Category Archives: Engineering

Eight ways to not fix the tower of Pisa, and one that worked.

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You may know that engineers recently succeed in decreasing the tilt of the “leaning” tower of Pizza by about 1.5°, changing it from about 5.5° to about to precisely 3.98° today –high precision given that the angle varies with the season. But you may not know how that there were at least eight other engineering attempts, and most of these did nothing or made things worse. Neither is it 100% clear that current solution didn’t make things worse. What follows is my effort to learn from the failures and successes, and to speculate on the future. The original-tilted tower is something of an engineering marvel, a highly tilted, stone on stone building that has outlasted earthquakes and weathering that toppled many younger buildings that were built straight vertical, most recently the 1989 collapse of the tower of Pavia. Part of any analysis, must also speak to why this tower survived so long when others failed.

First some basics. The tower of Pisa is an 8 story bell tower for the cathedral next door. It was likely designed by engineer Bonanno Pisano who started construction in 1173. We think it’s Pisano, because he put his name on an inscription on the base, “I, who without doubt have erected this marvelous work that is above all others, am the citizen of Pisa by the name of Bonanno.” Not so humble then, more humble when the tower started to lean, I suspect. The outer diameter at the base is 15.5 m and the weight of the finished tower is 14.7 million kg, 144 million Nt. The pressure exerted on the soil is 0.76 MPa (110 psi). By basic civil engineering, it should stand straight like the walls of the cathedral.

Bonanno’s marvelous work started to sink into the soil of Pisa almost immediately, though. Then it began to tilt. The name Pisa, in Greek, means swamp, and construction, it seems, was not quite on soil, but mud. When construction began the base was likely some 2.5 m (8 feet) above sea level. While a foundation of clay, sand and sea-shells could likely have withstood the weight of the tower, the mud below could not. Pisano added length to the south columns to keep the floors somewhat level, but after three floors were complete, and the tilt continued, he stopped construction. What to do now? What would you do?

If it were me, I’d consider widening the base to distribute the force better, and perhaps add weight to the north side. Instead, Pisano gave up. He completed the third level and went to do other things. The tower stood this way for 99 years, a three-floor, non-functional stub. 

About 1272, another engineer, Giovanni di Simone, was charged with fixing the situation. His was the first fix, and it sort-of worked. He strengthened the stonework of the three original floors, widened the base so it wold distribute pressure better, and buried the base too. He then added three more floors. The tower still leaned, but not as fast. De Simone made the south-side columns slightly taller than the north to hide the tilt and allow the floors to be sort-of level. A final two stories were added about 1372, and then the first of the bells. The tower looked as it does today when Gallileo did his famous experiments, dropping balls of different size from the south of the 7th floor between 1589 and 1592.

Fortunately for the construction, the world was getting colder and the water table was dropping. While dry soil is stronger than wet, wet soil is more plastic. I suspect it was the wet soil that helped the tower survive earthquakes that toppled other, straight towers. It seems that the tilt not only slowed during this period but briefly reversed, perhaps because of the shift in center of mass, or because of changes in the sea level. Shown below is 1800 years of gauge-based sea-level measurements. Other measures give different sea-level histories, but it seems clear that man-made climate change is not the primary cause. Sea levels would continue to fall till about 1750. By 1820 the tilt had resumed and had reached 4.5°.

Sea level height history as measured by land gauges. Because of climate change (non man-made) the sea levels rise and fall. This seems to have affected the tilt of the tower. Other measures of water table height give slightly different histories, but still the sense that man change is not the main effect.

The 2nd attempt was begun in 1838. Architect, Alessandro Della Gherardesca got permission to dig around the base at the north to show off the carvings and help right the tower. Unfortunately, the tower base had sunk below the water table. Further, it seems the dirt at the base was helping keep the tower from falling. As Della Gherardesca‘s crew dug, water came spurting out of the ground and the tower tilted another few inches south. The dig was stopped and filled in, but he dig uncovered the Pisano inscription, mentioned above. What would you do now? I might go away, and that’s what was done.

The next attempt to fix the tower (fix 3) was by that self-proclaimed engineering genius, Benito Mussolini. In 1934. Mussolini had his engineers pump some 200 tons of concrete into the south of the tower base hoping to push the tower vertical and stabilize it. The result was that the tower lurched another few inches south. The project was stopped. An engineering lesson: liquids don’t make for good foundations, even when it’s liquid concrete. An unfortunate part of the lesson is that years later engineers would try to fix the tower by pumping water beneath the north end. But that’s getting ahead of myself. Perhaps Mussolini should have made tests on a model before working on the historic tower. Ditto for the more recent version.

On March 18, 1989 the Civic Tower of Pavia started shedding bricks for no obvious reason. This was a vertical tower of the same age and approximate height as the Pisa tower. It collapsed killing four people and injuring 15. No official cause has been reported. I’m going to speculate that the cause was mechanical fatigue and crumbling of the sort that I’ve noticed on the chimney of my own house. Small vibrations of the chimney cause bits of brick to be ejected. If I don’t fix it soon, my chimney will collapse. The wet soils of Pisa may have reduced the vibration damage, or perhaps the stones of Pisa were more elastic. I’ve noticed brick and stone flaking on many prominent buildings, particularly at joins in the chimney.

John Burland’s team cam up with many of the fixes here. They are all science-based, but most of the fixes made things worse.

In 1990, a committee of science and engineering experts was formed to decide upon a fix for the tower of Pisa. It was headed by Professor John Burland, CBE, DSc(Eng), FREng, FRS, NAE, FIC, FCGI. He was, at the time, chair of soil mechanics at the Imperial College, London, and had worked with Ove, Arup, and Partners. He had written many, well regarded articles, and had headed the geological aspects of the design of the Queen Elizabeth II conference center. He was, in a word, an expert, but this tower was different, in part because it was an, already standing, stone-on stone tower that the city wished should remain tilted. The tower was closed to visitors along with all businesses to the south. The bells were removed as well. This was a safety measure, and I don’t count it as a fix. It bought time to decide on a solution. This took two years of deliberation and meetings

In 1992, the committee agreed to fix no 4. The tower was braced with plastic-covered, steel cables that were attached around the second and third floors, with the cables running about 5° from the horizontal to anchor points several hundred meters to the north. The fix was horribly ugly, and messed with traffic. Perhaps the tilt was slowed, it was not stopped.

