http://www.flyingcircusofphysics.html

Editors note: These passages are not written strictly in the past passive and they are not always in the third person. The anthropomorphic fallacy creeps in at times. Do not use this conversational writing style as a model for you own formal report writing. Note also, that in common with most self published works, it has not been proof read as strictly as it could have been.

Fingers in molten lead, beer gushing, entropy and the campus police, meandering rivers, and many more subjects

Sunday, April 01, 2007

Here are the stories I have posted since the website was launched and the new edition of The Flying Circus of Physics was published. I usually post new stories around the first day of each month. If you want all the references (and all the stories) in PDF form, choose Topics from the menu at the left, choose a chapter, and then click on the PDF icon next to the armadillo. Those PDF lists are updated with the stories and new references about once a month. If you want to tell me about any of this, use the blog site.   ---- Jearl Walker

Sound mirrors detecting enemy aircraft

March 2007

During World War I, German airships (Zeppelin and Shutte-Lanz) bombed regions around the Thames estuary (southern England) and Humber estuary (northern England). To detect the airships before they arrived, the English built an early warning system of sound mirrors that would intercept and concentrate the sound waves of an approaching airship so that it could be heard before it was within normal hearing range. The first sound mirror was simply a hemispherical cavity dug into a chalk cliff on the southeast coast. The sound waves, at least those with wavelengths smaller than the radius of the hemisphere, reflected from the wall of the cavity and passed through the center of curvature (the point that would be the center of the sphere were the sphere complete). At that point, a horn was mounted to collect the waves and send them through rubber tubes to someone listening at the other end of the tubes.

Although listening for the sounds of enemy airships must have been mind-numbing work, because of the background noise that was also reflected into the collecting horn, this early-warning system functioned reasonably well. If the listener moved the collecting horn horizontally to the point at which the airship sound was loudest, the direction of the airship could be determined. If the airship headed directly toward the sound mirror, the reflected sound was loudest when the collector was at the center of curvature. If (as was more likely) the airship was off to one side of the direct approach, the sound was loudest at a point on the opposite side of the center of curvature. Several sound mirrors were built during the war, and enemy airships were detected on at least two occasions, allowing several extra minutes of warning.

After the war, free-standing concrete sound mirrors were deployed on several English shores. The size was increased so that longer sound wavelengths could be properly reflected to the collecting device at the center of curvature. In 1930, a long curved sound mirror (in the shape of a curved wall) was built at Denge. The wall was designed to collect sound over a wide horizontal range and focus the waves onto a collector. It was capable of detecting aircraft that was 20 or 30 miles away, whereas normal hearing was limited to about 6 or 7 miles. By 1935, all the sound mirrors became outdated because radar came into use and shown capable of detecting aircraft that was 40 miles away.

You can find similar sound mirrors in the equipment used by bird enthusiasts to hear bird calls or spies to hear conversions. Today's devices are small, portable metal dishes with sensitive electronic microphones placed at the concentration points. Two larger-scale versions are set up in the lobby of the physics building at the University of Florida, where students can listen to whispers from across the width of the large lobby. (Hearing whispers across the domed interior of Saint Paul's Cathedral depends on entirely different physics. Check out item 3.63 in The Flying Circus of Physics.)

Web pages by Andrew Grantham, lots of photos and brief descriptions of the sound mirrors in England and Malta:
http://www.ajg41.clara.co.uk/mirrors/
Excellent review of sound mirrors on the south coast of England by Phil Hide:
http://www.doramusic.com/soundmirrors.htm
The Sound Mirrors Project, an artistic venture to send performances across the English Channel, between a sound mirror on the English coast and a sound mirror on the French coast
http://www.soundmirrors.org/
Historic look at listening devices, many of them quaint or even comical, with illustrations:
http://www.dself.dsl.pipex.com/MUSEUM/COMMS/ear/ear.htm
Short description by Claire Barrett:
http://www.c20society.org.uk/docs/building/sound.html

Stacking blocks to get an overhang

March 2007

Stacking blocks to make a leaning tower has long fascinated both mathematicians and normal people, including those students who have built a tower of books that leans from a library table out over an aisle, threatening to collapse onto a careless library patron. (Don't you dare do this. Librarians are usually calm and helpful, but if you mess with their books, they transform into the orcs of Tolkien's Middle Earth.) The standard question is, "What is the maximum overhang?" The standard answer is, "If you stack the blocks properly, there is, in principle, no limit."

M. R. Khoshbin-e-Khoshnazar of the Physics Department at the Research Institution for Curriculum Development & Educational Innovations in Tehran recently pointed out that a practical matter limits the stacking: The bottom block gets squashed by all the higher bricks and if the number of higher blocks exceeds a certain limit, the bottom block "yields," that is, it deforms and collapses.

If the usual stacking scheme is followed, you put the center of mass of the top block just over the outer edge of the underlying second block. Then you put the center of mass of those two top blocks just over the edge of the underlying third block. And so on. If a block has the physical characteristics of a standard rigid brick and a height of 20 cm, the maximum number of blocks for a stable tower is about 853 and the maximum height of the tower is about 171 m. If you switch to bricks with another height, the number of bricks is different but the maximum height of the stack does not change.

Khoshbin-e-Khoshnazar, M. R., "Simplifying modeling can mislead students," Physics Education, 42, No. 1, 14-15 (January 2007)

White beetles

March 2007

My blue shirt is blue because of pigmentation; that is, the fabric holds certain molecules that absorb in the red end of the visible spectrum, allowing the blue end to be reflected by the fabric. The top surface of a Morpho butterfly wing is iridescent blue because wavelengths of blue light undergo constructive interference when they reflect from the terrace-shaped structures on the wing. That is, those wavelengths leave the wing in step with one another and thus reinforce one another. Other wavelengths of visible light leave the wing out of step with one another and thus cancel one another. One or both effects color other colored surfaces, but what "colors" a white surface, such as the surface of milk? Milk is white because all the colors in the visible spectrum scatter equally well from the various particles in the milk. So, white light goes in and white light comes out. Is something similar responsible for the brilliant white of Cyphochilus beetles, which is a very rare coloration among beetles and other animals?

Recently Pete Vukusic, Benny Hallam, and Joe Noyes (of Exeter University in Exeter UK and Imerys Minerals Limited in Cornwall UK) attributed the whiteness to the internal structure of the very thin scales on the beetle. Each scale is partially filled with cuticle-like filaments that scatter all the wavelengths in visible light equally well. Were the scales fully filled with the filaments, light could scatter only on the surface, which would give just a dull white. Were the scales barely filled, not much light would be scattered back out of them and they again would be just a dull white. The scales seem to be filled just right for lots of light to be scattered to back to the observer from the interiors, producing the intense white seen on the beetles.

The white is much whiter than human teeth, where the incoming light is scattered by crystals in a shallow layer on the enamel. Since very white teeth are a fashion trend in many countries, perhaps the teeth could be coated with thin layers resembling the scales on the beetle. Well, maybe. A smile might then be like the headlamps of an oncoming car, which would be more a threat than a fashion statement.

Abstract of the paper: http://www.sciencemag.org/cgi/content/abstract/315/5810/348
Photos and news releases:
http://news.bbc.co.uk/2/hi/science/nature/6272485.stm
http://www.aaas.org/news/releases/2007/0118beetle.shtml
http://www.livescience.com/animalworld/070118_white_beetles.html

Lifting a glass from a tabletop wet with whiskey

March 2007

Someone happens to put a beverage glass down onto liquid that has been spilt on a barroom table. When the glass is then lifted from the table, some of the liquid clings to the bottom of the glass before the glass breaks free. Does the effort of lifting (either the required force or the required energy) depend on the concentration of alcohol in that liquid? That is, is the effort different when the liquid is strong whiskey than when it is just water?

Answer

Considering the long history of whiskey, you would think that there has been considerable experimental research on the subject. Little has been published on the subject, perhaps because the experimental research interfered with the ability to write.

Recently, David van der Spoel of Uppsala University (Sweden) and Erik J. W. Wensink and Alex C. Hoffmann of University of Bergen (Norway) investigated the subject with mathematical simulations of a liquid layer between two separating quartz surfaces, one representing the table and the other the bottom of the beverage glass. They found that as the surfaces separate, the required force first increases and then decreases. The variation stems from the behavior of the liquid during the separation. Initially, as the surfaces begin to move apart, the liquid begins to form a cylinder between the two quartz surfaces and thus must increase its surface area. Surface tension is the force between molecules located along the air-liquid surface of the column. That force tends to decrease the surface area, as if the air-liquid surface on the column were an elastic membrane attempting to contract. So, as the quartz surfaces move apart, lengthening the column and adding to the air-liquid surface area, surface tension fights against the separation.

The sides of the liquid cylinder become progressively more concave (roughly shaped like a wide hourglass) and the pull by surface tension becomes less vertical. Thereafter, with progressively less fight by the surface tension, the quartz surfaces are easier to move apart. When the separation reaches a certain distance, one or more cavities of air and water vapor form within the liquid cylinder, until there is only one or two "liquid bridges" running between the quartz surfaces.

All this action occurs between a tabletop and a beverage glass when the glass is lifted. And it occurs whether the liquid is strong whiskey or just water. When the liquid contains alcohol, the alcohol molecules interfere with the attraction between nearby water molecules and thus reduce the surface tension. The stronger the alcohol is, the weaker the surface tension is. So, strong whiskey puts up a weaker fight as the beverage glass is pulled away from the table. In short, lifting a glass when there is strong whisky clinging to the bottom is easier than when there is just water clinging to the bottom.

Stress dip below a sandpile

March 2007

What is something you really enjoyed as a child but now find utterly boring? Among many possible answers is playing with sand. Building sandpiles was loads of fun years ago but not now. Many physicists are still fascinated by sandpiles and have managed to build their careers on them. The reason is that a sandpile is a treasure trove of puzzles that figure into the general science of granular flow (that is the flow of grains of anything from powder to apples, in environments from the cosmetic industry to the dunes on a desert). Here is one puzzle.

