Category Archives: electricity

Hydrogenation, how we’ve already entered the hydrogen economy

The hydrogen economy is generally thought to come in some distant future, where your car (and perhaps your home) runs on hydrogen, and the hydrogen, presumably, is made by clean nuclear or renewable solar or wind power. This is understood to be better than the current state of things where your car runs on dirty gasoline, and your home runs on coal or gas, except when the sun is shining bright and the wind is blowing hard. Our homes and cars can not run on solar or wind alone, although solar cells have become quite cheap, because solar power is only available in the daytime, basically for 6 hours, from about 9AM to 3PM. Hydrogen has been proposed as a good way to store solar and wind energy that you can’t use, but it’s not easy to store hydrogen — or is it? I’d like to suggest that, to a decent extent, we already store green hydrogen and use it to run our trucks. We store this hydrogen in the form of Diesel fuel, so you don’t realize it’s hydrogen.

Much of the oil in the United States these days comes from tar sands and shale. It doesn’t flow well at room temperature, and is too heavy and gooey for normal use. We could distill this crude oil and use only the light parts, but that would involve throwing away a huge majority of the oil. Instead we steam reform it to gasoline, ethylene and other products. The reaction is something like this, presuming an input feed of naphtha, C10H8:

C10H8 + 2 H2O –> C7H8 + C2H4 + CO2.

The C2H4 component is ethylene. We use it to make plastics. The C7H8 is called toluene. It is a component of high octane gasoline (octane rating about 114). The inventor of the process, Eugene Jules Houdry claimed to have won WWII for the allies because his secret process (Houdryflow catalytic cracking) allowed high production of lots of gasoline of very high octane, giving US and British planes and trucks higher mpg than the Germans or Japanese had. It was a great money maker, but companies can make even more by adding hydrogen.

Schematic of the hydrocracking process, from the US energy information agency

Over the last 2-3 decades, refineries have been adding catalytic hydrogenation processes. These convert high octane aromatic products, like toluene to low -octane diesel and jet fuel. These products sell for more. Aromatic toluene is exposed to hydrogen at about 500°C and 300 psi (20 bar) to produce heptane, an excellent diesel fuel with about 7% more energy content than toluene per gallon.

C7H8 + 4H2 –> C7H16.

Diesel fuel sell for about 20% more than gasoline per gallon, in part because of the higher energy content, and because Diesel engines are more efficient than gas engines. What’s more, toluene expands as it’s converted to heptane. One gallon of toluene converts to 1.16 gallons of heptane. As a result hydrogenation adds about 40% to the sales price per molecule. Refineries have found that they can make significant money this way if they can buy cheap hydrogen. Over the last few years, several refineries in Norway and Texas (high sun and wind areas) have added hydrogenators along with electrolysis units to produce the cheap hydrogen when no one needs the unwanted electricity generated when supply exceeds demand. Here is an analysis of the thermodynamics of this type of hydrogen generation.

Robert Buxbaum, May 11, 2023

Plans to Raise-the-Dead-Sea

The Dead Sea in Israel is a popular tourist attraction and health resort-area. It is also the lowest point on the planet, with a surface about 430m below sea level. Its water is saturated with an alkaline salt, and quite devoid of life, and it’s shrinking fast, loosing about 1 m in height every year. The Jordan river water that feeds the sea is increasingly drawn off for agriculture, and is now about 10% of what it was in the 1800s. The Dead Sea is disappearing fast, a story that is repeated with other inland seas: the Aral Sea, the Great Salt Lake, etc. In theory, one could reverse the loss using sea water. In theory, you could generate power dong this too: 430m is seven times the drop-height of Niagara Falls. The problem is the route and the price.

Five (or six) semi-attractive routes have been mapped out to bring water to the Dead Sea, as shown on the map at right. The shortest, and least expensive is route “A”. Here, water from the Mediterranean enters a 12 km channel near Haifa; it is pumped up 50m and travels in a pipe for about 52 km over the Galilean foothills, exiting to a power station as shown on the elevation map below. In the original plan the sea water feeds into the Jordan river, a drop of about 300m. The project had been estimated to cost $3 B. Unfortunately, it would make much of the Jordan river salty. It was thus deemed unacceptable. A variation of this would run the seawater along the Jordan in a pipe or an open channel. This would add to the cost, and would likely diminish the power that could be extracted, but you would not contaminate the Jordan.

A more expensive route, “B”, is shorter but it requires extensive tunneling under Jerusalem. Assuming 20 mies of tunnel at $500 MM/mile, this would cost $10B. It also requires the sea water to flow through the Palestinian West Bank on its way to the sea. This is politically sensitive and is unlikely to be acceptable to the West Bank Palestinians.