In 1993, fix number 5. This was the most exciting engineering solution to date: 600 tons of lead ingots were stacked around the base, and water was pumped beneath the north side. This was the reverse of the Mussolini’s failed solution, and the hope was that the tower would tilt north into the now-soggy soil. Unfortunately, the tower tilted further south. One of the columns cracked too, and this attempt was stopped. They were science experts, and it’s not clear why the solution didn’t work. My guess is that they pumped in the water too fast. This is likely the solution I would have proposed, though I hope I would have tested it with a scale model and would have pumped slower. Whatever. Another solution was proposed, this one even more exotic than the last.

For fix number 6, 1995, the team of experts, still overseen by Burland, decided to move the cables and add additional tension. The cables would run straight down from anchors in the base of the north side of the tower to ten underground steel anchors that were to be installed 40 meters below ground level. This would have been an invisible solution, but the anchor depth was well into the water table. So, to anchor the ground anchors, Burland’s team had liquid nitrogen injected into the ground beneath the tower, on the north side where the ground anchors were to go. What Burland did not seem to have realized is that water expands when it freezes, and if you freeze 40 meters of water the length change is significant. On the night of September 7, 1995, the tower lurched southwards by more than it had done in the entire previous year.  The team was summoned for an emergency meeting and the liquid nitrogen anchor plan was abandoned.

Tower with the two sets of lead ingots, 900 tons total, about the north side of the base. The weight of the tower is 14,700 tons.

Fix number 7: Another 300 tons of lead ingots were added to the north side as a temporary, simple fix. The fix seems to have worked stabilizing things while another approach was developed.

Fix number 8: In order to allow the removal of the ugly lead bricks another set of engineers were brought on, Roberto Cela and Michele Jamiolkowski. Using helical drills, they had holes drilled at an angle beneath the north side of the tower. Using hoses, they removed a gallon or two of dirt per day for eleven years. The effect of the lead and the dirt removal was to reduce the angle of the tower to 4.5°, the angle that had been measured in 1820. At this point the lead could be removed and tourists were allowed to re-enter. Even after the lead was removed, the angle continued to subside north. It’s now claimed to be 3.98°, and stable. This is remarkable precision for a curved tower whose tilt changes with the seasons. (An engineering joke: How may engineers does it take to change a lightbulb? 1.02).

The bells were replaced and all seemed good, but there was still the worry that the tower would start tilting again. Since water was clearly part of the problem, the British soils expert, Burland came up with fix number 9. He had a series of drainage tunnels built to keep the water from coming back. My worry is that this water removal will leave the tower vulnerable to earthquake and shedding damage, like with the Pavia tower and my chimney. We’ll have to wait for the next earthquake or windstorm to tell for sure. So far, this fix has done no harm.

Robert Buxbaum, October 9, 2020. It’s nice to learn from other folks mistakes, and embarrassments, as well as from their successes. It’s also nice to see how science really works, not with great experts providing the brilliant solution, but slowly, like stumbling in the dark. I see this with COVID-19.

If nothing sticks to teflon, how do you stick teflon to a pan? PFAS.

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When I was eight or nine year old, I went to the 1963-64 World’s Fair in New York. Among the attractions, in “the kitchen of the future”, I saw the first version of an amazing fry-pan that was coated with plastic. You could cook an egg on that plastic without any oil, and the egg didn’t stick. The plastic was called teflon, a DuPont innovation, whose molecule is shown below.

The molecular structure of Teflon. There is an interior carbon backbone that is completely enclosed with tightly bound fluorine atoms. The net result is a compound that does not bind readily to anything else.

Years later, I came to understand that Teflon’s high-temperature stability and non-stick properties derive from the carbon-fluorine bonds. These bonds are much stronger than the carbon-hydrogen bonds found in food, and most solid, organic things. Because of the strength of the carbon-fluorine bond, Teflon is resistant to oxidation, and to chemical interaction with other molecules, e.g. in food. It does not even interact with water, making it hydrophobic and non-wetting on metals. The carbon-carbon bonds in the middle remained high temperature stable, in part because they were completely shielded by the fluorine atoms.

This is a PFAS. The left side is just like teflon, and very hydrophobic. The right side is hydrophilic and highly bonding to pans, and many other things like water or cotton.

But as remarkable as teflon’s non-stick properties are, perhaps the most amazing thing was that it somehow sticks to the pan. For the first generation pans I saw, it didn’t stick very well. Still, the DuPont engineers had found a way to stick non-stick Teflon to a metal for long enough to cook many meals. If they had not found this trick, teflon would not have the majority of its value, but how did they do it? It turns out they used a thin coating of a di-functional compound called PFAS, a a polyfluoro sulphonyl (or polyfluoroalkyl) substance. The molecular structure of a common PFAS, is shown above.

Each molecule of PFAS has one end that’s teflon-like and another end that’s different. The non-Teflon end, in this case a sulfonyl group, is chosen to be both high temperature stable and sticky to metal oxides. The sulphonyl group above is highly polar, and acidic. Acidic will bind to bases, like metal oxides. The surface of the metal pan is prepared by applying a thin layer of oxide or amidine, making it a polar base. The PFAS is then applied, then Teflon. The Teflon-end of the PFAS is bound to teflon by the hydrophobicity of everything else rejecting it.

There are many other uses for PFAS. For example, PFAS is applied to clothing to make it wrinkle free and stain resistant. It can also be used as a super soap, making uncommonly stable foams and bubbles. It is also used in fire-fighting and plane de-icing. Finally, PFAS is the main component of Nafion, the most common membrane for PEM fuel cells. (I can think of yet other applications..) There is just one small problem with PFAS, though. Like teflon, this molecule is uncommonly stable. It doesn’t readily decompose in nature. That would be a small problem if we were sure that PFAS was safe. As it happens it seems safe, but we’re not totally sure.