If you were measuring the stress (or pressure) under a sandpile from the outer edge to the center, you would expect that stress to be greatest under the highest point, where the supporting surface must support the most weight. Measurements show that although the stress increases toward the center of the pile, it actually decreases in the region of the highest point. That decrease is called the stress dip.

As explained in The Flying Circus of Physics, the stress dip is most likely due to the formation of arcs of sand grains that are produced when the sand is poured to make the pile. Such arcing creates force chains, which are lines of support among the grains that form a skeletal structure hidden from view within the pile. This generation of force chains shifts support away from the center of the pile.

Recently, I. Zuriguel and T. Mullin of the University of Manchester and J. M. Rotter of the University of Edinburgh described a method to make the force chains visible in a two-dimensional granular pile. The "grains" are cut from a photoelastic polymer layer that is birefringent. That is, if the layer is placed between polarizing sheets, the stress in the polymer material shows up as a pattern.

A narrow rectangular container was made to hold the grains. The front and back were made of Perspex plates that were held 7 millimeters apart. The grains were carefully poured into the container. A polarizing sheet was mounted on the rear Perspex and a second sheet was mounted on the front Perspex, with the polarizing directions of the sheets perpendicular to each other. When light is sent through the apparatus, the light becomes polarized by the first sheet and would not nomally be passed by the second sheet because of the perpendicular arrangement. The stressed regions in the polymer grains rotate the polarization of the light, so that in some regions the light gets through the second polarizing sheet, revealing where the grains are stressed.

When the polymer grains are a mixture of circular grains with two different diameters, the grain pile has a slight stress dip under the highest section. When the grains are elliptical and identical, the pile has a dramatic stress dip under the highest section. Presumably, the elliptical shape naturally forms the supporting arcs that shift support away from the center.

Getting charged by walking

February 2007

Here is a common dorm prank: On a day with low humidity, you walk quietly up behind a friend and reach a finger out toward his ear lobe. When your finger is close to the lobe, a spark jumps between the two surfaces and your friend jumps up into the air with a shriek of surprise. Obviously you became charged as you walked toward him, but why?

Unless you live in continuously humid conditions, you have probably been shocked by a spark after walking over certain types of floors and then reaching for a computer, door knob, faucet, or some other conducting object. In those sparking circumstances, walking over the floor charges you up and then the charge can be neutralized with a spark. The process can also be described in terms of electric potential (or voltage). As you walk, the electric potential of your body increases. When you reach for a conducting object, the electric field between you and the object becomes large enough to ionize some of the air molecules (tear electrons out of the molecules). Then the air becomes conducting and electrons can move along a path between you and the object. Those moving electrons collide with the air molecules along the way. The molecules emit light, and the energy dumped into the air along the spark's path causes the air to rapidly expand, which sends out the sound of the spark.

This much has been known for a long time, but the lingering question has been, "Why does your body become charged and the electric potential increase?" Here is a recently published explanation by T. Ficker of the Technical University of Brno in the Czech Republic, based on his measurements on someone walking over a nonconducting floor (electrons cannot easily move through the floor). Suppose you wear shoes with rubber soles and walk on such a floor. Electrons can move from the sole of the shoe onto the floor, leaving the sole positively charged and the floor negatively charged.

The culprits. If both the sole and the floor do not conduct well (charge cannot move through them easily), the charges stay put. But your body and the floor support are both conducting. So electrons come down from your body to your foot, to be near the positive charge on the sole. And electrons in the floor support move away from the floor surface. You get two double layers (closely lying layers of positive and negative charge): (1) the sole and your foot, (2) the floor surface and just below the surface.

Walking. As you walk, you leave the double layer on the floor in your trail but your shoe continuously touches fresh points on the floor and loses even more electrons. The result is that the double layer of charge of the sole and your foot grows stronger. Moreover, each time you raise your foot, the increased distance from the floor increases the electric potential (the voltage) on your body. So, you become more and more charged and each step increases the electric potential. If the air humidity is high, the water moisture quickly neutralizes the charge, and then putting your finger near the ear lobe of a friend is just weird. But if the air humidity is low, you eventually become charged enough to send a spark between finger and ear lobe.

Walking in place. If you walked in place, touching the same points on the floor, you would not lose so many electrons and your electric potential would not increase very much. If you walked barefooted across the floor, you wouldn't become charged at all because, with the foot conducting, you cannot build up a double layer of charge.
Cats. Oh, by the way, you might enjoy sparking to a friend but never ever spark to a cat because its claws will extend outward by 20 cm (like Wolverine in X-Men) and then it will slice the clothes from your body, which is very embarrassing to explain to the emergency medical crew (and then to the animal protection agency).

Ficker, T., "Charging by walking," Journal of Physics D: Applied Physics, 39, 410-417 (2006)
Ficker, T., "Electrification of human body by walking," Journal of Electrostatics, 64, 10-16 (2006)

Projectile penguin from an ice hole

February 2007

For those of you using Fundamentals of Physics, the textbook that I write, you know that I am greatly amused by the deadpan comic look of emperor penguins. But those penguins must be very smart to survive in their extremely harsh environment. Here is one example. When a penguin returns from foraging for food in the water, it might need to leave the water through a hole in an overlying ice layer. If the ice surface is only a centimeter or so above the water surface, the penguin just plops out onto the ice and then wiggles its way free of the water. If the ice surface is higher, the penguin must "leap" from the water, much like you might leap across a stream.

To leap, the penguin moves toward the hole either almost vertically (if the hole is narrow) or at an appreciable angle to the vertical (if the hole is wider). Buoyancy alone may propel it sufficiently, but if the ice surface is high, the penguin must increase its speed by stroking. In a successful leap, the penguin clears the hole in a parabolic path and lands belly-first on the ice. Use the URL listed below here to watch a movie of projectile penguins. You'll laugh. There is no way you can watch it without laughing. Gosh, life might be tough in a physics class, but at least you don't have to shoot yourself through a hole in an ice sheet to survive. (Well, you won't have to IF you graduate.)

Students using my textbook or any other introductory physics textbook learn how to calculate the launch speed and launch angle that is required for such projectile motion if an object must reach a certain height, here the height of the ice surface. They also learn that during the flight, an object's initial kinetic energy is converted to potential energy as the object rises. Students usually struggle with both ideas and are quick to slide open their calculators for the "equation-solving" function available on one of the keys.

An emperor penguin can make the calculation without any equation-solving calculator. (Just imagine a penguin trying to push in those little keys.) Instead, a penguin can judge the height of the ice above the water and then mentally determine what speed is required to reach the top of the ice and thus whether it should just be buoyed upward or if it should stroke for a greater speed. The leap can be critical because the penguin is in a hostile environment and must be able to escape from the water on the first try and with as little wasteful expenditure of energy as possible. If it fails to leap up onto the ice, it falls back into the water, where it might become the lunch of a predatory seal. (Becoming something's meal is a great motivator to do calculations correctly.)

Depending on the angle of launch, there is always a least speed to reach a given height of ice. A penguin usually uses a somewhat greater speed because its view of the height of the ice can be misleading. When the light from the top of the ice travels down through the water surface, its path is bent (refracted) toward the vertical. When a penguin looks back along the light to make sense of its origin, the ice looks higher than it truly is. So, the penguin uses a speed that is greater than it truly needs. This overshoot costs the penguin some extra energy, which is precious in that harshly cold environment, but the cost is minor compared to the cost of being eaten by a seal.

http://jeb.biologists.org/cgi/content/full/208/13/2549/DC1
A movie showing penguins "leaping" through an ice hole.
Sato, K., P. J. Ponganis, Y. Habara, and Y. Naito, "Emperor penguins adjust swim speed according to the above-water height of ice holes through which they exit," Journal of Experimental Biology, 208, 2549-2554 (2005)

Backpacks on bungee cords are easier to carry

February 2007

The main reason that a heavy backpack is difficult to carry is that as you walk, your torso rises and falls by several centimeters and thus you must repeatedly accelerate the backpack through that vertical distance. The force on your back is greatest when the torso begins to move upward and the backpack is accelerated upward. That demand automatically limits the speed at which you can walk, and running, such as running after a bus, is usually out of the question. More serious, the demand can severely limit an emergency crew member from moving rapidly with a heavy backpack of rescue equipment.

The difficulty of moving with a heavy backpack can be significantly reduced if the backpack is suspended by bungee cords from a pack frame. A person with such arrangement can even run. Although you might think a suspended backpack would be unwieldy, research conducted by Lawrence C. Rome, Louis Flynn, and Taeseung D. Yoo of the University of Pennsylvania showed that the vertical motion of the load is significantly decreased when the load is suspended than when it is rigidly attached to the back in the normal fashion. The reduction is primarily due to the out-of-step oscillations of the load with the torso. That is, when the torso moves upward, the load moves downward, and vice versa. There are two results: (1) The reduced vertical oscillation means that less force is required to accelerate the load. (2) When the load begins to move upward, the bungee cords accelerate the load instead of only the torso accelerating it.
This physics is similar to that discovered long ago in Asia, where some people carry light to moderately heavy loads by tying them to opposite ends of a spring pole such as a bamboo pole and placing the center of the pole over one shoulder (check the URL listed below). As I discuss in the Flying Circus book, when such a person walks or runs, the two loads oscillate vertically and out of step with the vertical oscillation of the supporting shoulder. As a result, less force is required of the shoulder in the upward portion of the motion, because the springy pole helps propel the loads upward.

http://www.iamtonyang.com/0609/farmers_carrying_rice.JPG
Rome, L. C., L. Flynn, and T. D. Yoo, "Rubber bands reduce the cost of carrying loads," Nature, 444, No. 7122, 1023-1024 (21/28 December 2006)

Toilet stall electric field

February 2007

In mid-winter, certain toilet stalls in the restrooms at Cleveland State University (my school) provide a hair-raising experience. When I enter such a stall, the hair on my arms and head rise away from the skin. What causes the motion, and why does it not occur during the summer?

