# Wind Physics and Gravity Batteries

1. Jul 5, 2011

### MarcoD

At the current rate of oil consumption, the world will run out of it in twenty years. The Netherlands is investing somewhat into wind energy since that's one of the few renewable resources around in our country.

Now the obvious problem with wind energy is that it is unreliable, so people are looking at manners in which to store that energy. The most popular solution is to store overspill energy into a lake, a gigantic gravity battery, by pumping water into, sometimes out of, it, and harvesting that energy at a later stage with generators. A proposal is to construct a massive lake, 40 metres deep, in the sea.

It sounds wasteful to me. What about storing energy directly at your house by lifting a mass? If you use lead instead of water, you need less volume/height, and a mechanical solution should have a better efficiency than a 'hydraulic' solution.

So I arrived at the following basic physics question: Suppose that you store energy by lifting matter, and suppose that system runs at 90% efficiency, and suppose the mass is lifted (at most) 5 metres. How big does the mass need to be to store the equivalent of one day of electric energy for one household?

Any idea?

2. Jul 5, 2011

### MarcoD

After a bit of Googling, the approximate annual household energy consumption for three bedroom house is 4200kWh.

3. Jul 5, 2011

### timthereaper

The potential energy stored in a mass is PE=mgh. Taking your estimate to be accurate, 4200 kWh is about 1.512e10 joules. Dividing by Earth's gravitational constant and your given height of 5 m, the average household would require a mass of 3e8 kilograms, approximately the weight of 226,470 cars (based on a 3000 lb average). That's also assuming a perfect 100% energy conversion. That's not entirely realistic.

What's wrong with hydroelectric power? It's pretty renewable and environmentally friendly (depending on your viewpoint). It's also fairly reliable. I agree that the oil reserves won't last indefinitely, but I (and Bill Gates) think the best solution is nuclear power. I'm not talking about uranium fission, but there has been talk about thorium-based reactors producing comparable amounts of energy with smaller reactors and a lot less harmful waste products. Today's energy needs are too large to rely on wind and solar energy. They simply do not produce the amounts we all require.

Last edited: Jul 5, 2011
4. Jul 5, 2011

### MarcoD

You forgot to divide by 365 I think? What about the following (I only had physics in high-school.)

After some Googling, the average annual household energy consumption is 4200kWh (unreliable answer, but good enough for the purpose).

That equals about 12kWh a day. That is about 43MJ a day. So far so good.

With 90% efficiency, we need to put in 43/0.9MJ = 48MJ. Problem is I would need efficiencies for the lifting and lowering of mass. I'll wave that away. Let's just assume we can lift a mass a metre with 10MJ. One joule is the equivalent of lifting 102g one metre.

So, about a mass of one million kilos, a thousand tonnes.

(I think we'll need all kinds of energy resources to continue after the end of the oil-powered industrial revolution. We hardly have hydroelectric power in the Netherlands; there's lots of water but only a 4 metre drop in height. But I am trying to avoid the energy debate here.)

Last edited by a moderator: Jul 5, 2011
5. Jul 5, 2011

### timthereaper

You're right. I was calculating energy per year. Even with 12 kWh a day (I know that I burn more than that every day) and 100% energy conversion, the mass required would be 845401 kilograms, or approximately 621 average cars. You also have to consider that's per household. I think you'd be better off storing that energy some other way.

Sorry about the energy debate hijack. I just we were talking about alternative energy.

6. Jul 5, 2011

### chrisbaird

You can cut down that mass by increasing the height. You could dam up a valley up in the mountains and pump water up into the valley to store energy. I think pumping water would be cheaper than lifting solid masses, because you just run a pipe up a mountain or tower instead of installing a long track for the mass.

7. Jul 5, 2011

### MarcoD

The mechanics which prompted my question was that some cars are very good at transforming electrical energy into mechanical energy (a flywheel). A braking car can transform 95% of it to mechanical energy, and again 95% back.

I just don't believe water pumps have the same efficiency, and flywheels cannot store energy over a prolonged period of time. And storing energy at your house demands a less robust power grid -which is a problem at the moment when transferring to wind energy,- so I thought of weights at your house, or an 'industrial' park. And I just wondered about the math of such a solution; i.e., if it's anywhere feasible that it could work. (I thought a system of pulleys should be more efficient than pumping. But it seems you'ld need to fill about a quarter of your house with lead, about 90m^3, to make this gravity battery work.)

