Monthly Archives: October 2013

An Aesthetic of Mechanical Strength

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Back when I taught materials science to chemical engineers, I used the following poem to teach my aesthetic for the strength target for product design:

The secret to design, as the parson explained, is that the weakest part must withstand the strain. And if that part is to withstand the test, then it must be made as strong as all the rest. (by R.E. Buxbaum, based on “The Wonderful, One-hoss Shay, by Oliver Wendell Holmes, 1858).

My thought was, if my students had no idea what good mechanical design looked like, they’d never  be able to it well. I wanted them to realize that there is always a weakest part of any device or process for every type of failure. Good design accepts this and designs everything else around it. You make sure that the device will fail at a part of your choosing, when it fails, preferably one that you can repair easily and cheaply (a fuse, or a door hinge), and which doesn’t cause too much mayhem when it fails. Once this failure part is chosen and in place, I taught that the rest should be stronger, but there is no point in making any other part of that failure chain significantly stronger than the weakest link. Thus for example, once you’ve decided to use a fuse of a certain amperage, there is no point in making the rest of the wiring take more than 2-3 times the amperage of the fuse.

This is an aesthetic argument, of course, but it’s important for a person to know what good work looks like (to me, and perhaps to the student) — beyond just by compliments from the boss or grades from me. Some day, I’ll be gone, and the boss won’t be looking. There are other design issues too: If you don’t know what the failure point is, make a prototype and test it to failure, and if you don’t like what you see, remodel accordingly. If you like the point of failure but decide you really want to make the device stronger or more robust, be aware that this may involve strengthening that part only, or strengthening the entire chain of parts so they are as failure resistant as this part (the former is cheaper).

I also wanted to teach that there are many failure chains to look out for: many ways that things can wrong beyond breaking. Check for failure by fire, melting, explosion, smell, shock, rust, and even color change. Color change should not be ignored, BTW; there are many products that people won’t use as soon as they look bad (cars, for example). Make sure that each failure chain has it’s own known, chosen weak link. In a car, the paint on a car should fade, chip, or peel some (small) time before the metal underneath starts rusting or sagging (at least that’s my aesthetic). And in the DuPont gun-powder mill below, one wall should be weaker so that the walls should blow outward the right way (away from traffic).Be aware that human error is the most common failure mode: design to make things acceptably idiot-proof.

Dupont powder mills had a thinner wall and a stronger wall so that, if there were an explosion it would blow out towards the river. This mill has a second wall to protect workers. The thinner wall should be barely strong enough to stand up to wind and rain; the stronger walls should stand up to explosions that blow out the other wall.

Dupont powder mills had a thinner wall and a stronger wall so that, if there were an explosion, it would blow out ‘safely.’ This mill has a second wall to protect workers. The thinner wall must be strong enough to stand up to wind and rain; the stronger walls should stand up to all likely explosions.

Related to my aesthetic of mechanical strength, I tried to teach an aesthetic of cost, weight, appearance, and green: Choose materials that are cheaper, rather than more expensive; use less weight rather than more if both ways worked equally well. Use materials that look better if you’ve got the choice, and use recyclable materials. These all derive from the well-known axiom, omit needless stuff. Or, as William of Occam put it, “Entia non sunt multiplicanda sine necessitate.” As an aside, I’ve found that, when engineers use Latin, we look smart: “lingua bona lingua motua est.” (a good language is a dead language) — it’s the same with quoting 19th century poets, BTW: dead 19th century poets are far better than undead ones, but I digress.

Use of recyclable materials gets you out of lots of problems relative to materials that must be disposed of. E.g. if you use aluminum insulation (recyclable) instead of ceramic fiber, you will have an easier time getting rid of the scrap. As a result, you are not as likely to expose your workers (or you) to mesothelioma, or similar disease. You should not have to pay someone to haul away excess or damaged product; a scraper will oblige, and he may even pay you for it if you have enough. Recycling helps cash flow with decommissioning too, when money is tight. It’s better to find your $1 worth of scrap is now worth $2 instead of discovering that your $1 worth of garbage now costs $2 to haul away. By the way, most heat loss is from black body radiation, so aluminum foil may actually work better than ceramics of the same thermal conductivity.