Answer

When different materials are put in contact, one surface can pull some of the electrons off the other surface, becoming negatively charged and leaving the other surface positively charged. If the air humidity is high, the water moisture can quickly neutralize both surfaces by removing electrons (if the surface is negatively charged) or providing electrons (if the surface is positively charged).

During the winter in Cleveland, the air humidity can be so low that charge can remain on a surface for hours. The plastic-coated metal walls forming the toilet stalls in the men's room are an example of such a surface. (I can only assume that the toilet stalls in the women's room are another example.) Most of the time, the walls have no net charge and are thus neutral. On the days when they are cleaned by someone rubbing cloth over them, they can become highly charged. Let's assume that the cloth pulls electrons off the plastic coating on a wall, leaving that region positively charged. Because plastic is a nonconductor, the positive charge cannot just be neutralized by electrons flowing up through the ground supports, and so it stays in place.

When I enter the stall and walk into the electric field of the positively charged walls, electrons on me tend to move toward the walls. They can get closest on the hair strands. Because those strands are then negatively charged by the collection of electrons, they move away from the skin and toward the walls ---- thus my hair stands up. If I move my hand within a few millimeters of the wall, I can hear small sparks as electrons jump across the air gap to the wall, neutralizing pockets of positive charge on the wall.

If you come to Cleveland State during midwinter, you might check out this effectfor yourself. (I will not be guiding personal tours through the restrooms).

Bridge chaos

February 2007

In the Flying Circus book, I discuss the embarrassing opening of the footbridge across the Thames in London, connecting the Tate Modern art gallery with the vicinity of St. Paul's Cathedral. The sleek, modern bridge was built to celebrate the new millennium and hence is called the Millennium Bridge. When the first surge of people began to walk over the bridge, the bridge began to oscillate so vigorously that many people had difficulty keeping their balance.

The bridge was closed while it was fitted with dampers to decrease or eliminate the oscillations. Later, researchers explored why the oscillations occurred on that opening day. The ultimate cause was the pedestrians themselves, which is surprising because they did not walk across locked in step like a marching band. Rather, their walking was nonsynchronous (independent). Studies revealed, then when the density of walkers exceeds a certain critical value, even the random impacts of the footsteps set up small oscillations of the bridge at its natural frequencies (the frequencies at which it would oscillate if it were somehow pulled to one side and released and then allowed to oscillate on its own). If the density of walkers is above a certain critical value, then the oscillations grow somewhat, causing some of the people to fall into step with them To better maintain their balance. In turn, that falling-into-step increases the extent of the oscillations, which causes even more people to fall into step. And so on.

Recently Bruno Eckhardt of Philipps-Universität Marburg in Marburg, Germany, and Edward Ott of the University of Maryland in College Park, Maryland presented color-coded graphs of the footfalls (left and right for each of 80 walkers) in a model of the bridge walkers. If the sensitivity of the walkers is low (in a real situation, the walkers don't notice the oscillations enough to adjust their walking), the bridge oscillations do not build up and the graphs show nonsynchronous walking. As the sensitivity is increased in the model, the walkers begin to adjust their walking and eventually become locked in step, and then the oscillations increase in strength. The onset of the synchronous walking is clearly visible on the graphs, and the onset occurs earlier the greater the sensitivity is.
You might experience similar synchronous oscillations in a stadium stand or a concert hall balcony if spectators stomp or jump in unison. That is always my signal to leave because I don't want to be part of the experiment to see if the engineers who designed the structure allowed for significant oscillations in the construction plans.

Eckhardt, B., and E. Ott, "Crowd synchrony on the London Millennium Bridge," Chaos, 16, article # 041104 (2006)

Gushing of beer and soda

January 2007

Here is puzzle to go with a new year's celebration. Shake a can of carbonated beverage (soda or beer) and then pop the top open as you point the can toward a friend. (Don't deny it---you've done this before, drenching someone with the beverage and then laughing as you claimed, "Gosh. I didn't know. Somebody must have shaken the can before I picked it up." Yeah, right.

Why does the shaken beverage undergo gushing as it is called in the technical literature? (I am really pleased that I have a job in which I can read and write Flying Circus type of physics all day, but maybe, just maybe, having a job where you get to study beer gushing might be better. What do you think? Or is that what many college students already do?)

Bubbles in a carbonated drink can form in two ways. In a drinking glass, they nearly always form on microscopic bits of cellulose that was left on the glass interior the last time it was wiped with a paper or cloth towel. The interior of the cellulose tubes are ideal for allowing carbon dioxide molecules (the "carbonation" of a carbonated beverage) to come out of solution to start and then expand a bubble until the bubble is large enough to pinch off from the tube and escape upward.

Bubbles can also form directly in the bulk liquid, but there is a hitch. A bubble must initially be larger than a critical size or otherwise it is squeezed out of existence immediately by the surface tension along its surface. The reason has to do with a competition taking place in each bubble that is formed in the bulk liquid: (1) Carbon dioxide passes through the bubble's surface to join the gas inside the bubble, tending to expand the bubble. (2) The mutual attraction of the liquid molecules (primarily water) for one another produces a force that squeezes the bubble. That inward force is usually said to be due to the surface tension along the surface of the bubble. The force is greater for a smaller bubble than for a larger one because the surface is more tightly curved.

 If a bubble is larger than a certain critical size, the influx of gas molecules wins and the bubble continues to exist and grow. If the bubble is smaller than the critical size, surface tension immediately squeezes it out of existence. When you pour a carbonated beverage into a glass, the turbulence may create bubbles in the bulk liquid but they are almost all too small and quickly disappear. So the bubbles you see are ones from the cellulose fibers, not from the bulk liquid.

 Well, that is the traditional explanation of bubble formation but it fails to explain why a shaken can of beer gushes when opened. There are no cellulose fibers in a can and so the bubbles must form in the bulk liquid. But how?

 The shaking can mix the gas that was at the top of the can (above the liquid) down into the liquid but it can also create points of turbulence where the pressure is momentarily reduced, allowing dissolved gas to come out of solution and form bubbles. Those bubbles might be expected to immediately disappear, not hang around for you to aim the can at a friend and pop the can open. Yet, the bubbles do last for tens of minutes. When you open the can, the pressure inside is suddenly reduced (it was about twice atmospheric pressure) and so the bubbles suddenly expand, shooting beverage out through the can's opening. The traditional explanation for bubble formation says this cannot happen, but that is of little comfort to your friend.

   K. K. Sahu, Y. Hazama, and K. N. Ishihara of Kyoto University have produced an alternate explanation that is based on a series of experiments using ultrasound to "shake" the liquid inside cans of Asahi beer and Coca Cola. After an ultrasound application, a can would be opened and the extent of gushing measured. In line with common experience, they found that if the can is allowed to sit undisturbed for a while before it is opened, the contents will not gush. Surprisingly, Coke Cola required less time than the beer.

  Apparently, the shaking, whether by hand or via ultrasound, produces microbubbles that are smaller than the critical size and yet which do not immediately disappear. They don't last very long in the Coca Cola (you have to squirt your friend right away) but they last tens of minutes in the beer (you can wait). Presumably something in the beer (some of the proteins), stabilizes the surface of a microbubble, allowing it to persist for a while. If the can is opened during this stage, the microbubbles suddenly expand and shoot the beer out through the opening.

 Here is something strange. Suppose that you shake a beer and then let it sit undisturbed just long enough (say, 10 or 15 minutes) so that it would be safe to open. If you shake it just as hard a second time and then finally open it, there is very little gushing. The researchers suggest that the microbubbles produced in the first shaking were transformed somehow during the rest period, perhaps by splitting into even smaller bubbles. When the can is shaken the second time and then opened, gas cannot readily enter these smaller bubbles and so the expansion of the bubbles is insufficient to blow liquid out of the can. I'll keep you posted if more is published on this explanation.

Here is a link on a discussion of the fact that bubbles in a freshly poured glass of Guinness stout move down the side of the glass.

http://www.stanford.edu/group/Zarelab/guinness/index.html

Frost circles and the danger of sinkholes

January 2007

During certain weather conditions, in certain parts of the British Isles, frost-free circles will appear in regions that are otherwise covered with frost. More than just a novelty, these circles (called frost circles in spite of the fact that they are frost free) are warnings that the underlying ground might be unstable and subject to collapse. Occasionally, the ground does collapse to form a sinkhole large enough to swallow up a car, large truck, or even part of a house. What causes frost circles?

Answer

The British Isles, California, and many other locations have many abandoned mines, often with little or no above-ground evidence of their presence. Gas, such as methane, can escape from the shafts of such a mine by flowing up through the ground to the surface. The gas may already be warm and might become warmer by oxidation once it reaches the surface. Either way, it can warm the region surrounding its escape point by several degrees. If frost or snow covers the ground, this warming can clear the ground in a circular region around the escape point.

The effect is most noticeable during changes in barometric pressure. If the barometric pressure is high for several days, air is forced down into the mines, either through mine openings, chance cracks, or even the overlying ground. Then if the barometric pressure drops, the pressure in the mine is then higher than the external pressure, and some of the mine gas is pushed outward.
Regions in which mine gas escapes may indicate that the ground overlying the mine is relatively thin. Weathering or the presence of a sudden heavy load on the ground might cause such a thin ground layer to collapse to form a sinkhole. When this occurs in an urban environment, a truck driver might suddenly be headed nose down into a pit or a homeowner might open up the front door to find that the front lawn is no longer there. Thankfully, slumping of the ground is more common than the sudden formation of a sinkhole. If the ground slumps, don't drive heavy machinery over the top of it!

http://www.psc.state.nd.us/issues/aml-consinfo.html
http://www.news10.net/storyfull2.aspx?storyid=17212

Fizzing in a glass container

January 2007

To reduce the splashing when pouring a carbonated beverage (soda, beer, or champagne) into a drinking glass, you can tilt the glass and pour onto the slanted interior surface, so that the stream hits a solid instead of the liquid already in the glass. There is still enough turbulence to create bubbles. Listen to their fizz as they form, merge, and pop open. Although the noise extends over a range of frequencies, you can hear a dominant frequency that shifts as the depth of liquid in the glass increases.

