Author Archives: R.E. Buxbaum

About R.E. Buxbaum

Robert Buxbaum is a life-long engineer, a product of New York's Brooklyn Technical High School, New York's Cooper Union to Science and Art, and Princeton University where he got a PhD in Chemical Engineering. From 1981 to 1991 he was a professor of Chemical Engineering at Michigan State, and now runs an engineering shop in Oak Park, outside of Detroit, Michigan. REB Research manufactures and sells hydrogen generation and purification equipment. He's married with 3 wonderful children who, he's told, would prefer to not be mentioned except by way of complete, unadulterated compliments. As of 2016, he's running to be the drain commissioner/ water resources commissioner of Oakland county.

Alice’s Restaurant and Nuclear Waste

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It’s not uncommon for scientists to get inspiration from popular music. I’d already written about how the song ‘City of New Orleans’ inspires my view of the economics of trains, I’d now like to talk about dealing with nuclear waste, and how the song Alice’s Restaurant affects my outlook.

As I see it, nuclear power is the elephant in the room in terms of clean energy. A piece of uranium the size of a pencil eraser produces as much usable energy as three rail cars of coal. There is no air pollution and the land use is far less than for solar or wind power. The one major problem was what to do with the left over eraser-worth of waste. Here’s the song, it’s 18 1/2 minutes long. The key insight appeared in the sixth stanza: “…at the bottom of the cliff there was another pile of garbage. And we decided that one big pile Is better than two little piles…”

The best way to get rid of nuclear waste would be (as I’ve blogged) to use a fast nuclear reactor to turn the worst components into more energy and less-dangerous elements. Unfortunately doing this requires reprocessing, and reprocessing was banned by Jimmy Carter, one of my least favorite presidents. The alternative is to store the nuclear waste indefinitely, waiting for someone to come up with a solution, like allowing it to be buried in Yucca Mountain, the US burial site that was approved, but that Obama decided should not be used. What then? We have nuclear waste scattered around the country, waiting. I was brought in as part of a think-tank, to decide what to do with it, and came to agree with several others, and with Arlo Guthrie, that one big pile [of waste] Is better than two little piles. Even if we can’t bury it, it would be better to put the waste in fewer places (other countries bury their waste, BTW).

That was many years ago, but even the shipping of waste has been held up as being political. Part of the problem is that nuclear waste gives off hydrogen — the radiation knocks hydrogen atoms off of water, paper, etc. and you need to keep the hydrogen levels low to be able to transport the waste safely. As it turns out we are one a few companies that makes hydrogen removal pellets and catalysts. Our products have found customers running tourist submarines (lead batteries also give off hydrogen) and customers making sealed electronics, and we are waiting for the nuclear shipping industry to open up. In recent months, I’ve been working on improving our products so they work better at low temperature. Perhaps I’ll write about that later, but here’s where you’d go to buy our current products.

Robert Buxbaum, July 4, 2021. I’ve done a few hydrogen-related posts in a row now. In part that’s because I’d noticed that I went a year or two talking history and politics, and barely talking about H2. I know a lot about hydrogen — that’s my business– as for history or politics, who knows.

Adding H2 to an engine improves mpg, lowers pollution.

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I month ago, I wrote to endorse hythane, a mix of natural gas (methane) and 20-40% hydrogen. This mix is ideal for mobile use in solid oxide fuel cell vehicles, and not bad with normal IC engines. I’d now like to write about the advantages of an on-broad hydrogen generator to allow adjustable composition fuel mixes.

A problem you may have noticed with normal car engines is that a high hp engine will get lower miles per gallon, especially when you’re driving slow. That seems very strange; why should a bigger engine use more gas than a dinky engine, and why should you get lower mpg when you drive slow. The drag force on a vehicle is proportional to speed squared. You’d expect better milage at low speeds– something that textbooks claim you will see, counter to experience.

