Einstein, Newton, and the two Pascal brothers are playing hide and seek. Einstein has his eyes covered and is counting. The two Pascal bothers run and hide but Isaac Newton does not. He draws a square around him in the dust and stands waiting. When Einstein finishes counting he says, “I see you Sir Isaac standing there.” “No you don’t.” says Newton. “You see two Pascals: there’s one Newton in half a square meter area.
Category Archives: Science: Physics, Astronomy, etc.
For parents of a young scientist: math
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It is not uncommon for parents to ask my advice or help with their child; someone they consider to be a young scientist, or at least a potential young scientist. My main advice is math.
Most often the tyke is 5 to 8 years old and has an interest in weather, chemistry, or how things work. That’s a good age, about the age that the science bug struck me, and it’s a good age to begin to introduce the power of math. Math isn’t the total answer, by the way; if your child is interested in weather, for example, you’ll need to get books on weather, and you’ll want to buy a weather-science kit at your local smart-toy store (look for one with a small wet-bulb and dry bulb thermometer setup so that you’ll be able to discuss humidity in some modest way: wet bulb temperatures are lower than dry bulb with a difference that is higher the lower the humidity; it’s zero at 100%). But math makes the key difference between the interest blooming into science or having it wilt or worse. Math is the language of science, and without it there is no way that your child will understand the better books, no way that he or she will be able to talk to others who are interested, and the interest can bloom into a phobia (that’s what happens when your child has something to express, but can’t speak about it in any real way).
Math takes science out of the range of religion and mythology, too. If you’re stuck to the use of words, you think that the explanations in science books resemble the stories of the Greek gods. You either accept them or you don’t. With math you see that they are testable, and that the versions in the book are generally simplified approximations to some more complex description. You also get to see that there the descriptions are testable, and that are many, different looking descriptions that will fit the same phenomena. Some will be mathematically identical, and others will be quite different, but all are testable as the Greek myths are not.
What math to teach depends on your child’s level and interests. If the child is young, have him or her count in twos or fives, or tens, etc. Have him or her learn to spot patterns, like that the every other number that is divisible by 5 ends in zero, or that the sum of digits for every number that’s divisible by three is itself divisible by three. If the child is a little older, show him or her geometry, or prime numbers, or squares and cubes. Ask your child to figure out the sum of all the numbers from 1 to 100, or to estimate the square-root of some numbers. Ask why the area of a circle is πr2 while the circumference is 2πr: why do both contain the same, odd factor, π = 3.1415926535… All these games and ideas will give your child a language to use discussing science.
If your child is old enough to read, I’d definitely suggest you buy a few books with nice pictures and practical examples. I’d grown up with the Giant Golden book of Mathematics by Irving Adler, but I’ve seen and been impressed with several other nice books, and with the entire Golden Book series. Make regular trips to the library, and point your child to an appropriate section, but don’t force the child to take science books. Forcing your child will kill any natural interest he or she has. Besides, having other interests is a sign of normality; even the biggest scientist will sometimes want to read something else (sports, music, art, etc.) Many scientists drew (da Vinci, Feynman) or played the violin (Einstein). Let your child grow at his or her own pace and direction. (I liked the theater, including opera, and liked philosophy).
Now, back to the science kits and toys. Get a few basic ones, and let your child play: these are toys, not work. I liked chemistry, and a chemistry set was perhaps the best toy I ever got. Another set I liked was an Erector set (Gilbert). Get good sets that they pick out, but don’t be disappointed if they don’t do all the experiments, or any of them. They may not be interested in this group; just move on. I was not interested in microscopy, fish, or animals, for example. And don’t be bothered if interests change. It’s common to start out interested in dinosaurs and then to change to an interest in other things. Don’t push an old interest, or even an active new interest: enough parental pushing will kill any interest, and that’s sad. As Solomon the wise said, the fire is more often extinguished by too much fuel than by too little. But you do need to help with math, though; without that, no real progress will be possible.