Vertical demand of the northern route

Two other routes, labeled “C” and “D” are likely even more expensive than route B. They require the water to be pumped over the Judaean hills near Bethlehem, south of Jerusalem. That’s perhaps 600m up. The seawater would flow from Ashkalon or Gaza and would enter the Dead Sea at Sodom, near Masada. Version C is the most politically acceptable, since it’s short and does not go through Palestinian land. Also, water enters the dead sea at its saltiest point so there is no disruption of the environment. Route D is similar to C, somewhat cheaper, but a lot more political. It goes through Gaza.

The longest route, “E” would go through Jordan taking water from the Red Sea. Its price tag is said to be $10 B. It’s a relatively flat route, but still arduous, rising 210m. As a result it’s not clear that any power would be generated. A version of this route could send the water entirely through Israel. It’s not clear that this would be better than Route C. Looking things over, it was decided that only routes that made sense are those that avoided Palestinian land. An agreement was struck with Jordan to go ahead with route D, with construction to begin in 2021. The project has been on hold though because of cost, COVID, and governmental inertia.

In order to make a $5-10B project worthwhile, you’ll have to generate $500MM to $1B/year. Some of this will come from tourism, but the rest must come from electrical power generation. As an estimate of power generation, let’s assume that that the flow is 65 m3/s, just enough to balance the evaporation rate. Assuming a 400 m power drop and an 80% efficient turbine, we should generate 80% of 255 MWe = about 204 MWe on average. Assuming a value of electricity of 10¢/kWh, that translates to $20,000/ hour, or $179 million per year. This is something, but not enough to justify the cost. We might increase the value of the power by including an inland pond for water storage. This would allow power production to be regulated to times of peak load, or it could be used for recreation, fish-farming, or cooling a thermal power station up to 1000 MWe. These options almost make sense, but with the tunnel prices quoted, the project is still too expensive to make sense. It is “on hold” for now.

It’s not like the sea will disappear if nothing is done. With 10% of the original in-flow of water to the Dead Sea, it will shrink to 10% its original size, and then stop shrinking. At that point evaporation will match in-flow. One could add more fresh water by increasing the flow from the sea of Galilee, but that water is needed. When more water is available, more is taken out for farming. This is what’s happened to the Arial Sea — it’s now about 10% the original size, and quite salty.

Elon Musk besides the prototype 12 foot diameter tunnel.

There’s a now a new tunnel option though and perhaps these routes deserve a second look: Elon Musk claims his “Boring company” can bore long tunnels of 12 foot diameter, for $10-20 MM/mile. This should be an OK size for this project. Assuming he’s right about the price, or close to right, the Dead Sea could be raised for $1B or so. At that price-point, it makes financial sense. It would even make sense if one built multiple seapools, perhaps one for swimming and one for energy storage, to be located before the energy-generating drop, and another for fish after. There might even be a pool that would serve as coolant for a thermal power plant. Water in the desert is welcome, even if it’s salt water.

Robert Buxbaum, February 14, 2023.

A clever range extender for EVs

Electric vehicles work well for short trips between places where you can charge with cheap electricity. Typically that’s trips from home to a nearby place of work, and to local shopping malls and theaters with low-cost charge spots. If you drive this way, you’ll pay about 3.2¢/mile for home electricity, instead of about 17¢/mile for gasoline transport (e.g. 24 mpg with $4/gallon gas). Using an EV also saves on oil changes, transmission, air filters, belts, etc., and a lot of general complexity. Battery prices are still high, but much lower than they were even a few years ago.

The 10 kW Aquarius Engine is remarkably small and light, about 10kg (22 lb).

EVs are less attractive for long trips, especially in the cold. Your battery must provide the heat, as there is no waste heat from the engine. Expect to have to recharge every 200 -250 miles, or perhaps twice in the middle of a long trip. Each charge will take a half-hour or more, and fast charging on the road isn’t low cost. Expect to pay about 15¢/mile, nearly as much as for gasoline. See my full comparison of the economics here.

One obvious solution is to have two cars: a short commuter and an EV. Another solution is a hybrid. The Toyota’s Prius and the Chevy Volt were cutting edge in their day, but people don’t seem to want them. These older hybrids provided quick fill-ups, essentially infinite range, and about double the gas milage of a standard automobile, 30-45 mpg. The problem is you have even more complexity and maintenance than with even a gas automobile.

Aquarius liner engine as a range extender

I recently saw a small, simple, super-efficient (they say) gas engine called Aquarius. It provides 9.5 kW electric output and weighs only 22 lbs (10 kg), see picture above. A Tesla S uses about 16 kW during highway driving, implying that this engine will more than double the highway range of a Tesla S at minimal extra weight and complexity. It also removes the fear of being stranded on the highway, far from the nearest charge-station.

