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Flying circus of physics

Chap 2 (fluids) archived stories part A

Friday, February 06, 2009

For Chapter 2, here is part A 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

First, a list
2.1  Upside down racing, as in Men in Black
2.1  Gurney flap in race car downforce
2.3  Aerodynamics of passing trains
2.4  Collapse of the old Tacoma Narrows Bridge
2.7  Scott Macarney crash in downhill ski racing
2.10  Cards as weapons
2.11  Falling cards and helicopter seeds
2.14  The best free kick ever
2.15  Golf ball dimples
2.18  Birds flying in V formation
2.23  Large bathtub-like vortexes
2.26  Meandering rivers
2.30  Canal effect

2.35  Swimming in dead water
2.36  Being inside (yes, actually inside) a tornado
2.36  Tornado versus house
2.39  Dust devil core
2.39  Martian dust devils
2.40  Vortex rings --- from hookahs to powerful air cannons
2.41  Pub trick---sucking liquid up a straw
2.41  Chain siphon that rises into the air

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

Now the stories:

2.1 Upside down racing, as in Men in Black
Jearl Walker
Oct 2011  A car traveling through a flat turn in a Grand Prix race depends on friction to stay in the turn. However, if the car is going too fast, friction fails and the car slides out of the turn. In earlier times, a car had to take the flat turns rather slowly. But modern race cars are designed so that they are literally pushed down onto the track to give the tires good grip. In fact, that push down, called negative lift, is so strong that some drivers boast they could drive their cars upside down on a long ceiling. What causes negative lift, and can a race car actually be driven upside down as done fictionally by a sedan in the first Men in Black movie?

About 70% of negative lift on a car is due to one or more wings that deflect the passing air upward.

race car.

The rest of the negative lift is called ground effect and has to do with the airflow beneath the car. The faster a car moves, the greater both aspects of negative lift are. At the high speeds typical in a Grand Prix, the negative lift is larger than the gravitational force on a car. Thus, if the car were to move from a normal track to a ceiling (without slowing), the now upward negative lift would more than offset the downward gravitational force. Thus, the car could indeed be driven upside down as in Men in Black.

Ground effect is due to the constricted flow of air below a car. As air is squeezed into a small passage beneath the car, its speed increases at the expense of its pressure.

So, there is lower air pressure below the car than above it, and the pressure difference presses the car onto the track. In a race, a driver can reduce air drag on the car by closely following another car, a procedure known as drafting. However, the leading car disrupts the steady flow of air under the trailing car, eliminating the ground effect on it. If the trailing driver does not anticipate that elimination and slow accordingly, sliding into the track wall may be unavoidable.

Here is a video from the television series Top Gear in which Jeremy Clarkson attempts to drive upside down in a large-diameter, long sewer pipe in Belfast

Well, he does not actually drive upside down. He actually drives in a loop-the-loop around the top of the pipe but falls off the pipe before he completes the loop.

However, even that much was ambitious considering the relative slow speed of the car. It certainly had no negative lift from wings or the ground effect.

What Clarkson is doing is mimicking a circus performance in which a small car is driven fast into a vertical, circular track that loops it around until it emerges onto the ground. Here is an image of such an act, in which stuntman Steve Truglia raced a Toyota around a vertical loop:

The stunt works provided that the car’s speed exceeds some critical value. In effect, the car is then continuously running into the curved track. But if the speed drops below the critical value, the force on the car from the track (the so-called normal force) decreases to zero and then the car loses contact with the track and falls while still moving forward, crashing somewhere on the lower, far side of the track.

If you are using the textbook that I write (Halliday, Resnick, and Walker, Fundamentals of Physics), you can find calculations involving upside-down racing in some of the sample problems:

In 7e, Chapters 6 and 14.

In 8e, Chapters 6 and 14.

In 9e, Chapter 6

Calculations about a bicycle (rather than a car) being driven upside down in a loop can be found in Chapter 6 in all recent editions.

I’ll leave you with this upside-down-racing cartoon from The Flying Circus of Physics book.