The primary noise of the fizzing is independent of the depth but the noise also creates a weak resonance in the air space between the liquid and the top of the glass. That air space acts as though it were an organ pipe that is closed at one end (at the liquid) and open at the other. The resonant frequency of such a pipe depends on the pipe length---a shorter length corresponds to a shorter wavelength of sound and thus a higher resonant frequency. As you pour in more liquid, the air space in the glass decreases, and so the resonant frequency you hear steadily increases.

Tunnel fires

January 2007

I love crawling through caves but I hate driving through tunnels. The big difference is that in a cave I am in control but in a tunnel I depend on the wisdom (and sobriety) of all the drivers around me. My big fear is a crash that results in a fire, which happens quite often somewhere in the tunnels around the world. Being trapped in a long tunnel by a fire with billowing smoke is the stuff of nightmares. Let's see if physics can offer any guidance on what to do in such a situation.

Because hot gas from a fire is less dense than the surrounding cooler air, the hot gas rises. In an open area, the hot gas would probably reach a considerable height but in a tunnel, the ceiling blocks the gas. So, the gas spreads in both directions along the ceiling. The motion creates an air flow: clear air moves along the roadway toward the fire, gets caught up in the burning, rises to the ceiling, and then spreads along the ceiling. Thus, near the fire (within 50 m to 100 m), someone in a car or on foot may be able to avoid the smoke by being in the inflow of clear air. Farther from the fire (200 m), the hot gas has cooled somewhat and become turbulent, and it begins to mix the smoke with the road-level air. This road-to-ceiling smoke front moves along the tunnel and may be dense enough to be life-threatening. Indeed, the smoke in a tunnel fire is the primary danger for anyone not involved in the crash that caused the fire. The smoke front moves at about 1.5 meters per second, which is about the pace of someone walking quickly. Thus, if people are trying to walk away from the fire, they can easily be overtaken by the smoke front.

Modern tunnels, especially long ones, are ventilated by an air flow of about 3 meters per second in the direction of the traffic flow (if the traffic flow is one way). The idea is not only to remove car exhaust fumes but also to provide a margin of safety in case of a fire. The speed of the air is chosen to prevent the smoke from moving upstream (against the air flow and thus also against the traffic flow). Motorists downstream are able (hopefully) to escape from the tunnel by driving out of the tunnel but motorists upstream cannot easily back up out of the tunnel. The air flow is designed to give the upstream motorists a chance of survival by preventing the smoke from reaching them. There is, of course, a flaw in the plan. If the downstream motorists are caught in a traffic jam and cannot drive out, then the smoke might overtake them because the smoke front is pushed along by the ventilation flow.

http://www.roadtraffic-technology.com/contractors/traffic_man/exor/exor4.html
http://irc.nrc-cnrc.gc.ca/fr/pfdss/detecttunnel_e.html
http://www.sintef.no/content/page1____2884.aspx
accidental fire:
http://www.answers.com/topic/summit-tunnel-fire

Freezing of water on icicles

January 2007

Although they have been studied for a very long time, icicles are still not well understood. Here is one curious feature: An active (still wet, still growing) icicle has a thin central core of liquid water that extends down to the pendant drop at the tip. The top of that core gradually freezes, which means that it loses thermal energy so that the water molecules can become locked up in solid ice. But to lose thermal energy, the water must send it toward a point with a lower temperature. So, it cannot send the energy downward through the liquid water because that water is at the freezing point or slightly warmer. It cannot send the energy out horizontally, because the liquid water sheathing the icicle is at the freezing point. The only direction left is upward: The core gradually freezes by sending thermal energy up to the icicle root at the top and only if the temperature of the root is below the freezing point.

Recently, researchers at the University of Arizona have investigated the carrot-like shape of an icicle, noting that common stalactites have the same shape. In particular, the investigators developed a mathematical model for icicle growth. A thin sheath of water coats the outside of an icicle, draining toward the tip. As the water descends, some of it freezes to the ice surface, adding to the icicle width. Again, freezing can occur only if the water can lose some of its thermal energy. The energy cannot go into the icicle because there is no lower temperature in that direction. It must come horizontally outward to the external surface of the water layer and then be transferred to the air. On a windy day, the transfer is easy to picture. How about on a calm day? As air molecules take up some of the energy, the density in that air decreases slightly and then that air begins to rise because of buoyancy. Thus, convection of the air up along the side of the icicle removes the thermal energy. The rate at which the energy is removed sets the rate at which the icicle can grow in size and therefore the ultimate shape of the icicle.

http://curiouslee.typepad.com/photos/best_of_curiouslee/icicle_tip.html tip of icicle
http://gallery.spacebar.org/f/a/photo/viewpic/1/91/1/
http://www.pbase.com/hsandler/image/53385966 drop falling from tip
http://www.raglanroad.org/weblog/archives/2005_12.html the ribs often seen on an icicle

Golf ball dimples

December 2006

Golfers have long realized that a dimpled golf ball will fly much farther than a smooth ball because the dimples somehow reduce the air drag on the ball. It is that drag force that opposes the ball's motion and drains energy from it. Understanding how the dimples decrease the drag force has been very challenging because the experiments with air flow past a ball are difficult to see or measure. Up until now, that is. 

The air drag is primarily due to a difference in the air pressure between the front and rear of the ball. Let's take the perspective of a smooth ball, as if we rode along with the ball and felt the air streaming past us. As the stream moves around the surface of the ball, the air layer rubbing against the surface slows until it reaches a stagnation point, and then the stream breaks free of the surface. On a smooth ball, the

This break-away of the air stream creates a vortex-filled wake behind the ball. Because the air pressure in a vortex is low, this condition means that the ball has high pressure along its front surface and low pressure along its rear surface. The difference in the pressures on front and rear is the air drag that slows the ball.

Dimples change the picture dramatically because somehow they delay the stagnation of the layer of air sliding past the surface of the ball. So, the layer clings to the ball until it reaches the point almost directly behind the front impact point. The break-away point (or the stagnation point) is said to be delayed because it occurs farther back on the rear surface of the ball.

The result is that the vortex wake is much narrower and so the pressure across the rear surface of the ball is not so low. That means that the pressure difference between the front and rear is lower than with a smooth ball, perhaps 50% lower, and so the drag force is less by that same amount. What matters to the golfer is that a long drive goes much farther toward the hole.

I've known all this since I wrote the first edition of The Flying Circus of Physics. For all those years the nagging question has been: "Yes, but why do the dimples delay the break-away point?"

Jin Choi, Woo-Pyung Jeon, and Haecheon Choi of Seoul National University in Seoul, Korea, have now published an answer based on experiment because they figured out a way to measure the speeds down within and just above the dimples on a golf ball. A dimple causes turbulence in the air flow next to the ball's surface. Bringing faster air down next to the surface prevents the air next to the surface from slowing, stagnating, and then breaking free of the surface. Thus, we have the seemingly contradictory statement that the dimples lower the air drag on a golf ball by creating turbulence in the air flowing past the ball. For a golfer, then, turbulence is a good thing. 

Sounds of putting

December 2006

A professional golfer has an intuitive feel for putting a golf ball toward the hole. Obviously years of experience and a keen eye for the lay of the green are essential. The golfer can also analyze the ball (perhaps subconsciously) via the sound it makes when the putter hits it. Indeed, often a player will test an unfamiliar ball by dropping it onto a hard surface, to hear the ball bounce. What clues lie in such sound?

Successful putting requires an exquisite control over the way the ball leaves the putter, both in direction and speed. The direction is obviously important, because putting away from the hole just brings laughter of onlookers. But the speed is also important because if the

Usually a golfer describes a "hard ball" as one that shoots off the putter with less control over direction and speed and a "soft ball" as one that leaves the putter more slowly and with more control. Such evaluations are, to be sure, highly subjective but may, on the average, allow a golfer to adjust the putting during a game when the putting has not been very good.

In a long drive off a tee, a golfer has three general ways to judge the hardness of a ball. One way obviously lies in the path that the ball takes (the height and distance). A second way lies in the pressure and oscillations on the hands due to the impact. The third way comes via the sound made when the club hits the ball. All three ways are important during a long drive, but only the sound is important during the milder impacts in putting.

The impact by a club causes the ball to oscillate much like a bell oscillates when struck. And, just like a bell, a ball tends to oscillate in a certain pattern, said to be a resonance pattern. As the ball's surface oscillates and pushes on the adjacent air, sound waves are radiated from the surface. The frequency of those waves depends not only on the oscillation pattern but also on the materials and design of the ball. Tests indicate that a softer (more compressible) ball tends to oscillate in a broader range of frequencies centered on a lower frequency than does a harder ball. A golfer can hear the difference: The softer ball emits a duller, lower frequency sound (a "thud") while a harder ball emits a sharper, higher frequency sound (a "ping"). In putting, a thud is desirable. If the ball pings, the golfer has a harder ball and needs to hit it more softly, to control how it runs over the green.

Katrina damage to New Orleans

December 2006

When hurricane Katrina slammed into New Orleans in 2005, the water damage to the city's infrastructure was devastating. Much of that damage was due to the impact of water and to the scouring of the ground, which undermined the support of many structures. But there was another damage mechanism that caught me by surprise, although I have experienced the effect countless times, and so have you.

When the water submerged structures such as bridges and buildings, the buoyancy on those structures created stresses that the structures were never designed to withstand. You have noticed the effect whenever you have been swimming---your effective weight in water is small or zero because the upward buoyant force on you counters the downward gravitational pull on you. The same effect acts on bridges and the concrete slabs forming the floors of buildings. Once an object is submerged, its weight of such an object is effectively decreased by the by upward buoyant force. Many of these structures were designed to be anchored onto their supports by their weight. So, when that weight was effectively reduced or even eliminated, the structures were no longer anchored and were easily swept aside by the rushing water and high-speed winds. Worse, as the water rose it trapped air under some bridge spans and floor slabs. The buoyancy of the air tended to cause the objects to bob upward like a cork in water, ripping apart any connection with the normal support structure. Such a bobbing tendency also ruined many of the empty or almost empty storage tanks. The buoyancy tended to rip the tanks away from their attachments and then they could be shifted sideways by the flowing water. 