The energy efficiency is 34%, far higher than that for normal automobile engines, but fairly typical of floating piston linear engines. The high efficiency of these engines is partly due to the lack of tapper valves, risers, crank-shaft, and partially due to the fact that the engine always runs at its maximum power. This is very close to the maximum efficiency point. Most car engines are over sized (200 hp or so) and thus must run at a small fraction of their maximum power. This hurts the efficiency, as I discuss here. The Aquarius Engine makes electricity by the back-forth motion of its aligner rods moving past magnetic stator coils. Slots in the piston rod and in the side of the cylinder operate as sliding valves, like in a steam engine. First versions of the Aquarius Engine ran on hydrogen, but the inventors claim it can also run on gasoline, and presumably hythane, my favorite fuel, a mix of hydrogen and natural gas.

At the moment shown, slit valves in the piston rod are open to both cylinder chambers. The explosion at left will vent to the exhaust at left and out the manifold at top. The sliding valve is currently sending fresh air into the cylinder at right, but will soon send it into both cylinders to help scavenge exhaust and provide for the next cycle; engine speed and impression are determined by the mass of the piston.

A video is available to show the basic operation (see it here). The drawing at right is from that video, modified by me. Air is drawn into the engine through a sliding valve at the middle of the cylinder. The valve opens and closes depending on where the piston is. At the instant shown in the picture, the valve is open to the right. Air enters that chambered is likely exiting through slits in the hollow piston rod. It leaves through the manifold t the top, pushing exhaust along with it. When the piston will have moved enough, both the slits and the intake will close. The continued piston motion (inertially driven) will compress the air for firing. After firing, the piston will move left, generating electricity, and eventually opening the slit-valve in the piston to allow the exhaust to leave. When it moves a little further the intake will open.

The use of side-opening exhaust valves is a novelty of the “Skinner UniFlow” double-acting, piston steam engines, seen on the Badger steamship on Lake Michigan. It’s one of my favorite steam engine designs. Normally you want a piston that is much thicker than the one in the drawing. This option is mentioned in the patent, but not shown in the drawing.

Aquarius is not the only company with a free-piston range extender. Toyota built a free-piston extender of similar power and weight; it was more complex but got higher efficiency. It has variable compression though, and looks like a polluter. (the same problems might affect the Aquarius) They dropped the project in 2014. Deutsch Aerospace has a two headed version that’s more powerful, but long and heavier: 56kg and 35kW. Lotus has a crank-piston engine, also 56kg, 35kW; it’s more complex and may have service life issues, but it’s compact and relatively light, and it probably won’t pollute. Finally, Mazda is thinking of bringing back its Wankel rotary engine as a range extender. Any of these might win in the marketplace, but I like the Aquarius engine for its combination of light weight, compact size, and simplicity.

This is not to say that Aquarius motors is a good investment. Aquarius automotive went public on the Toronto exchange in December, 2021, AQUA.TA. The company has no profits to date, and the only chance of them making a profit resides in them getting a good licensing deal from an established company. The major car companies have shown no interest so far, though they clearly need something like this. Their plug in hybrids currently use standard-size, 4 stroke engines: 110-150 kW, 100-150 kg, complex, and low efficiency. Consumers have not been impressed. Tesla autos could benefit from this engine, but Musk shows no interest either.

Robert Buxbaum May 5, 2022. I have no stock in Aquarius motors, nor have I received any benefits from them, or any auto company.

Lithium Battery prices fell 98%, solar prices fell more.

Most people have heard of Moor’s law, the law that computing power keeps doubling every two years, with the price remaining the same, but the same law is observed with other tech products, notably lithium ion batteries and solar cells.

By my calculation the price of lithium ion batteries has fallen 98% so far, at a rate of 12.5% per year. That’s a remarkable drop given that the chemistry has hardly changed. The size has dropped too; it’s nowhere near as much as the price but enough to make batteries a reasonable choice for powering automobiles, scooters, and power tools. Batteries still lack the range and fast charging for some applications, but even there the low cost means that hybrids become attractive, combining for cars and truck, the long range of gas with a reduced cost per mile. The rate of decrease suggests that prices will be below $100 per kWh by 2025. That’s an $8000 cost for a battery powered car with 300 miles of range.

As for where the electricity comes from, the price of electricity is going up and becoming less reliable. In part that’s because of regulations on coal and nuclear power and the inherent problems with large-scale wind and solar. But decentralized solar may turn out to be a winner. Solar prices have fallen 99.6% since 1976. Even though the rate of decrease is slower, about an 8% drop in price per year, there is a sense that solar power has entered the mainstream. Combined with cheap, home batteries, it may soon make sense to power your home and car by solar cells on the house; there isn’t enough area on a car to quite power it.