2.1  Gurney flap in race car downforce
Jearl Walker
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 and thus should have obstructed the stream and added to the air drag on the car. After all, engineers go to great care to streamline a car in order 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? (A modern version is shown in the image here, from The359. Do you see the short upright gray ridge that runs along the right-hand edge of the wing?) There are two reasons for the flap's increase in downforce: (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,"

· · ·  Mukherji, T., “Investigating the aerodynamic response of a NACA 0012 airfoil with gurney flap,” (2006)
· · ·  Troolin, D. R., E. K. Longmire, and W. T. Lai, “Time resolved PIV analysis of flow over a NACA 0015 airfoil with Gurney flap,” Experiments in the Fluids, 41, 241-254 (2006)

Want more references? Use the link at the top of this page.

2.3  Aerodynamics of passing trains
Jearl Walker
Dec 2008     If you stand next to a rail track as a high-speed train passes you, you can be knocked down by the pressure wave shed by the front of the train. As the train plows through the air, it compresses the air. If you could see the compressed air, it would roughly form a cone with the apex located at the front of the train. As the train moves, the pressure cone is continuously being formed.

If you are near the track, the pressure cone will sweep past you, followed by a rapid decrease in air pressure as the air attempts to regain its initial pressure. This cone of high pressure and then low pressure is also shed by high speed airplanes and is sometimes made visible if water moisture condenses to form a fog of water drops in the low pressure portion of the wave. Below I give a link to photographs and videos where you can see conical fogs hugging high-speed airplanes.

The situation with a high-speed train, however, is different in that a train can be much longer than an airplane. Air tends to be entrained (pulled along) by the cars behind the front of the train, which causes a suction action on the air somewhat farther from the train.

Although we cannot see the high pressure cone or the entrainment of air directly, we can see the effects in the following video. You may want to watch it twice because the first part is horrifying --- two people dash across the track of an oncoming, very high speed train. The woman just barely misses being hit. Try to watch the man that is already on the platform; in particular, watch his stance and his clothing.

Can you see when he is hit by the high-pressure wave and then when he is pulled toward the train? Can you also see airborne debris that is pulled along with the train?

In England and other places, a danger line is marked on the platforms, near the outer edge --- you are to stand behind the line. One reason is so that you are not hit by any side projection from a train. The other reason is that if a train passes rapidly through the station (instead of slowing to a stop), you will not be knocked off balance by the high-pressure cone and then pulled onto the side of the train by the suction action of the entrainment of air.

You can also hear and see the pressure effects from inside a train if the train passes another, nearby train at high speed. I notice the effects on the trains running between Gatwick Airport and London whenever a train passes an oncoming train. Both trains are moving fairly rapidly but the relative speed between the two (the speed of either relative to the other) is the sum of the two speeds. Thus, the relative speed is high, which causes a significant decrease in the air pressure between the trains as they pass each other. I can feel the sudden drop in pressure. I can also hear the effect as the passenger doors facing the other train are yanked outward against their restraints by the decreased air pressure between the trains. In earlier days, when train speeds were first being increased and side-by-side tracks were being laid, train designers did not know about the low pressure that could develop between passing trains. One result was that the glass would be sucked out of the windows that faced one another.

In this video

people leaving an apparently stalled train walk over an adjacent track as another train approaches at a fairly high speed. My first reaction to the video was to say, “Oh no, someone is going to be hit.” But then I noticed the several people caught in the narrow space between the stalled train and the moving train. They were caught in a low pressure region where the air was being entrained and pulled along by the moving train. They were very lucky they were not pulled onto the moving train. Video of two fast trains passing each other in opposite directions. Note the uncontrollable motion of the camera.

Videos and photos of condensation cones created by high-speed aircraft: go to

and then scroll down to item 3.54 Photo of a shock wave shed by an aircraft.