Oh, one more thing, don’t be disappointed if your child isn’t interested in science; most kids aren’t interested in science as such, but rather in something science-like, like the internet, or economics, or games, or how things work. These areas are all great too, and there is a lot more room for your child to find a good job or a scholarship based on their expertise in theses areas. Any math he or she learns is certain to help with all of these pursuits, and with whatever other science-like direction he or she takes. — Good luck. Robert Buxbaum (Economics isn’t science, not because of the lack of math, but because it’s not reproducible: you can’t re-run the great depression without FDR’s stimulus, or without WWII)
Heisenberg joke and why water is wet
I love hydrogen in large part because it is a quantum fluid. To explain what that means and how that leads to water being wet, let me begin with an old quantum physics joke.
Werner Heisenberg is speeding down a highway in his car when he’s stopped by a police officer. “Do you know how fast you were going?” asks the officer. “No idea” answers Heisenberg, “but I know exactly where I am.”
The joke relates to a phenomenon of quantum physics that states that the more precisely you can know the location of something, the less precisely you can infer the speed. Thus, the fact that Heisenberg knew precisely where he was implied that he could have no idea of the car’s speed. Of course, this uncertainty is mostly seen with small things like light and electrons –and a bit with hydrogen, but hardly at all with a car or with Dr. Heisenberg himself (and that’s why it’s funny).
This funky property is related to something you may have wondered about: why is water wet? That is, why does water cling to your hands or clothes while liquid teflon repels. Even further, you may have wondered why water is a liquid at normal conditions when H2S is a gas; H2S is a heavier analog, so if one of the two were a liquid, you’d think it was H2S.
Both phenomena are understood through hydrogen behaving as the quantum car above. Oxygen atoms are pretty small, and hydrogen atoms are light enough to start behaving in a quantum way. When a hydrogen atom attaches to an oxygen atom to form part of a water molecule, its location becomes fixed rather precisely. As a result, the hydrogen atom gains velocity (the hydrogen isn’t going anywhere with this velocity, and it’s sometimes called zero-point energy), but because of this velocity or energy, its bond to the oxygen becomes looser than it would be if you had heavier hydrogen. When the oxygen of another water molecule or of a cotton cellulose molecule comes close, the hydrogen starts to hop back and forth between the two oxygen atoms. This reduces the velocity of the hydrogen atom, and stabilizes the assemblage. There is now less kinetic energy (or zero-point energy) in the system, and this stability is seen as a bond that is caused not by electron sharing but by hydrogen sharing. We call the reasonably stable bond between molecules that share a hydrogen atom this way a “hydrogen bond.” (now you know).
The hydrogen bond is why water is a liquid and is the reason water is wet. The hydrogen atom jumping between water molecules stabilizes the liquid water more than it would stabilize liquid H2S. Since sulfur atoms are bigger than oxygen atoms, the advantage of hydrogen jumping is smaller. As a result, the heat of vaporization of water is higher than that of H2S, and water is a liquid at normal conditions while H2S is a gas.
Water sticks to cotton or your skin the same way, hydrogen atoms skip between the oxygen of water molecules and of these surfaces creating a bond. It is said to whet these surfaces, and the result is that water is found to be wet. Liquid teflon does not have hydrogen atoms that can jump so there is no band that could be made from that direction (there are some hydrogen atoms on the cotton that can jump to the teflon, but there is no advantage to bonding of this sort as there are only a few hydrogen atoms, and these already jump to other oxygens in the cotton. Thus, to jump to the teflon would mean breaking a bond with other oxygen atoms in the cotton — there would be no energy advantage. This then is just one of the reasons I love hydrogen: it’s a quantum-y material.
Why isn’t the sky green?
Yesterday I blogged with a simple version of why the sky was blue and not green. Now I’d like to add mathematics to the treatment. The simple version said that the sky was blue because the sun color was a spectrum centered on yellow. I said that molecules of air scattered mostly the short wavelength, high frequency light colors, indigo and blue. This made the sky blue. I said that, the rest of the sunlight was not scattered, so that the sun looked yellow. I then said that the only way for the sky to be green would be if the sun were cooler, orange say, then the sky would be green. The answer is sort-of true, but only in a hand-waving way; so here’s the better treatment.
