Monthly Archives: June 2019

Shakespeare’s plays, organized.

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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

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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

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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?

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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 (Abase/Atop) = 5.55 x 10-6 ∆H,

Here, (Abase/Atop) = Abase 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√Abase.  But since

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

5.55 x 10-6 √Abase = 4.

At the base, the length of a building side is Lbase = √Abase=  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 (Abase/Atop)/ 5.55 x 10-6 inches =  15.1/ 5.55 x 10-6 inches = 2,720,400 inches = 226,700 feet = 42.94 miles.

Hmax-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.