The safety of PFAS was studied extensively before PFAS-teflon pans was put on the market, but the methodology has been questioned. Large doses of PFAS were fed to test animals, and their health observed. Since the test animals showed no real signs of ill-health though some showed a slight liver enlargement, PFAS was accepted as safe for humans at a lower exposure dose. PFAS was approved for use on pans and allowed to be dumped under conditions where humans would be exposed to 1/1000 of that used on the animals. The assumption was that there would be little or no health hazard at these low exposure levels.

But low risk is not no risk, and today one can sue for even the hint of an effect though use of a class action suit. That is, lawyers sue on behalf of all the people who might have been damaged. My city was sued successfully this way for complicity in sewage over-flows. Of course, since the citizens being paid by the suit are the same ones who have to pay for the damage, only the lawyers benefit. Still, the law is the law, and at least for some judges, putting anyone at risk is enough evidence of willful disregard to hand down a stinging judgement against the evil doer. Judges have begun awarding large claims for PFAS too. While no individual can get the claim more than a tiny amount of money, the lawyers can do very well.

There is no new evidence that PFAS is dangerous, but none is needed if you can get yourself the right judge. In this regard, an industry of judicial tourism has sprung up, where class-action lawyers travel to districts where the judges are favorable. For Teflon suits, the bust hunting grounds are in New York, New Hampshire, and California, and the worst are blood-red states like Wyoming and Utah. Just as different judges promote different precedents, different states allow vastly different PFAS concentrations in the water. A common standard, one used by Michigan, is 70 ppt, 1 billion times stricter than the amounts tested on animals. This is roughly 500 times stricter than the acceptable concentratios for lead, a known poison. The standard in New York is 7 times stricter than Michigan, 10 ppt. The standard in North Carolina is 140,000 ppt, in in several states there is no legal limit to PFAS dumping. There is no scientific logic to all of this, and skeptical view is that the states that rule more strictly for PFAS than lead do so make money for lawyers. Lead is everyone in the natural environment, so you can’t sue as easily for lead. PFAS is a man-made intruder, though, and a strict standard helps lawyers sue. You can find a summary of state by state regulations here.

Any guideline stricter than about 1000 ppt, presents a challenge to the water commissioner who must measure it and enforce the law. There are tricks, though. You can use the surfactant quality of PFAS to concentrate it by a factor of 100 or more. To do this, you take a sample of river water and create bubbles. Any bubbles that form will be highly concentrated in PFAS. Once PFAS can be identified this way, and the concentrators estimated, the polluters can be held liable. Whether we benefit from the strict rulings is another story. If I were making the law for Michigan, I’d probably choose a limit about 1 ppb, but I’m not making the law. The law, as written, may be an idiot, as Bumble said, but the Law is the Law.

In terms of Michigan fishing, while some rivers have PFAS concentrators above the MI-legal limit, they are generally not far over the line. I would trust the fish in the Huron River, even west of Wixom road but I’d suggest you avoid any foam you find floating there. The PFAS content of foam will be much higher than that of the water in general.

Robert E. Buxbaum, June 30, 2020, edited July 8, 2020. There are seven compounds known as PFAS’s: perfluorooctanesulfonic acid (PFOS), perfluorooctanoic acid (PFOA), perfluorononanoic acid (PFNA), perfluorohexanesulfonic acid (PFHxS), perfluoroheptanoic acid (PFHpA), and perfluorobutanesulfonic acid (PFBS).

Italian Engineering and the Kennedy assassination.

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There are several unbelievable assertions surrounding the Kennedy assassination, leading many to conclude that Oswald could not have killed Kennedy alone. I believe that many of these can be answered once you realize that Oswald used an Italian gun, and not a US gun. Italian engineering differs from our in several respects that derive from the aesthetic traditions of the countries. It’s not that our engineers are better or worse, but our engineers have a different idea of what good engineering is and thus we produce designs that, to an Italian engineer, are big, fat, slow, and ugly. In our eyes Italian designs are light, fast, pretty, low-power, and unreliable. In the movie, Ford vs Ferrari, the American designer, Shelby says that, “If races were beauty contests, the Ferrari would win.” It’s an American, can-do, attitude that rings hollow to an Italian engineer. 

Three outstanding questions regarding the Kennedy assassination include: How did Oswald fire three bullets, reasonably accurately in 5 to 8 seconds. How did he miss the limousine completely on the first, closest shot, then hit Kennedy twice on the next two, after previously missing on a close shot at retired general, Edwin Walker. And how could the second shot have gone through Kennedy’s neck, then through his wrist, and through Connolly twice, emerging nearly pristine. I will try to answer by describing something of the uniquenesses of the gun and bullets, and of Italian engineering, in general. 

Oswald cartridge.

The rifle Oswald used was a Modello 91/38, Carcano (1938 model of a design originally used in 1891) with an extra-long, 20.9″ barrel, bought for only $19.95 including a 4x sight. That’s $12.50 for the gun, the equivalent of $100 in 2020). The gun may have been cheep, but it was a fine Italian weapon: it was small, fast, pretty, manual, and unreliable. The small size allowed Oswald to get the gun into the book depository without arousing suspicion. He claimed his package held curtain rods, and the small, narrow shape of the gun made the claim believable.

The first question, the fast shooting, is answered in part by the fact that loading the 91/38 Carcano rifle takes practice. Three American marksmen who tried to duplicate the shots for the Warren commission didn’t succeed, but they didn’t have the practice with this type of gun that Oswald had. The Carcano rifle used a bolt and clip loading system that had gone out of style in the US before WWI. To put in a new shell, you manually unlock and pull back the bolt. The old casing then flies out, and the spring–clip loads a new shell. You then have to slam the bolt forward and lock it before you can fire again. For someone practiced, loading this way is faster than with a semi-automatic. To someone without practice it is impossibly slow, like driving a stick shift car for the first time. Even with practice, Americans avoid stick shift cars, but Italians prefer them. Some time after the Warren report came out, Howard Donahue, an American with experience on this type of rifle, was able to hit three moving targets at the distance in 4.8 seconds. That’s less than the shortest estimate of the time it took Oswald to hit twice. Penn of Penn and Teller recreates this on TV, and shows here that Kennedy’s head would indeed have moved backward.