Behind these two problems are issues of fuel combustion range and pollution. You can solve both issues with hydrogen. With normal gasoline or Diesel engines, you get more or less the same amount of air per engine rotation at all rpm speeds, but the amount of air is much higher for big engines. There is a relatively small range of fuel-air mixes that will burn, and an even smaller range that will burn at low pollution. You have to add at least the minimal fuel per rotation to allow the engine to fire. For most driving that’s the amount the carburetor delivers. Because of gearing, your rpm is about the same at all speeds, you use almost the same rate of fuel at all speeds, with more fuel used in big engines. A gas engine can run lean, but normally speaking it doesn’t run at all any leaner than about 1.6 times the stoichiometric air-to-fuel mix. This is called a lambda of 1.6. Adding hydrogen extends the possible lambda range, as shown below for a natural gas – fired engine.

Engine efficiency when fueled with natural gas plus hydrogen as a function of hydrogen amount and lambda, the ratio of air to stoichiometric air.

The more hydrogen in the mix the wider the range, and the less pollution generally. Pure hydrogen burns at ten times stoichiometric air, a lambda of ten. There is no measurable pollution there, because there is no carbon to form CO, and temperature is so low that you don’t form NOx. But the energy output per rotation is low (there is not much energy in a volume of hydrogen) and hydrogen is more expensive than gasoline or natural gas on an energy basis. Using just a little hydrogen to run an engine at low load may make sense, but the ideal mix of hydrogen and ng fuel will change depending on engine load. At high load, you probably want to use no hydrogen in the mix.

As it happens virtually all of most people’s driving is at low load. The only time when you use the full horse-power is when you accelerate on a highway. An ideal operation for a methane-fueled car would add hydrogen to the carburetor intake at about 1/10 stoichiometric when the car idles, turning down the hydrogen mix as the load increases. REB Research makes hydrogen generators based on methanol reforming, but we’ve yet to fit one to a car. Other people have shown that adding hydrogen does improve mpg.

Carburetor Image from a course “Farm Power”. See link here. Adding hydrogen means you could use less gas.

Adding hydrogen plus excess air means there is less pollution. There is virtually no CO at idle because there is virtually no carbon, and even at load because combustion is more efficient. The extra air means that combustion is cooler, and thus you get no NOx or unburned HCs, even without a catalytic converter. Hydrogen is found to improve combustion speed and extent. A month ago, I’d applied for a grant to develop a hydrogen generator particularly suited to methane engines. Sorry to say, the DoT rejected my proposal.

Robert Buxbaum June 24, 2021

Upgrading landfill and digester gas for sale, methanol

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We live in a throw-away society, and the majority of it, eventually makes its way to a landfill. Books, food, grass clippings, tree-products, consumer electronics; unless it gets burnt or buried at sea, it goes to a landfill and is left to rot underground. The product of this rot is a gas, landfill gas, and it has a fairly high energy content if it could be tapped. The composition of landfill gas changes, but after the first year or so, the composition settles down to a nearly 50-50 mix of CO2 and methane. There is a fair amount of water vapor too, plus some nitrogen and hydrogen, but the basic process is shown below for wood decomposition, and the products are CO2  and methane.

System for sewage gas upgrading, uses REB membranes.

C6 H12 O6  –> 3 CO2  + 3 CH4 

This mix can not be put in the normal pipeline: there is too much CO2  and there are too many other smelly or condensible compounds (water, methanol, H2S…). This gas is sometimes used for heat on site, but there is a limited need for heat near a landfill. For the most part it is just vented or flared off. The waste of a potential energy source is an embarrassment. Besides, we are beginning to notice that methane causes global-warming with about 50 times the effect of CO2, so there is a strong incentive to capture and burn this gas, even if you have no use for the heat. I’d like to suggest a way to use the gas.

We sell small membrane modules too.

The landfill gas can be upgraded by removing the CO2. This can be done via a membrane, and REB Research sells a membranes that can do this. Other companies have other membranes that can do this too, but ours are smaller, and more suitable to small operations in my opinion. Our membrane are silicone-based. They retain CH4 and CO and hydrogen, while extracting water, CO2 and H2S, see schematic. The remainder is suited for local use in power generation, or in methanol production. It can also be used to run trucks. Also the gas can be upgraded further and added to a pipeline for shipping elsewhere. The useless parts can be separated for burial. Find these membranes on the REB web-site under silicone membranes.