Light scatters off of dispersed small particles in proportion to wavelength to the inverse 4th power of the wavelength. That is to say, we expect air molecules will scatter more short wavelength, cool colors (purple and indigo) than warm colors (red and orange) but a real analysis must use the actual spectrum of sunlight, the light power (mW/m2.nm) at each wavelength.
intensity of sunlight as a function of wavelength
The first thing you’ll notice is that the light from our sun isn’t quite yellow, but is mostly green. Clearly plants understand this, otherwise chlorophyl would be yellow. There are fairly large components of blue and red too, but my first correction to the previous treatment is that the yellow color we see as the sun is a trick of the eye called additive color. Our eyes combine the green and red of the sun’s light, and sees it as yellow. There are some nice classroom experiment you can do to show this, the simplest being to make a Maxwell top with green and red sections, spin the top, and notice that you see the color as yellow.
In order to add some math to the analysis of sky color, I show a table below where I divided the solar spectrum into the 7 representative colors with their effective power. There is some subjectivity to this, but I took red as the wavelengths from 620 to 750nm so I claim on the table was 680 nm. The average power of the red was 500 mW/m2nm, so I calculate the power as .5 W/m2nm x 130 nm = 65W/m2. Similarly, I took orange to be the 30W/m2 centered on 640nm, etc. This division is presented in the first 3 columns of the following table. The first line of the table is an approximate of the Rayleigh-scatter factor for our atmosphere, with scatter presented as the percent of the incident light. That is % scattered = 9E11/wavelength^4.
To use the Rayleigh factor, I calculate the 1/wavelength of each color to the 4th power; this is shown in the 4th column. The scatter % is now calculated and I apply this percent to the light intensities to calculate the amount of each color that I’d expect in the scattered and un-scattered light (the last two columns). Based on this, I find that the predominant wavelength in the color of the sky should be blue-cyan with significant components of green, indigo, and violet. When viewed through a spectroscope, I find that these are the colors I see (I have a pocket spectroscope and used it an hour ago to check). Viewed through the same spectroscope (with eye protection), I expect the sun should look like a combination of green and red, something our eyes see as yellow (I have not done this personally). At any rate, it appears that the sky looks blue because our eyes see the green+ cyan+ indigo + purple in the scattered light as sky blue.
At sunrise and sunset when the sun is on the horizon the scatter percents will be higher, so that all of the sun’s colors will be scattered except red and orange. The sun looks orange then, as expected, but the sky should look blue-green, as that’s the combination of all the other colors of sunlight when orange and red are removed. I’ve not checked this last yet. I’ll have to take my spectroscope to a fine sunset and see what I see when I look at the sky.
Why isn’t the sky green and the sun orange?
Part of the reason the sky isn’t green has to do with the color of the sun. The sun’s color, and to a lesser extent, the sky color both are determined by the sun’s surface color, yellow. This surface color results from black body radiation: if you heat up a black object it will first glow red, then orange, yellow, green etc. Red is a relatively cool color because it’s a low frequency (long wavelength) and low frequencies are the lowest energy photons, and thus are the easiest for a black body to produce. As one increases the temperature of a black object, the total number of photons increases for all wavelengths, but the short wavelength (high frequency) colors increase faster than the of long wavelength colors. As a result, the object is seen to change color to orange, then yellow, or to any other color representative of objects at that particular temperature.
Our star is called a yellow sun because the center color of its radiation is yellow. The sun provides radiation in all colors and wavelengths, even colors invisible to the eye, infra red and ultra violet, but because of its temperature, most of the radiated energy appears as yellow. This being said, you may wonder why the sky isn’t yellow (the sky of Mars mostly is).
The reason the sky is blue, is that some small fraction of the light of the sun (about 10%) scatters off of the molecules of the air. This is called Rayleigh scatter — the scatter of large wavelegth waves off of small objects. The math for this will be discussed in another post, but the most relevant aspect here is that the fraction that is scattered is proportional to the 4th power of the frequency. This is to say, that the high frequencies (blue, indigo, and violet) scatter a lot, about 20%, while the red hardly scatters at all. As a result the sky has a higher frequency color than the sun does. In our case, the sky looks blue, while the sun looks slightly redder from earth than it does from space — at least that’s the case for most of the day.