Coal fires and Earth's magnetic field

December 2006

Earth's magnetic field is continuously changing in both strength and direction for reasons that are only poorly understood. Recorded measurements usually go back for only a few hundred years, and scientists have long sought ways of inferring the field for more remote times. One way involves the rock layers lying just above coal ash, which can be found in some naturally exposed coal veins. How can the rocks there (but not meters away on either side of the exposed vein) reveal the magnetic field of long ago?

A vein of coal can become exposed to air if faults develop in the overlying rock layers or rivers cut down through the vein and then weathering further exposes the coal. When air becomes available, the coal can undergo exothermic reactions (energy is released) and the coal can spontaneously ignite, heating the overlying rocks. The temperature can then become high enough to exceed the Curie temperature of the magnetic grains in the rock. This temperature, named after Pierre Curie, marks the temperature at which certain naturally magnetic materials become demagnetized.

Ferromagnetic materials, such as in the magnets that you might use to attach notes to a refrigerator door, are magnetic because of a quantum mechanical effect that organizes the magnetic fields of the individual atoms, to give an overall magnetic field to the material. This organization can be ruined by the thermal energy associated with the oscillations of the atoms. If the temperature increases, so do the oscillations and the thermal energy. At the Curie temperature for a material, the thermal oscillations win and the overall magnetic field of the material disappears.

When coal burns in a vein and heats the overlying rocks above the Curie point, the magnetic properties in the grains in those rocks disappear. Once the fire burns out and the rocks cool, the magnetic organization of the atoms is reinstated. Because they lie in Earth's magnetic field, many of the atoms in the grains line up with that field. Thus, they record the direction of the Earth's field at the time of the cooling. 

When scientists find such burnt rock and remove a sample, they carefully note its orientation relative to the current direction of the magnetic field. If they can determine a date for when the coal became exposed to air (they might, for example, be able to calculate when a river had cut down to the level of the vein), then they can associate a date with the recorded direction of the field. We do not know why Earth's field wanders about (and sometimes disappears or flips over, north pole for south pole), but thanks to the burnt rocks, we know that these variations are not just recent events.

Fingers in molten lead

November 2006

First, a serious caution. This stunt is really, really dangerous, and don't you dare think about trying it. I have been badly hurt by it, but because I was the one who first did it in modern times, my name is associated with it and so I still do it.

Back in the 1970s, when I toured the U.S. and Canada with my Flying Circus of Physics talk, I showed the stunt to lots of physics instructors. They were amused by it, but most of them had the good sense (sense of self preservation) not to repeat it. A few failed the good-sense test and went off to hurt themselves in front of students. 

As described in The Flying Circus of Physics, the stunt requires that I dip my fingers first into water and then into the molten lead. Lead melts at 328 degrees Celsius but I take care to get the lead even hotter so that there is less chance that the lead will solidify when my fingers enter it. Its temperature exceeds the so-called Leidenfrost point for water (about 200 degrees Celsius), a temperature named for Johann Gottlieb Leidenfrost. He did not dip his fingers into molten lead (thus, he was smarter than I am, but about 300 years ago he wrote about how a drop of water can last much longer on a very hot metal spoon than on a moderately hot spoon. His explanation was that when the metal is very hot, the bottom of the drop vaporizes and then the vapor layer holds the remaining liquid water above the hot metal surface, thereby slowing the transfer of thermal energy to the water. So, the water can take a lot longer before it vaporizes.

Do you know that many people can remember where they were when something really dramatic happened? Well, I can remember exactly where I was standing when I discovered a copy of the article by Leidenfrost, in the engineering library at the University of Maryland. (All right, all right, I fully realize just how nerdy this makes me sound.) When I was a graduate student at Maryland, I always worked on my Ph.D. dissertation till midnight and then switched to working on the original version of The Flying Circus of Physics, until I passed out due to sleep depravation.

In those days before search engines, looking for FCP ideas was demanding because I had to physically search page by page through books and research journals. Curiously, some of the old physics books of about 1900 described how a carnival daredevil would stick fingers into molten metal, but I shrugged off the accounts, thinking the daredevil somehow faked the stunt. After all, how could a person touch a very hot surface without the finger being burnt?

When I discovered Leidenfrost's article, I immediately realized how the stunt was done. If the finger is wet, the water immediately vaporizes when it enters the lead and then the finger is coated with a thin vapor layer that slows the transfer of thermal energy to the finger. I say "slows" and not "stops" because thermal energy will still be transferred to the skin, so the vapor layer's brief protection is indeed brief.

After I graduated and came to Cleveland State University as a professor, I decided to try the stunt myself. As my common sense screamed at my foolishness, I first touched some molten lead with a wet finger and then plunged four wet fingers into it. The stunt proved to be a great treat for my classes. (Ah, let's watch the professor burn off his fingers! He won't be able to write exams after that!)

My second "Amateur Scientist" article in Scientific American magazine was about the Leidenfrost effect and the fingers-into-lead stunt. While making measurements and drafting the article late one night at school, I wondered: Is the water on my fingers really necessary for a plunge into the molten lead? I was so tired that I threw aside all rational thought and stuck a dry finger down into the molten lead.

What is the shortest amount of time that you know about? A microsecond? A nanosecond? A zeptosecond? Well, whatever your answer is, I realized in less time than that just how incredibly stupid I was. The pain rushed up my finger, faster through the fingernail than the fleshy part of the finger, presumably because either the fingernail conducts better or it is simply faster to heat. "Yes," I screamed to no one but myself (because, thankfully, no one else was at school that late), "water is indeed necessary."

If you want to see numbers and graphs about the Leidenfrost effect, here is a link to an essay I wrote for the textbook Fundamentals of Physics (David Halliday, Robert Resnick, Jearl Walker):

http://www.wiley.com/college/phy/halliday320005/pdf/leidenfrost_essay.pdf

The photograph of me in the essay is old and was taken under pretense because a few weeks later it appeared, not in a Swiss newspaper as I had been promised, but in a tabloid newspaper here in the U.S. The photographer was so good that even after I realized that I had been tricked (when someone told me that my photograph was in the National Enquirer), I still wanted the photograph.

In the blog site (click on the blog choice in the menu at the left here), you can find a link to an excellent (and recent photograph of me as my fingers enter molten lead, splashing the lead toward me (and my brand new Flying Circus of Physics tee shirt, which ended up with bits of lead melted into the fabric).

Again, do not dare try this stunt yourself. There are several subtle dangers---you can end up badly burned or even blinded. In the coming months, I shall tell you more about those dangers and how I painfully discovered them.

Rattlebacks

November 2006

A rattleback is the name of a plastic toy that exhibits a very headstrong behavior. It looks simple enough, resembling half of a long cylinder that is flat on top and curved on bottom. You spin it on a table with the curved side down by flicking it with your fingers. The curious feature is that the toy prefers one direction of spin. If you spin it in the other direction, it quickly slows, momentarily rocks in place, and then rotates in its preferred direction. It reminds me of certain people who insist that THEIR way is the ONLY way.

The behavior is very difficult to explain in detail but I can give a quick explanation, as I do in the book. The curved bottom is asymmetric (it is curved more on one side than the other). When the rattleback begins to turn in the wrong direction, the motion is unstable and the rattleback wobbles. Because of the shape on the bottom side, the wobbling sets up and then builds a vertical rocking motion. That motion requires energy, which comes from the energy of the rotation, and so the spinning rate decreases. The rocking motion increases until it has all the energy.

But the rocking motion is also unstable because of the shape of the bottom. With each bob up and down, the rattleback effectively falls toward one side rather than straight down. So, it begins to rotate in that direction of fall, which is its preferred direction of spinning. Thus, energy is transferred from the rocking motion to the rotation motion and the rattleback is then rotating as it wants. Throughout this entire process, friction between the bottom surface and the table drains energy from the rattleback, until the rattleback finally slows to a stop.

In the 19th century, stones that (by chance) had the right shape to exhibit the headstrong behavior were known as celts because their behavior was discovered by archaeologists studying the prehistoric axes and adzes they had already called celts. My guess is that a bored researcher happened to idly spin a celt that happened to be shaped to be biased in the spin direction.

Descriptions of the odd behavior and the name celt made their way into 19th century books about rotation but attention to them disappeared until I wrote about this curious physics in the first edition of The Flying Circus of Physics (1975). Later, A. D. Moore of the University of Michigan sent me several of the hundreds of celts that he had fashioned from dental stone. I included their description and his name for them --- rattlebacks--- in my Amateur Scientist article for the October 1979 issue of Scientific American. Some of Moore's rattlebacks exhibited a second, weaker reversal. (These too resemble people I have known: "I insist on this way. No, no. I mean this other way." Argh!)

My old article has provoked at least eight mathematically-sophisticated articles about rattlebacks. Although simple explanations are (well, er) simple, explaining the details of how the energy is shuffled from rotation to rocking and then back to rotation by instabilities and wobbling is mathematically challenging.

http://www.tedcotoys.com      This link takes you to Tedco, from which you can buy plastic rattlebacks via the internet.

Meandering rivers

November 2006

Nearly all rivers meander, that is, curve to one side and then the other as the water generally moves downhill. In some cases, the meander is so extreme that water even moves (briefly) uphill along a loop. This tendency of meandering and looping has long fascinated hydraulic engineers, environmentalists, and physicists. After all, except when meeting a solid obstacle, water flows directly downhill because of the gravitational pull on it. The next time you fly over land, examine the rivers that you pass---they all meander, even the ones that do not have solid obstacles, such as rock outcroppings, deflecting them.