Oswald’s magic bullet, shot two.

That Oswald was so accurate is explained, to great extent by the way the sight was mounted and by the unusual bullets. The model 38 Carcano that Oswald bought fired light, hollow, 6.5×52mm cartridges. This is a 6.5 mm diameter bullet, with a 52 mm long casing. The cartridge was adopted by the Italians in 1940, and dropped by 1941. These bullets are uncommonly bullet is unusually long and narrow (6.5 mm = .26 caliber), round-nosed and hollow from the back to nearly the front. In theory a cartridge like this gives for greater alignment with the barrel., and provides a degree of rocket power acceleration after it leaves the muzzle. Bullets like this were developed in the US, then dropped by the late 1800s. The Italians dropped this bullet for a 7.5 mm diameter version in 1941. The 6.5 mm version can go through two or three people without too much damage, and they can behave erratically. The small diameter and fast speed likely explains how Oswald’s second shot went through Kennedy and Connolly twice without dong much. An American bullet would have done a lot more damage.

Because of the light weight and the extra powder, the 6.5 mm hollow bullet travels uncommonly fast, about 700 m/s at the muzzle with some acceleration afterwards, ideally. Extra powder packs into the hollow part by the force of firing, providing, in theory, low recoil, rocket power. Unfortunately these bullets are structurally weak. They can break apart or bend and going off-direction. By comparison the main US rifle of WWII, the M1, was semi-automatic, with bullets that are shorter, heavier, and slower, going about 585 m/s. Some of our bullets had steel cores too to provide a better combination of penetration and “stopping power”. Only Oswald second shot stayed pristine. It could be that his third shot — the one that made Kennedy’s head explode — flattened or bent in flight.

Oswald fragment of third bullet. It’s hollow and seems to have come apart in a way a US bullet would not.

The extra speed of Oswald’s bullets and the alignment of his gun would have given Oswald a great advantage in accuracy. At 100 yards (91 m), test shots with the rifle landed 2 1⁄2 to 5 inches high, within a 3-to-5-inch circle. Good accuracy with a sight that was set to high for close shot accuracy. The funky sight, in my opinion , explains how Oswald managed to miss Walker, but explains how he hit Kennedy accurately especially on the last, longest shot, 81 m to Kennedy’s head

Given the unusually speed of the bullets (I will assume 750 m/s) Oswald’s third shot would have taken 0.108 s to reach the target. If the sight were aligned string and if Kennedy were not moving, the bullet would have been expected to fall 2.24″ low at this range, but given the sight alignment we’d expect him to shoot 3-6″ high on a stationary target, and dead on, on the president in his moving vehicle. Kennedy was moving at 5 m/sand Oswald had a 17° downward shot. The result was a dead on hit to the moving president assuming Oswald didn’t “lead the shot”. The peculiarities of the gun and bullets made Oswald more accurate here than he’d been in the army, while causing him to miss Walker completely at close range.

comparison of the actual, second shot, “magic bullet,” left, with four test-shot bullets. Note that one of the test bullets collapsed, two bent, and one exploded. This is not a reliable bullet design.

We now get to the missed, first shot: How did he miss the car completely firing at the closest range. The answer, might have to do with deformation of the bullets. A hollow base bullet can explode, or got dented and fly off to the side. More prosaically, it could be that he hit a tree branch or a light pole. The Warren commission blamed a tree that was in the way, and there was also a light pole that was never examined. For all we know the bullet is in a branch today, or deflected. US bullets would have a greater chance to barrel on through to at least hit the car. This is an aspect of Italian engineering — when things are light, fast, and flexible, unusual things happen that do not expect to happen with slow, ugly, US products. It’s a price of excellence, Italian style.

Another question appears: Why wasn’t Oswald stopped when the FBI knew he’d threatened Kennedy, and was suspected of shooting at Walker. The simple answer, I think, is that the FBI was slow, and plodding. Beyond this, neither the FBI nor the CIA seem to have worried much about Kennedy’s safety. Even if Kennedy had used the bubble top, Oswald would likely have killed him. Kennedy didn’t care much for the FBI and didn’t trust Texas. Kennedy had a long-running spat with the FBI involving his involvement with organized crime, and perhaps running back to the days when Kennedy’s father was a bootlegger. His relation with the CIA was similar.

The Mateba, Italian semi-automatic revolver, $3000, available only in 357 Magnum and 44 magnum.

I should mention that the engineering styles and attitudes of a country far outlast the particular engineer.We still make big, fat, slow, ugly cars — that are durable and reasonably priced. Germans still overbuild, and Italian cars and guns are as they ever were: beautiful, fast, expensive, and unreliable. The fastest production car is Italian, a Bugatti with a top speed of 245 mph; the fastest rollercoaster is at Ferrari gardens, 149 mph, and in terms of guns, let me suggest you look at the Mateba, left, a $3000 beautiful super fast semi-automatic revolver (really), produced in Italy, and available in 357 magnum and .44 magnum only . It’s a magnificent piece of Italian engineering beautiful, accurate, powerful, and my guess is it’s unreliable as all get out. Our, US pistols typically cost 1/5 to 1/10 as much. A country’s cars, planes, and guns represent the country’s aesthetics. The aesthetics of a county changes only slowly, and I think the world is better off because of it

Robert Buxbaum, February 14, 2020. One of my favorite courses in engineering school, Cooper Union, was in Engineering Aesthetics and design.

Sewage reactor engineering, Stirred tank designs

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Over the past few years, I’ve devoted several of these essays to analysis of first-stage sewage treatment reactors. I described and analyzed the rotating disc reactor found at the plant is Holly here, and described the racetrack,“activated sludge” plug reactor found most everywhere else here. I also described a system without a primary clarifier found near Cincinatti. All of these were effective for primary treatment; soluble organics are removed by bio-catalyzed oxidation:

2 H-C-O-H + O2 –> CO2 + H2O.

A typical plant in Oakland county treats 2,000,000 gallons per day of this stuff, with the bio-reactor receiving liquid waste containing about 200 ppm of soluble and colloidal biomass. That’s 400 dry gallons for those interested, or about 3200 dry lbs./day. About half of this will be oxidized to CO2 and water. The rest (cell bodies) are removed with insoluble components, and applied to farmers fields or buried, or burnt in an incinerator.