Garbage trucks in New York powered by natural gas. They could use landfill gas.

There is another gas source whose composition is nearly identical to that of landfill gas; it’s digester gas, the output of sewage digesters. I’ve written about sewage treatment mostly in terms of aerobic bio treatment, for example here, but sewage can be treated anaerobically too, and the product is virtually identical to landfill gas. I think it would be great to power garbage trucks and buses with this. Gas. In New York, currently, some garbage trucks are powered by natural gas.

As a bonus, here’s how to make methanol from partially upgraded landfill or digester gas. As a first step 2/3 of the the CO2 removed. The remained will convert to methanol. by the following overall chemistry:

3 CH4 + CO2 + 2 H2O –> 4 CH3OH. 

When you removed the CO2., likely most of the water will leave with it. You add back the water as steam and heat to 800°C over Ni catalyst to make CO and H2. That’s done at about 800°C and 200 psi. Next, at lower temperature, with an appropriate catalyst you recombine the CO and H2 into methanol; with other catalysts you can make gasoline. These are not trivial processes, but they are doable on a smallish scale, and make economic sense where the methane is essentially free and there is no CNG customer. Methanol sells for $1.65/gal when sold by the tanker full, but $5 to $10/gal at the hardware store. That’s far higher than the price of methane, and methanol is far easier to ship and sell in truckload quantities.

Robert Buxbaum, June 8, 2021

The solar powered automobile

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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

Brown’s gas for small scale oxygen production.

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Some years ago I wrote a largely negative review of Brown’s gas, but the COVID crisis in India makes me want to reconsider. Browns gas can provide a simple source of oxygen for those who are in need. First, an explanation, Browns gas is a two-to-one mix of hydrogen and oxygen; it’s what you get when you do electrolysis of water without any internal separator. Any source of DC electricity will do, e.g. the alternator of a car or a trickle charger of the sort folks buy for their car batteries, and almost any electrode will do too (I’d suggest stainless steel). You can generate pressure just by restricting flow from the electrolysis vessel, and it can be a reasonable source of small-scale oxygen or hydrogen. The reaction is:

H2O –> H2 + 1/2 O2.

The problem with Brown’s gas is that it is explosive, more explosive than hydrogen itself, so you have to handle it with care; avoid sparks until you separate the H2 from the O2. Even the unseparated mix has found some uses, e.g. as a welding gas, or for putting in cars to avoid misfires, increase milage, and decrease pollution. I think that methanol reforming is a better source of automotive hydrogen: hydrogen is a lot safer than this hydrogen-oxygen mix.

Browns gas to oxygen for those who need it.

The mix is a lot less dangerous if you separate the oxygen from the hydrogen with a membrane, as I show in the figure. at right. If you do this it’s a reasonable wy to make oxygen for patients who need oxygen. The electrolysis cell can be a sealed bottle with water and the electrodes; add a flow restriction as shown to create the hydrogen pressure that drives the separation. The power can be an automotive trickle charger. You can get this sort of membranes from REB Research, here and many other suppliers. REB provide consulting services if you like.

In a pinch, you don’t even need the membrane, by the way. You can rely on your lungs to make the separation. A warning, though, the mix is dangerous. Avoid all sparks. Also, don’t put salt into the water. You can can put in some baking soda or lye to speed the electrolysis, but If you put salt in, you’ll find you don’t make oxygen, but will instead make chlorine. And chlorine is deadly. If you’re not sure, smell the gas. If it smells acrid, don’t use it. This is the chlorine-forming reaction.

2NaCl + 2 H2O –> H2 + Cl2 + 2NaOH

Ideally you should vent the hydrogen stream out the window, but for short term, emergency use, the hydrogen can be vented into your home. Don’t do this if anyone smokes (not that anyone should smoke about someone on oxygen). This is a semi-patentable design, but I’m giving it away; not everything that can be patented should be.

Robert Buxbaum, May 13, 2021.

Hythane and fuel cells to power buses and trains.