Robert Buxbaum, September 27, 2021

Automobile power 2021: Batteries vs gasoline and hydrogen

It’s been a while since I did an assessment of hydrogen and batteries for automobile propulsion, and while some basics have not changed, the price and durability of batteries has improved, the price of gasoline has doubled, and the first commercial fuel cell cars have appeared in the USA. The net result (see details below) is that I find the cost of ownership for a gasoline and a battery car is now about the same, depending on usage and location, and that hydrogen, while still more pricey, is close to being a practical option.

EV Chargers. They look so much cooler than gasoline hoses, and the price per mile is about the same.

Lithium battery costs are now about $150/kwh. That’s $10,000 for a 70 kWh battery. That’s about 1/5 the price of a Tesla Model 3. The reliability that Tesla claims is 200,000 miles or more, but that’s with slow charging. For mostly fast charging, Car and Driver’s expectation is 120,000 miles. That’s just about the average life-span of a car these days.

The cost of the battery and possible replacement adds to the cost of the vehicle, but electricity is far cheaper than gasoline, per mile. The price of gasoline has doubled to, currently, $3.50 per gallon. A typical car will get about 24 mpg, and that means a current operation cost of 14.6¢/mile. That’s about $1,460/year for someone who drives 10,000 miles per year. I’ll add about $150 for oil and filter changes, and figure that operating a gas-powered car engine costs about $1,610 per year.

If you charge at home, your electricity costs, on average, 14¢/kWh. This is a bargain compared to gasoline since electricity is made from coal and nuclear, mostly, and is subsidized while gasoline is taxed. At level 2 charging stations, where most people charge, electricity costs about 50¢/kWh. This is three times the cost of home electricity, but it still translates to only about $32 for a fill-up that take 3 hours. According to “Inside EVs”, in moderate temperatures, a Tesla Model 3 uses 14.59 kWh/100 km with range-efficient driving. This translates to 11.7¢ per mile, or $1170/year, assuming 10,000 miles of moderate temperature driving. If you live in moderate climates: Californian, Texas or Florida, an electric car is cheaper to operate than a gasoline car. In cold weather gasoline power still makes sense since a battery-electric car uses battery power for heat, while a gasoline powered car uses waste heat from the engine.

Battery cars are still somewhat of more expensive than the equivalent gasoline car, but not that much. In a sense you can add $400/year for the extra cost of the Tesla above, but that just raises the effective operating cost to about $1,570/year, about the same as for the gasoline car. On the other hand, many folks drive less than 50 miles per day and can charge at home each night. This saves most of the electric cost. In sum, I find that EVs have hit a tipping point, and Tesla lead the way.

Now to consider hydrogen. When most people think hydrogen, they think H2 fuel, and a PEM fuel cell car. The problem here is that hydrogen is expensive, and PEM FCs aren’t particularly efficient. Hydrogen costs about $10/kg at a typical fueling station and, with PEM, that 1 kg of hydrogen takes you only about 25 miles. The net result is that the combination hydrogen + PEM results in a driving cost of about 40¢/mile, or about three times the price of gasoline. But Toyota has proposed two better options. The fist is a PEM hybrid, the hydrogen Prius. It’s for the commuter who drives less than about 40 miles per day. It has a 10kWh battery, far cheaper than the Tesla above, but enough for the daily commute. He or she would use charge at home at night, and use hydrogen fuel only when going on longer trips. If there are few long trips, you come out way ahead.

Toyota 2021 Mirai, hydrogen powered vehicle

Toyota also claims to have a hydrogen powered Corolla or debut in 2023. This car will have a standard engine, and I would expect (hope) will drive also — preferably — on hythane, a mix of hydrogen and methane. Hythane is much cheaper per volume, and more energy dense, see my analysis. While Toyota has not said that their Corolla would run on hythane, it is supposed to have an internal combustion engine, and that suggests that hythane will work in it.

A more advanced option for Toyota or any other car/truck manufacturer would be to design to use solid oxide fuel cells, SOFCs, either with hydrogen or hythane. SOFCs are significantly more efficient than PEM, and they are capable of burning hythane, and to some extent natural gas too. Hythane is not particularly available, but it could be. Any station that currently sells natural gas could sell hythane. As for delivery to the station, natural gas lines already exist underground, and the station would just blend in hydrogen, produced at the station by electrolysis, or delivered. Hythane can also be made locally from sewer gas methane, and wind-power hydrogen. Yet another SOFC option is to start with natural gas and convert some of the natural gas to hydrogen on-board using left-over heat from the SOFC. I’ve a patent for this process.

