Backyard gravitational energy storage

 kw: analytical projects, energy, energy storage, batteries, gravitational energy storage

The Federal subsidy for installing solar panels on houses' roofs continues. I can't take advantage of it because the huge trees in my back yard shade too much of the roof too much of the time. I was told there is an extra subsidy to pay for removing big trees. Hmm, I wonder what the carbon "pollution" balance is between removing several 150-foot trees and using solar power…produced with panels that were manufactured using large amounts of fossil fuel-powered equipment. Is anybody producing solar panels using only solar power?

Anyway, at my latitude, I must use air conditioning about one-third of the year. On the warmest days, the A/C runs periodically all night long, particularly when the overnight low temperature is in the 80's (°F of course; that's about 30°C). It's no longer possible in most states to have the solar panels "run the meter backward" during the day, to build up an energy credit with the utility. Thus, I would have to purchase electricity to run my A/C, and the rest of the house, at night.

I'd like to store energy during the day to use at night. The Tesla Powerwall is one expensive option, and it is probably insufficient. Let's do some figuration.

My electricity bill shows monthly usage between 500 and 1,100 kwh/month. The smaller amount is characteristic of spring and autumn. My A/C unit is a heat pump, so my highest usage is actually in slightly warmer winters, when the heat pump usually runs rather than the backup oil furnace. Let's take 600 kwh/month as the top end of A/C-heat pump usage. That's about 20 kwh/day on the "worst" days, from an energy consumption perspective. Not every day is the same, so there are probably peak days with usage in the 30-40 kwh range. In the summer, more cooling is needed during the day; in winter, more heating is needed at night. Considering that these are very approximate figures, I can begin with the likelihood that an energy storage solution in the range of 20 kwh is appropriate.

First possible option: Tesla Powerwall 2. At a web page for This Old House, I find that the Powerwall 2 has a current (early 2023) price of $11,500 for one battery with a capacity of 13.5 kwh, and $18,500 for a unit with two batteries (27 kwh total). The warranty life is 10 years, with a guarantee of 70% remaining capacity at the end of 10 years. That brings the effective storage of an older unit as low as 9.45 kwh or 18.9 kwh. My benchmark figure of 20 kwh thus requires a two-battery system, with replacement needed 9-10 years down the road. Also, such a unit weighs about 500 pounds (230 kg).

If you're enough of a maker (we used to say "handyman"), what about buying a bunch of car batteries and wiring them together with a charger and a large inverter for converting the DC output to AC at 110 volts (or 220V, for your A/C)? Lead-acid batteries have an energy density of about 40 watt-hours per pound (wh/lb) or 88 (or 90) wh/kg. To achieve 20 kwh we need 500 pounds of car batteries. Hmm, that's about the same as the Tesla unit. Of course, adding the charger and inverter will probably add 100 lbs, and the supporting structure would be another hundred or so. A typical car battery costs $200 or more and weighs 45 pounds; we need 11 of these, perhaps 12 for good measure (even numbers are better for balancing charging and discharge circuits). Not knowing what large, fast chargers cost, nor large inverters, this is still looking pretty good at a battery cost of about $2,400.

That sets some sidebars on direct electricity storage. But I've been wondering about gravitational energy storage. This picture shows one company's proposal for using concrete cylinders and a six-arm crane that uses wind turbine-generated electricity to raise the cylinders, and generates electricity when they are lowered during periods of less wind. They claim overall efficiency of 90%.

The concept is by Energy Vault. The tower is 33 storeys tall (about 100 meters). However, I couldn't make much sense of the numbers in the report, which describes 5,000 concrete blocks with a total weight of 35 tons. That doesn't add up; it works out to 14 pounds per block. I suspect the actual weight of each block is 1,400 lb (640 kg). Such a cylinder would have a volume of a little less than a third of a cubic meter (or about 1/3 of a cubic yard), which is almost twice the volume of an oil drum. From the picture, that looks about right.

What kind of weight would I need to make a backyard gravitational power "tower"? In most neighborhoods, one cannot construct anything taller than a 2-story house; perhaps 30 feet (9 m) at the very most. More figuration is needed, to convert weight and distance to watt-hours.

