The free press isn’t

4 Replies

Newspapers remain the primary source for verified news. Facts presumed to be sifted to avoid bias, while opinions and context is presumed to be that of the reporter whose name appears as the byline. We may look to other media sources for confirmation and fact-checking: news magazines, Snopes, and Facebook. Since 2016 these sources have been unanimous in their agreement about the dangers of biassed news. Republicans, including the president have claimed that the left-media spreads “fake news”, against him, while Democrats claim that Trump and the Russians have been spreading pro-Trump, fake news, While Trump and the Republicans claim that the left-media spreads fake news. In an environment like this, it’s worthwhile to point out that the left-wing and right-wing press is owned by a very few rich people, and none of it is free of their influence. An example of this is the following compilation of many stations praising their news independence: CBS, ABC, NBC, and FOX, praising their independence in exactly the same words.

It costs quite a lot to buy a newspaper or television station, and a lot more to keep it running. Often these are money-losing ventures, and as a result, the major newspapers tend to be owned by a few mega-rich individuals who have social or political axes to grind. As the video above shows, one main axe they have is convincing you of their own independence and reliability. The Sinclair news service, owned by the Smith news family came up with the text, and all the independent journalists read it in as convincing a voice as they could muster. This is not to say. that all the news is this bad or that the mega rich don’t provide a service by providing us the news, but it’s worth noting that they extract a fee by controlling what is said, and making sure that the news you see fits their agendas – agendas that are often obvious and open to the general view.

Perhaps the most prominent voice on the right is Rupert Murdoch who owns The New York Post, and The Wall Street Journal. He used to own Fox too, and is still the majority controller and guiding voice, but Fox is now owned by Disney who also owns ABC. Murdoch uses his many media outlets to make money and promote conservative and Republican causes. You might expect him to support Trump, but he has a person feud with him that boils up in the Post’s cover pages. Disney’s ABC tends to present news on the left, but as in the compilation above, left and right journalists have no problem parroting the same words. Here is another, older compilation, more journalistl saying the same thing in the same words, e.g. playing up the Conan O’Brian show.

Another media master is Ted Turner. He tends to own media outlets on the left including CNN. Turner manages to make CNN, and his other properties profitable, in part by courting controversy. His wife for a time was Jane Fonda, otherwise known as Hanoi Jane.

Another left-leaning media empire (whatever that means) is MSNBC. It is owned by Time-Warner, also owner of The Huffington Post. Both are anti-israel, and both promote zero-tariff, Pacific-rim trade, but as seen above, MSNBC anchors will read whatever trash they are told to read, and often it’s the same stuff you’d find on Fox.

Rounding out the list of those with a complete US media empires, I include the Emir of Qatar, perhaps the richest man in the world. He operates Al Jazeera, “the most respected news site for Middle east reporting” as an influence-buying vehicle. Al Jazeera is strongly anti-fracking, anti nuclear, and anti oil (Qatar is Asia’s latest supplier of natural gas). It is strongly anti-Israel, and anti Saudi. Qatar propagandist, Jamal Khashoggi worked for AlJazeera, and was likely killed for it. They’re also reliably pro-Shia, with positive stories about Hamas, The Muslim Brotherhood, and Iran, but negative stories about Sunni Egypt and Turkey. They present news, but not unbiassed.

But you don’t have to buy a complete media empire to present your politics as unbiassed news. Jeff Bezos, founder Amazon, bought The Washington Post for $250 million (chump change to hm). For most of the past two years, the paper mostly promoted anti-tariff views, and liberal causes, like high tax rates on the rich. Amazon thrives on cheep Chinese imports, and high tax rates don’t hurt because Amazon manages to not pay any taxes on $11 billion/year profits (by clever accounting they actually get a rebate). Recently Joe Biden made the mistake of calling out Amazon for not paying on $11 billion in profits, and The Washington Post has returned the favor by bashing Biden. As for why Bezos bought the money-losing Post, he said: “It is the newspaper in the Capital City of the most important country in the world… [As such] … “it has an incredibly important role to play in this democracy.”

Moving on to The New Your Times, its editorial slant is controlled by another contestant for world’s richest man: telecom mogul, Carlos “Slim” Helú. Carlos’s views are very similar to Bezos’s, with more of an emphasis on free trade with Mexico. Steve Jobs’s widow runs “The Atlantic” for the same reasons. It’s free on line, well written and money losing. Like with the above, it seems to be a vanity project to promote her views. It’s a hobby, but sh can afford it.

Like her, Chris Hughes, Facebook’s Co-founder and Zuckerberg room-mate, bought and runs the money losing “The New Republic“. He was Facebook’s director of marketing and communications before joining the Obama campaign as it internet marketing head. The New Republic’s had a stellar reputation, back in the day. Zuckerberg himself runs a media empire, but it’s different from the above: it’s social media where people pay for placement, and where those whose views he doesn’t like get censored: put in Facebook jail. He’s gotten into trouble over it, but as a media giant, there seem to have been no consequences.

H.L. Menken on the fake news of the early – mid 20th century.

And it’s not only rich individuals who turn trusted news sources into propaganda outlets. The US CIA did this for years, and likely still do. Then there are the Russians, the Chinese, the Israelis, the British (BBC) and our very own NPRt. These sources present news that benefits them in the most positive light and scream about dangers to democracy and the world if their position is touched or their veracity is questioned. As these sources are all government funded, there is a they are unanimous supporters big governments as a cure to all ills. Closer to home, I’d like to mention that Detroit has two major papers, but only one owner. The left leaning Detroit Free Press, and the right-leaning Detroit News are owned by the same people, share a considerable staff, and generally agree on important issues. There are a dozen smaller papers in Metro Detroit; all but one is owned by one media group.