Speaking of supply network, I should mention the brown outs we’ve been having in Detroit. Electric cars are part of the stress to the electric grid, but I believe that, with intelligent charging (and discharging) the concern is more than manageable. The driver who goes 10,000 miles per year only adds about 2,350 kWh/year of extra electric demand. This is a small fraction of the demand of a typical home, 12,154 kWh/year.It’s manageable. Then again, hythane adds no demand to the electric grid and the charge time is quicker — virtually instantaneous.

Robert Buxbaum, September 3, 2021

A useful chart, added September 20, 2021. Battery prices are likely to keep falling.

The solar powered automobile

The typical car has about 60 ft2 of exposed, non glass surface area, of which perhaps 2/3 is exposed to the sun at any time. If you covered the car with high-quality solar cells, the surfaces in the sun would generate about 15W per square foot. That’s about 600W or 0.8 horsepower. While there is no-one would would like to drive a 0.8 hp car, there is a lot to be said for a battery powered electric car that draws 6000 Wh of charge every sunny day — 6kWh per day– moving or parked — especially if you use the car every day, but don’t use it for long trips.

Owners of the Tesla sedans claim you can get 2.5 to 3 miles/kWhr for average driving suggesting that if one were to coat a sedan with solar cells, one day in the sun would generate 15 to 20 miles worth of cost-free driving power. This is a big convenience for those who only drive 15 to 20 miles each day, to work and back. As an example, my business is only 3 miles from home. That’s enough for the lightyear one, pictured below. The range would be higher for a car with a lighter battery pack, and some very light solar cars that have been proposed.

Lightyear one solar boosted plug in electric vehicle.

Solar power also provides a nice security blanket boost for those who are afraid of running out of charge on the highway, or far from home. If a driver gets worried during the day, he or she could stop at a restaurant, or park in the sun, and get enough charge to go a few miles, especially if you stick to country roads. Unlike gas-powered cars, where mpg is highest on the highway, electric vehicles get more miles per kWh at low speeds. It seems to me that there is a place for the added comfort and convenience of solar.

Robert Buxbaum, May 21, 2021

China keeps building coal-fired plants so we can close ours.

Part of the mandate to the 2020 election was to join with Europe and the rest of the western world in agreeing to stop the use of coal. It’s a low cost way to generate energy. Of course we still like to buy things, and we’ve largely turned to China, a country that still burns coal, and thus makes things cheap. The net result of this shift to Chinese goods is that China keeps building coal-fired plants while we shut ours. As it happens, China is worse than the US in terms of CO2 per output, but at least when China pollutes, we don’t see the smoke directly, and we don’t see their new coal plants at all. So we feel better buying things from China than from the US. Besides, slave labor is cheap.

From th eEconomist, December 2020.

Buying Chinese goods is good for the importers, and for the non-manufacturing consumer, at least in the short term. It has the effect of exporting jobs though, and eventually we have to support the displaced workers. It also means we don’t keep up our manufacturing technology. Long term, that affects innovation, and that starts to displace other industries. Antibiotic production has already left the US and along with it semiconductors. Still, we feel good about it since the Chinese don’t let us see the slave labor camps. We do get to see the haze of the pollution.

The Chinese expect this pattern to continue. China is building new coal-fired plants at a furious rate. Presently China has most of the world’s coal-fired power plants. Mostly these are only 4 to 12 years old, far younger than our forty year old plants China plans to build more, and keeps encouraging us to shut down ours. Even 10 years ago, China lead the world in CO2 output. And their fraction of the CO2 keeps climbing.

China is popular with the press. In part, I expect, that’s because they pay the international experts. lAlso, writers and editors are consumers industrial products, but not manufacturers. Consumers benefit from slave labor, or maybe not, but displaced American workers certainly suffer. Also, of course, the news requires pictures and personal stories to keep viewer interest. If you can’t get pictures of young protesters, like Grey Thunberg, you can get an interesting story. Our Chinese pollution is out of sight, and not in the press.

Robert Buxbaum, January 6, 2021. BTW, if we wanted preserve jobs and stop CO2 pollution, we’d go nuclear.

Water Towers, usually a good thing.

Most towns have at least one water tower. Oakland county, Michigan has four. When they are sized right, they serve several valuable purposes. They provide water in case of a power failure; they provide increased pressure in the morning when people use a lot of water showering etc.; and they allow a town to use smaller pumps and to pump with cheaper electricity, e.g. at night. If a town has no tower, all these benefits are gone, but a town can still have water. It’s also possible to have a situation that’s worse than nothing. My plan is to show, at the end of this essay, one of the ways that can happen. It involves thermodynamic properties of state i a situation where there is no expansion headspace or excess drain (most towers have both).

A typical water tower — spheroidal design. A tower of the dimensions shown would contain about 1/2 million gallons of water.