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Fuel cells are highly efficient and hardly polluting. They have a long history of use in space, and as a power source for submarines. They are beginning to appear powering city buses and intercity trains, at least in Europe, but not so much in the US or Canada. The business case for fuel cells is that they provide clean electric power to the train or bus, without the need for overhead wires. Avoiding wires helps make up for the high cost of hydrogen as a fuel. The reluctance to switch to fuel cells is the US is due to the longer distances that must be covered. The very low volumetric energy density of hydrogen means you need many filling stations with hydrogen fuel cells, and many fill ups per trip.

Energy density CNG, hydrogen, hythane.

On a mass-basis, hydrogen is energy dense, with 1 kg providing the same energy as 2-3 kg of gasoline. The problem with hydrogen (aside from the cost) is that its mass density is very low, less than 50g/liter, even at high pressure. This is terribly un-dense on a volume basis. It would take 20 liters of high pressure hydrogen (about 5 gallons) to take a car or bus as far as with one gallon of gasoline. Even with a huge tank of high pressure hydrogen, 150 gallons or so, a cross country trip would require some 12 fill ups, one every 250 miles, and this is an annoyance, besides being an infrastructure problem.

Then there is cost. In California, hydrogen costs far more than gasoline, between $12 and $15 per kg. That’s ten times as expensive as gasoline on a weight basis and 4 times as expensive on an energy basis. What’s needed is a cheaper, more energy-dense version of hydrogen, ideally one that can be used in both fuel cells and IC engines, and the version I’d like to suggest is hythane, a mix of methane (natural gas) and 20-30% hydrogen.

Hythane dispenser

Hythane has about 3 times the volumetric energy density of hydrogen, and about 1/3 the price. It makes less CO and CO2 pollution because there is far less carbon. On an energy basis, hythane costs just slightly more than gasoline, and requires less infrastructure. Natural gas is cheap and available, delivered by pipeline, without the need for hydrogen delivery trucks. Because hythane has about three times the volumetric energy density of hydrogen, the tank described above, that would give a 250 mile ride with hydrogen, would give 750 miles with hythane. This means a lot fewer fueling stations are needed, and a lot fewer forced stops. As a bonus, hythane can be used in (some) IC engines as well as in fuel cells.

Hydrogen for hythane-automotive use can be made on site, by electrolysis of water. Because there is relatively little hydrogen in the mix, only 25% by volume, or 8% on an energy basis, there is relatively little burden on the electric grid, and fueling will be a lot faster than with battery chargers. Hythane is already in use in buses in China and Canada. These are normal combustion buses but hythane works even better — more efficiently — with fuel cells (solid oxide fuel cells) and thus hythane provides a path to efficiency and greater fuel cell use.

Hythane bus, Montreal.

Natural gas does not work as well in fuel cells; it requires a pre-reformer to make some H2, and even then tends to coke. To be used in most fuel cells, the methane has to be converted, at lest partially into hydrogen and this takes heat energy and water.

CH4 + H2O + energy –> 3H2 + CO

Reforming is a lot easier with hythane; it can be done within the fuel cell. Within a SOFC, the hydrogen combustion, H2 + 1/2 O2 –> H2O, provides heat and water that helps feed the reforming reaction and helps prevent coking. Long term, fuel cells will likely dominate the energy future, but for now it’s nice to have a fuel that will work well in normal IC engines too.

Robert Buxbaum, April 28, 2021

Are fewer people better?

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Part of the push to help the oppressed and save the plant is push to decrease the birthrate both in the developed and undeveloped world. Putting of childbirth is supposed to lead to a more meaningful life, while academic excellence is considered meaningful. Child-raising is considered male oppression of women, while writing mediocre poetry is, we’re told elevating, it’s finding your voice. It’s the new mood, at least in the developed world.

In the undeveloped world, political activism and wealth accumulation are presented as more meaningful, and fewer children is presented as a responsible route to wealth and happiness (see Indian advertisement below). My sense is otherwise, that children bring happiness and long term wealth. My sense is that the best two ways to change the world for the better is to work on yourself and to raise good children. And these Idas are connected; children are little mirrors, sometimes showing hidden flaws, sometimes revealing enthusiasm and greatnesses.