Dots ·  through · · ·  indicate level of difficulty
Journal reference style: author, title, journal, volume, pages date)

· Price, B. T., “I. Social significance of airflow problems. Airflow problems related to surface transport systems,” Philosophical Transactions of the Royal Society of London A, 269, 327-333 (1971)
· ·  Camerlingo, C., and A. Varlamov, “An incident on the train,” Quantum, ??, 42-44 (November-December 1990)
·  Fuji, K., and T. Ogawa, “Aerodynamics of high speed trains passing by each other,” Computers & Fluids, 24, No. 8, 897-908 (1995)
· · ·  Howe, M. S., “Pressure transients generated when high-speed trains pass in a tunnel,” IMA Journal of Applied Mathematics, 65, 315-334 (2000)
· ·  Schetz, J. A., “Aerodynamics of high-speed trains,” Annual Review of Fluid Mechanics, 33, 371-414 (2001)
· · ·  Howe, M. S., “On the infrasound generated when a train enters a tunnel,” Journal of Fluids and Structures, 17, 629-642 (2003)

2.4  Collapse of the old Tacoma Narrows Bridge
Jearl Walker
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. If 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.
    However, 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.
Movies and newsreels Newsreel with narration and music

Still photos


· · ·  Matsumoto, M., H. Shirato, T. Yagi, R. Shijo, A. Eguchi, and H. Tamaki, “Effects of aerodynamic interferences between heaving and torsional vibration of bridge decks: the case of Tacoma Narrows Bridge,” Journal of Wind Engineering and Industrial Aerodynamics, 91, 1547-1557 (2003)
· · ·  Ricciardelli, F., “On the wind loading mechanism of long-span bridge deck box sections,” Journal of Wind Engineering and Industrial Aerodynamics, 91, 1411-1430 (2003)
· · ·  Schmit, R. F., M. N. Glauser, and G. Ahmadi, “Flow and turbulence conditions in the wake of a H-section in cross flow,” Journal of Fluids and Structgures, 19, 193-207 (2004)
·  Ulam, A., “A bridge too far?” Discover, 25, 40-43 (May 2004)
·  Petroski, H., “Past and future failures,” American Scientist, 92, No. 6, 500-504 (November-December 2004)
· · ·  Green, D., and W. G. Unruh, “The failure of the Tacoma Bridge: a physical model,” American Journal of Physics, 74, No. 8, 706-716 (August 2006)
·  Cardno, C. A., “New Tacoma Narrows Bridge officially opens,” Civil Engineering, 77, 16-18 (September 2007)

Want more references? Use the link at the top of this page.

2.7  Scott Macarney crash in downhill ski racing
Jearl Walker
Feb 2008
   In January a terribly frightening video raced across many media outlets. It shows the American skier Scott Macarney making the final jump in a downhill ski race at Kitzbuehel, Austria. Here is a link to one of many places running the video, but let me warn you that this is shocking. However, let me also reassure you that Macarney appears to be ok. Although he was airlifted from the race to Innsbruck and put into a forced coma to protect his brain, he was flown back home several days later and is predicted to make a full recovery. Scott Macartney crash lands on the final jump in a ski race at Kitzbuehel  Same video  News report with video

In the video you see Macarney leave the top slope of the jump at a measured 140 kilometers per hour. During flight to the lower slope, he loses control and then crashes on his side and back, breaking his helmet. Very dangerous.

Anyone can say what I just wrote: high speed, loss of control, thus bad crash. But with physics we can say more because we can say why he lost control.

Especially telling is the shot from behind Macarney as he leaves the upper slope. Notice that at the last instant, he leans to his right. He is shifting his weight to the right leg to make his upward jump as he comes off the edge. The leap upward from his right side put a slight spin on him around two axes. From the rear, we see him begin to rotate clockwise around a horizontal axis extending from us through him. If we could see him from above, we would also see him rotate clockwise around a vertical axis.

Because Macarney went into free flight with spin, he had a certain amount of angular momentum around the two spin axes. Only an outside torque can change that angular momentum; Macarney could not himself change it. Now, in some sports such as snowboarding, leaving the surface with angular momentum is desirable. The jumper knows how to manipulate the body’s orientation to alter the spin rate, so as to perform some fancy rotation during the flight. The angular momentum does not change, but the spin rate can. But that ability to manipulate the spin rate takes training.