There is another type of reactor used in Oakland County. It’s mostly used for secondary treatment, converting consolidated sludge to higher-quality sludge that can be sold or used on farms with less restriction, but it is a type of reactor used at the South Lyon treatment plant, for primary treatment. It is a Continually stirred tank reactor, or CSTR, a design that is shown in schematic below.

As of some years ago, the South Lyon system involved a single largish pond lined with plastic with a volume about 2,000,000 gallons total. About 700,000 gallons per day of sewage liquids went into the lagoon, at 200 ppm soluble organics. Air was bubbled through the liquid providing a necessary reactant, and causing near-perfect mixing of the contents. The aim of the plant managers is to keep the soluble output to the, then-acceptable level of 10 ppm; it’s something they only barely managed, and things got worse as the flow increased. Assume as before, a value V and a flow Q.

We will call the concentration of soluble organics C, and call the initial concentration, the concentration that enters,  Ci. It’s about 200 ppm. We’ll call the output concentration Co, and for this type of reactors, Co = C.  The reaction is first order, approximately, so that, if there were no flow into or out of the reactor, the concentration of organics would decrease at the rate of

dC/dt = -kC.

Here k is a reaction constant, dependent on temperature oxygen and cell content. It’s typically about 0.5/hour. For a given volume of tank the rate of organic removal is VkC. We can now do a mass balance on soluble organics. Since the rate of organic entry is QCi and the rate leaving by flow is QC. The difference must be the amount that is reacted away:

QCi – QC = VkC.

We now use algebra, to find that

Co = Ci/(1 + kV/Q).

V/Q is sometimes called a residence time; for the system. At normal flow, the residence time of the South Lyon system is about 2.8 days or 68.6 hours. Plugging these numbers in, we find that the effluent from the reactor leaves at 1/35 of the input concentration, or 5.7 ppm, on average. This would be fine except that sometimes the temperature drops, or the flow increases, and we start violating the standard. A yet bigger problem was that the population increased by 50% while the EPA standard got more stringent to 2 ppm. This was solved by adding another, smaller reactor, volume = V2. Using the same algebraic analysis, as above you can show that, with two reactors,

Co = Ci/ [(1 + kV/Q)(1+kV2/Q)].

It’s a touchy system, but it meets government targets, just barely, most of the time. I think it is time to switch to a plug-flow reactor system, as used in much of Oakland county. In these, the fluid enters a channel and is reacted as it flows along. Each gallon of fluid, in a sense moves by itself as if it were its own reactor. In each gallon, we can say that dC/dt = -kC. We can thus solve for Co in terms of the total residence time, where t again is V/Q. We can rearrange this equation and integrate: ∫dC/C = – ∫kdt. We then find that, 

      ln(Ci/Co) = kt = kV/Q

To convert 200 ppm sewage to 2 ppm we note that Ci/Co = 100 and that V = Q ln(100)/k = Q (4.605/.5) hours. An inflow of 1000,000 gallons per day = 41,667 gal/ hour, and we find the volume of tank is 41,667 x 9.21 = 383,750 gallons. This is quite a lot smaller than the CSTR tanks at South Lyon. If we converted the South Lyon tanks to a plug-flow, race-track design, it would allow it to serve a massively increased population, discharging far cleaner sewage. 

Robert Buxbaum, November 17, 2019

Maximum height of an NYC skyscraper, including wind.

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Some months ago, I demonstrated that the maximum height of a concrete skyscraper was 45.8 miles, but there were many unrealistic assumptions. The size of the base was 100 mi2, about that of Sacramento, California; the shape was similar to that of the Eiffel tower, and there was no wind. This height is semi-reasonable; it’s about that of the mountains on Mars where there is a yellow sky and no wind, but it is 100 times taller than the tallest skyscraper on earth. the Burj Khalifa in Dubai, 2,426 ft., shown below. Now I’d like to include wind, and limit the skyscraper to a straight tower of a more normal size, a city-block square of manhattan, New York real-estate. That’s 198 feet on a side; this is three times the length of Gunther’s surveying chain, the standard for surveying in 1800.

Burj Khalifa, the world’s tallest building, Concrete + glass structure. Dubai tourism image.

As in our previous calculation, we can find the maximum height in the absence of windby balancing the skyscrapers likely strength agains its likely density. We’ll assume the structure is made from T1 steel, a low carbon, vanadium steel used in bridges, further assume that the structure occupies 1/10 of the floor area. Because the structure is only 1/10 of the area, the average yield strengthener the floor area is 1/10 that of T1 steel. This is 1/10 x 100,000 psi (pounds per square inch) = 10,000 psi. The density of T1 steel is 0.2833 pounds per cubic inch, but we’ll assume that the density of the skyscraper is about 1/4 this; (a skyscraper is mostly empty space). We find the average is 0.07 pounds per cubic inch. The height, is the strength divided by the density, thus

H’max-tower = 10,000psi / 0.07 p/in3 = 142, 857 inches = 11, 905 feet = 3629 m,

This is 4 1/4 times higher than the Burj Khalifa. The weight of this structure found from the volume of the structure times its average density, or 0.07 pounds per cubic inch x 123 x 1982x 11,905 = 56.45 billion pounds, or, in SI units, a weight of 251 GNt.

Lets compare this to the force of a steady wind. A steady wind can either either tip over the building by removing stress on the upwind side, or add so much extra stress to the down-wind side that the wall fails. The force of the wind is proportionals to the wind’s energy dissipation rate. I’ll assume a maximum wind speed of 120 mph, or 53.5 m/s. The force of the wind equals the area of the building, times a form factor, ƒ, times the rate of kinetic energy dissipation, 1/2ρv2. Thus,

F= (Area)*ƒ* 1/2ρv2, where ρ is the density of air, 1.29kg/m3.