Buildings can be recycled too. Buy them and sell them as needed. Shipping containers make for great lab buildings because they are cheap, strong, and movable. You can sell them off-site when you’re done. We have a shipping container lab building, and a shipping container storage building — both worth more now than when I bought them. They are also rather attractive with our advertising on them — attractive according to my design aesthetic. Here’s an insight into why chemical engineers earn more than chemists; and insight into the difference between mechanical engineering and civil engineering. Here’s an architecture aesthetic. Here’s one about the scientific method.

Robert E. Buxbaum, October 31, 2013

Lets make a Northwest Passage

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The Northwest passage opened briefly last year, and the two years before allowing some minimal shipping between the Atlantic and the Pacific by way of the Arctic ocean, but was closed in 2013 because there was too much ice. I’ve a business / commercial thought though: we could make a semi-permanent northwest passage if we dredged a canal across the Bootha peninsula at Taloyoak, Nunavut (Canada).Map of Northern Canada showing cities and the Perry Channel, the current Northwest passage. A canal north of the Bootha Peninsula would seem worthwhile.

Map of Northern Canada showing cities and the Perry Channel, the current Northwest passage. A canal north or south of the Bootha Peninsula would seem worthwhile.

 

 

As things currently stand, ships must sail 500 miles north of Taloyoak, and traverse the Parry Channel. Shown below is a picture of ice levels in August 2012 and 2013. The proposed channels could have been kept open even in 2013 providing a route for valuable shipping commerce. As a cheaper alternative, one could maintain the Hudson Bay trading channel at Fort Ross, between the Bootha Peninsula and Somerset Island. This is about 250 miles north of Taloyoak, but still 250 miles south of the current route.

Arctic Ice August 2012-2013; both Taloyoak and Igloolik appear open this year.

The NW passage was open by way of the Perry Channel north of Somerset Island and Baffin Island in 2012, but not 2013. The proposed channels could have been kept open even this year.

Dr. Robert E. Buxbaum, October 2013. Here are some random thoughts on Canadian crime, the true north, and the Canadian pastime (Ice fishing).

Arctic and Antarctic Ice Increases; Antarctic at record levels

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Good news if you like ice. I’m happy to report that there has been a continued increase in the extent of both Antarctic and Arctic Ice sheets, in particular the Antarctic sheet. Shown below is a plot of Antarctic ice size (1981-2010) along with the average (the black line), the size for 2012 (dotted line), and the size for 2013 so far. This year (2013) it’s broken new records. Hooray for the ice.

Antarctic ice at record size in 2013, after breaking records in 2012

Antarctic ice at record size in 2013, after a good year in 2012

The arctic ice has grown too, and though it’s not at record levels, the Arctic ice growth  is more visually dramatic, see photo below. It’s also more welcome — to polar bears at least. It’s not so welcome if you are a yachter, or a shipping magnate trying to use the Northwest passage to get your products to market cheaply.

Arctic Ice August 2012-2013

Arctic Ice August 2012-2013

The recent (October 2013) global warming report from NASA repeats the Arctic melt warnings from previous reports, but supports that assertion with an older satellite picture — the one from 2006. That was a year when the Arctic had even less ice than in 2012, but the date should be a warning. From the picture, you’d think it’s an easy sail through the Northwest passage; some 50 yachts tried it this summer, and none got through, though some got half way. It’s a good bet you can buy those ships cheap.

I should mention that only the Antarctic data is relevant to Al Gore’s 1996 prediction of a 20 foot rise in the sea level by 2100. Floating ice, as in the arctic, displaces the same amount of mass as water. Ice floats but has the same effect on sea level as if it were melted; it’s only land-based ice that affects sea level. While there is some growth seen in land-ice in the arctic photos above — compare Greenland and Canada on the 2 photos, there is also a lot of glacier ice loss in Norway (upper left corners). The ocean levels are rising, but I don’t think this is the cause, and it’s not rising anywhere near as fast as Al Gore said: more like 1.7mm/year, or 6.7 inches per century. I don’t know what the cause is, BTW. Perhaps I’ll post speculate on this when I have a good speculation.