The sun looks orange-red at sundown because the sunlight has to go through more air. Because of this, a lot more of the yellow, green, and blue scatter away before we see it. Much more of the scatter goes off into space, with the result that the sky to looks dark, and somewhat more greenish at sundown. If the molecules were somewhat bigger, we’d still see a blue sky, maybe somewhat greener, with a lot more intensity. That’s the effect that carbon dioxide has — it causes more sunlight to scatter, making the sky brighter. If the sun were cooler (orange say), the sky would appear green. That’s because there would be less violet and blue in the sunlight, and the sky color would be shifted to the longer wavelengths. On planets where the sun is cooler than ours, the sky is likely green, but could be yellow or red.
Rayleigh scatter requires objects that are much smaller than the light wavelength. A typical molecule of air is about 1 nm in size (1E-9 of a meter), while the wavelength of yellow light is 580 nm. That’s much larger than the size of air molecules. Snow appears white because the size of the crystals are the size of the sun wavelengths, tor bigger, 500-2000 nm. Thus, the snow looks like all the colors of the sun together, and that’s white. White = the sum of all the colors: red + orange + blue + green + yellow + violet + indigo.
Robert Buxbaum Jan. 27, 2013 (revised)
Physics joke (neutron)
So a neutron walks into a bar and orders a drink.
The bar tender says, it’s on the house for you. No charge.
Robert E. Buxbaum, Jan 22, 2013.
What causes the swirl of tornadoes and hurricanes
Some weeks ago, I presented an explanation of why tornadoes and hurricanes pick up stuff based on an essay by A. Einstein that explained the phenomenon in terms of swirling fluids and Coriolis flows. I put in my own description that I thought was clearer since it avoided the word “Coriolis”, and attached a video so you could see how it all worked — or rather that is was as simple as all that. (Science teachers: I’ve found kids love it when I do this, and similar experiments with centrifugal force in the class-room as part of a weather demonstration).
I’d like to now answer a related question that I sometimes get: where does the swirl come from? hurricanes that answer follows, though I think you’ll find my it is worded differently from that in Wikipedia and kids’ science books since (as before) I don’t use the word Coriolis, nor any other concept beyond conservation of angular momentum plus that air flows from high pressure to low.
In Wikipedia and all the other web-sits I visited, it was claimed that the swirl came from “Coriolis force.” While this isn’t quite wrong, I find this explanation incomprehensible and useless. Virtually no-one has a good feel for Coriolis force as such, and those who do recognize that it doesn’t exist independently like gravity. So here is my explanation based on low and high pressure and on conservation of angular momentum. I hope it will be clearer.
All hurricanes are associated with low pressure zones. This is not a coincidence as I understand it, but a cause-and-effect relationship. The low pressure center is what causes the hurricane to form and grow. It may also cause tornadoes but the relationship seems less clear. In the northern hemisphere, the lowest low pressure zones are found to form over the mid Atlantic or Pacific in the fall because the water there is warm and that makes the air wet and hot. Static air pressure is merely the weight of the air over a certain space, and as hot air has more volume and less density, it weighs less. Less weight = less pressure, all else being equal. Adding water (humidity) to air also reduces the air pressure as the density of water vapor is less than that of dry air in proportion to their molecular weights. The average molecular weight of dry air is 29 and the molecular weight of water is 18. As a result, every 9% increase in water content decreases the air pressure by 1% (7.6 mm or 0.3″ of mercury).
Air tends to flow from high pressure zones to low pressure zones. In the northern hemisphere, some of the highest high pressure zones form over northern Canada and Russia in the winter. High pressure zones form there by the late fall because these regions are cold and dry. Cold air is less voluminous than hot, and as a result additional hot air flows into these zones at high altitude. At sea level the air flows out from the high pressure zones to the low pressure zones and begins to swirl because of conservation of angular momentum.