I’d like to end with a positive note. Not every reporter is in this sad grab-bag. In Detroit, Setve Neveling, “the motor-city muckraker” manages to present is independent, active news. Then there is Los Angeles’s Biotech billionaire, Patrick Soon-Shiong. He bought the LA Times in June 2018, claiming he will use it to fight fake news, “the cancer of our time.” I wish him luck. So far, I’d say, he’s made the LA Times is the best Newspaper in the US with The NY Post a close second ( love the snarky headlines).

Robert Buxbaum, July 15, 2019.

Bitcoin v cash to avoid Trump’s tariffs or ransom a sailor

Thermal stress failure

1 Reply

Take a glass, preferably a cheap glass, and set it in a bowl of ice-cold water so that the water goes only half-way up the glass. Now pour boiling hot water into the glass. In a few seconds the glass will crack from thermal stress, the force caused by heat going from the inside of the glass outside to the bowl of cold water. This sort of failure is not mentioned in any of the engineering material books that I had in college, or had available for teaching engineering materials. To the extent that it is mentioned mentioned on the internet, e.g. here at wikipedia, the metric presented is not derived and (I think) wrong. Given this, I’d like to present a Buxbaum- derived metric for thermal stress-resistance and thermal stress failure. A key aspect: using a thinner glass does not help.

Before gong on to the general case of thermal stress failure, lets consider the glass, and try to compute the magnitude of the thermal stress. The glass is being torn apart and that suggests that quite a lot of stress is being generated by a ∆T of 100°C temeprarture gradient.

To calcule the thermal stress, consider the thermal expansivity of the material, α. Glass — normal cheap glass — has a thermal expansivity α = 8.5 x10^-6 meters/meter °C (or 8.5 x10^-6 foot/foot °C). For every degree Centigrade a meter of glass is heated, it will expand 8.5×10^-6 meters, and for every degree it is cooled, it will shrink 8.5 x10^-6 meters. If you consider the circumference of the glass to be L (measured in meters), then
∆L/L = α ∆T.

where ∆L is the change in length due to heating, and ∆L/L is sometimes called the “strain.”. Now, lets call the amount of stress caused by this expansion σ, sigma, measured in psi or GPa. It is proportional to the strain, ∆L/L, and to the elasticity constant, E (also called Young’s elastic constant).

σ = E ∆L/L.

For glass, Young’s elasticity constant, E = 75 GPa. Since strain was equal to α ∆T, we find that

σ =Eα ∆T

Thus, for glass and a ∆T of 100 °C, σ =100°C x 75 GPa x 8.5 x10^-6 /°C = 0.064 GPa = 64MPa. This is about 640 atm, or 9500 psi.

As it happens, the ultimate tensile strength of ordinary glass is only about 40 MPa = σ_u. This, the maximum force per area you can put on glass before it breaks, is less than the thermal stress. You can expect a break here, and wherever σ_u < Eα∆T. I thus create a characteristic temperature difference for thermal stress failure:

The Buxbaum failure temperature, ß = σ_u/Eα

If ∆T of more than ß is applied to any material, you can expect a thermal stress failure.

The Wikipedia article referenced above provides a ratio for thermal resistance. The usits are perhaps heat load per unit area and time. How you would use this ratio I don’t quite know, it includes k, the thermal conductivity and ν, the Poisson ratio. Including the thermal conductivity here only makes sense, to me, if you think you’ll have a defined thermal load, a defined amount of heat transfer per unit area and time. I don’t think this is a normal way to look at things. As for including the Poisson ratio, this too seems misunderstanding. The assumption is that a high Poisson ratio decreases the effect of thermal stress. The thought behind this, as I understand it, is that heating one side of a curved (the inside for example) will decrease the thickness of that side, reducing the effective stress. This is a mistake, I think; heating never decreases the thickness of any part being heated, but only increases the thickness. The heated part will expand in all directions. Thus, I think my ratio is the correct one. Please find following a list of failure temperatures for various common materials.

Stress strain properties of engineering materials including thermal expansion, ultimate stress, MPa, and Youngs elastic modulus, GPa.

You will notice that most materials are a lot more resistant to thermal stress than glass is and some are quite a lot less resistant. Based on the above, we can expect that ice will fracture at a temperature difference as small as 1°C. Similarly, cast iron will crack with relatively little effort, while steel is a lot more durable (I hope that so-called cast iron skillets are really steel skillets). Pyrex is a form of glass that is more resistant to thermal breakage; that’s mainly because for pyrex, α is a lot smaller than for ordinary, cheap glass. I find it interesting that diamond is the material most resistant to thermal failure, followed by invar, a low -expansion steel, and ordinary rubber.

Robert E. Buxbaum, July 3, 2019. I should note that, for several of these materials, those with very high thermal conductivities, you’d want to use a very thick sample of materials to produce a temperature difference of 100*C.

Shakespeare’s plays, organized.

1 Reply

One remarkable thing about Shakespeare’s plays is how varied they are. There are comedies and tragedies; histories of England, and of Rome, musings on religion, and on drink, and lots of cross-dressing. He wrote at least thirty seven plays between 1590 and 1613, alone or as a major collaborator, and the chart below gives a sense of the scope. I have seen less than half of these plays, so I find the chart below both useful and humorous. The humor of the chart is partly that it presents the common man (us) access to the godly (Shakespeare). That access is the root of the best comedy, in my opinion. Shakespeare also has a comic dog, some total idiots, comic violence to women, and a few other cringeworthy laugh-getters, but we’ll not mention those; it’s low comedy. You’ll notice that Merchant of Venice is listed here as a comedy; I think it was seen that way by Shakespeare. The hero of the play in my opinion, is a woman, Portia, who outsmarts all others by her legal genius at the end. Tragedy is when the great individual can not access great things. At least that’s how I see it. As for History; it’s been said, that it starts as tragedy, and ends as comedy. Shakespeare’s histories include some of each. And as for our, US history, Lincoln was tragedy, like LBJ; Truman was comedy, and Andrew Jackson too. And, as for Trump, who knows?