When a skier makes a long jump, such as in a downhill race or in a ski jump, the focus is to avoid any spinning because the skis and the skier each must function as a wing. To do this, the skier holds the skis in front to “catch” the wind and also leans toward the skis so that the body also “catches” the wind. When the skier does all this, each wing provides a steady lift to carry the skier out over and then down onto the slower slope. Each wing also provides stability so that chance buffeting by the passing air does not ruin the proper orientation.

When Macarney began to rotate as he left the upper slope, he quickly moved out of the correct orientation. His body rotated to his right while his skis came up on his left. Whatever lift he then got on his skis made the situation worse because it pushed the skis up higher and thus rotated his body lower. By then he was straightening his body instead of leaning over to catch the wind, and so any upward push on his body by the air was insufficient to stop the rotation. When he reached the lower slope, he was rotated by enough that the impact was on his side and back, causing his head to hit so hard that the helmet broke.

Physics is everywhere, even in tragic events. Thankfully, Macarney’s crash was only frightening and threatening but not lethal.

2.10 Cards as weapons
Jearl Walker
June 2010  If you throw a common playing card haphazardly in the air, it simply tumbles and then flops onto the floor. Why does spinning the card as you launch it greatly increase the distance it will go? The current Guinness record is about 65.9 meters (216 feet and 4 inches), set by Rick Smith, Jr. When Rick was a student here at Cleveland State University, he was a pitcher for the school’s baseball team. In fact, when he now throws a card, he uses almost the same throw as he used for a curve ball when he was on the team. Here is a video of him on the Wayne Brady television show, where he throws cards directly through a banana, slicing it in two places:

Just as remarkable is this video in which business cards are thrown with great accuracy through hoops, flames, and balloons.

And here is the legendary Ricky Jay breaking a pencil with a thrown card.

In the several more video links gathered below, you can see cards thrown into various fruits (even through the thick skin of a watermelon) and into a common wall.

My acquaintance with throwing cards began when I read the now famous book Cards as Weapons by Ricky Jay, who explains how cards really can be used in self defense. (Well, I am not sure that you could actually stop a charging ox or fend off a giant squid, as implied by the cover.)

However, you can seriously hurt someone, especially if an eye is hit. Indeed metal cards for throwing (shuriken) have long been associated with the fighting skills of ninja.


Launching the card

There are various styles of holding a card. Here are a few:

They all have one common feature: The card must easily slip from your grip after you have snapped your wrist in the launch. In that way, you the card spins rapidly around its central axis (the axis that is perpendicular to its face and through its center point).


You can launch the card with its plane at any angle to the horizontal but the card will tend to stay in the air longest (and travel farthest) if the plane is approximately horizontal. Then the card receives the greatest lift on its bottom face due to its continuous collision with the air in its path.


A spinning top

The primary purpose of the rotation around the central axis is to stabilize the card’s orientation, much like spin stabilizes a top. Here is a side view of a spinning top consisting of a disk (seen on edge) and a vertical central spindle.


If the top were not spinning, then it would be unstable and pulled over by the gravitational force after any slight chance disturbance. However, with it spinning, it is stabilized by its angular momentum. That quantity is the product of its angular speed and a property called its rotational inertia, which depends on the mass and how the mass is distributed relative to the central axis. That description may sound terribly abstract, but angular momentum is the quantity that is responsible for the magic of any spinning top.

In the figure, the top is rotating clockwise as seen from above, which means that the associated angular momentum is a vector that points down along the central axis. When the top is upright as shown, the angular momentum is fully vertical.

That vertical angular momentum can be changed only if a force acts in the plane of the disk, to increase or decrease the top’s angular speed. If, instead, the force leans the central axis off to one side, it cannot change the vertical angular momentum. The top still rotates around its central axis with the same angular momentum but now only a component (a portion) of it is vertical. Because the vertical angular momentum cannot change, the central axis itself must now move around the vertical, to make up the difference. This motion of the central axis is precession.


However, there is a hitch to this process. Is there enough energy for the precession? If there is not, then the top simply cannot lean over and must remain upright, a condition known in both street play and physics textbooks as the sleeping top.