Early investigations tended to concentrate on the mathematics behind a meandering shape because other things tend to buckle in similar shapes. For example, if you hold a thin metal strip (such as a metal ruler) between your hands and then compress it by moving your hands toward each other, the strip's sideways buckle resembles a typical loop in a river meander. The buckled shape has to do with the energy associated with the compressed parts of the rod. That energy is reduced to a minimum if the rod takes on the buckled shape instead of remaining straight. Could a similar energy reduction be attributed to river meander?

Recently Brian Hayes examined that question's history in an article in American Scientist (vol. 94, no. 6, pages 490-494, November-December 2006). In particular, he explored the research of Luna Leopold who coauthored a delightful article in Scientific American in June 1966. Both Hayes and I were captured by that article, and I eagerly included the subject of river meandering when I began writing the original Flying Circus of Physics material.

Although an explanation of river meander due to a mathematical reduction in energy is very tempting, the situation in an actual water flow is far too complex for the explanation. Instead, we must consider how, once chance has diverted the flow slightly to one side, the deflection is enhanced when water moves into the deflection. The deflected water's path is (roughly) spiral, with downward motion along the outer bank in the deflection. That downward portion tends to carve away the outer bank, making the deflection even more pronounced. Given enough time, the deflection forms a loop. Further erosion can even cut off a loop, leaving it isolated from the rest of the river. The loop is then usually called an oxbow, or in Australia a bilabong.

http://www.stacey.peak-media.co.uk/Year7/7-7Rivers/7-7Meanders/7-7Meanders.htm
River meander images

Strange ice sounds

November 2006

When a thin layer of ice lies over a pond, you might be able to hear a strange sound if you toss a stone out over the ice. Just after the stone hits, you might hear a slightly prolonged sound resembling the chirp of a bird. Why don't you hear just a single pulse of sound?

Neil Basescu of Westchester Community College (Valhalla, New York) told me how he happened to generate this chirping sound and then how he worked out its source. The stone's impact on thin ice causes the ice to fracture at the point of impact and in the surrounding area. Both the impact and fracturing send out sound waves through the air and the ice. The speed of sound is higher in the ice, and so that sound reached him first, and then slightly later, the sound through the air reached him. Thus, the total sound that come back to him was noticeably longer lasting than what he would have heard had the stone merely bounced off (thicker) ice.

Desert ant naviation

November 2006

The desert ant Catglyphis fortis can find its way back to its nest after traveling a long complicated path away from the nest to search for food. In spite of the hundreds of course changes, when it is ready to return, the ant simply turns toward the nest and moves along a straight line until it reaches the nest. The ant knows the way home because during the outward trip it continuously performs vector addition of all its displacements, both the length and direction of the displacements. So, the way home from any spot is the reversal of the net vector from the nest to that point.

This is astonishing, especially to my students who struggle to add only two or three vectors (using a calculator). Here, this tiny ant with a tiny brain (and no calculator) can add hundreds of vectors (and with no guidance from a physics instructor)!

Recent research shows that the ant's ability to find the direct route home works even when the terrain is hilly. Apparently, the ant can projects its motion onto a horizontal plane. So, if it follows a complicated outward route involving a lot of up and down travel, it knows the direct route home even if that direct route involves lots of up and down travel over other portions of the hills. That is, it can find the horizontal components of all the individual displacements and then sum those components. Somehow, this mathematical ability must be genetically coded in the ants. Too mathematics is not coded in your genes---math classes would have been a lot easier.

Musical echoes at a Mayan pyramid

November 2006

A handclap at the base of the ancient Mayan pyramid at Chichen Itza in Mexico produces a drawn-out musical echo instead of just a single echo that simply repeats the handclap sound. The reason has to do with the fact that the sound waves reflect head-on from the lower steps but obliquely from the higher, more distant steps. So, the pulses from the lower steps reach you, one after another, at a certain rate, which you hear as a certain frequency. Shortly later, the pulses from the higher steps reach you, one after another, at a lower rate (because of the oblique path), which you hear as a lower frequency. Thus, the echo begins with a higher frequency and ends with a lower frequency.

In 1693, Christian Huygens, a famous figure in the history of optics, described a similar experience in the garden of the Chantilly de la Cour in France. The sound from a water fountain reflected to him from a large stone staircase, giving him an echo at a certain frequency. This echo is due to a continuous source of sound (the fountain) instead of a pulse of sound (a handclap).

http://www.ocasa.org/MayanPyramid.htm
David Lubman, information and recordings, Chichen Itza Pyramid 

Echoes at rock art sites

November 2006

Rock art is art that has been left on rock walls by ancient people. It often depicts animals, such as deer, that the people probably hunted. In recent times, researchers have realized that the site of rock art is often a point where strong echoes can be heard. If you stand back away from the art and, say, clap your hands, the echoes returning to you can give the illusion that the sound originated from the animals in the art. Moreover, if you strike two stones together, the echoes resemble hoof beats, as if the animals are running.

Some rock art can be found in the caves of southern France, at points where a handclap or yell produces strong echoes. The reflecting sound waves briefly travel through one another, from one end of a passageway to the other, and set up a temporary acoustic resonance, somewhat like you might set up while singing in a shower stall. Such resonance may have been magical to ancient people, provoking them into drawing animals and signs on the walls to mark those special points in a cave. If the cave passageway was too tight, rough, or wet for extensive drawings, the point was marked with a red dot (usually ochre, which is a mixture of clay and ferric oxide). Such a dot was effectively a sign saying, "This is a magical point. Chant or hum here to contact the greater spirits."

http://www.geocities.com/capecanaveral/9461/
S. J. Waller, "Rock Art Acoustics," sound recordings and lots of additional material   

Rubber bands and the direction of time, me in entropy trouble at MIT

October 2006

Inflating a balloon with your breath and stretching a rubber band with your hands require effort because the rubber (or rubber-like material) resists being stretched. In most materials, the resistance to stretching is due to the forces that bind the atoms and molecules together. Because any stretching tends to separate the atoms and molecules, the binding forces resist the stretching. Rubber is very different because it is elastic and, for small extensions, the stretching does not tend to increase the separation of the atoms and molecules. Thus, its resistance is not due binding forces. What causes a rubber band or balloon to resist stretching?

Rubber consists of cross-linked polymer chains (long molecules with cross links) that resemble three-dimensional zig-zags. When the rubber band is at its rest length, the polymers are coiled up in a spaghetti-like arrangement. Because of the large disorder of the molecules, this rest state has a high value of entropy, the measure of disorder. When we stretch a rubber band, we uncoil many of the polymers, aligning them in the direction of stretch. Because the alignment decreases the disorder, the entropy of the stretched rubber band is less. Thus, the force on our hands from the rubber band is due to the tendency of the polymers to return to their former disordered state and higher value of entropy.

Because entropy naturally increases in the world, it is often said to give direction to the "flow" of time. That is, the flow is in the direction of increased disorder. For example, the molecules that bring the stench of a skunk to you (as time flows in the "proper" direction with the molecules spreading out) will not naturally recollect at the skunk (as if time could be reversed like a video run backwards). Thus, the force on our hands from a stretched rubber band is related to the direction of time. 

When I was at MIT in Boston, I lived in the East Campus Dorm, which consists of two parallel buildings. When spring arrived, the buildings would fight each other with giant slingshots made of surgical hose. Typically, the window in a dorm room was removed and then two lengths of the hose were fastened to opposite sides of the window frame. The lengths of hose were connected to a pouch that was pulled with great effort almost to the hallway. After a water balloon was fitted into the pouch, the pouch was released and the rapidly contracting hose hurled the water balloon at the opposite building of the dorm. If we were lucky, the water balloon would hit a window on the opposite building, crashing through the glass and into the room, spraying water everywhere. This was especially fun when we added dye to the water, to color the other room. "Festive," I thought.

Now, you might think that we were an unruly bunch. What we were really doing was studying how the force due to entropy can result in the mechanical energy of a projectile. At least, that is what we were going to tell the campus police if they ever caught us. We were always able to dismantle and move the slingshot before the police could pinpoint our position.

Halloween physics

October 2006

To celebrate Halloween (well, more to the point, to scare small children senseless), Americans transform pumpkins into Jack O'Lanterns. Triangular eyes and nose and an elongated mouth with a few sharp teeth are cut into the side of a pumpkin, and then a top section is cut out so that the seeds can be removed and a candle can be mounted inside the pumpkin. At night, the candle is lit so that the light escaping through the eyes, nose, and mouth give the glowing impression of a demon.

A practical question often arises: Should the top section be put back in place, or should it be removed so that the candle does not burn its underside, creating a stink? From a recent study by Whitehead and Mossman of the University of British Columbia, we can answer that question with some physics.

The Jack O'Lantern is a gothic version of an integrating sphere---a sphere with a reflecting interior and a small exit port. Such a sphere can be used to measure the total light output from a source, which is mounted inside. If a source emits light in many directions, measuring the total output is normally difficult. With the source inside the sphere, the light is effectively trapped except for a predictable fraction that escapes through the exit port. By measuring that escaping amount of light, you can easily determine the total light output from the source.

In a Jack O'Lantern, the exit ports are the carved-out facial features. Usually enough light escapes through those features to rival the brightness of a full Moon, which is, of course, just right to scare children on a dark night. The scare effect is almost eliminated if you remove the top piece, because then too much of the light escapes through the open top instead of reflecting around the interior and escaping through the facial features. The features are then just a dull glow.

None of this would matter if the interior of a pumpkin did not reflect so well, because then the light would just be absorbed by the interior. A dark Jack O'Lantern on a dark night wouldn't scare anyone.

Cocktail-party effect

October 2006

The cocktail-party effect is a name given to your general ability to pick out a conversation in the midst of many sound sources, such as other partygoers. The fact that you hear with two ears instead of one is certainly involved, because the signal from one ear may be delayed from the signal from the other ear. For example, if a speaker is on your right side, your right ear receives a spoken word from the speaker slightly before your left ear. Based on experience, your brain can use the difference in arrival times to determine the direction of the speaker amid the noise in the room. Also, your ability to make sense of a sentence after hearing only portions of it (you mentally fill in missing sounds and even words) can also help. And your ability to read the lips and body language certainly helps. (If the speaker throws her hands upward while scowling, she is certainly not telling a joke.)