• One horsepower is 33,000 ft-lbs per minute, or 550 ft-lbs per second
• One kilowatt = 1.36 HP = 738 ft-lbs/s
• 1 kwh = 738×3,600 = 2,692,800 ft-lbs = 372,400 kg-m
• 20 kwh comes to 7,448 Tonne-m (nearly 7½ million kg-m)
• Divide by 9: About 830 Tonnes (910 tons) raised to a 9 m height

Ok, just to run my overnight energy storage, I need to be able to raise and lower upwards of 900 one-ton blocks, using motors that can function as generators with a 4000-watt capacity. Standard concrete weighs 2,400 kg (2.4 Tonnes) per cubic meter, or 4,000 lbs (2 tons) per cubic yard. 830/2.4 = 346 cubic meters of concrete, a mass 18 by 19 meters, one meter thick (English units: 455 cubic yards, about 64 by 64 feet, and 3 feet thick).

My back yard is rather small, only 30 feet deep, though it's 90 feet wide. I do have a side yard that's plenty large enough. I wonder what my neighbors would think if I built a structure as tall as my house, with a footprint of more than 4,000 sq ft. And the big electric motors/generators would most likely whine when in use. I'd probably have to remove some soil and seat it 2-3 feet below grade (with drainage infrastructure for rainy weather) to keep the total height below 30 feet.

Maybe I can use iron (I can't afford 900 tons of lead!). Iron's density is 7,874 kg/cubic meter, or 3.28 times that of concrete. This would shrink the volume needed to 105.5 cubic meters or 138 cubic yards. Reducing the vertical depth to 2 feet means the footprint would be no longer 4,000 sq ft but 1,860 sq ft, or about 43 feet square. My 2,000 square-foot house is two storeys, so it's size is only 25 by 40 feet.

The picture is a bit ridiculous. The primary virtue of such a system is that its energy capacity doesn't reduce over time the way the Powerwall will. But it illustrates the amazing energy density of batteries, even lead-acid car batteries, compared to big blocks of iron or concrete and big motors to lift and lower them.

This is a fun mental exercise. It convinces me to wait for better batteries to be developed. Systems based on something besides lithium, for sure! Sodium-sulfur can have 2-4 times the energy density of lithium-ion, and sodium-ion is in the two-times range. Recent research has produced prototypes that don't have to be kept at 300°C (570°F) to operate efficiently. I can wait.

A hierarchy of energy

kw: references, energy, combustion, fission, fusion, kerr black holes, annihilation

From time to time I find or gather a synthesis of related ideas, and this is as good a place to store them as any. Reading recently about the energy released from matter falling into a spinning black hole, often called a Kerr black hole after the New Zealander who first worked out the math, I sought to place it in the context of more familiar sources of energy. Not that a Kerr black hole is going to be easy to harness as a "source" of energy, but perhaps a sufficiently advanced civilization could do so.

Sundry classifications have been made of speculative levels of civilization, and they frequently hinge on the level of energy use. Here I present one based on energy source. The characteristic figure for an energy source is the fraction of the mass-energy that is made available at each level.

Level 0 would have to be pre-Human, based on what follows. The only source of energy is food energy, a type of slow combustion; overt, external combustion is not used.

The primary energy source of Level 1 civilizations is combustion. The genus Homo began using combustion (very) roughly a million years ago, and that is still the primary source of energy used by the human race, though our fuel supply has changed from time to time. One of our most efficient combustion systems is hydrogen-oxygen, so far primarily used for rocket propulsion. Burning a gram of hydrogen releases about 142 kJ of energy, while also consuming 8 grams of oxygen. By Einstein's energy equation, e=mc², we find that the combustion products must be lighter than the uncombusted gases by 15.8 trillionths of a gram per gram of hydrogen burnt, or 1.75 trillionths of a gram per gram of combined gases. Note that hydrocarbon combustion is somewhat less energy intensive on a gram per gram basis, when oxygen consumption is included.

Some nations are on the boundary of Level 2, in that a large fraction of their total energy is derived by nuclear fission. In the fission of U-235, a large variety of reactions may occur, but on average we find that the fission products and neutrons emitted weigh about 0.2 AMU less than the original uranium nucleus. Thus the mass conversion is about 0.00085 grams per gram of uranium fuel. This is about 490 million times as much energy per gram as hydrogen combustion.

Nuclear fusion has been a holy grail for many. Success in developing economical fusion power would yield a Level 3 civilization. Note, however, that the 4H-to-He system is only about 8 times as powerful as uranium fission, or 0.0071 grams per gram of H consumed. The methods being studied are mostly based on deuterium fusion, which has very little advantage over uranium fission, on a grams released per gram converted basis. If we could, however, capture large fractions of the Sun's energy output (such as by a Dyson sphere), we could sidestep our way to energy use characteristic of this Level, as the Sun uses the 4-hydrogen reaction.