If the force is slight and brief, the only source of the energy for the precession must be from the fall of the center of the top as it leans over. That fall can transfer energy from the gravitational potential energy of the top to the kinetic energy of the precession. However, the required amount of kinetic energy depends on the rate at which the top is spinning. If the top is spinning slowly, then the procession needed to maintain the vertical angular momentum is also slow and only a small energy transfer is required. In that case, the fall can provide enough energy. But if the top is spinning rapidly, then the procession must also be rapid and the required energy is more than can be supplied by the fall. In that case, the top cannot lean over. Thus, the spin stabilizes the top.


The spinning card

Essentially the same physics is behind the stability of a spinning playing card as it flies through the air. When launched from the right hand, the card spins clockwise as seen from overhead and its angular momentum vector points downward.


If the card is spinning rapidly, its orientation is stable in spite of the irregular buffeting by the air. Once air drag slows the spinning, the card becomes increasingly unstable and eventually flops onto the ground.


Loss of lift

I have trouble putting a large spin on a card and find that soon after I launch the card (with my right hand), the plane of the card rotates from being horizontal to being vertical. In my view, the plane of the card rotates counterclockwise. Of course, as the plane becomes more vertical, there is progressively less lift and the card then slides down to the ground (while still spinning).

This rotation of the plane of the card is due to the uneven lift on the card’s bottom surface --- there is more lift on the underside of the front of the card (whatever part is foremost as the card rotates around its central axis), as shown in this figure from a side view.


Because that lift is forward of the card’s center, it creates a torque on the card (toward your right in your view of the card), which rotates the angular momentum vector (and thus the plane of the card) counterclockwise.


Boomeranging cards

If you throw a rapidly spinning card upward at about 45 degrees from the horizontal, it will move up along that path until it reaches a highest point, and then it will move back down to you along almost the same path.

As previously, the rapid spinning stabilizes the orientation of the card and its angular momentum. As the card moves upward, the increase in its gravitational potential energy comes from the decrease in the kinetic energy associated with translational motion of the card (that is, the motion of the center of mass of the card). The kinetic energy associated with the rotation does not change.

The card climbs the path until the translational kinetic energy is exhausted, just as a ball thrown straight up moves up to the point where its translational kinetic energy has been fully transferred to potential energy. Then the card (or the ball) reveres the transfer by moving downward.


Other objects

You could try throwing other flat objects, such as a CD or even a CD case. (Being a rock fan, I take great pleasure in throwing CDs of country music. Actually, I think the resulting scratches on the CD improves the music.) The physics is the same as with a card unless the object is too blunt or thick. Then the air drag will quickly bring it down. One last note: Be safe. You could really hurt and blind someone if you are not careful. quick tutorial Master of Champions with Rick Smith Jr Ricky Jay card slices into apple slices bananas quick lesson card stuck in wall Rick Smith Jr on Attack of the Show Rick Smith Jr with Steve Harvey lots of tricks by Jav Jarquin instructions on throwing cards


Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Jay, R., Cards as Weapons, Warner Books, 1977. WARNING: mature content
··· Lugt, H. J., “Autorotation,” Annual Review of Fluid Mechanics, 15, 123-147 (1983)
··· Jones, M. A., and M. J. Shelley, “Falling cards,” Journal of Fluid Mechanics, 540, 393-425 (2005)

2.11 Falling cards and helicopter seeds
Jearl Walker
October 2010  Release a credit card (or any other stiff card) with its long edge down and horizontal (and its faces left and right). Why doesn’t the card merely slip through the air to hit the floor directly below the release point? Similarly, why doesn’t a falling leaf simply fall straight down instead of fluttering and gliding like the falling card? Why do some seeds spin like the blades on a helicopter. Such spinning seeds have the advantage of falling slowly so that any chance breeze will blow it away from the parent tree.

Falling card

The flight of a card (or leaf) released long edge down is very challenging to explain, and mathematical attempts have been made to do so since 1854. The flight can be chaotic but instead it might show the following patterns: (1) Flutter is where the card slides through the air, alternating between sliding leftward and sliding rightward. (2) Tumbling occurs when the card rotates around an axis while it also glides either leftward or rightward. Which behavior occurs depends on the dimensions of the card. A standard playing card usually develops a steady tumbling while drifting at a certain angle to the vertical. Starting from the initial vertical orientation, the release deflects the lower end either left- or rightward. Then as the card slides at an angle to the vertical, the airflow past it creates a high-pressure point below the leading edge and above the trailing edge. These high-pressure regions rotate the card around the central axis along its length. As the card reaches the face-down orientation, its fall slows but the rotation continues until the card approaches being vertical again. As it does this, it slides through the air more easily and so its downward speed increases. The process is then repeated.