The typical tower stands at the highest point in the town, with the water level about 170 feet above street level. It’s usable volume should be about as much water as the town uses in a typical day. The reason for the height has to do with the operating pressure of most city-level water pipes. It’s about 75 psi and each foot of water “head” gives you about 0.43 psi. You want pressures about 75 psi for fire fighting, and to provide for folks in apartment buildings. If you have significantly higher pressures, you pay a cost in electricity, and you start losing a lot of water to leaks. These leaks should be avoided. They can undermine the roads and swallow houses. Bob Dadow estimates that, for our water system the leakage rate is between 15 and 25%.

Oakland county has four water towers with considerably less volume than the 130 million gallons per day that the county uses. I estimate that the South-east Oakland county tower, located near my home, contains, perhaps 2 million gallons. The other three towers are similar in size. Because our county’s towers are so undersized, we pay a lot for water, and our water pressure is typically quite low in the mornings. We also have regular pressure excursions and that leads to regular water-boil emergencies. In some parts of Oakland county this happens fairly often.

There are other reasons why a system like ours should have water towers with something more like one days’ water. Having a large water reserve means you can benefit from the fact that electric prices are the lowest at night. With a days’ volume, you can avoid running the pumps during high priced, day times. Oakland county loses this advantage. The other advantage to having a large volume is that it gives you more time to correct problems, e.g. in case of an electric outage or a cyber attack. Perhaps Oakland thinks that only one pump can be attacked at one time or that the entire electric grid will not go out at one time, but these are clearly false assumptions. A big system also means you can have pumps powered by solar cells or other renewable power. Renewable power is a good thing for reliability and air pollution avoidance. Given the benefits, you’d expect Oakland county would reward towns that add water towers, but they don’t, as best I can tell.

Here’s one way that a water column can cause problems. You really need those pressure reliefs.

Now for an example of the sort of things that can go wrong in a water tower with no expansion relief. Every stand-pipe is a small water tower, and since water itself is incompressible, it’s easy to see that a small expansion in the system could produce a large pressure rise. The law requires that every apartment hose water system has to have expansion relief to limit these increases; The water tower above had two forms of reliefs, a roof vent, and an overflow pipe, both high up so that pressure could be maintained. But you can easily imagine a plumber making a mistake and installing a stand pipe without an expansion relief. I show a system like that at left, a 1000 foot tall water pipe, within a skyscraper, with a pump at the bottom, and pipes leading off at the sides to various faucets.

Lets assume that the pressure at the top is 20 psi, the pressure at the bottom will be about 450 psi. The difference in pressure (430 psi) equals the weight of the water divided by the area of the pipe. Now let’s imagine that a bubble of air at the bottom of the pipe detaches and rises to the top of the pipe when all of the faucets are closed. Since air is compressible, while water is not, the pressure at the bubble will remain the same as the bubble rises. By the time the bubble reaches the top of the pipe, the pressure there will rise to 450 psi. Since water has weight, 430 psi worth, the pressure at the bottom will rise to 880 psi = 450 + 430. This is enough to damage pump and may blow the pipes as well. A scenario like this likely destroyed the New Horizon oil platform to deadly consequences. You really want those pressure reliefs, and you want a competent plumber / designer for any water system, even a small one.

Robert Buxbaum, September 28- October 6, 2019. I ran for water commissioner is 2016.

Why the earth is magnetic with the north pole heading south.

The magnetic north pole, also known as true north, has begun moving south. It had been moving toward the north pole thought the last century. It moved out of Canadian waters about 15 years ago, heading toward Russia. This year it passed as close to the North pole as it is likely to, and begun heading south (Das Vedanga, old friend). So this might be a good time to ask “why is it moving?” or better yet, “Why does it exist at all?” Sorry to say the Wikipedia page is little help here; what little they say looks very wrong. So I thought I’d do my thing and write an essay.

The motion of the magnetic (true) north pole over the last century; it's nearly at the north pole.

Migration of the magnetic (true) north pole over the last century; it’s at 8°N and just passed the North Pole.

Your first assumption of the cause of the earth’s magnetic field would involve ferromagnetism: the earth’s core is largely iron and nickel, two metals that permanent magnets. Although the earth’s core is very hot, far above the “Curie Temperature” where permanent magnets form, you might imagine that some small degree of magnetizability remains. You’d be sort of right here and sort of wrong; to see why, lets take a diversion into the Curie Temperature (Pierre Curie in this case) before presenting a better explanation.