Other good news: For the past 15 years global warming appears to have taken a break. And the ozone hole shrunk in 2012 to near record smallness. Yeah ozone. The most likely model for all this, in my opinion, is to view weather as chaotic and fractal; that is self-similar. Calculus works on this, just not the calculus that’s typically taught in school. Whatever the cause, its good news, and welcome.

Robert E. Buxbaum, October 21, 2013. Here are some thoughts about how to do calculus right, and how to do science right; that is, look at the data first; don’t come in with a hypothesis.

Calculus is taught wrong, and is often wrong

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The high point of most people’s college math is The Calculus. Typically this is a weeder course that separates the science-minded students from the rest. It determines which students are admitted to medical and engineering courses, and which will be directed to english or communications — majors from which they can hope to become lawyers, bankers, politicians, and spokespeople (the generally distrusted). While calculus is very useful to know, my sense is that it is taught poorly: it is built up on a year of unnecessary pre-calculus and several shady assumptions that were not necessary for the development, and that are not generally true in the physical world. The material is presented in a way that confuses and turns off many of the top students — often the ones most attached to the reality of life.

The most untenable assumption in calculus teaching, in my opinion, are that the world involves continuous functions. That is, for example, that at every instant in time an object has one position only, and that its motion from point to point is continuous, defining a slow-changing quantity called velocity. That is, every x value defines one and only one y value, and there is never more than a small change in y at the limit of a small change in X. Does the world work this way? Some parts do, others do not. Commodity prices are not really defined except at the moment of sale, and can jump significantly between two sales a micro-second apart. Objects do not really have one position, the quantum sense, at any time, but spread out, sometimes occupying several positions, and sometimes jumping between positions without ever occupying the space in-between.

These are annoying facts, but calculus works just fine in a discontinuous world — and I believe that a discontinuous calculus is easier to teach and understand too. Consider the fundamental law of calculus. This states that, for a continuous function, the integral of the derivative of changes equals the function itself (nearly incomprehensible, no?) Now consider the same law taught for a discontinuous group of changes: the sum of the changes that take place over a period equals the total change. This statement is more general, since it applies to discrete and continuous functions, and it’s easier to teach. Any idiot can see that this is true. By contrast, it takes weeks of hard thinking to see that the integral of all the derivatives equals the function — and then it takes more years to be exposed to delta functions and realize that the statement is still true for discrete change. Why don’t we teach so that people will understand? Teach discrete first and then smooth as a special case where the discrete changes happen at a slow rate. Is calculus taught this way to make us look smart, or because we want this to be a weeder course?

Because most students are not introduced to discrete change, they are in a very poor position  to understand, or model, activities that are discreet, like climate change or heart rate. Climate only makes sense year to year, as day-to-day behavior is mostly affected by seasons, weather, and day vs night. We really want to model the big picture and leave out the noise by considering each day or year as a whole, keeping track of the average temperature for noon on September 21, for example. Similarly with heart rate, the rate has no meaning if measured every microsecond; it’s only meaning is as a measure of the time between beats. If we taught calculus in terms of discrete functions, our students would be in a better place to deal with these things, and in a better place to deal with total discontinuous behaviors, like chaos and fractals, an important phenomena when dealing with economics, for example.

A fundamental truth of quantum mechanics is that there is no defined speed and position of an object at any given time. Students accept this, but (because they are used to continuous change) they come to wonder how it is that over time energy is conserved. It’s simple, quantum motion involves a gross discrete changes in position that leaves energy conserved by the end, but where an item goes from here to there without ever having to be in the middle. This helps explain the old joke about Heisenberg and his car.

Calculus-based physics is taught in terms of limits and the mean value theorem: that if x is the position of a thing at any time, t then the derivative of these positions, the velocity, will approach ∆x/∆t more and more as ∆x and ∆t become more tightly defined. When this is found to be untrue in a quantum sense, the remnant of the belief in it hinders them when they try to solve real world problems. Normal physics is the limit of quantum physics because velocity is really a macroscopic ratio of difference in position divided by macroscopic difference in time. Because of this, it is obvious that the sum of these differences is the total distance traveled even when summed over many simultaneous paths. A feature of electromagnetism, Green’s theorem becomes similarly obvious: the sum effect of a field of changes is the total change. It’s only confusing if you try to take the limits to find the exact values of these change rates at some infinitesimal space.