The form factor, ƒ, is found to be 1.15 for a flat plane. I’ll presume that’s also the form factor for a skyscraper. I’ll take the wind area as

Area = W x H,

where W is the width of the tower, 60.35 m in SI, and the height, H, is what we wish to determine. It will be somewhat less than H’max-tower, =3629 m, the non-wind height. As an estimate for how much less, assume H = H’max-tower, =3629 m.
For this height tower, the force of the wind is found to be:

F = 3629 * 60.35* 2123 = 465 MNt.

This is 1/500 the weight of the building, but we still have to include the lever effect. The building is about 60.1 times taller than it is wide, and as a result the 465 MNt sideways force produces an additional 28.0 GNt force on the down-wind side, plus and a reduction of the same amount upwind. This is significant, but still only 1/9 the weight of the building. The effect of the wind therefore is to reduce the maximum height of this New York building by about 9 %, to a maximum height of 2.05 miles or 3300 m.

The tallest building of Europe is the Shard; it’s a cone. The Eiffel tower, built in the 1800s, is taller.

A cone is a better shape for a very tall tower, and it is the shape chosen for “the shard”, the second tallest building in Europe, but it’s not the ideal shape. The ideal, as before, is something like the Eiffel tower. You can show, though I will not, that even with wind, the maximum height of a conical building is three times as high as that of a straight building of the same base-area and construction. That is to say that the maximal height of a conical building is about 6 miles.

In the old days, one could say that a 2 or 6 mile building was inconceivable because of wind vibration, but we’ve found ways to deal with vibration, e.g. by using active damping. A somewhat bigger problem is elevators. A very tall building needs to have elevators in stages, perhaps 1/2 mile stages with exchanges (and shopping) in-between. Yet another problem is fire. To some extent you eliminate these problems by use of pre-mixed concrete, as was used in the Trump tower in New York, and later in the Burj Khalifa in Dubai.

The compressive strength of high-silica, low aggregate, UHPC-3 concrete is 135 MPa (about 19,500 psi), and the density is 2400 kg/m3 or about 0.0866 lb/in3. I will assume that 60% of the volume is empty and that 20% of the weight is support structure (For the steel building, above, I’d assumed 3/4 and 10%). In the absence of wind,

H’max-cylinder-concrete = .2 x 19,500 psi/(0.4 x.0866  lb/in3) = 112,587″ = 9,382 ft = 1.77 miles. This building is 79% the height of the previous, steel building, but less than half the weight, about 22,000,000,000 pounds. The effect of the wind will be to reduce the above height by about 14%, to 1.52 miles. I’m not sure that’s a fire-safe height, but it is an ego-boost height.

Robert Buxbaum. December 29, 2019.

The chemistry of lead in drinking water

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Our county, like many in the US and Canada, is served by thousands of miles of lead pipes. Some of these are the property of the government, others sit beneath our homes and are the property of the home-owner. These pipes are usually safe, but sometimes poison us. There is also problem of lead-tin solder. It was used universally to connect iron and copper pipes until it was outlawed in 1986. After years of sitting quietly, this lead caused a poisoning crisis in DC in 2004, and in Flint in 2015-16. Last month my town, Oak Park, registered dangerous lead levels in the drinking water. In an attempt to help, please find the following summary of the relevant lead chemistry. Maybe people in my town, or in other towns, will find some clue here to what’s going on, and what they can do to fix it.

lead pipes showing the three oxides: brown, yellow, and red, PbO2, PbO, and Pb2O3.

Left to itself, lead and solder pipe could be safe; lead is not soluble in clean water. But, if the water becomes corrosive, as happens every now and again, the lead becomes oxidized to one of several compounds that are soluble. These oxides are the main route of poisoning; they can present serious health issues including slow development, joint and muscle pain, memory issues, vomiting, and death. The legal limit for lead content in US drinking water is 15 ppb, a level that is far below that associated with any of the above. The solubility of PbO, lead II oxide, is more than 1000 times this limit 0.017 g/L, or 17,000 ppb. At this concentration serious health issues will show up.

PbO is the yellow lead oxide shown in the center of the figure above, right; the other pipes show other oxides, that are less-soluble, and thus less dangerous. Yellow lead oxide and red lead oxides on the right were used as paint colors until well into the 20th century. Red lead oxide is fairly neutral, but yellow PbO is a base; its solubility is strongly dependent on the PH of the water. In neutral water, its solution can be described by the following reaction.

PbO + H2O(l) –> Pb2+(aq) + 2 OH–(aq).

In high pH water (basic water), there are many OH–(aq) ions, and the solubility is lower. In low pH, acidic water the solubility is even higher. For every 1 point of lower pH the lowubility increases by a factor of 10, for every 1 point of higher pH, it decreases by a factor of ten. In most of our county, the water is slightly basic, about pH 8. It also helps that our water contains carbonate. Yellow lead forms basic lead carbonate, 2PbCO3·Pb(OH)2, the white lead that was used in paint and cosmetics. Its solubliity is lower than that of PbO, 110 ppb, in pure water, or within legal limit in water of pH 8. If you eat white lead, though, it reacts with stomach acid, pH 2, and becomes quite soluble and deadly. Remember, each number here is a factor of ten.

A main reason lead levels a very low today are essentially zero, even in homes with lead solder or pipe, involves involves the interaction with hypochlorite. Most water systems add hypochlorite to kill bacteria (germs) in the water. A side benefit is significant removal of lead ion, Pb2+(aq).

Pb2+(aq) + 2 ClO–(aq) –> Pb(ClO)2(s). 

Any dissolved lead reacts with some hypochlorite ion reacts to form insoluble lead hypochlorite. Lead hypochlorite can slowly convert to Lead IV oxide — the brown pyrophilic form of lead shown on the left pipe in the figure above. This oxide is insoluble. Alkaline waters favor this reaction, decreasing solubility, but unlike with PbO, highly alkaline waters provide no significant advantage.