Helicopter seeds

A seed from an ash, elm, or maple tree is winged and prolongs its fall by spinning. For example, a single-wing samara from a maple tree spins around its center of mass (the center of its mass distribution), which lies between the bulge portion and the flat-wing portion.

Here is my photograph of single-wing seeds and double-wing seeds (the latter usually break apart into single-wing seeds).

The plane of the wing may be tilted by as much as 45°. As the wing spins around during the seed’s fall, it propels air downward, and so the seed undergoes a force that is upward. The force can also push the seed off to the side so that it takes a helical path to the ground.

Here is a slow motion video of a samara seed that is rotating in a controlled upward current of air. autorotating seed

Probably the action is easier to picture if you ride along with the seed. As the air comes up past you, it pushes against the underside of the wing portion. The component (or part) of the push that is perpendicular to the wing is lift, the force that helps support the seed. The push of the air makes the wing spin like a helicopter blade and also allows the seed to glide off to one side. Often the combination of spin and glide allows the seed to come down on a spiral while also spinning around its center of mass, in a motion called autorotation.

Many seeds depend on aerodynamic forces for dispersion, so as to spread away from the parent planet. Some of those dispersion techniques are shown in the following video, along with the seeds that are dispersed by explosions of the seed pod. seed dispersal

I’ll come back to those explosive dispersals later here at the FCP site.

Several currently available toys are modeled after samaras.
For the two in my photograph, the center of mass lies between the relatively heavy “head” and the lighter “wing.” Both are shot into the arrow by means of a stretched rubber band. Once they begin to fall, they spin just like the single-wing samaras.


Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
·· Norberg, R. A., “Autorotation, self-stability, and structure of single-winged fruits and seeds (samaras) with comparative remarks on animal flight,” Biological Review, 48, 561-596 (1973)
··· Rosen, A., and D. Seter, “Vertical autorotation of a single-winged samara,” Journal of Applied Mechanics. Transactins of the ASME, 58, 1064-1071 (December 1991)
· Walker, J., “The aerodynamics of the samara: winged seed of the maple, the ash and other trees,” in “The Amateur Scientist,” Scientific American, 245, No. 4, 226-236 (October 1981)
··· Lugt, H. J., “Autorotation,” Annual Review of Fluid Mechanics, 15, 123-147 (1983)
··· Seter, D., and A. Rosen, “Study of the vertical autorotation of a single-winged samara,” Biological Reviews of the Cambridge Philosophical Society, 67, No. 2, 175-197 (May 1992)
··· Mahadevan, L., “Tumbling of a falling card,” Comptes rendus de l’Academie des Sciences. Series II. Mecanique, Physique, Chimie, Astronomie, 323, No. 11, 729-736 (2 December 1996)
··· Belmonte, A., H. Eisenberg, and E. Moses, “From flutter to tumble: inertial drag and Froude similarity in falling paper,” Physical Review Letters, 81, No. 2, 345-348 (13 July 1998)
·· Mahadevan, L., W. S. Ryu, and A. D. T. Samuel, “Tumbling cards,” Physics of Fluids, 11, No. 1, 1-3 (January 1999)
··· Seter, D., and A. Rosen, “Dynamics of systems that include wings in autorotation,” Journal of Dynamic Systems Measurement and Control – Transactions of the ASME, 121, No. 2, 248-254 (June 1999)
··· Mittal, R., V. Seshadri, and H. S. Udaykumar, “Flutter, tumble and vortex induced autorotation,” Theoretical and Computational Fluid Dynamics, 17, 165-170 (2004)
··· Kolomenskiy, D., and K. Schneider, “Numerical simulations of falling leaves using a pseudo-spectral method with volume penalization,” Theoretical and Computational Fluid Dynamics, 24, Nos. 1-4, 169-173 (March 2010)
··· Tam, D., J. W. M. Bush, M. Robitaille, and A. Kudrolli, “Tumbling dynamics of passive flexible wings,” Physical Review Letters, 104, article #184504 (4 pages) (7 May 2010)

More references are listed under items 2.10 and 2.11 at the pdf file
for Chapter 2 of the FCP book.