By Myra Gosling, www.goodticklebrain.com

A Shakespeare collaboration. The collaborator, Fletcher, is cited by name.

Ms Gosling’s graphic, wonderful as it is, lists some but not all of Shakespeare’s collaborations. Two listed ones, “Henry VIII,” and “The Two Noble Kinsmen” were with John Fletcher. The cover shown at right, shows Fletcher named as first author. Since Fletcher outlived Shakespeare and took over the company after his death, I’ll assume these are later plays.

“Henry IV, part 1” is thought to be from Shakespeare’s early career, and seems to have been a mass collaboration: something written by a team the way situation comedies are written today. And “Pericles, Prince of Tyre,” listed near the bottom right, seems to have been a mid-career collaboration with George Wilkins. At least four of Shakespeare’s collaborations don’t appear at all in the graphic. “Edward III” and “The Spanish Tragedy”, appear to have been written with Thomas Kyd, likely early in Shakespeare’s career. Perhaps Gosling felt they don’t represent the real Shakespeare, or perhaps she left them off because they are not performed often. Another collaboration, “Sir Thomas More” (an intentional misspelling of Moore?), is well regarded today, and still put on. An existing manuscript includes 300+ lines written in Shakespeare’s hand. Still, Shakespeare’s main contribution seems to have been editing the play to get it past the censors. Finally, “Cardenio,” is a lost play, likely another collaboration with Fletcher. It got good reviews.

The cool thing about Shakespeare’s play writing, in my opinion, is his willingness to let the characters speak for themselves. Even characters who Shakespeare doesn’t like have their say. They speak with passion and clarity; without interruption or mockery. Writing this way is difficult, and most writers can’t avoid putting themselves and their opinions in the forefront. I applaud Ms Gosling for making Shakespeare accessible. Here’s this month’s issue of her blog, GoodTickleBrain.

Robert Buxbaum, June 26, 2019. As a side note, Shakespeare appears to have been born and died on the same date, April 23; in 1564 and 1616, respectively.

Making The City of New Orleans profitable

1 Reply

The City of New Orleans is the name of the only passenger train between Chicago and New Orleans. It’s also the name of a wonderful song by Steve Goodman, 1971. Hear it, sung by Arlo Guthrie with scenes from a modern ride.

“Riding on the City of New Orleans
Illinois Central Monday morning rail
Fifteen cars and fifteen restless riders
Three conductors and twenty-five sacks of mail
All along the southbound odyssey
The train pulls out at Kankakee
Rolls along past houses, farms and fields
Passin’ trains that have no names
Freight yards full of old black men
And the graveyards of the rusted automobiles…”

Every weekday, this train leaves Chicago at 9:00 PM and gets into New Orleans twenty hours later, at 5:00 PM. It’s a 925 mile trip at a 45 mph average: slow and money-losing, propped up by US taxes. Like much of US passenger rail, it “has the disappearing railroad blues.” It’s a train service that would embarrass the Bulgarians: One train a day?! 45 mph average speed!? It’s little wonder is that there are few riders, and that they are rail-enthusiasts: “the sons of Pullman porters, and the sons of engineers, Ride[ing] their father’s magic carpets made of steel.” The wonder, to me was that there was ever fifteen cars for these, “15 restless riders”.

A sack of mail being picked up on the fly.

I would be happy to see more trips and a faster speed, at an average speed of at least 60 mph. This would require 85 mph or higher between stops, but it would save on salaries, and it would bring in some new customers. But even if these higher speeds cost nothing extra, in net, you’d still need something more to make the trip profitable; a lot more if the goal is to add another train. Air-traffic will always be faster, and the automobile, more convenient. I find a clue to profitability in the fifteen cars of the song and in the sacks of mail.

Unless I’m mistaken, mail traffic was at least as profitable as passenger traffic, and those “twenty-five sacks of mail” were either very large, or just the number on-loaded at Kankakee. Passenger trains like ‘the city of New Orleans’ were the main mail carriers till the late 1970s, a situation that ended when union disputes made it unprofitable. Still, I suspect that mail might be profitable again if we used passenger trains only for fast mail — priority and first class — and if we had real fast mail again. We currently use trucks and freight trans for virtually all US mail, we do not have a direct distribution system. The result is that US mail is vastly slower than it had been. First class mail used to arrive in a day or two, like UPS now. But these days the post office claims 2 to 4 business days for “priority mail,” and ebay guarantees priority delivery time “within eight business days”. That’s two weeks in normal language. Surely there is room for a faster version. It costs $7.35 for a priority envelope and $12.80 for a priority package (medium box, fixed price). That’s hardly less than UPS charges.

Last day of rail post service New York to Washington, DC. .June 30, 1977.

Passenger trains could speed our slow mail a lot, if it were used for this, even with these slow speeds. The City of New Orleans makes this trip in less than a day, with connections available to major cities across the US. If priority mail went north-south in under one day, people would use it more, and that could make the whole operation profitable. Trains are far cheaper than trucks when you are dealing with large volumes; there are fewer drivers per weight, and less energy use per weight. Still there are logistical issues to making this work, and you want to move away from having many post men handling individual sacks, I think. There are logistical advantages to on-loading and off-loading much larger packages and to the use of a system of standard sizes on a moving conveyor.