Now we come to Kerr black holes. The theoretical maximum energy that could be extracted is 28% of the rest mass of the infalling matter. Thus, if a Level 4 civilization could harness a rapidly spinning black hole (in the range of 10,000-100,000 rotations per second if it is stellar-sized), 0.28 grams of effective mass-energy per gram consumed is 39 times the energy available from hydrogen fusion.

Is a higher proportion of energy release attainable? Could a Level 5 civilization arise that makes effective use of total annihilation? In the Star Trek civilization, "antimatter generators" produce antimatter fuel for use in starships (at least), moderated by "dilithium" and "rubindium" and other special materials. The matter-antimatter reaction does result in annihilation, but if you are generating the antimatter somewhere, rather than having found an antimatter mine, it may be assumed that you are using energy characteristic of a lower Level to do so.

For those of us on the threshold of Level 2, we find there is no political will, and great public opposition, to expanding energy sources that release large amounts of radioactivity or produce radioactive waste. Thus I favor sidestepping our way to Level 3 by effective use of solar energy. So far, we barely have a bit of a toe in the water on this. The side of earth facing the Sun at any one time intercepts about 64 quadrillion watts of solar energy, at ground level. Total human energy use is presently less than 20 trillion watts, or about 1/3200 of what is available. Of course, paving land and sea with solar cells is a formula for ecological suicide, but covering 0.1% of the total (because much is in darkness at any one time) would be enough to meet all our needs and then some.

A rosy look at energy future

kw: energy, speeches

I have been out of pocket a few days, at a company conference. I was particularly interested in today's keynote speech, given by Dr. Stephen Chu, the Nobel laureate physicist who is the Secretary of Energy. The opening section of his address was the most compelling case I have so far seen supporting the theory that humans are at least partly responsible for the current climatic warming, AKA "global warming". While he acknowledged that scientists are still uncertain about all the parameters, that uncertainty is a scattering of opinion around a very bad prognosis. For example, the carbon dioxide proportion of the atmosphere has varied quite a lot over the past million years, but has not exceeded 350 ppm. The present level is 420 ppm, and the debate is whether, by the year 2100, it will be closer to 550 ppm or 900 ppm. There is no realistic scenario of future energy use that predicts a level below 500 ppm.

Much more of his talk was devoted to some hopeful trends. The best batteries now used in hybrid and electric autos have a performance factor of about 200, which I think is in w-h/kg. 200 something, anyway. Prototypes in the lab right now are performing in the 400 range, and technologies being studied promise to push energy densities into the 600-800 range. That means a battery pack for the Chevy Volt, which can drive the car about 60-80 miles between charges, might one day be replaced with one that can take it 250-300 miles, yet be recharged in less than an hour. That's great, as long as you don't have to replace a $5,000 pack every year or so. They need to last ten years, like the rest of the car.

He also showed a number of "experience charts", showing how the price of an item drops as manufacturers get more and more experience making it. For certain appliances, such as refrigerators, not only has the cost of making them gone down, but the imposition of standards for energy use have made their lifetime cost go down even more, yet the purchase price has continued to fall. Compared to 1975, a refrigerator is twice as large, costs less (in constant dollars), and uses one-third the energy. Other appliances have followed a similar path.

In answer to a question, he said that the level of energy per capita translates into GDP in an almost linear fashion, up to a point, then levels off. That means that many of the world's poorest couple of billion people can be brought to a much more prosperous level with an increase in energy use that is quite modest, compared with the "western standard".

I am inclined to take another look at the speech, which was recorded, and take notes. I want to check some of the rosy predictions he makes. If enough of them bear up, I will have a greater level of comfort that the world we are leaving to our children and grandchildren may not be the dystopian nightmare so many of my contemporaries predict.

Minimizing energy cost on the interplanetary express

kw: analysis, energy, space travel, economics

It is frustrating. Space fiction is filled with 35^th Century, or 135^th Century folks flitting about space in their interstellar runabouts, going to Mars or Neptune like we might go to Omaha or Yokohama, and catching some kind of hyperspace express to cruise out to Aldebaran or some other locale a few hundred parsecs distant, for a rather modest cost.

The fact is, space travel requires a lot of energy, and energy costs something. At the moment, though, it costs more than it should because a space vehicle has to carry the fuel to make its entire journey, and we take advantage of tricks like using the atmosphere of Earth to slow the return module to parachute speed (or landing speed, for a shuttle-type vehicle, not that any currently exist).