All the air in the world is spinning with the earth. At the north pole the spin rate is 360 degrees every 24 hours, or 15 degrees per hour. The spin rate is slower further south, proportionally to the sine of the latitude, and it is zero at the equator. The spin of the earth at your location is observable with a Foucault pendulum (there is likely to be one found in your science museum). We normally don’t notice the spin of the air around us because the earth is spinning at the same rate, normally. However the air has angular momentum, and when air moves into into a central location the angular speed increases because the angular momentum must be conserved. As the gas moves in, the spin rate must increase in proportion; it eventually becomes noticeable relative to the earth’s spin. Thus, if the air starts out moving at 10 degrees per hour (that’s the spin rate in Detroit, MI 41.8° N), and moves from 800 miles away from a low pressure center to only 200 miles from the center, the angular momentum must increase four times, or to 40 degrees per hour. We would only see 30 degrees/hr of this because the earth is spinning, but the velocity this involves is significant: V= 200 miles * 2* pi *30/360 = 104 mph.
To give students a sense of angular momentum conservation, most science centers (and colleges) use an experiment involving bicycle wheels and a swivel chair. In the science centers there is usually no explanation of why, but in college they tend to explain it in terms of vectors and (perhaps) gauge theories of space-time (a gauge is basically a symmetry; angular momentum is conserved because space is symmetric in rotation). In a hurricane, the air at sea level always spins in the same direction of the earth: counter clockwise in the northern hemisphere, clockwise in the southern, but it does not spin this way forever.
The air that’s sucked into the hurricane become heated and saturated with water. As a result, it becomes less dense, expands, and rises, sucking fresh air in behind it. As the hot wet air rises it cools and much of the water rains down as rain. When the, now dry air reaches a high enough altitude its air pressure is higher than that above the cold regions of the north; the air now flows away north. Because this hot wet air travels north we typically get rain in Michigan when the Carolinas are just being hit by hurricanes. As the air flows away from the centers at high altitudes it begins to spin the opposite direction, by the way, so called counter-cyclonally because angular momentum has to be consevered. At high altitudes over high pressure centers I would expect to find cyclones too (spinning cyclonally) I have not found a reference for them, but suspect that airline pilots are aware of the effect. There is some of this spin at low altitudes, but less so most of the time.
Hurricanes tend to move to the US and north through the hurricane season because, as I understand it, the cold air that keeps coming to feed the hurricane comes mostly from the coastal US. As I understand it the hurricane is not moving as such, the air stays relatively stationary and the swirl that we call a hurricane moves to the US in the effective direction of the sea-level air flow.
For tornadoes, I’m sorry to say, this explanation does not work quite as well, and Wikipedia didn’t help clear things up for me either. The force of tornadoes is much stronger than of hurricanes (the swirl is more concentrated) and the spin direction is not always cyclonic. Also tornadoes form in some surprising areas like Kansas and Michigan where hurricanes never form. My suspicion is that most, but not all tornadoes form from the same low pressure as hurricanes, but by dry heat, not wet. Tornadoes form in Michigan, Texas, and Alabama in the early summer when the ground is dry and warmer than the surrounding lakes and seas. It is not difficult to imagine the air rising from the hot ground and that a cool wind would come in from the water and beginning to swirl. The cold, damp sea air would be more dense than the hot, dry land air, and the dry air would rise. I can imagine that some of these tornadoes would occur with rain, but that many the more intense?) would have little or none; perhaps rain-fall tends to dampen the intensity of the swirl (?)
Now we get to things that I don’t have good explanation for at all: why Kansas? Kansas isn’t particularly hot or cold; it isn’t located near lakes or seas, so why do they have so many tornadoes? I don’t know. Another issue that I don’t understand: why is it that some tornadoes rotate counter cyclonicly? Wikipedia says these tornadoes shed from other tornadoes, but this doesn’t quite seem like an explanation. My guess is that these tornadoes are caused by a relative high pressure source at ground level (a region of cold ground for example) coupled with a nearby low pressure zone (a warm lake?). My guess is that this produces an intense counter-cyclonic flow to the low pressure zone. As for why the pressure is very low in tornadoes, even these that I think are caused by high pressure, I suspect the intense low pressure is an epee-phenomenon caused by the concentration of spin — one I show in my video. That is, I suspect that the low pressure in the center of counter-cyclonic tornadoes is not the cause of the tornado but an artifact of the concentrated spin. Perhaps I’m wrong here, but that’s the explanation that seems to fit best with the info I’ve got. If you’ve got better explanations for these two issues, I’d love to hear them.