How would a revised mail service work? I’d suggest using a version of intermodal logistics. Currently this route consists of 20 stops including the first and last, Chicago and New Orleans. This suggests an average distance between stops of 49 Miles. Until the mid 70s, , mail would be dropped off and picked up at every stop, with hand sorting onboard and some additional on-off done on-the-fly using sacks and hooks, see picture above. For a modern version, I would suggest the same number of passenger stops, but fewer mail pick ups and drop offs, perhaps only 1/3 as many. These would be larger weight, a ton or more, with no hand sorting. I’d suggest mail drop offs and pick ups every 155 miles or so, and only of intermodal containers or pods: ten to 40 foot lengths. These containers plus their contents would weigh between 2,500 and 25,000 pounds each. They would travel on flatcars at the rear of the passenger cars, and contain first class and priority mail only. Otherwise, what are you getting for the extra cost?

The city of New Orleans would still leave Chicago with six passenger cars, but now these would be followed by eight to ten flatcars holding six or more containers. They’d drop off one of the containers at a stop around the 150 mile mark, likely Champaign Urbana, and pick up five or so more (they’d now have ten). Champaign Urbana is a major east-west intermodal stop, by the way. I’d suggest the use of six or more heavy forklifts to speed the process. At the next mail-stop, Centralia, two containers might come off and four or more might come on. Centralia is near St. Louis, itself a major rail hub for trains going west. See map below. The next mail stop might be Memphis. Though it’s not shown as such, Memphis is a major east-west rail hub; it’s a hub for freight. A stripped down mail-stop version of passenger train mail like this seems quite do-able — to me at least. It could be quite profitable, too.

Amtrak Passenger rail map. The city of New Orleans is the dark blue line going north-south in the middle of the map.

Intermodal, flat-bed trucks would take the mail to sorting locations, and from there to distribution points. To speed things, the containers might hold pre-sorted sacks of mail. Intermodal trucks might also carry some full containers east and west e.g. from Centralia to St. Louis, and some full flatcars could be switched on and off too. Full cars could be switched at the end, in New Orleans for travel east and west, or in the middle. There is a line about “Changing cars in Memphis Tennessee.” I imagine this relates to full carloads of mail joining or leaving the train in Memphis. Some of these full intermodal containers could take priority mail east and west. One day mail to Atlanta, and Houston would be nice. California in two days. That could be a money maker.

At this point, I would like to mention “super-fast” rail. The top speeds of these TGV’s “Transports of Grande Vitess” are in the range of 160 mph (265 km/hr) but the average speeds are lower because of curves and the need to stop. The average speeds are roughly 125 mph on the major routes in Europe, but they require special rails and rail beds. My sense is that this sort of special-use improvement is not worth the cost for US rail traffic. While 60 -90 mph can be handled on the same rails that carry freight, the need for dedicated track comes with a doubling of land and maintenance costs. And what do you have when you have it? The bullet rail is still less than half as fast as air travel. At an average speed of 125 mph, the trip between Chicago and New Orleans would take seven hours. For business travelers, this is not an attractive alternative to a two hour flight, and it is not well suited for intermodal mail. The fuel costs are unlikely to be lower than air travel, and there is no easy way to put mail on or off a TGV. Mail en-route would slow the 125 mph speed further, and the use of intermodal containers would dramatically increase the drag and fuel cost. Air travel has less drag because air density is lower at high altitude.

Meanwhile, at 60 mph average speeds, train travel can be quite profitable. Energy use is 1/4 as high at 60 mph average as at 120 mph. An increase of average speed to 60 mph would barely raise the energy use compared to TGV, but it would shorten the trip by five hours. The new, 15 hour version of “The City of New Orleans” would not be competitive for business travel, but it would be attractive for tourists, and certainly for mail. Having fewer hours of conductor/ engineer time would save personnel costs, and the extra ridership should allow the price to stay as it is, $135 one-way. A tourist might easily spend $135 for this overnight trip: leaving Chicago after dinner and arriving at noon the next day. This is far nicer than arriving at 5:00 PM, “when the day is done.”

Robert Buxbaum, June 21, 2019. One summer during graduate school, I worked in the mail room of a bank, stamping envelopes and sorting them by zip code into rubber-band tied bundles. The system I propose here is a larger-scale version of that, with pre-sorted mail bags replacing the rubber bands, and intermodal containers replacing the sacks we put them in.

How to avoid wet basements

1 Reply

My house is surrounded my mulch — it absorbs enough rainwater that I rarely have to water.

Generally speaking water gets to your basement from rain, and the basic way you avoid wet basements is by providing some more attractive spot for the rainwater to go to. There are two main options here: divert the water to a lake or mulch-filled spot at least 8 feet away from your home, or divert it to a well-operated street or storm drain. My personal preference is a combination of both.

At right I show a picture of my home taken on a particularly nice day in the spring. Out front is a mulch-filled garden and some grass. On the side, not shown is a driveway. Most of the rain that hits our lawn and gardens is retained in 4 inches of mulch, and waters the plants. Four inches of mulch-covered ground will hold at least four inches of rainwater. Most of the rain that hits the house is diverted to downspouts and flows down the driveway to the street. Keeping some rainwater in the mulch means you don’t have to pay so much to water the trees and shrubs. The tree at the center here is an apple tree. I like fruit trees like this, they really suck up water, and I like the apples. We also have blueberries and roses, and a decorative pear (I like pears too, but they are messy).

In my opinion, you want some slope even in the lawn area, so excess rainwater will run to the sewers and not form a yard-lake, but that’s a professional preferences; it’s not always practical and some prefer a brief (vernal ) lake. A vernal lake is one that forms only in the spring. If you’ve got one, you may want to fill it with mulch or add trees that are more water tolerant than the apple, e.g. swamp oak or red cedar. Trees remove excess water via transpiration (enhanced evaporation). Red Cedars grow “knees” allowing them to survive with their roots completely submerged.