A number of new technologies have been proposed to get a vehicle off the Earth without using any on-board fuel, such as laser propulsion. I don't propose to get into such a discussion here. Rather, given that some kind of remote assist is developed, what is the lowest cost of getting something from point A to point B?

For comparison, we might consider that it costs a few dollars ($20 or less) to ship a kilogram of any legal substance via public carriers or even the US Postal Service, say from western Pennsylvania to Massachusetts, a distance of about 800 km. If I were to personally deliver the package by driving both ways, it would cost more. My car gets 30 miles per gallon, or 48 km/gal, on the highway. That's also about 12.7 km/l. Gas (petrol) cost alone for the 1,600 km trip comes to 33.3 gallons at $4, or $133. But that's partly because the material being moved now weighs a metric ton, not just one kg. On a per kilo basis, the cost is thirteen cents. So the USPS or other carrier is only a few percent efficient, compared to my own costs, if I were carrying lots of packages in my one-ton car (and if I worked for free).

In actuality, the energy costs to the Postal Service or FedEx or whoever, are still a minor portion of total costs. But let's consider that energy-only cost a baseline: $0.133/kg to go 1,600 km, or about 8 cents per 1,000 km. Now let's consider moving a more modest 200 km, but straight up. That'll get us in the neighborhood of the ISS. USPS might charge only $5, but I doubt it. We'll consider achieving orbital velocity separately.

What's the gravitational potential difference between Earth's surface and an altitude of 200 km? Considering the Earth as a point object, which is mathematically valid from its surface outward, potential V = -GM/r. At the surface, V_s = -6.64×10^-11×5.97×10²⁴/6.37×10⁶ = -6.255×10⁷ J/kg. Add 200 to the 6,370 km radius of the earth and recalculate, and we get V_orbit = -6.065×10⁷ J/kg. Subtracting these two, we get 1.90×10⁶ J/kg. So what does that amount of energy cost?

In the US, gasoline costs $4 per gallon, and has an energy content of 3.2×10⁷ J/l or 1.2×10⁸ J/gal. The most efficient methods of using gasoline are only 30% efficient, however, so the usable energy cost is about ten cents per megajoule, or 10^-7 $/J. Liquid hydrogen can be bought for about $0.40/l, and running the figures I find it costs about 20% more than gasoline for a joule of energy obtained from hydrogen. We can use the 10¢/MJ figure for our calculations. Thus, lifting a kilogram to orbital altitude costs nineteen cents.

Keeping it there requires moving it at orbital velocity, however, which is 7,910 m/s. E_k = ½MV² = 3.13×10⁷ J/kg. This comes to $3.13/kg, more than sixteen times the cost of achieving altitude. That's an important fact about getting around in space: δv (delta vee), or change in velocity, can be a larger factor than the gravitational potential. However, at this point, let's consider that, if we truly could achieve costs as low as $3/kg to get an object into orbit, it would be revolutionary: Attaining orbit presently costs about $10,000/kg. With such a reduced cost we could think about visiting the outer planets.

The major factor going from planet to planet is the gravitational potential relative to the Sun. At Earth, this comes to -8.85×10⁸ J/kg; at Neptune, it is much smaller: -2.95×⁷ J/kg. Subtracting these yields 8.55×10⁸ J/kg, which costs $88.50/kg. Getting out of Earth's gravity well is a fraction of this (about $6/kg, similar to the cost of going to the Moon). But now there is a time factor to consider. It takes fifteen to twenty years to get to Neptune on a ballistic orbit. In other words, if some kind of energy deposition mechanism gives our one kilogram package an initial velocity of about 40 km/s, it will coast out to Neptune, and have nearly no kinetic energy left, but it might take twenty years or more.

If we increase that to Solar escape velocity, measured from Earth vicinity, or 42 km/s, it'll arrive with velocity comparable to Neptune's orbital velocity of 5.4 km/s. However, it will have required 15-16 years to travel some five billion km. To get there in one year requires a lot more initial velocity, and almost as much δv at the other end to slow down. Initial velocity needs to be of the order of 158 km/s. Kinetic energy comes to 1.25×10¹⁰, which costs $1,250. So, take your choice. A decade and a half for $88.50 or a one year delivery time for $1,250, plus another thousand-dollar slowdown fee.

These costs assume we are not accelerating fuel, just the kilogram we want to deliver. Perhaps there will one day be installations, set up by earlier generations (plural, to be sure!), that use something like laser boosting to push a projectile to these velocities, or to push against an incoming package to slow it back down. These costs are just the incremental energy costs for moving a package about. I am ignoring amortization of sunk costs (you know, the odd quadrillion or quintillion dollars to get the laser boosters into Earth orbit—or onto the Moon—, Neptune orbit, and sundry places between).