Apart from that, the Netherlands is flat. Your solution of pumping up a lake only works if all energy is transported to Norway or Switzerland which means lots of waste and major adjustments to the electrical grids. Moreover, I doubt that there are enough lakes in Europe to hold the spare capacity in the future.

(Can everyone please check the calculations. I am certainly not proficient at physics, even classical. Ah well, at least I managed to invent a nice physics exam question.)

Last edited by a moderator: Jul 5, 2011
8. Jul 5, 2011

### Drakkith

Staff Emeritus
There are plenty of good options for storing energy, and we only have more options as time passes. The main issues between all the options are cost and size. From my knowledge they all have about the same efficiency, some a little more or less, so that's not too big a deal. Some are generally very costly, but not very big in physical size, while others are very big but can be very inexpensive for the amount of power stored. (I'm talking about the size of industrial use, not household)

Something like lifting weights probably isn't a very good idea, as they are extremely limited by weight and size constraints. A flywheel would be much better, as you can simply accelerate the flywheel further to almost any speed you want as long as you have the power. They have magnetic bearings and other things that can greatly reduce the friction, so that the flywheel loses very little energy over time. I believe there is a city in Alaska or something that is using this method as a means to store power.

9. Jul 5, 2011

### MarcoD

Yeah, I guess flywheels will be the way of the future. Although I wonder what happens if you leave them spinning for two weeks.

It was just a goofy question. ;-)

10. Jul 6, 2011

### timthereaper

That's not entirely true. The limit of flywheels is really the hoop stress. The faster you accelerate a flywheel, the greater the circumferential stress. Carbon fiber composite flywheels with the fibers oriented in the circumferential direction has seen the most promise due to its large tensile strength and relatively cheap cost and manufacturability.

They won't lose much power over if you have little friction or drag, like with magnetic bearings.

11. Jul 6, 2011

### MarcoD

Dunno, it's just about the numbers, right? And potential energy is potential energy; it doesn't matter whether you lift 10 litres of water a meter, or 1 litre of lead. In the end, it just boils down to how much money you need to invest to build a battery which can hold all that spare energy.

I doubt flywheels will be cost-effective. And I guess you'ld need to build one factory full of weights just to serve fifty households. So, I guess it's back to lakes. (I found the number for lakes btw. Such a solution operates at 70%.)

[Swapped kinetic for potential. Oops ;-)]

Last edited by a moderator: Jul 6, 2011
12. Jul 6, 2011

### timthereaper

I wasn't trying to say that flywheels were the best option for energy storage. They're really a curiosity for the time being, but the technology is still being developed. I was just trying to say that if you were going to make a flywheel, make it out of carbon fiber.

A good system for energy storage really depends on your application. Flywheels are nice because they're small. You don't have to have a large factory of flywheels if all you want is a sizable amount of energy stored somewhere (e.g. for a house). If you're thinking of a country-wide energy solution, lakes or reservoirs are convenient because all you have to do is dam up a river and nature fills up a store of energy for you. The capacity of energy you can store in a lake really only depends on the strength of the dam.

Arguably, that's why oil is so useful and why it's so widely used. It's kind of abundant (at least it was), it's available to anyone who drills for it (very simplistic view of the oil industry, I know), and it packs a lot of energy in a small amount. The energy storage capacity for gasoline is really as big as the tank it's being stored in. It can be easily distributed to consumers and it stores well (I don't know if it tends to break down into other chemicals after extended periods of time). If you want to replace dependence on oil, then you have to address these issues with alternative energy.

13. Jul 6, 2011

### MarcoD

You hijacked the debate anyway, right? ;) So, okay, my opinion:

Oil will run out[1]. I imagine a small part of the current chain of oil will be replaced by biofuels (to be used for food production or aircrafts for example). But the numbers don't add up, there's no way biofuel can replace oil completely. Actually, I think there's no way that we can continue to consume 15 TW world energy with renewable sources in the coming decades - note that more than 80% of that consumption stems from non-renewable sources. But a substantial part of world energy consumption can be generated as electricity, and solar/wind/hydro power is there in abundance - as long as we can store it.

The 'battery' problem is real: the sun doesn't shine at night and wind is unreliable. If we shift to producing and consuming more electricity, and I think we will be forced to, it needs to be solved. Maybe we will need to build gigantic lakes (but I estimate that for the Netherlands that means transforming 15% of the country into a lake with 40 metres high dikes). We can also build a city full of weights which can be lifted to fifty metres (it is the same thing, but more expensive), or we can try to store it in chemical batteries, or we can try to store it locally at each house with flywheels.