For many homes, the trick to avoiding a flooded basement is to get the water away from your home and to the street or a retention area.

When it comes to rain that falls on your hose, one option is to send it to a vernal lake, the other option is to sent it to the street. If neither is working, and you find water in your basement, your first step is to try to figure out where your rainwater goes and how it got there. Follow the water when it’s raining or right after and see where it goes. Very often, you’ll discover that your downspouts or your driveway drain into unfortunate spots: spots that drain to your basement. To the extent possible, don’t let downspout water congregate in a porous spot near your house. One simple correction is to add extenders on the downspouts so that the water goes further away, and not right next to your wall. At left, I show a simple, cheap extender. It’s for sale in most hardware stores. Plastic or concrete downspout pans work too, and provide a good, first line of defense agains a flood basement. I use several to get water draining down my driveway and away from the house.

Sometimes, despite your best efforts, your driveway or patio slopes to your house. If this is the case, and if you are not quite ready to replace your driveway or patio, you might want to calk around your house where it meets the driveway or patio. If the slope isn’t too great, this will keep rainwater out for a while — perhaps long enough for it to dry off, or for most of the rainwater to go elsewhere. When my driveway was put in, I made sure that it sloped away from the house, but then the ground settled, and now it doesn’t quite. I’ve put in caulk and a dirt-dam at the edge of the house. It keeps the water out long enough that it (mostly) drains to the street or evaporates.

A drain valve. Use this to keep other people’s sewer water out of your basement.

There is one more source of wet basement water, one that hits the houses in my area once a year or so. In our area of Oakland county, Michigan, we have combined storm and sanitary sewers. Every so often, after a big rain, other people’s rainwater and sanitary sewage will come up through the basement drains. This is really a 3rd world sewer system, but we have it this way because when it was put in, in the 1900s, it was first world. One option if you have this is to put in a one-way drain valve. There are various options, and I suggest a relatively cheap one. The one shown at right costs about $15 at Ace hardware. It will keep out enough water, long enough to protect the important things in your home. The other option, cheaper and far more hill-billy, is to stuff rags over your basement drains, and put a brick over the rags. I’ll let you guess what I have in my basement.

Robert Buxbaum, June 13, 2019

How tall could you make a skyscraper?

3 Replies

Built in 1931, the highest usable floor space of the Empire State building is 1250 feet (381m) above the ground. In 1973, that record was beaten by the World Trade Center building 1, 1,368 feet (417 m, building 2 was eight feet shorter). The Willis Tower followed 1974, and by 2004, the tallest building was the Taipei Tower, 1471 feet. Building heights had grown by 221 feet since 1931, and then the Burj Khalifa in Dubai, 2,426 ft ( 739.44m):. This is over 1000 feet taller than the new freedom tower, and nearly as much taller than the previous record holder. With the Saudi’s beginning work on a building even taller, it’s worthwhile asking how tall you could go, if your only limitations were ego and materials’ strength.

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

Having written about how long you could make a (steel) suspension bridge, the maximum height of a skyscraper seems like a logical next step. At first glance this would seem like a ridiculously easy calculation based on the math used to calculate the maximum length of a suspension bridge. As with the bridge, we’d make the structure from the strongest normal material: T1, low carbon, vanadium steel, and we’d determine the height by balancing this material’s yield strength, 100,000 psi (pounds per square inch), against its density, .2833 pounds per cubic inch.

If you balance these numbers, you calculate a height: 353,000 inches, 5.57 miles, but this is the maximum only for a certain structure, a wide flag-pole of T1 steel in the absent of wind. A more realistic height assumes a building where half the volume is empty space, used for living and otherwise, where 40% of the interior space contains vertical columns of T1 steel, and where there’s a significant amount of dead-weight from floors, windows, people, furniture, etc. Assume the dead weight is the equivalent of filling 10% of the volume with T1 steel that provides no structural support. The resulting building has an average density = (1/2 x 0.2833 pound/in³), and the average strength= (0.4 x 100,000 pound/in²). Dividing these numbers we get a maximum height, but only for a cylindrical building with no safety margin, and no allowance for wind.

H’_max-cylinder = 0.4 x 100,000 pound/in²/ (.5 x 0.2833 pound/in³) = 282,400 inches = 23,532 ft = 4.46 miles.

This is more than ten times the Burj Khalifa, but it likely underestimates the maximum for a steel building, or even a concrete building because a cylinder is not the optimum shape for maximum height. If the towers were constructed conical or pyramidal, the height could be much greater: three times greater because the volume of a cone and thus its weight is 1/3 that of a cylinder for the same base and height. Using the same materials and assumptions,

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

H’_max-cone = 3 H’_max-cylinder = 13.37 miles.

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 we’ll see, is something like the Eiffel tower.

Before speaking about this shape, I’d like to speak about building materials. At the heights we’re discussing, it becomes fairly ridiculous to talk about a steel and glass building. Tall steel buildings have serious vibration problems. Even at heights far before they are destroyed by wind and vibration , the people at the top will begin to feel quite sea-sick. Because of this, the tallest buildings have been constructed out of concrete and glass. Concrete is not practical for bridges since concrete is poor in tension, but concrete can be quite strong in compression, as I discussed here. And concrete is fire resistant, sound-deadening, and vibration dampening. It is also far cheaper than steel when you consider the ease of construction. The Trump Tower in New York and Chicago was the first major building here to be made this way. It, and it’s brother building in Chicago were considered aesthetic marvels until Trump became president. Since then, everything he’s done is ridiculed. Like the Trump tower, the Burj Khalifa is concrete and glass, and I’ll assume this construction from here on.

let’s choose to build out of high-silica, low aggregate, UHPC-3, the strongest concrete in normal construction use. It has a compressive strength of 135 MPa (about 19,500 psi). and a density of 2400 kg/m³ or about 0.0866 lb/in³. Its cost is around $600/m³ today (2019); this is about 4 times the cost of normal highway concrete, but it provides about 8 times the compressive strength. As with the steel building above, I will assume that, at every floor, half of the volume is living space; that 40% is support structure, UHPC-3, and that the other 10% is other dead weight, plumbing, glass, stairs, furniture, and people. Calculating in SI units,

H’_{max-cylinder-concrete} = .4 x 135,000,000 Pa/(.5 x 2400 kg/m³ x 9.8 m/s²) = 4591 m = 2.85 miles.