This month’s cover article of National Geographic includes economic justifications for fewer children and ecological justifications. Apparently we’re making life difficult for the polar bears. The assumption is that the bears like it cold, and their opinion is more important than that of animals that like it warm, like most humans.

There is also an assumption that there will be more jobs and better food if we have fewer children, or that people will be happier. Who are the “we” who are better off. I personally would not trade a billion randomly selected lives to lower the earth’s temperature 1 degree, or for the supposed happiness benefit of 1 million empty-nest households.

Robert Buxbaum, April 18, 2021. I like people more than polar bears, sue me.

Dark Academia, the new mood.

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Old libraries and old books play a big part in the aesthetic.

The movie version of academia is typically a leafy campus, with great libraries, bright minds, and deep intellectual discussions. It’s a happy grove where the young and talented go to bloom to superiority, eclipsing their parents and their well-meaning, but fuddy-duddy teachers. It’s also where oppressed middle-agers go to complete a journey of self -discovery. To the extent that professors are there in older movies, it’s to confer degrees and, eventually praise.

But there is a new mood in literature and movies where professors are sinister, and competition is darker and more dangerous place, both for the body and the soul. It’s called “Dark Academia.” Consider the recent hit movie and book, “The Secret History,” by Danna Tartt. It follows a talented person without any particular view or direction. The person arrives, looking to make friends and to become special, and through misguided efforts, students end up damaged or killed. Any friendships that result are sinister, and often exploitive.

An early version was Hitchcock’s “Rope,” where two students get excited by a professor expounding the ideas of Nietzsche. They go on to kill one of their fellows who they come to decide isn’t, quite as enlighten as they. Secret History is similar, except that the professor teaches Greek. Another early version was Frankenstein, whose early chapters are of crazed collegians pushing the limits of science in a dark laboratory and similarly dark library settings. For Dr. Frankenstein, the crushing pressure is from inside the student, and not so much from his professors or classmates. University is still a place of refuge, without the pressure of drugs, sex, or fashion.

Harry Potter and friends in dark academic garb. Casual, clean, active, hip-academic.

The evil professor trope of Dark Academia first appears in Harry Potter, I think. The school is both helpful and hurtful, both refuge and enemy. It’s education in a building that tries to trip you, with sadistic professors, plus slave labor, and some murderers or “death eaters.” There are friends too, with the friendship bound by fire-whiskey, or butter-beer, and an intense desire to excel over each other at ones craft, in this case magic. Fashion becomes important in dark academia. Harry Potter’s round glasses, robes, and school neckties, but the alcohol isn’t excessive in HP and the books are pretty chaste where sex is concerned.

Alcohol abuse, fashion, and sex are more central in “The Secret History”. There is a cultish professor, Morrow, and students fashions are described in detail. Most dress in tweeds, and all of them wear round glasses, like Harry Potter’s– in this case with metal rims. All are rich. And as in Hitchcock’s “Rope,” they conspire to murder the least special of their group in the goal of understanding the ancient Greeks. Unlike in Rope, they get away with it.

A yet more recent example is “Kill your darlings” — the main character is played by Daniel Radclift, the same actor who was Harry in the HP movies. It takes place in Columbia University in 1943-46 and portrays the young Alan Ginsberg. As in “Secret History” there is a cultish leader and a murder. Alan enters school not knowing what sort of poetry he’d like to write, or if he’ll write poetry. In the movie, Jack Kerouac, William Burrows and a few others who introduce him to drugs, including heroin, gay sex, wanton destruction, and benzedrine. As in Secret History, there are no bad effects from the drugs, though he tries suicide and one of his group murders another — the least special one as in other dark academia. He gets away with it, as in Secret History, the cult leader is rejected, and the others become special — a happy ending of sorts. Ginsberg writes a great “absurdist” essay and goes on to become a great poet.

Danna Tartt, author models the Dark Academic look. Notice the cigarette.