The joy of curtains
By Dr. Robert E. Buxbaum January 18, 2013
In our northern climates most homes have double-paned windows; they cost a fortune, and are a lot better than plain glass, but they still lose a lot of heat: far more than the equivalent area of wall. The insulation value is poor mostly because the thickness is low: a typical double pane window is only ½” thick. The glass panes have hardly any insulation value, so the majority of the insulation is the 0.3″ air space between them. Our outer walls, by contrast, are typically 6” thick filled with glass –wool. The wall is 12 times as thick as the window, and it turns out that the R value is about 12 times as great. Since window area is about 1/10 the wall area, we can expect that about half your homes heat goes out through the windows (about half the air-conditioner cooling in the summer too). A good trick to improve your home’s insulation, then, is to add curtains as this provides a fairly thick layer of stagnant air inside the room, right next to your windows.
To see how much you can save by adding curtains, it’s nice (for me, and my mind-set mostly) to talk in terms of R values. In the northern USA, the “R” value of a typical, well-insulated outer wall is about 24. What that means is that it takes 24°F and one square foot of wall to remove 1 BTU per hour. That is, the resistance to heat loss is 24 °F.hr.ft2/BTU. The R value for a typical double pane window is about 2 in the same units, and is only 1 if you have single panes. The insulating quality of our windows is so poor that, for many homes, more heat is lost through the windows than through the rest of the wall space.
To figure out how much heat is lost through your windows take the area in square feet multiply by a typical temperature differential (50°F might be typical in Michigan), and divide by the R value of your paned windows (1 or 2) depending on whether it’s single or double paned. Since heat costs about $10/MMBTU ($10 per million BTU) for a gas heated house, you can figure out what a small, 10 ft2 window costs a typical Michigan householder as follows, assuming a single pane (R=1):
Q = Area* ∆T/R = 10 ft2 * 50°F/1 = 500 BTU/hr. Here Q is the heat lost per unit time, ∆T is the temperature difference between the window surface and the room, and A is the ara of the window surface.
Since there are 24 hours in a day, and 30.5 days in a month the dollar cost of that window is 500*24*31.5*10/1,000,000 = $3.78/month. After a few years, you’ll have paid $200 for that small window in lost heat and another $200 in air conditioning.
A cheap solution is to add curtains, shades, or plastic of some sort. These should not be placed too close to the window, or you won’t have a decent air gap, nor so far that the air will not be static in the gap. For small gaps between the window glass and your plastic or curtain, the heat transfer rate is proportional to the thermal conductivity of air, k, and inversely proportional to the air gap distance, ∂.
Q = ∆T A k /∂.
R = ∂/k.
The thermal conductivity of air, k, is about .024 BTU/ft. hr°F. We thus confirm that the the R-value for an air gap of 9/16” or 1/20 foot is about 2 in these units. Though the typical air gap between the glass is less, about .3″ there is some more stagnant air outside the glass an that counts towards the 9/16″ of stagnant air. The k value of glass or plastic is much higher than of air, so the layers of glass or plastic add almost nothing to the total heat transfer resistance.
Because the R value of glass and plastic is so low, if you cover your window with a layer of plastic sheet that touches the window, the insulation effect is basically zero. To get insulation value you want to use a gap between about ½” and 1” in thickness. If you already have a 2 paned window of R value 2, you can expect to be able to raise your insulation value to 4 by adding a plastic sheet or single curtain at 9/16” from the glass.
Sorry to say, you can’t raise this insulation value much higher than 4 by use of a single air gap that’s more than 1″ thick. When a single gap exceeds this size, the insulating value drops dramatically as gas circulation in the gap (free convection) drives heat transfer. That’s why wall insulation has fiber-glass fill. For your home, you will want something more attractive than fiberglass between you and the window pane, and typical approaches include cellular blinds or double layer drapes. These work on the same principle as the single sheet, but have extra layers that stop convection.
My favorite version of the double drapes is the federalist version, where the inner drape is near transparent, shim cloth hangs close to the window, with a heavier drape beyond that. The heavier curtain is closed at night and opened in daytime; where insulation is needed, the lighter cloth hangs day and night. This looks a lot better than a roll-type window shade, or bamboo screen. Besides, with a roll-shade or bamboo, you must put it close to the window where it will interfere with the convection flow, that is cold shedding from the shut window.