The factor 9.8 m/s² is necessary when using SI units to account for the acceleration of gravity; it converts convert kg-weights to Newtons. Pascals, by the way, are Newtons divided by square meters, as in this joke. We get the same answer with less difficulty using inches.

H’_{max-cylinder-concrete} = .4 x 19,500 psi/(.5 x.0866 lb/in³) = 180,138″ = 15,012 ft = 2.84 miles

These maximum heights are not as great as for a steel construction, but there are a few advantages; the price per square foot is generally less. Also, you have fewer problems with noise, sway, and fire: all very important for a large building. The maximum height for a conical concrete building is three times that of a cylindrical building of the same design:

H’_{max–cone-concrete} = 3 x H’_{max-cylinder-concrete} = 3 x 2.84 miles = 8.53 miles.

Mount Everest, picture from the Encyclopedia Britannica, a stone cone, 5.5 miles high.

That this is a reasonable number can be seen from the height of Mount Everest. Everest is rough cone , 5.498 miles high. This is not much less than what we calculate above. To reach this height with a building that withstands winds, you have to make the base quite wide, as with Everest. In the absence of wind the base of the cone could be much narrower, but the maximum height would be the same, 8.53 miles, but a cone is not the optimal shape for a very tall building.

I will now calculate the optimal shape for a tall building in the absence of wind. I will start at the top, but I will aim for high rent space. I thus choose to make the top section 31 feet on a side, 1,000 ft², or 100 m². As before, I’ll make 50% of this area living space. Thus, each apartment provides 500 ft² of living space. My reason for choosing this size is the sense that this is the smallest apartment you could sell for a high premium price. Assuming no wind, I can make this part of the building a rectangular cylinder, 2.84 miles tall, but this is just the upper tower. Below this, the building must widen at every floor to withstand the weight of the tower and the floors above. The necessary area increases for every increase in height as follows:

dA/dΗ = 1/σ dW/dH.

Here, A is the cross-sectional area of the building (square inches), H is height (inches), σ is the strength of the building material per area of building (0.4 x 19,500 as above), and dW/dH is the weight of building per inch of height. dW/dH equals A x (.5 x.0866 lb/in³), and

dA/dΗ = 1/ ( .4 x 19,500 psi) x A x (.5 x.0866 lb/in³).

dA/A = 5.55 x 10^-6 dH,

∫dA/A = ∫5.55 x 10^-6 dH,

ln (A_base/A_top) = 5.55 x 10^-6 ∆H,

Here, (A_base/A_top) = A_{base sq feet} /1000, and ∆H is the height of the curvy part of the tower, the part between the ground and the 2.84 mile-tall, rectangular tower at the top.

Since there is no real limit to how big the base can be, there is hardly a limit to how tall the tower can be. Still, aesthetics place a limit, even in the absence of wind. It can be shown from the last equation above that stability requires that the area of the curved part of the tower has to double for every 1.98 miles of height: 1.98 miles = ln(2) /5.55 x 10^-6 inches, but the rate of area expansion also keeps getting bigger as the tower gets heavier. I’m going to speculate that, because of artistic ego, no builder will want a tower that slants more than 45° at the ground level (the Eiffel tower slants at 51°). For the building above, it can be shown that this occurs when:

dA/dH = 4√A_base. But since

dA/dH = A 5.55 x 10^-6 , we find that, at the base,

5.55 x 10^-6 √A_base = 4.

At the base, the length of a building side is L_base = √A_base= 4 /5.55 x 10^-6 inches = 60060 ft = 11.4 miles. Artistic ego thus limits the area of the building to slightly over 11 miles wide of 129.4 square miles. This is about the area of Detroit. From the above, we calculate the additional height of the tower as

∆H = ln (A_base/A_top)/ 5.55 x 10^-6 inches = 15.1/ 5.55 x 10^-6 inches = 2,720,400 inches = 226,700 feet = 42.94 miles.

H_max-concrete = 2.84 miles + ∆H = 45.78 miles. This is eight times the height of Everest, and while air pressure is pretty low at this altitude, it’s not so low that wind could be ignored. One of these days, I plan to show how you redo this calculation without the need for calculus, but with the inclusion of wind. I did the former here, for a bridge, and treated wind here. Anyone wishing to do this calculation for a basic maximum wind speed (100 mph?) will get a mention here.

From the above, it’s clear that our present buildings are nowhere near the maximum achievable, even for construction with normal materials. We should be able to make buildings several times the height of Everest. Such Buildings are worthy of Nimrod (Gen 10:10, etc.) for several reasons. Not only because of the lack of a safety factor, but because the height far exceeds that of the highest mountain. Also, as with Nimrod’s construction, there is a likely social problem. Let’s assume that floors are 16.5 feet apart (1 rod). The first 1.98 miles of tower will have 634 floors with each being about the size of Detroit. Lets then assume the population per floor will be about 1 million; the population of Detroit was about 2 million in 1950 (it’s 0.65 million today, a result of bad government). At this density, the first 1.98 miles will have a population of 634 million, about double that of the United States, and the rest of the tower will have the same population because the tower area contracts by half every 1.98 miles, and 1/2 + 1/4 + 1/8 + 1/16 … = 1.