The reason there is no magnetism above the Curie temperature is similar to the reason that you can’t have a plague outbreak or an atom bomb if R-naught is less than one. Imagine a magnet inside a pot of iron. The surrounding iron will dissipate some of the field because magnets are dipoles and the iron occupies space. Fixed dipole effects dissipate with a distance relation of r-4; induced dipoles with a relation r-6. The iron surrounding the magnet will also be magnetized to an extent that augments the original, but the degree of magnetization decreases with temperature. Above some critical temperature, the surrounding dissipates more than it adds and the effect is that the original magnetic effect will die out if the original magnet is removed. It’s the same way that plagues die out if enough people are immunized, discussed earlier.

The earth rotates, and the earth's surface is negatively charged. There is thus some room for internal currents.

The earth rotates, and the earth’s surface is negatively charged. There is thus some room for internal currents.

It seems that the earth’s magnetic field is electromagnetic; that is, it’s caused by a current of some sort. According to Wikipedia, the magnetic field of the earth is caused by electric currents in the molten iron and nickel of the earth’s core. While there is a likely current within the core, I suspect that the effect is small. Wikipedia provides no mechanism for this current, but the obvious one is based on the negative charge of the earth’s surface. If the charge on the surface is non-uniform, It is possible that the outer part of the earth’s core could become positively charged rather the way a capacitor charges. You’d expect some internal circulation of the liquid the metal of the core, as shown above – it’s similar to the induced flow of tornadoes — and that flow could induce a magnetic field. But internal circulation of the metallic core does not seem to be a likely mechanism of the earth’s field. One problem: the magnitude of the field created this way would be smaller than the one caused by rotation of the negatively charged surface of the earth, and it would be in the opposite direction. Besides, it is not clear that the interior of the planet has any charge at all: The normal expectation is for charge to distribute fairly uniformly on a spherical surface.

The TV series, NOVA presents a yet more unlikely mechanism: That motion of the liquid metal interior against the magnetic field of the earth increases the magnetic field. The motion of a metal in a magnetic field does indeed produce a field, but sorry to say, it’s in the opposing direction, something that should be obvious from conservation of energy.

The true cause of the earth’s magnet field, in my opinion, is the negative charge of the earth and its rotation. There is a near-equal and opposite charge of the atmosphere, and its rotation should produce a near-opposite magnetic field, but there appears to be enough difference to provide for the field we see. The cause for the charge on the planet might be due to solar wind or the ionization of cosmic rays. And I notice that the average speed of parts of the atmosphere exceeds that of the surface —  the jet-stream, but it seems clear to me that the magnetic field is not due to rotation of the jet stream because, if that were the cause, magnetic north would be magnetic south. (When positive charges rotate from west to east, as in the jet stream, the magnetic field created in a North magnetic pole a the North pole. But in fact the North magnetic pole is the South pole of a magnet — that’s why the N-side of compasses are attracted to it, so … the cause must be negative charge rotation. Or so it seems to me.  Supporting this view, I note that the magnet pole sometimes flips, north for south, but this is only following a slow decline in magnetic strength, and it never points toward a spot on the equator. I’m going to speculate that the flip occurs when the net charge reverses, thought it could also come when the speed or charge of the jet stream picks up. I note that the magnetic field of the earth varies through the 24 hour day, below.

The earth's magnetic strength varies regularly through the day.

The earth’s magnetic strength varies regularly through the day.

Although magnetic north is now heading south, I don’t expect it to flip any time soon. The magnetic strength has been decreasing by about 6.3% per century. If it continues at that rate (unlikely) it will be some 1600 years to the flip, and I expect that the decrease will probably slow. It would probably take a massive change in climate to change the charge or speed of the jet stream enough to reverse the magnetic poles. Interestingly though, the frequency of magnetic strength variation is 41,000 years, the same frequency as the changes in the planet’s tilt. And the 41,000 year cycle of changes in the planet’s tilt, as I’ve described, is related to ice ages.

Now for a little math. Assume there are 1 mol of excess electrons on a large sphere of the earth. That’s 96500 Coulombs of electrons, and the effective current caused by the earth’s rotation equals 96500/(24 x3600) = 1.1 Amp = i. The magnetic field strength, H =  i N µ/L where H is magnetizability field in oersteds, N is the number of turns, in this case 1, µ is the magnetizability. The magnetizability of air is 0.0125 meter-oersteds/ per ampere-turn, and that of a system with an iron core is about 200 times more, 2.5 meter-tesla/ampere-turn. L is a characteristic length of the electromagnet, and I’ll say that’s 10,000 km or 107 meters. As a net result, I calculate a magnetic strength of 2.75×10-7 Tesla, or .00275 Gauss. The magnet field of the earth is about 0.3 gauss, suggesting that about 100 mols of excess charge are involved in the earth’s field, assuming that my explanation and my math are correct.