PbClO+(aq) + H2O(l) –> PbO2(s) + 2 H+(aq) + Cl–(aq)

Lead IV oxide, PbO2 was used in old-fashioned matches; it reacts violently with phosphorus or sulfur. People were sometimes poisoned by sucking on these matches. In the stomach, or the presence of acidic drinking water, PbO2 is decomposed forming soluble PbO:

PbO2(s) +2 H+(aq) + 2 e– –> PbO(s) + H2O(l).

You may wonder at the presence of the two electrons in the reaction above. A common source in water systems is the oxidation of sulphite:

SO3-2(aq)–> SO4-2(aq) + 2 e–.

The presence of sulphite in the water means that hypochlorite is removed.

ClO–(aq) + 2 H+(aq) + 2 e– —> Cl–(aq) + H2O(l).

Removal of hypochlorite can present a serious danger, in part because the PbO2(s) slowly reverts to PbO and becomes soluble, but mostly because bacteria start multiplying. In the Flint crisis of 2016, and in a previous crisis in Washington DC, the main problem, in my opinion was a lack of hypochlorite addition. The lead crisis was preceded by an uptick in legionnaires disease; It killed 12 people in Flint in 2014 and 2015, and 87 were sickened, all before the lead crisis. Eventually, it was the rise of legionaries disease that alerted water officials in Virginia that there was something seriously wrong in Flint. Most folks were unaware because Flint water inspectors seem to have been fudging the lead numbers to make things look better.

Most US systems add phosphate to remove lead from the water. Flint water folks could have stopped the lead crisis, but not the legionnaires, by adding more phosphate. Lead phosphate solubility is 14 ppb at 20°C, and my suspicion is that this is the reason that the legal limit in the US is 15 ppb. Regulators chose 15 ppb, I suspect, not for health reasons, but because the target could be met easily through the addition of phosphate. Some water systems in the US and Canada disinfect with chloramine, not hypochlorite, and these systems rely entirely on phosphate to keep lead levels down. Excess phosphate is used in Canada to lower lead levels below 10 ppb. It works better on systems with hypochlorite.

Chloramine is formed by reacting hypochlorite with ammonia. It may be safer than hypochlorite in terms of chlorite reaction products, a real problem when the water source is polluted. But chloramine is not safe. It sickened 72 soldiers, 36 male and 36 female in 1998. They’d used ammonia and bleach for a “cleaning party” on successive days. Here’s a report and first aid instructions for the poisoning. That switching to chloramine can expose people to lead is called “the chloramine catch”.

Unlike PbO, PbO2 is a weak acid. PbO2 and PbO can react to form red lead, PbO•PbO2(s), the red stuff on the pipe at right in the picture above. Red lead can react with rust to form iron plumbable, an insoluble corrosion resister. A simple version is:

PbO•PbO2(s) + Fe2O3(s) —> 2FePbO3(s).

This reaction is the basis of red-lead, anti-rust compounds. Iron plumbable is considered to be completely insoluble in water, but like PbO it is soluble in acid. Bottom line, slightly basic water is good, as are hypochlorite in moderation, and phosphate.

Robert Buxbaum, November 18, 2019. I ran for water commissioner, and might run again. Even without being water commissioner, I’ll be happy to lend my expertise, for free, to any Michigan town or county that is not too far from my home.

Ladder on table, safe till it’s not.

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via GIFER

Two years ago I wrote about how to climb a ladder safely without fear. This fellow has no fear and has done the opposite. This fellow has chosen to put a ladder on a table to reach higher than he could otherwise. That table is on another table. At first things are going pretty well, but somewhere about ten steps up the ladder there is disaster. A ladder that held steadily, slips to the edge of the table, and then the table tips over. It’s just physics: the higher he climbs on the ladder the more the horizontal force. Eventually, the force is enough to move the table. He could have got up safely if he moved the tables closer to the wall or if he moved the ladder bottom further to the right on the top table. Either activity would have decreased the slip force, and thus the tendency for the table to tip.

Perhaps the following analysis will help. Lets assume that the ladder is 12.5′ long and sits against a ten foot ledge, with a base 7.5′ away from the wall. Now lets consider the torque and force balance at the bottom of the ladder. Torque is measured in foot-pounds, that is by the rotational product of force and distance. As the fellow climbs the ladder, his weight moves further to the right. This would increase the tendency for the ladder to rotate, but any rotation tendency is matched by force from the ledge. The force of the ledge gets higher the further up the ladder he goes. Let’s assume the ladder weighs 60 lbs and the fellow weighs 240 pounds. When the fellow has gone up ten feet up, he has moved over to the right by 7.5 feet, as the diagram shows. The weight of the man and the ladder produces a rotation torque on the bottom of 60 x 3.75 + 240 x 7.5 = 1925 foot pounds. This torque is combatted by a force of 1926 foot pounds provided by the ledge. Since the ladder is 12.5 feet long the force of the ledge is 1925/12.5 = 154 pounds, normal to the ladder. The effect of this 154 lbs of normal force is to push the ladder to the left by 123.2 lbs and to lift the ladder by 92.4lbs. It is this 123.2 pounds of sideways push force that will cause the ladder to slip.

The slip resistance at the bottom of the ladder equals the net weight times a coefficient of friction. The net weight here equals 60+240-92.4 = 217.6 lbs. Now lets assume that the coefficient of friction is 0.5. We’d find that the maximum friction force, the force available to stop a slip is 217.6 x 0.5 = 108.8 lbs. This is not equal to the horizontal push to prevent rotation, 123.2 lbs. The net result, depending on how you loot at things, is either that the ladder rotates to the right, or that the ladder slips to the left. It keeps slipping till, somewhere near the end of the table, the table tips over.

Force balance of man on ladder. Based on this, I will go through the slippage math in gruesome detail.

I occasionally do this sort of detailed physics; you might as well understand what you see in enough detail to be able to calculate what will happen. One take home from here is that it pays to have a ladder with rubber feet (my ladders do). That adds to the coefficient of friction at the bottom.

Robert Buxbaum, November 6, 2019.

Water Towers, usually a good thing.

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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.