Nimrod examining the tower, Peter Breugel

We thus expect the tower to hold 1.28 Billion people. With a population this size, the tower will develop different cultures, and will begin to speak different languages. They may well go to war too — a real problem in a confined space. I assume there is a moral in there somewhere, like that too much unity is not good. For what it’s worth, I even doubt the sanity of having a single government for 1.28 billion, even when spread out (e.g. China).

Robert Buxbaum, June 3, 2019.

Vitamin A and E, killer supplements; B, C, and D are meh.

How long could you make a suspension bridge?

1 Reply

The above is one of the engineering questions that puzzled me as a student engineer at Brooklyn Technical High School and at Cooper Union in New York. The Brooklyn Bridge stood as a wonder of late 1800s engineering, and it had recently been eclipsed by the Verrazano bridge, a pure suspension bridge. At the time it was the longest and heaviest in the world. How long could a bridge be made, and why did Brooklyn bridge have those catenary cables, when the Verrazano didn’t? (Sometimes I’d imagine a Chinese engineer being asked the top question, and answering “Certainly, but How Long is my cousin.”)

I found the above problem unsolvable with the basic calculus at my disposal. because it was clear that both the angle of the main cable and its tension varied significantly along the length of the cable. Eventually I solved this problem using a big dose of geometry and vectors, as I’ll show.

Vector diagram of forces on the cable at the center-left of the bridge.

Consider the above vector diagram (above) of forces on a section of the main cable near the center of the bridge. At the right, the center of the bridge, the cable is horizontal, and has a significant tension. Let’s call that T°. Away from the center of the bridge, there is a vertical cable supporting a fraction of roadway. Lets call the force on this point w. It equals the weight of this section of cable and this section of roadway. Because of this weight, the main cable bends upward to the left and carries more tension than T°. The tangent (slope) of the upward curve will equal w/T°, and the new tension will be the vector sum along the new slope. From geometry, T= √(w² +T°²).

Vector diagram of forces on the cable further from the center of the bridge.

As we continue from the center, there are more and more verticals, each supporting approximately the same weight, w. From geometry, if w weight is added at each vertical, the change in slope is always w/T° as shown. When you reach the towers, the weight of the bridge must equal 2T Sin Θ, where Θ is the angle of the bridge cable at the tower and T is the tension in the cable at the tower.

The limit to the weight of a bridge, and thus its length, is the maximum tension in the main cable, T, and the maximum angle, that at the towers. Θ. I assumed that the maximum bridge would be made of T1 bridge steel, the strongest material I could think of, with a tensile strength of 100,000 psi, and I imagined a maximum angle at the towers of 30°. Since there are two towers and sin 30° = 1/2, it becomes clear that, with this 30° angle cable, the tension at the tower must equal the total weight of the bridge. Interesting.

Now, to find the length of the bridge, note that the weight of the bridge is proportional to its length times the density and cross section of the metal. I imagined a bridge where the half of the weight was in the main cable, and the rest was in the roadway, cars and verticals. If the main cable is made of T1 “bridge steel”, the density of the cable is 0.2833 lb/in3, and the density of the bridge is twice this. If the bridge cable is at its yield strength, 100,000 psi, at the towers, it must be that each square inch of cable supports 50,000 pounds of cable and 50,000 lbs of cars, roadway and verticals. The maximum length (with no allowance for wind or a safety factor) is thus

L(max) = 100,000 psi / 2 x 0.2833 pounds/in3 = 176,500 inches = 14,700 feet = 2.79 miles.

This was more than three times the length of the Verrazano bridge, whose main span is ‎4,260 ft. I attributed the difference to safety factors, wind, price, etc. I then set out to calculate the height of the towers, and the only rational approach I could think of involved calculus. Fortunately, I could integrate for the curve now that I knew the slope changed linearly with distance from the center. That is for every length between verticals, the slope changes by the same amount, w/T°. This was to say that d²y/dx² = w/T° and the curve this described was a parabola.

Rather than solving with heavy calculus, I noticed that the slope, dy/dx increases in proportion to x, and since the slope at the end, at L/2, was that of a 30° triangle, 1/√3, it was clear to me that

dy/dx = (x/(L/2))/√3

where x is the distance from the center of the bridge, and L is the length of the bridge, 14,700 ft. dy/dx = 2x/L√3.

We find that:
H = ∫dy = ∫ 2x/L√3 dx = L/4√3 = 2122 ft,

where H is the height of the towers. Calculated this way, the towers were quite tall, higher than that of any building then standing, but not impossibly high (the Dubai tower is higher). It was fairly clear that you didn’t want a tower much higher than this, though, suggesting that you didn’t want to go any higher than a 30° angle for the main cable.

I decided that suspension bridges had some advantages over other designs in that they avoid the problem of beam “buckling.’ Further, they readjust their shape somewhat to accommodate heavy point loads. Arch and truss bridges don’t do this, quite. Since the towers were quite a lot taller than any building then in existence, I came to I decide that this length, 2.79 miles, was about as long as you could make the main span of a bridge.

I later came to discover materials with a higher strength per weight (titanium, fiber glass, aramid, carbon fiber…) and came to think you could go longer, but the calculation is the same, and any practical bridge would be shorter, if only because of the need for a safety factor. I also came to recalculate the height of the towers without calculus, and got an answer that was shorter, for some versions, a hundred feet shorter, as shown here. In terms of wind, I note that you could make the bridge so heavy that you don’t have to worry about wind except for resonance effects. Those are the effects are significant, but were not my concern at the moment.

The Brooklyn Bridge showing its main cable suspension structure and its catenaries.