At this point, I should mention that Venus has about 1/100 the magnetic field of the earth despite having a molten metallic core like the earth. It’s rotation time is 243 days. Jupiter, Saturn and Uranus have greater magnetic fields despite having no metallic cores — certainly no molten metallic cores (some theorize a core of solid, metallic hydrogen). The rotation time of all of these is faster than the earth’s.

Robert E. Buxbaum, February 3, 2019. I have two pet peeves here. One is that none of the popular science articles on the earth’s magnetic field bother to show math to back their claims. This is a growing problem in the literature; it robs science of science, and makes it into a political-correctness exercise where you are made to appreciate the political fashion of the writer. The other peeve, related to the above concerns the game it’s thoroughly confusing, and politically ego-driven. The gauss is the cgs unit of magnetic flux density, this unit is called G in Europe but B in the US or England. In the US we like to use the tesla T as an SI – mks units. One tesla equals 104 gauss. The oersted, H is the unit of magnetizing field. The unit is H and not O because the English call this unit the henry because Henry did important work in magnetism One ampere-turn per meter is equal to 4π x 10−3 oersted, a number I approximated to 0.125 above. But the above only refers to flux density; what about flux itself? The unit for magnetic flux is the weber, Wb in SI, or the maxwell, Mx in cgs. Of course, magnetic flux is nothing more than the integral of flux density over an area, so why not describe flux in ampere-meters or gauss-acres? It’s because Ampere was French and Gauss was German, I think.

Alkaline batteries have second lives

Most people assume that alkaline batteries are one-time only, throwaway items. Some have used rechargeable cells, but these are Ni-metal hydride, or Ni-Cads, expensive variants that have lower power densities than normal alkaline batteries, and almost impossible to find in stores. It would be nice to be able to recharge ordinary alkaline batteries, e.g. when a smoke alarm goes off in the middle of the night and you find you’re out, but people assume this is impossible. People assume incorrectly.

Modern alkaline batteries are highly efficient: more efficient than even a few years ago, and that always suggests reversibility. Unlike the acid batteries you learned about in highschool chemistry class (basic chemistry due to Volta) the chemistry of modern alkaline batteries is based on Edison’s alkaline car batteries. They have been tweaked to an extent that even the non-rechargeable versions can be recharged. I’ve found I can reliably recharge an ordinary alkaline cell, 9V, at least once using the crude means of a standard 12 V car battery charger by watching the amperage closely. It only took 10 minutes. I suspect I can get nine lives out of these batteries, but have not tried.

To do this experiment, I took a 9 V alkaline that had recently died, and finding I had no replacement, I attached it to a 6 Amp, 12 V, car battery charger that I had on hand. I would have preferred to use a 2 A charger and ideally a charger designed to output 9-10 V, but a 12 V charger is what I had available, and it worked. I only let it charge for 10 minutes because, at that amperage, I calculated that I’d recharged to the full 1 Amp-hr capacity. Since the new alkaline batteries only claimed 1 amp hr, I figured that more charge would likely do bad things, even perhaps cause the thing to blow up.  After 5 minutes, I found that the voltage had returned to normal and the battery worked fine with no bad effects, but went for the full 10 minutes. Perhaps stopping at 5 would have been safer.

I changed for 10 minutes (1/6 hour) because the battery claimed a capacity of 1 Amp-hour when new. My thought was 1 amp-hour = 1 Amp for 1 hour, = 6 Amps for 1/6 hour = ten minutes. That’s engineering math for you, the reason engineers earn so much. I figured that watching the recharge for ten minutes was less work and quicker than running to the store (20 minutes). I used this battery in my firm alarm, and have tested it twice since then to see that it works. After a few days in my fire alarm, I took it out and checked that the voltage was still 9 V, just like when the battery was new. Confirming experiments like this are a good idea. Another confirmation occurred when I overcooked some eggs and the alarm went off from the smoke.

If you want to experiment, you can try a 9V as I did, or try putting a 1.5 volt AA or AAA battery in a charger designed for rechargeables. Another thought is to see what happens when you overcharge. Keep safe: do this in a wood box outside at a distance, but I’d like to know how close I got to having an exploding energizer. Also, it would be worthwhile to try several charge/ discharge cycles to see how the energy content degrades. I expect you can get ~9 recharges with a “non-rechargeable” alkaline battery because the label says: “9 lives,” but even getting a second life from each battery is a significant savings. Try using a charger that’s made for rechargeables. One last experiment: If you’ve got a cell phone charger that works on a car battery, and you get the polarity right, you’ll find you can use a 9V alkaline to recharge your iPhone or Android. How do I know? I judged a science fair not long ago, and a 4th grader did this for her science fair project.

Robert Buxbaum, April 19, 2018. For more, semi-dangerous electrochemistry and biology experiments.