Recycle nuclear waste

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In a world obsessed with stopping global warming by reducing US carbon emissions, you’d think there would be a strong cry for nuclear power, one of the few reliable sources of large-scale power that does not discharge CO2. But nuclear power produces dangerous waste, and I have a suggestion: let’s recycle the waste so it’s less dangerous and so there is less of it. Used nuclear fuel rods, in particular. We burn perhaps 5% of the uranium, and produce a waste that is full of energy. Currently these, semi-used rods are stored in very expensive garbage dumps waiting for us to do something. Let’s recycle.

I’ve called nuclear power the elephant in the room for clean energy. Nuclear fuel produces about 25% of America’s electricity, providing reliable baseline generation along with polluting alternatives: coal and natural gas, and less-reliable renewables like solar and wind. Nuclear power does not emit CO2, and it’s available whether or not the sun shines or the wind blows. Nuclear power uses far less land area than solar or wind too, and it provides critical power for our navy aircraft carriers and submarines. Short of eliminating our navy, we will have to keep using nuclear.

Although there are very little nuclear waste per energy delivered, the waste that there is, is hard to manage. Used nuclear fuel rods in particular. For one thing, the used rods are hot, physically. They give off heat, and need to be cooled. At first they give off so much heat that the rods must be stored under water. But rod-heat decays fractally. After ten years or so, rods can be stored in naturally cooled concrete; it’s still a headache, but a smaller one The other problem with the waste rods is that they contain about 1.2% plutonium, a material that can be used for atomic bombs. A major reason that you can’d just dump the waste into the ocean or into a salt mine is the fear that someone will dig it up and extract the plutonium for an a- bomb. The extraction is easy compared to enriching uranium to bomb-grade, and the bombs work at least as well. Plutonium made this way was used for the bomb that destroyed Nagasaki.

The original plan for US nuclear power had been that we would extract the plutonium, and burn it up by recycling it to the nuclear reactor. We’d planned to burry the rest, as the rest is far less dangerous and far less, long-term radioactive. We actually did some plutonium recycling of this sort but in the 1970s a disgruntled worker named Silkwood stole plutonium and recycling was shut down in the US. After that, political paralysis set in and we’ve come to just let the waste sit in more-or-less guarded locations. There was a thought to burry everything in a guarded location (Yucca Mountain, Nevada) but the locals were opposed. So the waste sits waiting to leak out or be stolen. I’d like to return to recycling, but not necessarily of pure plutonium as we did before Silkwood: there is no guarantee that there won’t be other plutonium thieves.

Instead of removing the plutonium for recycling, I’d like to suggest that we remove about 40% of the uranium in the rod, and all of the “ash”, this is all of the lighter atom elements created from the split uranium atoms. This ash is about 5% of the total. The resultant rods would have about 2% plutonium, 97.5% enriched uranium (about 1% enriched at this stage) plus about 0.5% higher transuranics. This composition would be a far less dangerous than purified plutonium. It would be less hot and it would not be possible to use it directly for atom bombs. It would still be fissionable, though, at the same energy content as fresh rods.

There is an uncommonly large amount of power available in nuclear fuel

Several countries recycle by removing the ash. Because no uranium is removed, the material they get has about half the usable life of a fresh rod. After one recycle, there is not much more they could do. If we remove uranium material is a lot more easily used, and more easily recycled again. If we keep removing ash and uranium, we could get many, many recycles. The result is a lot less uranium mining, and more power per rod, and fewer rods to store under guard.

The plutonium of multiply recycled rods is also less-usable for fission bombs. With each recycle, the rods build up a non-fisionabl isotope of plutonium: Pu 240. This isotope is not readily separated from the fissionable isotope, Pu 239, making multiply used rods relatively useless for fission bombs.

Among the countries that do some nuclear waste recycling are Canada, France, Russia, China, and Germany. Not a bad assortment. I would be happy to see us join them.

Robert Buxbaum September 9, 2019

Why does water cost what it does?

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Water costs vary greatly about Oakland county, and around the US, and I have struggled in vain to find out why. In part the problem is that each city gets to add as much maintenance and management costs as the city government thinks appropriate. High management and infrastructure fees can increase to the cost of water, but I also not that different cities about Oakland County Michigan get their water at different rates from the multi-county organization that oversees water in South East Michigan: GLWA, The Great Lakes Water Authority.

$112 water bill for zero usage. The base charge is so large that prices are essentially independent of useage.

I’ve attended meetings, both local and multi county and have tried to find out why one town gets its water at a far lower rate than another, near by. Towns get lower rates if they have a water tower, but it is not at all clear what the formula is. It also helps to separate the storm sewage from the sanitary sewage — something that I have proposed for all of Oakland county, but if there is fixed formula of how that affects rates, I’ve not seen it. And I wonder how well communities monitor the amount of storm sewage they generate.

The water itself is free. For the most part, in this county, we pump it from the Detroit river. Some of the rest of the water is pumped from wells. None of this costs anything. There is a pump cost, but it is manicure. Pumping 1 gallon of water up 75 feet, costs about 0.002¢ in pumping cost. The rest of the cost is infrastructure: the cost of the pumps, the pipes, the treatment, the billing and sewage. Among the sewage fees is a pollution penalty, and Oakland county pays plenty of pollution penalties. When it rains, we generate more sewage than the system will handle, and we dump the rest into the rivers and lakes. This results in closed beaches and poisoned fish, and fines too. The county pays the EPA when we do this, and the county passes the cost to the cities. I don’t know what the formula for fee distribution is, and don’t even know what it should be. What I do know is that we do this vastly too often.

Another oddity is that we bill on a per gallon basis. For my home, the bill is about 2¢/ gallon — 100 times the pumping cost. Though the city can claim that we are paying for infrastructure, both clean water infrastructure and sewage infrastructure, it seems odd to bill on a per-gallon used basis, and 1000 times the true per-gallon price. Since most of the price of water is the infrastructure and management cost, it seems like a regressive tax to charge people on the basis of per-gallon used. I also find it odd that cities do a propaganda campaign to tell folks to use less water. Why? I’d much prefer to charge a far lower base charge, and then bill significantly per-gallon. As with much that is socialist, the current system is inefficient, but pleasant for the management.

August 21, 20019, Robert Buxbaum