Another nice alternative is a “cell shade” These are folded lengths of two or more stiff cloths that are formed into honeycombs ½” to 2” apart. This empty thickness provides the insulating power of the shade. Placed at the right distance from the window, the cell shade will add 3 or more to the overall R value of the window (1/12 ft / .024 BTU/ft. hr°F = 3.5 ft2hr°F/BTU). As with a bamboo screen, all this R value goes away if the shade is set at more than about 1” from the window or an interior shade. At a greater thickness that this, the free convection flow of cold air between the window and the shade dominates, and you get a puddle of cold air on the floor.
I would suggest a cellular shade that opens from the bottom only and is translucent. This provides light and privacy; a shade that is too dark will be left open. Behind this, my home has double-pane windows (when I was single the window was covered by a layer of plastic too). The see-through shade provides insulation while allowing one to see out the window (or let light in) when the shade is drawn. You want to be able to see out; that’s the reason you had a window in the first place. Very thick, insulating curtains and blinds seem like a waste to me – they are enough thicker to add any significant R-value, they block the light, and if they end up far from the window, the shedding heat loss will more than offset any small advantage from the thick cloth.
One last window insulation option that’s worth mentioning is a reflective coating on the glass (an e-coating). This is not as bad an idea as you might think, even in a cold climate as in Detroit. A surprising amount of heat tends to escape your windows in the form of radiation. That is, the heat leaves by way of invisible (infra –red) light that passes unimpeded through the double pane glass. In hot climates even more heat comes in this way, and a coating is even more useful to preserve air conditioning power. Reflective plastic coats are cheap enough and readily available, though they can be hard to apply, and are not always attractive.
You can expect to reduce the window heat loss by a factor of 3 or more using these treatments, reducing the heat loss through the small window to $1.00 or so per month, far enough that the main heat loss is through the walls. At that point, it may be worth putting your efforts elsewhere. Window treatments can save you money, make a previously uninhabitable room pleasant, and can help preserve this fair planet of ours. Enjoy.
Updated, Feb 9, 2022, REB.
Engineering joke
An optimist says the cup is half full.
A pessimist says the cup is half empty.
An engineer says the cup is twice as big as it has to be.
(A quantum physicist might say that the water isn’t in the cup till he looks at it; then again, the quantum physicist isn’t there until someone looks at him. And that’s why I’m an engineer).
How much wood could a woodchuck chuck?
How much wood could a woodchuck chuck, if a woodchuck could chuck wood. It’s a classic question with a simple answer: The woodchuck, also known as a groundhog or marmot, is a close relative to the beaver: it looks roughly the same, but is about 1/5 the weight (10 pounds versus 50 pounds), and beavers do chuck wood, using their teeth to pile it onto their dams. I’ll call the tooth piling process chucking, since that’s what we would call it if a person did it by hand.
A beaver dam. From the size of this dam, and the rate of construction (one night) you can figure out how much wood a beaver could chuck, and from that how much a woodchuck could.
A reasonable assumption, is that a wood chuck would chuck about 1/5 as much wood as a beaver does. You might think this isn’t very much wood — and one researcher claimed it would be less than 1/2 lb. — but he’s wrong. A beaver is able to build a dam like the one shown in a single night. From the size of the dam and the speed of building you can estimate that the beaver chucked on the pile about 1000 lbs of wood per night (beavers work at night). To figure out how much wood a woodchuck would chuck, divide this rate by 5. Based on this, I’d estimate that a woodchuck would chuck some 200 lbs per day, if it chose to.
Woodchucks don’t chuck wood, as the question implies. Unlike beavers they do not build wood dams or lodges. Instead they live in burrows in the ground. Also woodchuck teeth are not so useful. Woodchucks do kick up a lot of dirt digging a burrow, as much as 700 lb/ day of dirt, but the question implies that this activity should not be counted as chucking. Well, now you know: it’s 200 lbs/night.
Robert Buxbaum. This post is revised January 30, 2020. My original estimate, from January 2013 was half the value here. I’d come to believe that wood-chucks/ groundhogs are 1/10 the size of a beaver, so I’d estimated 100 lb/night.