If getting to Earth orbit drops to some $3/kg, then there is some hope for a 100 kg guy like me to afford an orbital vacation. I'd gladly pay $300 each way for tickets to visit a space station, particularly if a more comfortable one than the ISS is assembled. Of course, I suspect the daily room cost will be more than at your average hotel! Going to Neptune would be more costly. Since the express trip takes a year each way (I don't have thirty years for the slower round trip!), I need some support systems, including plenty of water, air and food. Call it a couple tons. At $1,250/kg to start, $1,200 to stop, and then the same amounts for the return trip, the energy costs alone will come to nearly ten million dollars.

I don't have even one million dollars, nor much prospect of obtaining it. Vacationing in the outer solar system will probably always remain available only to the rich. What about going farther out? Stellar travel has huge time requirements, and to make it practical, the energy has to be balanced against that time.

For a number of reasons, various researchers have settled on a tradeoff velocity of 0.13c, or 39,000 km/s. That'll get you to Proxima Centauri in 33 years and Barnard's Star in 46 years. What is the energy cost? You really need laser boosting, at least at the near end, to make it practical. The relativistic kinetic energy is 7.69×10¹⁴ J/kg, at a cost of $76.9 million/kg. How many kg will a vehicle weigh, that can keep a few people alive for decades? 10,000 tons? Assuming that would do it, the energy cost is now $769 billion, or about what each of the "stimulus" packages of 2008 and 2009 cost the US government.

That is the bottom line. Sending people to a star is going to cost trillions. It may be that bombing around the inner solar system will become affordable for many of us, but even visiting the outer solar system will never be within reach to folks like me. Just getting a useful-sized spacecraft up to 0.13c is a project for a nation or a consortium of nations. Getting a kg or two in the form of a Von Neumann self-replicating robot up to such a speed is no cheap undertaking, and sending along fuel enough to allow it to slow down is another huge cost, but much less than the cost of sending people.

This doesn't mean I don't think it will be done. I expect it to take a lot more time, ingenuity, and fortitude. We especially need the planetary will to invest in technologies that enable getting off Earth, into orbit, and off to the planets, at the very least, at greatly reduced incremental cost. In today's dollars, we spent a pretty good chunk of a trillion dollars going to the Moon a few times. With any luck at all, we ought to be able to return to the Moon for one percent of that cost. The Moon is a good base for big lasers to accelerate packages once they are outside the atmosphere; an Earth-based laser facility ought to be able to get them that far. That is step one, and further steps are up to future generations of dreamers.

If you think OIL is a trap...

kw: book reviews, science fiction, energy, political drama

I got about halfway through The Green Trap by Ben Bova and realized he'd presented all the technical secrets; the second half of the book would continue the chase-capture-violence-escape-sex sequence that I'd already grown tired of. So I "ruined" it and jumped to the last twenty pages to see the denouement. The title actually gives it away; there is no happy ending here. The "hero" dies, the girl proves false, the minor villain does die while the major one wins everything. Kind alike real life.

The core idea: Cyanobacteria (which I once knew as "blue-green algae") have been cracking water for its hydrogen, and releasing the oxygen they don't want just then, for three billion years. A little genetic tinkering, and they can be forced to overdo it, so they release both gases, which people can then separate and burn together to recapture the solar energy the critters used in the first place.

Secondary idea: Should it work, it's worth billions, or trillions, but will wreck the current oil-based economy, foreign relations, and a number of other dominoes. So of course, people get killed right and left by the varying powerful factions.

Interesting side idea: Rather than have big central hydrogen-producing stations, put a bug-containing membrane in each vehicle to produce it on demand.

Bottom line: Cyanobacteria are less than five percent efficient in catching sunlight. Suppose they are tinkered with until they catch 25%. Then you need that membrane to be the size of a barn, about ten meters on a side, to grab sufficient sunlight to power a 20HP (i.e. quite small) car motor. Secondly, consider the waste problem. Photosynthesis runs best when a plant or green cell is growing and multiplying, so you create a lot of waste. LOTS of waste. Perhaps a ton per driving mile. We have silicon solar cells that do 25% now, and all the waste that is going to be produces has been produced once you buy it.

Bova's writing style keeps one going, but the content eventually wore me down so I skipped half the book. It didn't take much thought to see the flaws enumerated above, so I give him only a D+ for this idea.