It is not a matter of if, but when it will (need to) happen.

Anyway, the numbers, from Wikipedia: In 2008, total worldwide energy consumption was 474 exajoules (474×1018 J=132,000 TWh). This is equivalent to an average annual power consumption rate of 15 terawatts (1.504×1013 W) The potential for renewable energy is: solar energy 1600 EJ (444,000 TWh), wind power 600 EJ (167,000 TWh), geothermal energy 500 EJ (139,000 TWh), biomass 250 EJ (70,000 TWh), hydropower 50 EJ (14,000 TWh) and ocean energy 1 EJ (280 TWh). The estimates of remaining non-renewable worldwide energy resources vary, with the remaining fossil fuels totaling an estimated 0.4 YJ (1 YJ = 10^24J) and the available nuclear fuel such as uranium exceeding 2.5 YJ. Fossil fuels range from 0.6 to 3 YJ if estimates of reserves of methane clathrates are accurate and become technically extractable. The total energy flux from the sun is 3.8 YJ/yr, dwarfing all non-renewable resources.

I don't know how much you can trust these numbers, or how fast we will run out of oil/coal/gas, or how much of the potential is concretely harvestable, but I am sure we will see some strange stuff happening over the coming decades.

[1] From wikipedia, again: World demand for oil is projected to increase 21% over 2007 levels by 2030 (104 million barrels per day (16.5×106 m3/d) from 86 million barrels (13.7×106 m3)), due in large part to increases in demand from the transportation sector. Sadad al-Huseini, former head of exploration and production at Saudi Aramco, estimates 300 Gbbl (48×109 m3) of the world's 1,200 Gbbl (190×109 m3) of proven reserves should be recategorized as speculative resources, though he did not specify which countries had inflated their reserves.

The twenty years estimate was for dramatic effect. ;-). With a reserve of 1000 billion barrels and a daily consumption of 100 million barrels, we got 27 years left. Of course there are lots more reserves to be discovered. But the question is not how many days are left, but how many days are left until substantial parts of the world economies start failing. I.e., with a 50% drop of availability the price of oil may as well become tenfold the current price, and farming and flying will become very expensive. So twenty years looked like a nice gloomy estimate. ;0)

(Anyway, it's called 'grid energy storage.' Wikipedia has some nice articles on it.)

Last edited by a moderator: Jul 6, 2011
14. Sep 6, 2011

### mheslep

Some comments:

o Serious sources on perishable energy sources (EIA, USGS) like oil focus on 'peak' production forecasts and on supply falling short of demand, not on when it will 'run out'. No serious forecasts predict all the world's oil in all forms (liquid/tar/shale) will actually be completely consumed even within the next hundred years, much less twenty. C.F. http://ogma.newcastle.edu.au:8080/vital/access/services/Download/uon:6530/SOURCE4?view=true".

o A more accurate term for describing wind turbine farm output power over time is intermittent, not unreliable, the latter implying high failure rates in equipment. Over the time of a year or more a given wind farm ( or large solar array) will very reliably produce its designed amount of energy, probably more reliably than a gas/coal plant of similar total power which are prone to central boiler, turbine, etc failures.

o Current US Oil consumption is http://www.indexmundi.com/g/g.aspx?c=us&v=91"countries will no doubt increase consumption, but the US example should lend caution to world consumption predictions.

o http://en.wikipedia.org/wiki/Pumped-storage_hydroelectricity" [Broken] is currently about 3% of US total electric capacity.

Last edited by a moderator: May 5, 2017
15. Sep 7, 2011

### klimatos

The world will never run out of oil. I know that this is a physics forum, but still I expect a certain minimum understanding of basic economics. Basic supply-demand-price theory will simply raise the price of oil until the supply and demand balance out once more. The end result may be that the average man can no longer afford to buy gasoline for his car, but this is nothing new. The rich will continue to enjoy things that the common man cannot afford.

My oldest daughter has her PHD in and consults in bio-fuels. She sees no alternative source of energy on the horizon that will replace coal and oil in her lifetime without massive subsidies. Nuclear power is probably the best alternative, but has almost prohibitive political baggage. Solar power, wind power, tidal power, and the like are all limited by transportation problems between where they are produced and where we want to consume them.

A major part of the problem is that people live where they want to and drive as much as they want to. Any new sources of power must enable them to continue doing what they want to do. Changing basic human nature is not easily done--ask the former Soviet Union!

16. Sep 7, 2011

### mheslep

You mean transmission?

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