The mood of dark academia is a mix of repressed anger and innocence that takes place on a campus, but might as easily taken place in bohemian Paris. The movie architecture includes vast dining halls, gothic bell towers and forbidding libraries. The devoted student searches here for hidden light but finds only darkness. Murder follows. Students stare into space like Oscar Wilde with a heartburn, smoking like well-dressed longshoremen on break. See Danna Tartt at left.

The main contributions of Dark Academia is the fashion: Shades of brown, black and gray mostly, casual and active, but clean. The look says, “I’m both sexually active and criminally active; I do drugs think great thoughts, but don’t do homework. I might do murder too, but it’s OK since I plan to submit a killer final project. Morality is for losers, and “Genuine beauty is always quite alarming.” It’s a line from “The secret History,” appears, slightly altered, in Hitchcock’s “Rope.” The tremendous desire to be pure and special; great in a word, and that involves a destruction of the ordinary: an academic aesthetic where murder is the crowning creative act.

Robert Buxbaum, April 2-5, 2021.

A high minimum wage killed Detroit, perhaps Seattle and NYC too.

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In July, eitght years ago, Detroit filed for bankruptcy protection. The US was well into an economic expansion, but the expansion had largely bypassed Detroit. The Detroit area unemployment rate was 9.7%, and the Detroit city rate was 17%, among the highest in the nation. Tax income was not sufficient to pay retirement or current employees. The city was riven by corruption and crime, and attendance in school was dismal, less that 25% in some districts, about 55% as an overall average. Kids no longer saw a value in education. After bankruptcy, things started to improve dramatically.

Detroit area unemployment rate, 2005 to 2021.

The largest cause of the problem, and of the solution, in my opinion, was a high Detroit minimum wage that applied before bankruptcy and that was voided by bankruptcy. It was called a “living wage”. In 2013 it was $16/ hour and applied to any business that dealt with the city and did not offer health insurance (see more on the specifics here).The stated purpose was to insure that all workers could support a family of four in some middle-class standard, by one wage-earner working 40 hours per week. It was a view of Detroit family life and economic need that didn’t match Detroit reality. In practice most of Detroit were not 4 person, one wage-earner households. It meant that most Detroiters could not find jobs, since most companies worked in some way with the city. The only workers who could find jobs were those with special skills or political connections. The alternative was criminal business including drug sales, prostitution and burglary. The unemployment rate was 70% among Detroit’s teenagers.

The high minimum wage bought loyalty for Detroit’s political bosses; they gave out jobs for kickbacks, and some went to jail, including the mayor. Most Detroiters could not find jobs, though, and this especially hurt those looking for their first job: the job that would demonstrate that math and spelling were important; that you had to show up on time, dressed clean, and that you were not to insult the customers. High unemployment meant low tax revenue, made worse by high city employment costs for basic services: janitors, secretaries, and mail room personnel. The city was a mess.

When Detroit went bankrupt, among the first changes was to eliminate the $!6/hour living wage for employees and others doing business with the city. This helped bring the city budget into balance, and it brought in residents, businesses, and developers. By January 2020 Detroit’s unemployment rate had fallen to 6%, and Detroit metro unemployment had fallen to 4.2%, the lowest rates on record. Employment gives a motivation to stay in Detroit and to stay in school: there are jobs to be had for those who could add and spell. I covered these improvements here.

Seattle are unemployment rate 2015 to 2021. Seattle’s unemployment rate is now higher than Detroit’s.

Meanwhile, Seattle voted to raise their minimum wage to $15, with the change law taking effect in stages. The law fully came into effect three months ago, in January, 2021. New York voted for similar changes more recently. It is hard to be sure of the effect of the high minimum wage but already it seems to have hit employment. By the latest data, Seattle’s unemployment rate has risen to 6.9%. That’s higher than in Detroit, a real reversal. While unemployment in New York City has yet to rise much, they have seen a drop in rent rates while Detroit has seen a rise. New York’s are also moving to be more out of balance, something that leads to corruption and bankruptcy. We’ll see how this works out.

Robert Buxbaum, March 25, 2021. Among my first blog posts were complaints about Detroit’s high “living wage”, see here for example. As Puerto Rico slid into bankruptcy, I complained about the same thing.

The remarkable efficiency of 22 caliber ammunition.