This idea is also helpful in finance, likely a chaotic and fractal system. Finance is not continuous: just because a stock price moved from $1 to $2 per share in one day does not mean that the price was ever $1.50 per share. While there is probably no small change in sales rate caused by a 1¢ change in sales price at any given time, this does not mean you won’t find it useful to consider the relation between the sales of a product. Though the details may be untrue, the price demand curve is still very useful (but unjustified) abstraction.

This is not to say that there are not some real-world things that are functions and continuous, but believing that they are, just because the calculus is useful in describing them can blind you to some important insights, e.g. of phenomena where the butterfly effect predominates. That is where an insignificant change in one place (a butterfly wing in China) seems to result in a major change elsewhere (e.g. a hurricane in New York). Recognizing that some conclusions follow from non-continuous math may help students recognize places where some parts of basic calculus allies, while others do not.

Dr. Robert Buxbaum (my thanks to Dr. John Klein for showing me discrete calculus).

Improving Bankrupt Detroit

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Detroit is Bankrupt in more ways than one. Besides having too few assets to cover their $18 Billion in debts, and besides running operational deficits for years, Detroit is bankrupt in the sense that most everyone who can afford to leaves. The population has shrunk from 2,000,000 in 1950 to about 680,000 today, an exodus that shows no sign of slowing.

The murder rate in Detroit is 25 times the state average; 400/year in 2012 (58/100,00) as compared to 250 in the rest of the state (2.3/100,000). The school system in 2009 scored the lowest math scores that had ever been recorded for any major city in the 21 year history of the tests. And mayor Kwame Kilpatrick, currently in prison, was called “a walking crime wave” by the mayor of Washington DC. The situation is not pretty. Here are a few simple thoughts though.

(1) Reorganize the city to make it smaller. The population density of Detroit is small, generally about 7000/ square mile, and some of the outlying districts might be carved off and made into townships. Most of Michigan started as townships. When they return to that status, each could contract their children’s education as they saw fit, perhaps agreeing to let the outlying cities use their school buildings and teachers, or perhaps closing failed schools as the local area sees fit.

This could work work well for outlying areas like the southern peninsula of Detroit, Mexicantown and south, a narrow strip of land lying along Route 75 that’s further from the center of Detroit than it is from the centers of 5 surrounding cities: River Rouge, Ecorse, Dearborn, Melvindale, and Lincoln Park. This area was Stillwell township before being added to Detroit in 1922. If removed from Detroit control the property values would likely rise. The people could easily contract education or police with any of the 5 surrounding cities that were previously parts of Stillwell township. Alternately, this newly created township might easily elect to join one of the surrounding communities entirely. All the surrounding communities offer lower crime and better services than Detroit. Most manage to do it with lower tax rates too.

Another community worth removing from Detroit is the western suburb previously known as Greenfield, This community was absorbed into Detroit in 1925. Like the Mexicantown area, this part of Detroit still has a majority of the houses occupied, and the majority of the businesses are viable enough that the area could reasonably stand on its own. Operating as a township, they could bring back whatever services they consider more suitable to their population. They would be in control of their own destiny.

 

How to make fine lemonade

As part of discussing a comment by H.L. Mencken, that a philosopher was a man in a dark room looking for a black cat that wasn’t there, I alluded to the idea that a good person should make something or do something, perhaps make lemonade, but I gave no recipe. Here is the recipe for lemonade something you can do with your life that benefits everyone around:

The key is to use lots of water, and not too much lemon. Start a fresh lemon and two 16 oz glasses. Cut the lemon in half and squeeze half into each glass, squeezing out all of the juice by hand (you can use a squeezer). Ideally, you should pass the juice through a screen for the pits, but if you don’t have one it’s OK — pits sink to the bottom. Add 8 oz of water and 2 tbs of sugar to each (1/8 cup). Stir well until the sugar dissolves, add the lemon rind (I like to cut this into 3rds); stir again and add a handful of ice. This should get you to 3/4″ of the top, but if not add more water. Enjoy.

For a more-adult version, use less water and sugar, but add a shot of Cognac and a shot of Cointreau. It’s called a side-car, one of the greatest of all drinks.

Robert E. Buxbaum *82