illustrate why it wouldn't rip itself apart, imagine gaps on the weight every 100 meters.)
The appeal of the cables is that they're cheap. And they're cheap because they're easy to make (all things considered). Once you start applying sophistication to the design the price gets higher, and it's already too high from having to drill the hole.
I would have thought that a better comparison would be oil wells, which cost about $500 per ft of depth, or $1.5M per km.
our total volume of mass will be about 25 m^2 1000 m = 25,000 cubic meters. If the weights are made from lead, that's a total mass of ~280,000 tons*
You seem to be assuming that the entire depth of the shaft is filled by weights. My impression was that the weight was much smaller than the shaft it fell down.
Disclaimer, not a geologist.
Also if you expose the weight to open air and wind the whole system would be much trickier than using an enclosed shaft.
[0] http://en.wikipedia.org/wiki/Second_Avenue_Subway
[0] http://facstaff.gpc.edu/~pgore/geology/geo101/interior.htm
You seem to have accidentally assumed that the weight will stretch the full height of the hole. Obviously this would leave it unable to move vertically.
I don't think this is the case. We dig vertical holes all the time for wells, geothermal, and pilings for buildings: http://www.bdonline.co.uk/Pictures/web/r/r/g/CCTV_17_foundat...
Look at all of them! For one building!
1. Digging mine shafts is dramatically cheaper than structal tunnels. They dig exploratory shafts frequently to roughly these depths for well under $1m
2. Using a disused mineshaft would have a negative cost associated with it because the security associated with keeping it safe is non zero.
For one type [0], the safe limit is a tensile load of about 134-150 MN/m^2 (= MPa) [1]. At a density of 8 g/cm^3, the limiting length of a uniform cable is ~1.7 - 1.9 kilometers. If you have a stationary, suspended cable of this length, its own weight puts it at its maximum load; it can't lift anything else.
Steel rope on McMaster is around $10,000/ton [of rope]. So, these assumptions are a dead end.
You can't solve this by using shorter cables, because that decreases your energy capacity at the same rate. If you use cables of 1/10th the length (~100 m), you get only 1/10th the potential energy storage per ton. The cable thickness per lifted ton is constant.
[0] http://www.engineeringtoolbox.com/wire-rope-strength-d_1518....
[1] The breaking limit of rope is far higher (~700 MPa), and the breaking limit of a single wire strand -- the tensile strength -- is higher still (1,770 MPa according to [2])
For the cross section area, I'm assuming a circular rope (not accurate).
[2] http://www.gabaswire.com/en/overview/grades-of-wire-rope.htm...
This is a simple "figure of merit" for cable in this problem,
The is the same as the cost / energy stored. The denominator is simply the work equation (distance * force) -- the mechanical work the cable can do before it runs out of length. This is actually sort-of constant, since the denominator is ~proportional to the cable volume. (The load capacity is ~ the cross sectional area d^2).For steel rope from [0], it looks like a lower bound of about $1,200/kWh.
[0] http://www.mcmaster.com/#standard-wire-rope/=upui3o
(E.g. item "3440T68", 5/8" plain steel, $5.16/foot for 9,080 lbf lifting capacity;
$5.16 / (9,080 lbf * 1 foot) = $1,509/kWh)
http://www.solarserver.com/solar-magazine/solar-energy-syste...
It is effectively 100% renewable, 100% distributable, using 100% commodities (ie: rocks in a hole).
As a thought experiment: if on average you can meet 110%+ daily power expenditure captured from renewables (solar, wind, whatever), and store it by lifting up these weights, then you've broken into the "free energy" loop.
More specifically, don't look at the power input or storage, look at the power output / usage. If your input + storage capacity is greater than your output rate then energy effectively becomes "free forever".
Simulate it on a small scale. Get a pinwheel to run a small motor that winds something up. Attach a small LED to it that you only run occasionally. Basically, just so long as you have a really small output draw compared to your input rate and storage capacity, this "battery" will give you energy when you want it with minimal maintenance costs and minimal consumables.
The figure of merit for Li-ion is 250x1000=2.5e5. My estimate (and those of others) is that this costs up to about $2000/KWh. So the figure of merit for this is 1000x18000=0.9e7. Two orders of magnitude better than Li-ion.
Edit: I am ignoring the cost of capital, interest rates etc. Somebody should do this analysis.
http://www.sandia.gov/ess/publications/SAND2013-5131.pdf
Model visible here - http://imgur.com/KmQPb8P
Finance uses something called 'equivalent annual cash flows' (EACFs) to compare projects of different lifespans. Using EACFs makes this analysis very simple.
Using abdullahkhalids' figures and assuming a single cycle per day, the equivalent annual cash flows per KWh are equal when the cost of capital is about 4.35%.
Something magical happens when you assume can get more than one cycle per day. At two cycles per day, your funding costs could be 10% and the project still feasible! At four cycles per day and with a 5% cost of capital, Li-ion costs almost four times as much as the proposed project.
Could someone shine some light on how many cycles per day is realistic for both Li-ion & the proposal?
PS if you find this sort of analysis interesting and want to hit me up to talk about such things, feel free to send me an email (available in my profile).
That said, they can already get more weight by making the weight taller, so density likely isn't a huge benefit. Whatever's the cheapest cost/kg (and without the other issues of Uranium) would probably be best.
Also, imagine if we have a base on the moon powered by solar cells: having the technology to drill quickly and cheaply would be indispensable in storing energy captured during lunar "days". Although I imagine you would need deeper holes because of the smaller g.