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22 long rifle shells contain early any propellant.

The most rifle cartridge in the US today is the 22lr a round that first appeared in 1887. It is suitable to small game hunting and while it is less–deadly than larger calibers, data suggests it is effective for personal protection. It is also remarkably low cost. This is because the cartridge in almost entirely empty as shown in the figure at right. It is also incredibly energy efficient, that is to say, it’s incredibly good at transforming heat energy of the powder into mechanical energy in the bullet.

The normal weight of a 22lr is 40 grains, or 2.6 grams; a grain is the weight of a barley grain 1/15.4 gram. Virtually every brand of 22lr will send its bullet at about the speed of sound, 1200 ft/second, with a kinetic energy of about 120 foot pounds, or 162 Joules. This is about twice the energy of a hunting bow, and it will go through a deer. Think of a spike driven by a 120 lb hammer dropped from one foot. That’s the bullet from a typical 22lr.

The explosive combustion heat of several Hodgdon propellants.

The Hodgdon power company is the largest reseller of smokeless powder in the US with products from all major manufacturers, with products selling for an average of $30/lb or .43¢ per grain. The CCI Mini-Mag, shown above, uses 0.8 grains of some powder 0.052 grams, or about 1/3¢ worth, assuming that CCI bought from Hodgdon rather than directly from the manufacturer. You will notice that the energies of the powders hardly varies from type to type, from a low of 3545 J/gram to a high of 4060 J/gram. While I don’t know which powder is used, I will assume CCI uses a high-energy propellant, 4000 J/gram. I now calculate that the heat energy available as 0.052*4000 = 208 Joules. To calculate the efficiency, divide the kinetic energy of the bullet by the 208 Joules. The 40 grain CCI MiniMag bullet has been clocked at 1224 feet per second indicating 130 foot pounds of kinetic energy, or 176 J. Divide by the thermal energy and you find a 85% efficiency: 176J/ 208 J = 85%. That’s far better than your car engine. If the powder were weaker, the efficiency would have to be higher.

The energy content of various 22lr bullets shot from different length barrels.

I will now calculate the pressure of the gas behind a 22lr. I note that the force on the bullet is equal to the pressure times the cross-sectional area of the barrel. Since energy equals force times distance, we can expect that the kinetic energy gained per inch of barrel equals this force times this distance (1 inch). Because of friction this is an under-estimate of the pressure, but based on the high efficiency, 85%, it’s clear that the pressure can be no more than 15% higher than I will calculate. As it happens, the maximum allowable pressure for 22lr cartridges is set by law at 24,000 psi. When I calculate the actual pressure (below) I find it is about half this maximum.

The change in kinetic energy per inch of barrel is calculated as the change in 1/2 mv2, where m is the mass of the bullet and v is the velocity. There is a web-site with bullet velocity information for many brands of ammunition, “ballistics by the inch”. Data is available for many brands of bullet shot from gun barrels that they cut shorter inch by inch; data for several 22lr are shown here. For the 40 grain CCI MiniMag, they find a velocity of 862 ft/second for 2″ barrel, 965 ft/second for a 3″ barrel, 1043 ft/second for a 4″ barrel, etc. The cross-section area of the barrel is 0.0038 square inches.

Every 22 cartridge has space to spare.

Based on change in kinetic energy, the average pressure in the first two inches of barrel must be 10,845 psi, 5,485 psi in the next inch, and 4,565 psi in the next inch, etc. If I add a 15% correction for friction, I find that the highest pressure is still only half the maximum pressure allowable. Strain gauge deformation data (here) gives a slightly lower value. It appears to me that, by adding more propellant, one could make a legal, higher-performance version of the 22lr — one with perhaps twice the kinetic energy. Given the 1/3¢ cost of powder relative to the 5 to 20¢ price of ammo, I suspect that making a higher power 22lr would be a success.

Robert Buxbaum, March 18, 2021. About 10% of Michigan hunts dear every year during hunting season. Another 20%, as best I can tell own guns for target shooting or personal protection. Just about every lawyer I know carries a gun. They’re afraid people don’t like them. I’m afraid they’re right.