Recent research suggests that the cocktail-party effect also depends on whether you mentally focus on the speaker. If you know where the speaker is in front of you, you can direct your attention to her and exclude much of the background sounds from other people and from sound bouncing off their bodies, the walls, and the ceiling. All that extra noise is still coming into your ears and its information is still being sent to your brain, but you tend to ignore it and concentrate on the speaker's voice. In contrast, if you don't know where the speaker is located and thus cannot focus on the speaker, you are less able to sort the speaker's voice out from the noise. You may have noticed this result if you have been in a crowded party when someone calls out your name and begins talking to you before you can locate the person in the surrounding crowd.

Killer shrimp

A type of shrimp kills its prey by snapping shut one of its claws to send out a lethal sound wave. High-speed photography reveals that the snapping of the shrimp claw is really a double punch. A strong sound wave is generated by the mechanical crash of the claw and then a second, sometimes even stronger, sound wave is generated by the collapse of the bubbles produced by the mechanical crash. This double punch can be devastating to the shrimp's prey but, strangely, it does not seem to hurt the shrimp. That is good, of course, because it would be embarrassing if the shrimp knocked itself out every time it knocked out its lunch.

Booming sand dunes

October 2006

Recent research indicates that avalanches on sand dunes can boom if the jostling of sliding sand grains becomes synchronized. The sound frequency is related to the depth of the sliding layer---greater depth means lower frequency. Booming is a rare phenomenon because the ability of the grain motion to become synchronized depends on the surface of the grains. The booming sand has acquired desert glaze, which is a silica gel layer. If the grains are made to slide against one another repeatedly, this glaze wears off and then the sound production ceases. Reasonably, this dependence on the surface must mean that the ability of the sliding to become synchronized depends on the friction of sand grain rubbing on sand grain.

Here is the web page by Stephane Douady, where he offers sound bites of the sand sounds, but I cannot get them to play. You can give them a try.

http://www.lps.ens.fr/~douady/

Oil and waves

October 2006

A delightful paper by Joost Mertens of the History Department of the University of Maastricht, the Netherlands, explores how Benjamin Franklin first noticed the calming effect oil has on water waves. In 1757, while on voyage to England in a fleet of ships, Franklin noticed that the wakes behind two of the ships were much flatter than behind other ships. His captain offered that the cooks on those two ships must have just thrown over the greasy water from the day's cooking. The captain thought that the effect was obvious; Franklin thought that the explanation was unfounded.

Franklin soon learned that the calming effect of oil or grease was well known to some groups of seamen. Indeed, many stories have been recorded about how seamen have purposely dumped various oily or greasy fluids on waters to calm them so that the ship could be brought safely through otherwise dangerous breakers. Eventually, through thought, experiment, and correspondence, Franklin realized that the oil "will not be held together by adhesion to the spot where it falls," but will spread out. (The oil actually forms a monolayer, one molecule thick, but Franklin did not have benefit of our modern concept of molecules.) "Now I imagine that the wind blowing over water thus covered with a film of oil, cannot easily catch upon it, so as to raise the first wrinkles, but slide over it, and leaves it smooth as it finds it."

Dust devil core

October 2006

The core of a dust devil can be defined in terms of the speed of the air around the center of the vortex. According to both theoretical models and measurements in natural dust devils, the speed is zero at the center and increases with distance from the center. At the edge of a core, the speed is maximum. The speed then decreases with greater distance from the center. So, were a dust devil to sweep over you (which is definitely not a good idea because of all the blown debris), you would feel the maximum wind speed as the near edge of the core passed you, almost no wind speed as the center of the core passed you, and then maximum wind speed again as the far edge passed you.

Although small children and animals have, on rare occasion, been picked up by especially large dust devils, chances are that you would be just pelted by the debris. Be thankful that you are not on Mars. There dust devils are huge, large enough to show up on satellite imagery. There you might go flying.

Freezing salty water and microwaving frozen foods

October 2006

If you freeze a container of salty water, the salt acts as an antifreeze, delaying the freezing and decreasing the freezing point (the temperature at which freezing occurs). Wherever the ice forms, the salt is forced into the regions that are still liquid. This is one reason why frozen foods can be thawed in a microwave oven. The microwave radiation (an invisible form of light) can heat food if the food has liquid water. The heating process involves the forced oscillations of water molecules in the water---the motion can break bonds that hold the molecules in temporary groups. As groups reform, the energy that went into breaking bonds is then transferred to thermal motion of the molecules; that is, the water becomes warmer.

When frozen food is put into a microwave oven, the microwave radiation can warm the food because there are pockets of liquid water throughout the food in spite of the low temperature. Food that has been in a common freezer may be at a temperature of -10 degrees Celsius, which is below the freezing point of pure water, but because of the salt content (or other ingredients), the food still has pockets of liquid water that can be heated by the microwave radiation.

The heating is best done slowly and at a low oven setting. Otherwise, the liquid water pockets overheat (and overcook the surrounding food) while the rest of food is still frozen. Slower heating at a lower setting allows the thermal energy from the liquid pockets to spread into the frozen sections, thawing those sections so that they too can be warmed by the microwave radiation.     

Collapse of the old Tacoma Narrows Bridge

September 2006

One of the most popular physics videos ever made shows the collapse of the Tacoma Narrows bridge, which dramatically began to oscillate in a moderate wind one morning soon after it was officially opened. The oscillations built up until the main span ruptured. As I describe in the book, the subsequent analysis of the bridge's collapse modified the role of aerodynamics in the construction of all large bridges thereafter.

A recent paper by Green and Unruh clarifies the role of the vortices in bringing down the bridge and builds on earlier modeling by Larson. As the wind encountered the bridge's girder at the left side (as seen in the video), it generated a series of vortices, alternating just above and just below the left edge of the bridge, each being swept rightward across the bridge. I you watch the video, you can see one of the votices as dust (presumably from disintegrating pavement) swirls around in it.

Each vortex was at a lower air pressure than the normal air pressure. Thus, when a vortex formed, say, below the left side of the bridge, the normal air pressure above that point tended to push the bridge downward. And when a vortex formed above the left side of the bridge, the normal air pressure below that point tended to push the bridge upward.

Whether this tendency of pushing feeds energy into the vertical oscillation of the bridge depends on the speed of the votices as they are swept rightward across the bridge's width. Below a certain critical speed, the vortices could not cross the width in the time of one bridge oscillation and the pushing actually opposed the oscillation, draining energy from it. (When part of the bridge was moving, say, upward, the pushing by the vortex there was downward.) At the critical speed, the crossing time matched the oscillation time, and the vortices did no net work on the oscillations (provided no change in energy).

The important thing that happened the morning of the bridge's collapse is that the wind exceeded the critical speed and the vortices crossed the width in less time than a full bridge oscillation. In that case, the forces from the vortices fed energy into the oscillations because their pushes were in the direction of the bridge's motion. Finally, the oscillations were severe enough to rip apart the bridge.

Danger of cell phone during lightning

September 2006

Talking on a cell phone while outdoors when lightning can occur may be dangerous. A person was seriously injured during such a conversation, although I do not see how the circuitry of a handheld device could possibly influence the huge discharge between ground and cloud. After all, the discharge jumps through several kilometers of poorly conducting air.

The person was probably just in the wrong place at the wrong time, but once the lightning hit, the conducting parts of the cell phone could have influenced the path of the current near the head. What is certain is that the rapid heating and resulting explosion of the phone caused extensive damage to the ear. So, if you think you are going to be hit by lightning, you best get off the phone.

If you are using a cell phone indoors (house, building, car, airplane, or train), there may be no danger at all because lightning rarely enters an enclosure through, say, a window or door, especially if the walls contain conducting materials such as metal. There is more danger in talking on a land phone, because the telephone wire could bring part of the lightning discharge indoors.

Cosmic rays and airplane flights

September 2006

Earth's atmosphere partially protects us from energetic particles from the Sun and outer space (cosmic radiation), but that protection is less when you are flying at high altitudes. The risk is negligible unless you fly frequently, such as members of aircrews must. Then the exposure to the radiation can be worrisome, especially when the flight is along a polar route (one at high latitudes, near the north pole), such as commonly used for flights between North America and Europe. Such a route is the shortest path between two points such as Toronto and Paris. The trouble is that the charged particles in the influx of radiation are caught by Earth's magnetic field and spiral down into the higher latitudes. Thus a polar route takes the aircrew through a region of incoming radiation. For this reason, a crew might wear radiation badges to monitor their exposure, and an airplane might be equipped with a radiation detector to sound an alarm if the radiation level is unusually high. Such higher radiation is expected if a giant solar flare explodes and shoots a stream of protons into space toward Earth. Usually an aircrew member is limited in the time per year that can be spent flying through the higher latitudes.

You might think that the worst radiation risk was on Concorde flights because, when that type of airplane was still flying, its supersonic speed required it to fly much higher than all other (slower) airplanes. In fact, the risk was less on Concorde flights because the flight times were so much shorter.

Gurney flap in race car downforce

September 2006

A race car is held onto a track by the downforce due to the flow of air above and below the car's body and (on some types of cars) the front and back wings. Part of the downforce can be due to a gurney flap, which made no sense at all when it was invented by Dan Gurney in 1971. Faced with a race car that was running too slowly, Gurney seemingly whimsically decided to fit an upright, short flap along the full length of the trailing edge on the car's rear wing. That did not make sense because the flap stuck up into the airstream passing over the wing, obstructing the stream and adding to the air drag on the car. After all, engineers go to great care to streamline a car To reduce obstructions and air drag.

When driver Bobby Unser took the modified car around the track, the car's speed was no better than previously, but after Unser climbed out, he took Gurney off to a point of privacy and explained: The car was no faster simply because there was now so much downforce on the rear wing that the car was no longer "balanced" in a turn. All they had to do was increase the downforce on the front and the car would be able to take the turns very fast.