Now to discuss catenaries, the diagonal wires that support many modern bridges and that, on the Brooklyn bridge, provide support at the ends of the spans only. Since the catenaries support some weight of the Brooklyn bridge, they decrease the need for very thick cables and very high towers. The benefit goes down as the catenary angle goes to the horizontal, though as the lower the angle the longer the catenary, and the lower the fraction of the force goes into lift. I suspect this is why Roebling used catenaries only near the Brooklyn bridge towers, for angles no more than about 45°. I was very proud of all this when I thought it through and explained it to a friend. It still gives me joy to explain it here.

Robert Buxbaum, May 16, 2019. I’ve wondered about adding vibration dampers to very long bridges to decrease resonance problems. It seems like a good idea. Though I have never gone so far as to do calculations along these lines, I note that several of the world’s tallest buildings were made of concrete, not steel, because concrete provides natural vibration damping.

The Japanese diet, a recipe for stomach cancer.

3 Replies

Japan has the highest life expectancy in the world, an average about 84.1 years, compared to 78.6 years for the US. That difference is used to suggest that the Japanese diet must be far healthier than the American. We should all drink green tea and eat such: rice with seaweed and raw or smoked fish. Let me begin by saying that correlation does not imply causation, and go further to say that, to the extent that correlation suggests causation, the Japanese diet seems worse. It seems to me that the quantity of food (and some other things) are responsible for Americans have a shorter life-span than Japanese, the quality our diet does not appear to be the problem. That is, Americans eat too much, but what we eat is actually healthier than what the Japanese eat.

Top 15 causes of death in Japan and the US in order of Japanese relevance.

Let’s look at top 15 causes of deaths in Japan and the US in order of significance for Japan (2016). The top cause of disease death is the same for Japan and the US: it’s heart disease. Per-capita, 14.5% of Japanese people die of this, and 20.9% of Americans. I suspect the reason that we have more heart disease is that we are more overweight, but the difference is not by that much currently. The Japanese are getting fatter. Similarly, we exceed the Japanese in lung cancer deaths (not by that much) a hold-over of smoking, and by liver disease (not by that much either), a holdover of drinking, I suspect.

Japan exceeds the US in Stroke death (emotional pressure?) and suicide (emotional pressure?) and influenza deaths (climate-related?). The emotional pressure is not something we’d want to emulate. The Japanese work long hours, and face enormous social pressure to look prosperous, even when they are not. There is a male-female imbalance in Japan that is a likely part of the emotional pressure. There is a similar imbalance in China, and a worse one in Qatar. I would expect to see social problems in both in the near future. So far, the Japanese deal with this by alcoholism, something that shows up as liver cancer and cirrhosis. I expect the same in China and Qatar, but have little direct data.

Returning to diet, Japan has more far more stomach cancer deaths than the US; it’s a margin of nine to one. It’s the number 5 killer in Japan, taking 5.08% of Japanese, but only 0.57% of Americans. I suspect the difference is the Japanese love of smoked and raw fish. Other diet-related diseases tell the same story. Japan has double our rate of Colon-rectal cancers, and higher rates of kidney disease, pancreatic cancer, and liver cancer. The conclusion that I draw is that green tea and sushi are not as healthy as you might think. The Japanese would do well to switch the Trump staples of burgers, pizza, fries, and diet coke.

The three horsemen of the US death-toll: Automobiles, firearms, and poisoning (drugs). 2008 data.

At this point you can ask why our lives are so much shorter than the Japanese, on average. The difference in smoking and weight-related diseases are significant but explain only part of the story. There is also guns. About 0.7% of Americans are killed by guns, compared to 0.07% of Japanese. Still, guns give Americans a not-unjustified sense of safety from worse crime. Then there is traffic death, 1.5% in the US vs 0.5% in Japan. But the biggest single reason that Americans live shorter lives is drugs. Drugs kill about 1.5% of Americans, but mostly the young and middle ages. They show up in US death statistics mostly as over-dose and unintentional poisoning (overdose deaths), but also contribute to many other problems like dementia in the old. Drugs and poisoning do not shown on the chart above, because the rate of both is insignificant in Japan, but it is the single main cause of US death in middle age Americans.

The king of the killer drugs are the opioids, a problem that was bad in the 60s, the days of Mother’s Little helper, but that have gotten dramatically worse in the last 20 years as the chart above shows. Often it is a doctor who gets us hooked on the opioids. The doctor may think it’s a favor to us to keep us from pain, but it’s also a favor to him since the drug companies give kickbacks. Often people manage to become un-hooked, but then some doctor comes by and re-hooks us up. Unlike LSD or cocaine, opioid drugs strike women and men equally. It is the single major reason we live 5 1/2 years shorter than the Japanese, with a life-span that is shrinking.

Drug overuse seems like the most serious health problem Americans face, and we seem intent on ignoring it. The other major causes of death are declining, but drug-death numbers keep rising. By 2007, more people died of drugs than guns, and nearly as many as from automobile accidents. It’s passed automobile accidents since then. A first suggestion here: do not elect any politician who has taken significant money from the drug companies. A second suggestion: avoid the Japanese diet.

Robert Buxbaum, April 28, 2019.

REB Research Blog

Random thoughts about hydrogen, engineering, business and life by Dr. Robert E. Buxbaum

The free press isn’t

Like this:

Bitcoin v cash to avoid Trump’s tariffs or ransom a sailor

Like this:

Thermal stress failure

Like this:

Shakespeare’s plays, organized.

Like this:

Making The City of New Orleans profitable

Like this:

How to avoid wet basements

Like this:

How tall could you make a skyscraper?

Like this:

Vitamin A and E, killer supplements; B, C, and D are meh.

Like this:

How long could you make a suspension bridge?

Like this:

The Japanese diet, a recipe for stomach cancer.

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this: