For Chapter 2, this is part D of the new stories and also the updates to the items in the book, including many video links and journal citations. If you want all the video links (hundreds) and journal citations (thousands) for this chapter, go to

http://www.flyingcircusofphysics.com/pdf/Chapter2_Ref_Com.pdf

First, a list
--------- New items (not in the book):
2.155  Shooting yourself down
2.156  Katrina damage to New Orleans
2.157  Lifting a glass from a tabletop wet with whiskey
2.158  Being sucked through an airplane window

2.159  Patterns in draining honey and yogurt
2.160  Geoffrey Pyke and the bergship of World War II
2.161  Sailboats
2.162  Pub trick --- escape from a cellophane pocket
2.163 Geysers exploding from rain runoff shafts
2.164  Water and block puzzle
2.165  Diffraction as seen from space
2.166  "The Birds" and flocking
2.167  Pub trick --- 1000 drops from an empty bottle
2.168  Pub trick --- vortex in a bottle and the vortex beer bottle 


Reference and difficulty dots
Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages

2.155   Shooting yourself down
Jearl Walker www.flyingcircusofphysics.com
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.)

· Friedlander, G. D., “The pilot who shot himself down,” Mechanical Engineering, 111, 130 (March 1989)

2.156  Katrina damage to New Orleans
Jearl Walker www.flyingcircusofphysics.com
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. 

· Robertson, I. N., H. R. Riggs, S. Yim, and Y. L. Young, “Lessons from Katrina,” Civil Engineering, 76, No. 4, 56-63 (April 2006)

2.157  Lifting a glass from a tabletop wet with whiskey
Jearl Walker www.flyingcircusofphysics.com
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? (The photo here is by Novanto.)

Answer Considering the long history of whiskey, you would think that there has been considerable experimental research on the subject. However, 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.
    However, 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. However, 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. 

· ·  van der Spoel, D., E. J. W. Wensink, and A. C. Hoffmann, “Lifting a wet glass from a table: a microscopic picture,” Langmuir, 22, 5666-5672 (2006)

2.158  Being sucked through an airplane window
Jearl Walker www.flyingcircusofphysics.com
August 2007  In the 1959 novel and 1964 movie Goldfinger, James Bond watches a person being sucked through an airplane window after the window panes have been broken out by a sharp point (novel) or a stray bullet (movie). On countless flights since reading the novel and seeing the movie, I have envisioned the horror of being sucked through an airplane window opening like toothpaste is squeezed from its dispenser. However, recent studies have shown that a small hole in an airplane window, such as a bullet hole, is probably of no immediate danger. I definitely will not be squeezed through a bullet hole.

Those studies calmed me up until last month when the story about flight nurse Chris Fogg hit the news outlets. While transporting a patient in an air ambulance, Fogg was sitting next to a window when the window panes blew out of the airplane. He was immediately sucked into the window opening, and when he finally realized what had happened, his head and right arm were outside the airplane and he could see the tail of the airplane. In addition, the air moving at 200 miles per hour (310 kilometers per hour) along the fuselage was pushing his exposed head and right arm back along the fuselage, which tended to pull him farther through the window.

The only reason he was not sucked or pulled entirely through the window was that his left hand and his legs were splayed desperately against the cabin wall and ceiling. By shear effort, Fogg forced his torso back away from the window opening so that the outward airflow could move around him and out through the opening. Several of the links below take you to interviews with Fogg; one link shows a terrifying animation of what happened to him; and several links show photos of the window.

Here’s the physics. Because the atmospheric air pressure decreases with altitude, the air pressure inside an airplane tends to decrease also. Most of us can adjust to the decrease up to an altitude of 8,000 feet (about 2.4 kilometers). However, at cruising altitudes of 25,000 to 35,000 feet, we would be unable to breathe in enough oxygen to remain conscious or to stay alive. So, all high-altitude commercial aircraft have pressurized cabins where the air pressure is kept at the atmospheric air pressure of 8,000 feet. If the cabin were to become depressurized, oxygen masks would drop from above each seat to provide oxygen to a passenger. Of course, with Fogg’s head outside the airplane, he was in danger of oxygen starvation and certainly did not have the advantage of an oxygen mask. Luckily, the pilot realized that the cabin had depressurized and dived to a lower altitude in order to increase the oxygen supply. However, he did not yet realize that Fogg was hanging on for dear life.

What author Ian Fleming envisioned when he wrote the James Bond novel Goldfinger was what would happen if the window panes broke while an airplane is at high altitude. The internal air pressure matches that at 8,000 feet; the external air pressure is much lower. The pressure difference would tend to push air and objects through the opening. We can say that the higher internal pressure pushes the objects through the opening or the lower external pressure sucks them through. Either description is correct; the point is that there is a pressure difference.

So, how can the James Bond situation not be dangerous but the Chris Fogg situation should have been lethal? The difference is the size of the opening.

Suppose an aircraft is flying at an altitude of 35,000 feet with the cabin pressure set to match that at 8,000 feet. The pressure difference between the inside and outside is about half of the atmospheric air pressure that is normally pushing on you. That is a huge difference!

But the danger lies in the net force that would be produced on an object positioned in the opening. To get the net force, we multiply the pressure difference by the area of the opening. For a small bullet hole, the area is quite small and thus so is the net force. However, if we consider a larger hole, with a larger area, the force can be considerable. If the entire window pane blows out, the net force can be several thousand newtons, which is several times my body weight. Thus, if I brought my finger near a window with a bullet hole, I could easily withstand the net force on the finger but if I am sitting near a window that entirely blows out, fighting the net force would be very difficult.

I am writing this story while sitting next to the window on an airplane at high altitude. As I type, I frequently flick my eyes to the window to see if it is secure. Just in case, I have my seat belt pulled tight so that I am anchored to the seat which is anchored to the floor. And if the whole window suddenly blows out and the seat belt seems to be giving way, I am going to slap the food tray or even my wide-screen computer across the width of the window opening like a Band-Aide, to decrease the area through which the pressure difference is felt. And just in case that is about to happen, I am typing as fast as I can.

http://www.ktvb.com/news/localnews/stories/ktvbn-jul0107-freak_accident.32f8dd86.html Video interview with Chris Fogg. Scroll down to the news story to see the window.
http://www.amtonline.com/article/article.jsp?id=4214&siteSection=1 News account

http://abcnews.go.com/GMA/story?id=3347262&CMP=OTC-RSSFeeds0312 Audio from ABC news (click on the “Sucked Out of a Plane” button to activate the video; good animation of Fogg being pushed into the window)
http://www.youtube.com/watch?v=EHGBQINW0B0 Airplane window blown outward; dummy pushed through window.

2.159  Patterns in draining honey and yogurt
Jearl Walker www.flyingcircusofphysics.com
September 2007 Honey is a fluid with particles held in suspension. It is said to be viscous because it does not readily flow, owing to internal friction within the liquid and because of the particles. If you examine a pool of pure honey, you have no chance of seeing the suspended particles---they are much too small to be visible to the eye.

Yogurt is a similar viscous fluid with suspended particles that are too small to see with the eye. (In some countries, the name is “yoghurt” or yoghourt.” In North America, some yogurt products are so thick as to almost be solid. Here I am talking about the more liquid type.) With either honey or yogurt, you could see the particles with a good microscope. However, is there is any way you can compare the sizes of the honey particles with the sizes of the yogurt particles in your kitchen during breakfast?

Recently, M. Buchanan, D. Molenaar, S. de Villiers of the University of Oslo and R. M. L. Evans of the University of Leeds published a study about pattern formation in draining thin film suspensions and used honey and yogurt as their examples. Here is a link to their photographs but you may need to copy it into the address line of your browser to reach the site:

http://www.fys.uio.no/pgp/pdf/thinfilm_pattern.pdf

At the left, we see honey draining on a vertical flat glass surface (inset) and in a jar. At the right we see yogurt draining on the wall in a glass beaker. Do you see a difference? The draining honey forms roughly horizontal bars while the draining yogurt forms clear vertical channels. This difference in behavior is of keen interest to scientists working in, say, an industry involving coatings such as paint and liquid cosmetics. Such behavior gets their hearts thumping hard because it can involve physics that will allow them to beat out the competition in their markets.

Buchanan and the other researchers conducted experiments in which suspensions of distilled water and quartz particles were allowed to drain along a vertical container wall. They used particles of two sizes, 20 microns (“large”) and 3.5 microns (“small”), in several different combinations. When the suspension contained only the small particles, it formed vertical clear channels. When the suspension contained only the large particles, it formed roughly horizontal bands. Both types of drainage are said to be examples of self-organizing patterns, a region of avid research in many disciplines. Scientists and engineers like to fashion their own patterns but are utterly fascinated when a system just naturally forms a pattern on its own, as dictated by some internal (often unseen) feature.

For intermediate mixtures of the two types of particles, the researchers found a transition stage from the clear channels to the horizontal bands. The really neat thing here is that the microscopic size of the particles determines the pattern that you see in the drainage; that is the internal feature that dictates the patterns. Here is a simplified explanation:

· Particles smaller than the thinned film: Gravitation initially pulls the film down the wall rather quickly but as the film thins and its weight decreases, it slows. At some points on the wall, a chance nonuniform spot in the film causes the flow to stop. Liquid above the spot is forced to flow around the spot, and as the liquid picks up speed, its viscosity decreases. The flow is then sufficient to sweep the particles down the wall, leaving a relatively clear vertical channels on the left and right of the nonuniform spot.

· Particles almost as large as the thinned film: As the film thins to the size of the particles, the particles become pinned (they are immobile) and jam against one another, forming a logjam. Additional particles flow downward to the region and then off to both sides, becoming pinned and adding to the logjam. Thus, the logjam builds to the left and right, forming a horizontal band.

So, the behavior of a draining film of yogurt and honey on a vertical container wall depends (in part) on the size of the suspended particles relative to the thickness of the film. The yogurt particles are small enough to be flushed out by the flow even when the flow stops in certain spots, and thus yogurt forms vertical clear channels. The honey particles are big enough to get pinned as the film thins and then they form logjams that build out horizontally. And you can see all this physics while sitting at your breakfast. (Do I need to repeat the mantra of FCP that physics is everywhere? No, probably not.)

http://www.ph.ed.ac.uk/cmatter/meetings/seminars/1147093200  Abstract of seminar by Mark Buchanan
http://members.fortunecity.com/templarseries/patterns.html Essay “World of Patterns” by Mark Buchanan

Reference
· Buchanan, M., D. Molenaar, S. de Villiers, and R. M. L. Evans, “Pattern formation in draining thin film suspensions,” Langmuir, 23, 3732-3736 (2007)

2.160  Geoffrey Pyke and the bergship of World War II
Jearl Walker www.flyingcircusofphysics.com
Feb 2008    Geoffrey Pyke was a scientific advisor to the British government in World War II and had the highly eccentric personality that would easily fit into a script from Doctor Who. He presented a continuous flow of ideas, many that a normal person might find quite strange. Here is one that caught the attention of Winston Churchill, who was Prime Minister during the German siege of the British Isles. Why not convert an iceberg or ice floe into an aircraft carrier?

And here is the reasoning that (strangely enough) won Churchill’s approval of the idea:

1. The aircraft that the Allies could send into distant battle areas from the existing carriers were inferior to the German aircraft, which were land based. A bigger carrier was needed, one that could handle the larger land-based aircraft of the Allies.

2. The consumption of common building materials, such as steel, was already fully committed to the war effort, and so, such materials could not be diverted to build aircraft carriers.

3. Ice is readily available in the North Atlantic Ocean and suffers relatively little damage in direct hits by both artillery shells and torpedoes. Although a conventional aircraft carrier could easily be sunk by the fierce German submarines, an aircraft carrier made of ice would hardly be affected by many torpedo strikes.

4. Ice floats because the water expands as it freezes, that is, as the molecules take up fixed positions as the liquid turns into a solid. So, an iceberg or an ice floe is naturally less dense than the surrounding ocean water and floats with a certain amount above the ocean surface.

Once convinced, Churchill commissioned the Habbakuk project, in which a model “bergship” would be built and studied in Canada, to see if a large- scale ship could be fashioned.

Of course, many military and scientific advisors shook their heads at the idea, but Churchill prevailed. Almost immediately snags were met: The ice would have to be thick, much thicker than an ice floe, and long, much longer than an iceberg. So, the plan was to make an artificial floating block of iceberg, about 2000 feet long (to allow the planes to take off and land) and 3oo feet wide (to allow many planes to be stored) and 40 feet thick (to support the weight of the airplanes (which were going to be Spitfires). Such a bergship would have been huge, much larger than conventional aircraft carriers. However, researchers quickly realized that the strength of ice is too unpredictable. Some slabs are very strong while others are much more brittle. Building even a moderate size ship to support aircraft seemed far too risky.

Then the researchers discovered that the strength of the ice was increased and made much more predictable if wood chips or sawdust were mixed with the water prior to freezing. The product was called pykrete, which was a contraction of “Pyke’s concrete.” Its ultimate strength, which is a measure of the stress due to compression or tension needed to rupture the material, was considerably higher than pure ice.

The wood does not act as glue, as you might think. When a material cracks under stress, the failure occurs in chance weak regions, probably where some flaw already exists. Once started, a crack can cut its way through a structure because the stress is concentrated at the tip of the crack and can tear apart the molecular bonds there. The added strength of pykrete was due to the pieces of wood interfering with that stress concentration at the tip of a crack, probably by bridging the tip and resisting further separation of its two sides. Not only could pykrete support heavy aircraft and other equipment, but a direct hit from a torpedo would do little more than leave a shallow crater. (For a small example, see the link showing pykrete before and after being shot by a .243 rifle.)

Still, in spite of the pykrete’s promising qualities, the plan for a pykrete aircraft carrier was doomed for many reasons. For one, the pykrete sagged (crept) with time, especially if the temperature rose above -15ºC. (The British would have to operate the carrier in warmer waters than that.) For another, the pykrete needed to build the aircraft carrier as planned would reportedly have required every wood chip throughout Canada. And, third, after the huge amount of work spent in building it, the ship would have ultimately melted. Not sunk in heroic defeat. Not retired in heroic glory. But melted. Nothing heroic about that.

http://www.simegen.com/writers/lois/pykrete.htm Photos of pykrete and ice before and after being shot by .243 rifle

http://www.shipwreckcentral.com/livedive/archives/habbakuk/ Videos about the production of a television special about the Habbakuk project in Canada.

http://www.stormy.ca/marine/habbakuk.html Article and drawing and photo about the Habbakuk project

http://www.slv.vic.gov.au/hwtports/0/0/2/doc/hp002626.shtml Photo of Pyke
http://www.abovetopsecret.com/forum/thread177273/pg1 blog

· Perutz, M. F., “A description of the iceberg aircraft carrier and the bearing of the mechanical properties of frozen wood pulp upon some problems of glacier flow,” Journal of Glaciology, 1, No. 3, 95-104 (1948)

2.161  Sailboats

Jearl Walker www.flyingcircusofphysics.com
April 2008    Bryon D. Anderson of Kent State University recently published an article, “The Physics of Sailing,” in Physics Today. The article is based on his delightful book The Physics of Sailing Explained, which you can buy from Amazon.com by clicking through the store link in the menu at the left. Sailing holds many physics surprises, which perhaps is one reason why many scientists love to sail. Here are two surprises as explained by Anderson.

Speed. When the wind is steady, in what direction should you sail the boat in order to get the greatest boat speed? Downwind? No, actually, the best direction is perpendicular to the wind. If the boat is traveling downwind, then the faster it goes, the less effective the wind is. In the ideal limit, the boat’s speed could match the wind speed, but then the air and the sail would be traveling at the same speed and the air would not push on the sail. In reality, because the boat meets resistance from the water, it cannot actually reach the wind speed.

If the boat moves perpendicular to the wind, with the sails set at about 45º to the wind, the wind delivers the greatest push on the sail, regardless of how fast the boat moves. Then the boat speed can actually exceed the wind speed, although resistance from the water limits the speed. If the resistance is minimized, as is done with some special sailboats, the boat might move at twice the wind speed. Anderson points out that the same physics applies to iceboats that glide over ice with little resistance. With them, the boat speed might reach three times the wind speed, perhaps moving at 150 kilometers per hour (over 90 miles per hour). Imagine zipping along an iced over lake at 150 km/h (just praying that there are no ice bumps along your path).

Hull speed. Some boats are designed to fly over a water surface, but let’s consider the more traditional type with a hull that displaces water because it is extends below the water surface. When such a boat moves through water, its bow produces a bow wave, with a crest at the bow and one or more crests alongside the boat’s hull. If the boat speed increases, the wavelength of the bow wave increases, shifting those other crests back along the hull. If the speed reaches a critical value called the hull speed, the second crest is located at the stern of the boat.

That critical speed marks a dramatic transition in the resistance to the boat’s motion. If the boat speed increases any more, the second crest moves to a point behind the boat, and then the boat’s stern lies in the valley between that crest and the crest at the bow. Thus, the boat is tilted upward, with its bow higher than its stern. That means that the boat is effectively sailing “uphill”, which significantly retards its forward motion. A boat is limited by its hull speed unless an engine can power the boat through the water. But, of course, that would destroy the serene enjoyment of sailing that most enthusiasts cherish.

· ·  Anderson, B. D., The Physics of Sailing Explained, Sheridan House (2003)

· · Anderson, B. D., “The Physics of Sailing,” Physics Today, 61, No. 2, 38-43 (February 2008)
 

2.162  Pub trick --- escape from a cellophane pocket

Jearl Walker www.flyingcircusofphysics.com
May 2008    Here is a simple little trick involving a cigarette hard-pack (with a cellophane covering) and the filter end of a cigarette, cut off from the rest of the cigarette. You can substitute other materials to avoid using cigarettes. What is essential is that the cellophane makes a fairly tight fit over a fairly rigid cardboard structure. Also, you need something short and lightweight like the filter.

To start, the hard-pack has been opened such that the top of the cellophane covering has been removed, as is normally done with a pack of cigarettes. The remaining cellophane covering is then slid half way off the hard-pack so as to form a cellophane pocket below the hard-pack. A hole is then burned into one side of this pocket by a lit cigarette, with the hole large enough to allow the filter to be pushed through it and into the cellophane pocket.

The bar challenge is to get the filter to come back out of the pocket through the hole. In such a challenge, someone will most likely try to shake the hard-pack so that the filter might happen to line up with the hole and slide through it. However, a person could shake the hard-pack for hours without success.

Here is the video that reveals the “trick” that anyone can use to get the filter out through the hole, but my challenge here is this: Can you explain why the trick works? After all, anyone can do a trick but the real power of physics is the ability to explain a trick.

http://easybartricks.com/magic-escape.html

By depressing the side of the hard-pack somewhat with the fingers, a person creates a tunnel between the side and the cellophane. However, the cellophane still makes a fairly tight fit where it meets the bottom edge of the hard-pack. When you blow into the tunnel, the air stream must force its way through that tight fit, so that it can then flow into the cellophane pocket. As the air stream squirts through the opening and into the pocket, it swirls; that is, it forms chaotic vortexes in the pocket. In the video you can see that the filter is caught up in that swirling.

With such chaotic motion, the chance of the filter lining up with the hole and slipping through it seems just as remote as when the hard-pack is merely shaken by hand. Indeed, the filter is more likely to straddle the hole than be perpendicular to it and neatly lined up for an escape.

However, the filter almost immediately escapes because in the chaotic motion it soon hits with one end extending only partway across the hole. Because air is escaping through the hole, the air pushes against that end of the filter, creating a torque on the filter about the edge of the hole. The torque rotates the filter around that edge until the filter is lined up with the hole, and then the air pushes the filter on through the hole. Another successful escape!

Similar physics can be seen in an air-mix machine that is used in many lottery drawings. Ping-pong balls, rather than cigarette filters, fill a plastic container into which air is blown, with a single-digit number printed on each ball. When the valve on an escape tube is opened to allow the air to flow out of the container, the air stream picks up a ball and carries it up into the tube, where it catches on a constriction in the tube. The number printed on that ball then forms part of the winning lottery number. In this way, the digits forming the winning number are chosen by chance because which ping-pong ball the air stream happens to carry up into the tube cannot be determined in advance.

However, as I often repeat on this web site, knowing physics gives you power. In 1980, some people “fixed” a major lottery game in the United States by applying a bit of physics. They realized that even a slight increase in the weight of certain ping-pong balls would decrease the chance that those balls would be carried into a tube by the air stream. So, they injected a small amount of white paint into all the balls except those with 4 and 6 on them. Then they purchased many lottery tickets for numbers that included 4 and 6. When the lottery machine was turned on, the lighter weight balls with those numbers were indeed preferentially picked up by the air stream, and the cheaters won a huge amount of money (before they were caught).

Physics is everywhere, even in cheating in a lottery system. Indeed, physics is behind cheating in other games, such as throwing dice, as I shall explain here sometime.

link to scandal story
http://www.tubecityonline.com/history/perry.html

link to photo of air-mix machine
http://static.howstuffworks.com/gif/lottery-gravity.jpg

link to description of lottery devices
http://entertainment.howstuffworks.com/lottery2.htm

2.163 Geysers exploding from rain runoff shafts
Jearl Walker www.flyingcircusofphysics.com
June 2008    In many cities, rainwater drains off roadways into underground pipes (or tunnels) in order to decrease the chance of deep pools of water on the road, which would certainly cause accidents. The water runs along a road until it reaches an opening with a grid on top, and there it drains through the grid and down through a vertical shaft to the underground pipe. The pipe is somewhat slanted so that the water runs down its length to a larger pipe or a holding tunnel. Usually many vertical shafts are connected to a very long pipe that may run for many kilometers along a road.

What could be dangerous about such a drainage system? Watch this video:

http://www.youtube.com/watch?v=DDfZdfeJ1nc&feature=related water pressure blows a huge cover into traffic

http://www.youtube.com/watch?v=4BkFp5CL4q0&feature=related same video

Over four million people have watched this video on the web and surely they have all gasped when the pickup truck ran into the huge shaft cover that was blown off into its path and then later laughed when the driver walked over to the cover to see what was going on, only to be caught up in another geyser. I think that fleeing the area was the wisest thing that driver did.

But do you see something strange here? Why was there a second geyser? (There could have been even more.)

We can easily create a simple explanation for the first geyser: Maybe there was a sudden heavy downpour of rain somewhere along the road and the point we see on the road was just above a low point in the pipe. So when the onrush of water through the pipe reached the low point, the water rushed out of the vertical shaft.

But if that explanation is correct, why was there a second geyser? Did the storm gods wait until that driver had the poor judgment to walk close to the drainage shaft before they cut loose with another downpour somewhere else along the road? In short, our simple explanation seems to fail.

Such geysers on an urban water runoff system are uncommon but occur frequently enough that they have been studied by civil engineers. To see the physics beyond them, consider a simple system consisting of three, widely separated vertical shafts that are connected by an underground pipe which slants downward from the first shaft (at your left) to the third shaft (at your right). Water drains down the three shafts and then along the pipe, collecting at the pipe’s low point at the right. Let’s next assume that the system is designed to hold the water at least temporarily.

If the rainfall increases dramatically, the water depth at the right end also increases dramatically until that section of the pipe is filled. An increase in water height then moves up the pipe as a steep wave called a hydraulic jump or surge front. Moreover, because water continues to come down the third shaft, water actually flows up the pipe even as water from shafts 1 and 2 is still moving down the pipe. The surge front moves past shaft 2 and then finally reaches shaft 1. The flow associated with this motion is said to be pressurized because the high water pressure in the surge front pushes the water up the pipe against the pull of gravity. When the surge front and pressurized water reach shaft 1, water is shoved up the shaft so rapidly that it shoots out the top of shaft 1, forming a brief geyser as you see in the video.

Now comes the surprising part. The sudden climb of water up shaft 1 first relieves the pressure at the base and then, when the water slumps, recreates the high pressure there. That sudden increase in pressure sends a pressure pulse back down the pipe.

When the pulse reaches the lower end at the right, it reflects and climbs back up the pipe. When it returns to shaft 1, it can shoot another geyser out of the shaft. If the pipe is long, the round trip of the pulse may take tens of minutes or even longer, plenty of time for the ground water around shaft 1 to subside and an overly curious driver to walk over to inspect the shaft. In fact, the pressure pulse in the pipe may oscillate between the two ends of the pipe several times, sending out several geysers at either end of the pipe.

Here is a physics lesson that is simple enough to be put on a tee-shirt. We could write equations for the water flow on the back of the shirt but on the front all we need to say is

  If stuff shoots out of the ground, run away!

http://www.youtube.com/watch?v=Sh0Jy_DJrAA another manhole geyser

http://www.youtube.com/watch?v=f_vk-lev6vI&NR=1 oscillating manhole cover due to oscillating air pressure in the air above the oscillating water in a water runoff system

http://www.metacafe.com/watch/yt-8NwNwCXUMqU/dancing_manhole_cover/ here too

http://www.youtube.com/watch?v=8NwNwCXUMqU same video

http://www.youtube.com/watch?v=xwar6VbgY-M&feature=related another oscillating manhole cover

http://www.youtube.com/watch?v=zl1vctvVbwY&feature=related

http://www.youtube.com/watch?v=fOxQ_XQmEec&NR=1
 

· · · Guo, Q., and C. C. S. Song, “Surging in urban storm drainage systems,” Journal of Hydraulic Engineering, 116, No. 12, 1523-1537 (December 1990)
· · · Guo, Q., and C. C. S. Song, “Dropshaft hydrodynamics under transient conditions,” Journal of Hydraulic Engineering, 117, No. 8, 1042-1055 (August 1991)
· · Zhou, F., F. E. Hicks, and P. M. Steffler, “Observations of air-water interaction in a rapidly filling horizontal pipe” Journal of Hydraulic Engineering, 128, No. 6, 635-639 (June 2002)
· · Vasconcelos, J. G., and S. J. Wright, “Experimental investigation of surges in a stormwater storage tunnel,” Journal of Hydraulic Engineering, 131, No. 10, 853-861 (October 2005)
· · · Politano, M., A. J. Odgaard, and W. Klecan, “Case study: numerical evaluation of hydraulic transients in a combined sewer overflow tunnel system,” Journal of Hydraulic Engineering, 133, No. 10, 1103-1110 (October 2007)
 
 

2.164  Water and block puzzle
Jearl Walker www.flyingcircusofphysics.com
Aug 2008    Sola Saba, a student at Cleveland State University, recently brought me a puzzling problem. Suppose that a container of water is placed on a sensitive balance to measure weight, and then a block of lightweight wood (less dense than water) is submerged and attached to a thread that is tied to the bottom of the container. Thus the block is held fully below the water surface and a short distance above the bottom of the container. Next suppose that the thread slowly dissolves in the water and eventually breaks, allowing the block to float up to the water surface. Here is the puzzle: From the instant just before the string breaks to the instant just after the block has settled into its final floating position, what does the weight-measuring scale read? That is, does the reading increase, decrease, or remain the same, or does it undergo some series of changes?
 
Answer: Rather than slug our way through equations (though we should eventually do just that), let's just give a quick answer. Initially the scale supported both the water and the block, and the reading on the scale matched their weight. Once the block reached its final floating position, the scale again supported the water and block, and the reading again matched the weight. However, when the block was ascending and water was filling it its former location, the scale had less to support and its reading was less than the weight. You might think of the process this way: A block of lightweight wood went up and a block of heavier water went down. The net effect is a descent of mass --- a block of material effectively fell and during that falling, the scale did not fully support the material.

2.165  Diffraction as seen from space
Jearl Walker www.flyingcircusofphysics.com


Aug 2008    Recently Paul Hambourger, my colleague here at Cleveland State University, used Google Earth to search for the harbor across which Julius Caesar swam to escape an Egyptian army. Caesar had sided with Cleopatra in a power struggle with her brother, who was supported by the army. When he was cut off from his men at Alexandria, Caesar found that swimming was his only way to avoid capture.

When Hambourger used Google Earth to zoom in on one of the modern-day harbors at Alexandria (at coordinates 31º 12’ 34.5” N and 29º 54’ 7.2” E), he found the image you see here. Waves can enter the harbor through two relatively small openings in a protective barrier but in doing so, the waves undergo diffraction. In this type of wave interference, the waves flare from a small opening (instead of going straight) and also overlap. Where overlapping waves are in phase (in step), they form taller waves (higher crests and deeper valleys). Where waves are out of phase, they tend to cancel one another, leaving the water almost flat.

In the Google Earth image, I can easily see the flaring from the openings, especially the more central one, but I cannot see any pattern of large waves and flat water. I suspect that the pattern is wiped out for two reasons: (1) the waves have a range of wavelengths instead of a single one and (2) the arrival of the waves at each opening is somewhat random.

We would see the pattern if we could somehow arrange for the waves to have a single wavelength and arrive in a continuous fashion. If we were then to change to a different wavelength, the positions of the large waves and flat water would shift. Thus, because there is a range of wavelengths, there are so many overlapping patterns, with different locations for the large waves and flat water, that no evidence of the interference is left.

You might use Google Earth to search the coastline of your own country for examples of water-wave diffraction. I’ll be posting more examples of such diffraction here, but they will probably lack the charm of Julius Caesar swimming for his life.

2.166  “The Birds” and flocking
Jearl Walker www.flyingcircusofphysics.com
Aug 2009 In Alfred Hitchcock’s legendary movie The Birds, a coastal town is attacked and eventually devastated by thousands of birds. Here is a collection of clips from the movie that will take you through the storyline:

http://www.youtube.com/watch?v=fjj32CavzU0

Many people are terrified of a flock of birds, fearing that it might suddenly swoop down in an attack. Although that is simply the stuff of movies, the sight of a flock of starlings is at least awesome, if not frightening. A flock can consist of hundreds to tens of thousands of birds, undergoing a fluid-like motion. Here are a few examples:

http://www.youtube.com/watch?v=RHHfynLYW1I Video showing flocking of birds
http://www.youtube.com/watch?v=XH-groCeKbE&NR=1&feature=fvwp flocks of starlings near Oxford, England
http://www.youtube.com/watch?v=8vhE8ScWe7w&NR=1 Gretna, Scotland

The stunning feature of starling flocks is that in spite of the flock’s three-dimensional twists and turns, none of the birds collide. How can tens of thousands of closely-spaced flying birds avoid collisions? How do they manage to fly and land without any leader? How is the “decision” for the flock to, say, turn to the left communicated across the flock, or is the flight simply a result of chance decisions, with many random decisions being made and changed? How do the birds respond when the density of the flock suddenly changes?

These questions have fascinated scientists in many disciplines, including physics, because the starling flocks are an example of collective behavior without a leader. The questions still have not been fully answered, but recent studies of starling flocks have led researchers to fairly successful models. In particular, the models suggest that any given bird within a flock monitors the six or seven closest birds, regardless of how close they really are. That is, the bird’s flight is affected by those closest birds regardless of the density of birds.

Presumably, the bird maintains its flight orientation relative to those six or seven closest birds. If they begin to, say, veer to the right, then the given bird does also. Then information about this veering is fairly rapidly transmitted across the flock so that it (or at least part of it) veers to the right. In the videos you can see that the flight change is not always transmitted to the full flock, with the flock tending to split into branches. But then corrections are made to bring the branches together.

The simulations also suggest that this flight behavior works to the advantage of the birds if they are attacked by a falcon. If each bird were affected by the density, then the flock would tend to splinter at the point of attack, leaving individual birds as easy prey for the falcon. However, if each bird tends to monitor only the six or seven closest birds, the flock tends to veer away from the falcon at the point of attack, without leaving any stragglers as prey for the falcon. However, in this next video, a falcon attack does seem to split several of the starlings.

http://www.youtube.com/watch?v=b8eZJnbDHIg

Unraveling the collective behavior of starlings will be challenging because, of course, you cannot just interview them afterwards as you could with, say, a mob of football fans pressing into a game area. However, a successful model of the flocks might then be applied to a leaderless mob, as well as to other animal groups such as herds and fish schools.

Here are videos showing starling flocks:

http://www.youtube.com/watch?v=Vq6Qmd5apI4&NR=1
http://www.youtube.com/watch?v=_V83ysbs7zE

http://www.youtube.com/watch?v=RFRjO0vTjjM&feature=related

http://www.youtube.com/watch?v=mLb3ON1Z_L8&feature=related

http://www.youtube.com/watch?v=TL8diH-I9EQ&feature=related

http://www.youtube.com/watch?v=MIzlcH2q6Vo&feature=related

http://www.youtube.com/watch?v=YadP3w7vkJA&feature=related

http://www.youtube.com/watch?v=XH-groCeKbE duplicate video
http://www.youtube.com/watch?v=8vhE8ScWe7w duplicate video
http://plus.maths.org/issue42/features/dartnell/index.html Essay about simulations of flocking

http://upload.wikimedia.org/wikipedia/commons/thumb/9/95/Red-billed_quelea_flocking_at_waterhole.jpg/300px-Red-billed_quelea_flocking_at_waterhole.jpg photo

References
Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
··· Gregoire, G., H. Chate, and Y. Tu, “Moving and staying together without a leader,” Physica D, 181, 157-170 (2003)
· Grunbaum, D., “Align in the sand,” Science, 312, 1320-1322 (2 June 2006)
· Feder, T., “Statistical physics is for the birds,” Physics Today, 60, No. 10, 28-30 (October 2007)
·· Ballerini, M., N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, and V. Zdravkovic, “Empiral inverstigation of starling flocks: a benchmark in study in collective animal behaviour,” Animal Behaviour, 76, Part 1, 201-215 (July 2008)
· Ballerini, M., N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, and V. Zdravkovic, “Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study,” Proceedings of the National Academy of Sciences of the United States of America (PNAS), 105, No. 4, 1232-1237 (29 January 2008)
· Castelvecchi, D., “Birds network too,” Science News, 173, No. 8, 125 (23 February 2008). Article available without photo at http://www.thefreelibrary.com/Birds+network+too.-a0175948910
· Daruka, I., “A phenomenological model for the collective landing of bird flocks,” Proceedings of the Royal Society B, 276, 911-917 (2009)
· Carere, C., S. Montanino, F. Moreschini, F. Zoratto, F. Chiarotti, D. Santucci, and E. Alleva, “Aerial flocking patterns of wintering starlings, Sturnus vulgaris, under different predation risk,” Animal Behaviour, 77, No. 1, 101-107 (January 2009)
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2.167  Pub trick --- 1000 drops from an empty bottle
Jearl Walker www.flyingcircusofphysics.com
June 2010 Pour the beer out of the bottle and then set the bottle down upright. The challenge is to get even more beer out of the bottle, in fact, to get 1000 drops of beer out of the bottle. Here is a video to show that it can be done:

http://www.metacafe.com/watch/1172003/1000_drops_bar_bet/

I don’t know if you get as many as 1000 drops, but you certainly get a lot. The question is, why do you get beer from the bottle after you have seemingly emptied it?

The answer is that beer (and beer bubbles) still clings to the interior of the bottle. If you put a drop of beer (which is largely water) on a horizontal glass surface, it tends to spread out over the glass. Although the water molecules attract one another and tend to minimize the surface area of the drop by forming a bead, they are also attracted to the glass molecules and tend to spread out. The shape you see is the compromise between the two tendencies. On another surface, where there is less attraction between the surface molecules and the water molecules, the drop will spread out less and thus form a tighter bead, with a greater curvature.

When you pour beer from the bottle, some of the beer spreads over the glass interior, held there by the attraction with the glass molecules. If you are patient, most of it will eventually drain out of the bottle, but if you put the bottle down soon, an appreciable amount still coats the interior. After a few minutes that coating and the liquid in any bubbles drain to the bottom of the bottle. If you then sling the bottle as shown in the video, you propel that liquid out the opening. The effect is more dramatic if you sling the liquid down onto a metal surface so that the drops rupture into many smaller drops with an audible collision.

The effect is far less dramatic with a beer can for two reasons.

(1) Slinging any remaining contents through the small opening in the can is difficult.

(2) The beer does not spread over the interior surface as much as with glass and thus not as much is left in the container when you put it down.

Although beer cans are made of aluminum, nearly all brands have a coated interior to prevent interaction between the aluminum and the beer. To check how well beer spreads over the coated surface, I (carefully) ripped a can in half, laid the bottom half on a table on its curved side, and then put a drop of beer down on the interior wall. Next to it, I placed a glass cup (of comparable curvature) on its side and put a comparable drop down on the interior wall. The drop on the coated aluminum was noticeably rounder.

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2.168 Pub trick --- vortex in a bottle and the vortex beer bottle
Jearl Walker www.flyingcircusofphysics.com
Aug 2010   Here is a popular physics demonstration: Fill a 1 liter bottle with water, invert it, and then time how long the water takes to pour out. The water outflow alternates with the air inflow, an action called glug-glug after the sound it makes.

The action begins, of course, because the water at the bottle’s opening is denser than the underlying air, an unstable situation. As I discussed in other pub tricks here, the unstable situation can remain in place if the opening is small enough (see the pub trick involving the inverted Red Bull can). However, the opening to a 1 liter bottle is too wide. The width allows chance disturbances to set up waves across the water surface at the opening. Where the wave moves the water surface up, an air column develops and air bubbles into the bottle. And where the wave moves the surface down, a water column develops and dumps water from the bottle. The action is rarely smooth and has plenty of stops and restarts, which adds to the time required to drain the bottle.

Now repeat the demonstration but this time, as soon as you invert the bottle, use one hand to rotate the top (actually the closed bottom surface) in a horizontal circle, swirling the water around the vertical axis. The direction of swirling can be either clockwise or counterclockwise. A visible vortex can develop inside the bottle, from the opening at the bottom to the top of the water surface. The water now drains from the bottle in much less time because air can easily move up into the bottle through the core of the vortex, while the water swirling around the core can easily flow downward along the interior surface of the bottle. Here is a video showing this trick, and more are given below this story. You can also buy an adaptor to connect two l liter bottles so that the water drains neatly from one bottle into the other.

http://www.youtube.com/watch?v=dv6vQU94wws

Recently the company that brews Miller Lite beer brought introduced the vortex bottle with much advertising attention. (This is an American beer product, where the misspelling of “light” means that the beer is watered down from the normal product.)

The vortex bottle is the regular size of 12 fluid ounces for an American beer, but the interior surface of the neck has shallow spiral grooves instead of the normal smoothness. The name of the bottle and the video advertisements suggest that the beer leaves the bottle faster because of a swirling action due to the grooves.

http://www.youtube.com/watch?v=vmne-Wmm7WU&feature=related

One blogger worried that the increased speed would allow college students to guzzle a bottle faster, leading to (increased) alcohol abuse on campuses. (The advertising firm must have done a collected dance when they read that blog --- their advertising claims were being taken seriously!)

Is there any noticeable effect? Can I see swirling or a vortex in the beer flowing from the bottle? Is the draining time measurably less? I checked but with water instead of the watery beer (because I did not want the foaming to block my view of the flow).

Tilting the beer at various angles while I looked into the open mouth allowed me to watch the water as it flowed over the grooves. As long as air could flow in at the top of the opening, there was no glug-glug, of course. The beer simply poured outward with no swirling, unlike what is shown in the television advertisements. The grooves were too shallow to have any effect.

Next I inverted the bottle to allow glug-glug. No swirling developed. Then I checked that bottle and a normal beer bottle of the same dimensions to see if my hand rotation could set up the vortex effect seen in a 1 liter bottle. No vortex --- the bottle is so much smaller than a 1 liter bottle that it empties too quickly.

Finally I filled the vortex bottle with water and placed the empty normal bottle on top, opening to opening. I connected the bottles with wide plastic packing tape wrapped around the opening. Then with one hand on the wrapped region, I inverted the structure while with the other hand I triggered an electronic timer to measure how long the water took to drain from the vortex bottle (now on top) into the normal bottle. Then I inverted the assembly again to measure how long the water took to drain from the normal bottle (now on top) back into the vortex bottle. I repeated the measurements about 15 times and then averaged the draining time for each bottle. Their averages were the same.

Alas, the only way a Miller Lite beer can set up swirling is if someone drinks so much that their vision begins to swirl.

http://www.physics.umd.edu/lecdem/services/demos/demosf4/f4-25.htm University of Maryland physics demonstration

http://www.youtube.com/watch?v=mzw3DcDblIg&feature=channel tornado tube

http://www.youtube.com/watch?v=iTwh3sByYUU&feature=related tornado tube

http://www.youtube.com/watch?v=rBaD2CA2OrY&feature=fvw tornado tube

http://www.youtube.com/watch?v=P7L3KPfGTPU&feature=related tornado tube

www.stevespanglerscience.com/experiment/00000056 description of the tornado tube demonstration

http://www.teachersource.com/AirPressure/AirPressure/VortexBottleConnectors.aspx?gclid=CLjN69yOkaMCFQTXnAodAnEStQ purchase a connector

http://www.examiner.com/x-32687-Augusta-Craft-Beer-Examiner~y2010m3d31-MillerCoors-introduces-new-marketing-gimmick-The-Vortex-Bottle blog

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