So, how is the downforce increased by a gurney flap, as it came to be known after other racing engineers finally caught on to Gurney's secret design? There are two reasons: (1) The airflow along the top of the wing is deflected slightly upward by the flap and thus pushes downward on the wing. You feel a similar (but more simple) downward force if you have ever angled your hand in passing air, with the trailing edge of the hand somewhat upward. (2) The air flows over and under the wing form oppositely rotating vortices just behind the flap and extending a bit higher than the flap. The extra height causes extra deflection of the airstream passing over the flap and thus extra push down on the wing. Also, the presence of the vortices allows additional tilting of the wing without the airflow resulting in stall, in which the stream under the wing breaks away from the wing prematurely. Such breakaway would ruin the downforce.

Source: Howard, K., "Gurney flap," http://www.allamericanracers.com/gurney_flap.html 

Water-walking insects and the Cheerios effect

September 2006

The Cheerios effect is the tendency of individual floating grains of breakfast cereal (such as Cheerios) to aggregate because of their distortions of the water surface. The water tends to rise up along the side of each Cheerio, and when two of them are near, the curved water surface between them pulls them together. A high school student told me about this effect just as I was writing the first edition of The Flying Circus of Physics. More recently, researchers have written several very nice papers about the effect.

Some water-walking insects may use the Cheerios effect to climb out of the water next to, say, a log. A water-walking insect avoids sinking by causing the water surface below its legs to indent, which creates upward forces to support it. The forces are generally attributed to the surface tension of the water, that is, the forces along a water surface due to the mutual attraction of the water molecules. The water surface near a log curves upward --- the water molecules are attracted to the log and to each other, and so the water is pulled a short distance upward onto the log. A water-walking insect should have a difficult time negotiating this curvature (it would be like you trying to climb up a hill of ideally slippery ice), but a least one type meets the challenge by pulling upward on its front legs to decrease the indentation at the front and pushing down on its rear legs to increase it at the rear. The result is that the surface tension along the curved surface helps pull the insect to the log, which it can then grab to climb out.

Description and videos (including "robostrider," the mechanical water strider that surely is the nightmare of any water strider) are at
http://www-math.mit.edu/~dhu/Press/Press03/MIT%20leaps%20to%20solution%20of%20walking-on-water%20mystery.htm

Vertical roller coaster loops

September 2006

Vertical roller coaster loops are often tear-shaped instead of circular To maintain a large acceleration of the passenger during the upward climb. The problem is that the roller coaster slows as it climbs, as kinetic energy is traded in for gravitational potential energy. So the acceleration (the centripetal acceleration, or "toward the center" acceleration, which depends on the speed) decreases. That's no fun for rabid coaster fans. To offset this effect, modern tracks are tear shaped so that the curvature increases with height. The passenger's speed still decreases with height, but the ever sharper curvature maintains the acceleration and thus also the thrill. On some tracks, the curvature increases even more, so that the acceleration increases near the top of the loop. Then the acceleration is greatest where the passenger might be upside down. Just lovely for the coaster fans.

Punches in boxing

September 2006

In a recent study, Olympic boxers (in the categories of flyweight, light welterweight, middle-weight, and super heavyweight) threw forward punches into a laboratory dummy's face, so that the force of a punch could be measured. Not surprisingly, the size of the force correlated with the weight of the boxer. (I don't know about you, but I have spent a lifetime in avoiding fights with a heavy opponent. Well, actually, any opponent, but especially anyone twice my size and wearing a motorcycle jacket.)

The size of the force in a collision (here, between the fist and the face) depends on the fist's change in momentum (the product of mass and speed) during the collision. A greater initial momentum means a greater change in momentum and thus a greater force. This is the reason why both boxers and karate fighters are taught to aim a punch "through" the opponent, so that the collision begins when the fist has the greatest momentum.

Surprisingly (at least to me), the recent study showed that all boxers (light weight to heavy weight) have about the same fist speed. Thus, the force size is greater for a heavier boxer primarily because the fist has more mass.

Shooting yourself down

August 2006

During a routine flight in September 1956, test pilot Tom Attridge put his Grumman F11F-1 jet fighter into a 20 degree dive for a test of the aircraft's 20 mm machine cannons. While traveling faster than sound at 4000 m altitude, he shot a burst of rounds. Then, after allowing the cannons to cool, he shot another burst at 2000 m. His speed was then 344 m/s, the speed of the rounds relative to him was 730 m/s, and he was still in a dive.

Almost immediately the canopy around Attridge was shredded and his right air intake was damaged. With little flying capability left, the jet crashed into a wooded area, but Attridge managed to escape the resulting explosion by crawling from the fuselage (in spite of four fractured vertebrae). What happened just after the second burst of cannon rounds?

When the bullets left the cannons, they were traveling much faster than the airplane but the air drag on them was apparently severe, especially as they moved down into denser air. Unlike the airplane, the bullets lacked engines that could maintain their speed. So, their speed soon dropped to less than the airplane's (supersonic) speed, and the airplane ran into them. (There must be a moral about life here, somewhere.)

Falls over Niagara Falls

August 2006

Many people have tried to ride contraptions (balls, tubes, and other shapes) over the edge of the Canadian side of Niagara Falls. Most paid with their lives; the others, especially in recent times, paid heavy fines for their stunts. What is deadly about the fall?

The fall itself, which lasts about 3 seconds, can be jarring because the contraption hits so hard that the water does not move out of the way. Still, the impact could be survivable, especially if a rider is surrounded by padding, which would prolong the collision and thus decrease the size of the collision force on the rider. (Because the force is inversely proportional to the duration of the collision, prolonging that duration by the use of padding decreases the size of the force.) 

If the contraption hits the rocks at the bottom of the falls, the impact is so abrupt that survival is unlikely, even with considerable padding. The contraption might even bounce, which could throw the rider around the contraption or severely jar the rider, compounding the danger. In the past, the stunt people had to contend with an additional, subtle danger. In those days the water flow at the bottom of the falls could submerge a contraption behind the falling water. Several people drowned after their contraption became trapped like this and then filled with water.
  
Shot putting and the football throw-in

July 2006

The optimum angle for putting a shot in shot put (I love to say that) is not the intuitive 45 degrees for two reasons: (1) The shot is launched at a point above where it lands. (2) The shot putter can accelerate the shot to a greater launch speed at a shallower angle just because the orientation of the arm is less awkward.

The same argument governs the throw-in of the ball in football (known as soccer in the U.S.). To throw the ball in from the sideline to teammates deep in the field, a player uses an overhead throw at a relatively shallow angle, perhaps 30 degrees. This launch angle is large enough for the ball to clear the heads of nearby opponents and is small enough that the player can greatly accelerate the ball during the launch.

Golf ball hopping out of a cup

July 2006

A golf ball might hop out of a cup if its forward rotation causes it to climb the cup wall up to the lip. An escape is also possible if the ball's center initially has a downward component of motion. Then the ball rolls around the interior of the cup while it also oscillates up and down, and it can escape the cup during the up phase.

Building sway

July 2006

You might not notice very low frequency swaying (less than 0.10 times per second) but swaying at somewhat higher frequencies (say, once per second) can affect the balance center in your inner ear and may lead to slight motion sickness. The problem is worse if you stand because your body then tends to sway about your feet, as if you were an inverted pendulum. Your head may then oscillate enough for you to be aware of the motion.

Opal coloration in a beetle

July 2006

The colors of an opal are due to the diffraction of light by an ordered stacking of tiny spheres: White light enters an opal but the stacking arrangement scatters back only light in a narrow color (or wavelength) range. The rest of the entering light undergoes destructive interference (the waves cancel one another) after scattering from the arrangement.

Similar diffraction of light occurs in the scales on the Australian beetle Pachyrhynchus argus. A scale contains an inner structure of tiny transparent spheres in an ordered packing, an arrangement known as a photonic crystal. If white light shines on the beetle, the light reflected (scattered) by the scales has a metallic color of yellow-green. The spacing of the sphere arrangement determines the color of the reflected light but the beetle is not iridescent like many types of butterflies because the spacing varies across the scales, giving an overall yellow-green appearance.

Stone skipping on water

June 2006

Recent experiments and wonderful high-speed photos reveal the mechanics of a stone skipping over water. The stone, actually an aluminum disk, was launched by a catapult device that could control both launch speed and rotation rate. The researchers discovered (or rediscovered) that if a stone is to skip, its speed must exceed a certain threshold value or the stone merely skims (surfs) over the water top for a short distance before stopping and sinking. The stone's rotational speed must also exceed a certain threshold value. The spinning stabilizes the stone much like spinning stabilizes a gyroscope. Then the stone maintains the same orientation (with the front end tilted upward by 10º to 20º from the water surface) for its entire skipping path. From skip to skip, its horizontal speed is almost constant, but its vertical speed (due to its being thrown upward by each crash into the water) decreases, until finally the stone just skims. A video of Kurt Steiner setting the world's record of 40 skips can be seen at www.pastoneskipping.com/steiner.htm on the Web.

Missing Moon in Munch painting

June 2006

In the painting Girls on the Pier, Edvard Munch shows two girls standing on a pier as the Moon hovers some 8º above the horizon (www.munch-raisonne.com). Strangely, a reflection of the Moon does not appear in the water below the pier, whereas reflections of other things, such as a house and a tree, are there. Was Munch being careless or profound? Was there a hidden philosophical meaning behind the Moon's lack of reflection?

Although Munch (and the girls) could see the Moon directly, the rays of light from the Moon that would normally have given them a reflected image were blocked by the house they saw (directly) just below the Moon. If Munch had moved down to the point on the water where the moon rays would normally have been reflected and then looked up toward the Moon, he would not have seen the Moon because it would have been behind the house. So, from that viewpoint, the lack of a Moon would not have been mysterious. From the viewpoint up on the pier, the blockage of Moon rays by the house is not obvious and the lack of a Moon reflection seems strange.