2.14  The best free kick ever
Jearl Walker
April 2011 How can a football (soccer) player use a free kick to send the ball along a curved path around a defensive wall of players and into the goal?

Such a kick, dubbed a banana kick because of the shape of the flight path, seems unearthly and can often take a goalkeeper completely by surprise, especially if the wall blocks his view of the first phase of the ball’s flight. Here is a video of what many people think is the best free kick ever. same kick

Here are more free kicks

To see the physics of the curved flight, let’s start with the figures here.
Part a of the figure shows an overhead view of a ball in flight through stationary air. Let’s ride along with the ball so that the air passes us, as in part b of the figure. If the ball does not spin, the air passes symmetrically on the sides of the ball, and then somewhere on the back side the two airstreams break free of the ball and form vortexes behind the ball.

If, instead, the ball spins—say, clockwise as in part c of the figure—the airstreams are not symmetrical. Instead, the stream moving against the spinning surface breaks up into vortexes early and the stream moving with the spinning surface clings to the surface and breaks free of it late. We can think of the airstream as being slung off the spinning ball, much as mud is slung off a rotating tire. Because the spin on the ball forces the airstreams to be deflected, the ball is forced off in the opposite direction. That is, the spinning ball’s deflection of the air causes the ball to veer off to one side. The effect is commonly called the Magnus effect after an earlier investigator.

In the soccer free kick, let’s assume that the ball is kicked toward the left side of the defensive wall (as opposed to the right side as in the video) and with a clockwise side spin (part d of the figure). The ball should be launched at an angle of about 17° with the ground and directed out of arm’s reach at the end player on the wall. As the ball travels through the air, the spin causes the airstream to be deflected to the left and thus the ball to veer to the right. If the kick is executed well, the ball neatly veers around the end of the wall just out of reach and then into the goal.

Part of the magic of the shot may come from the change in the ball’s speed during the flight. The air drag on the ball is largely due to the difference in the high-pressure impact of air on its front surface and the low-pressure vortexes on the rear surface. As the ball slows, the extent of the vortex region changes, first increasing and then decreasing, and so the air drag varies in the same way. Thus, the slowing of the ball first increases and then decreases, which can trick a goalkeeper.

Other sports balls will veer during flight if spinning, including tennis balls, Ping-Pong balls, and volleyballs. (Early on, veering was noticed in the flight of spinning cannonballs and rifle bullets.) Of course, sending the ball along a curved path in any direction can confuse an opponent. A spinning ball also has an advantage of bouncing from the field, court, or wall in a surprising direction. However, a smooth beach ball seems to be different in that it can veer first one way and then another, following a path that is more S-shaped than banana-shaped. This perplexing last deflection, called a reverse Magnus effect, occurs when the ball’s speed and spin rate fall to low values.
Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Briggs, L. J., “Effect of spin and speed on the lateral deflection (curve) of a baseball; and the Magnus effect for smooth spheres,” American Journal of Physics, 27, 589-596 (1959)
·· Smith, N. F., “Bernoulli and Newton in fluid mechanics,” Physics Teacher, 10, 451-455 (November 1972)
· Johnson, W., “The Magnus effect---early investigations and a question of priority,” International Journal of Mechanical Sciences, 28, No. 12, 859-872 (1986)
··· Stepanek, A., “The aerodynamics of tennis balls—The topspin lob,” American Journal of Physics, 56, 138-142 (1988); reprinted in The Physics of Sports, Volume One, A. Armenti Jr., editor, American Institute of Physics, 1992, ISBN 0-88318-946-1, pages 159-163
· Glenn, G., personal communication about beach-ball deflection, 1989
··· Fuchs, P. M., “Physical model. Theoretical aspects and applications of the flight of a ball in the atmosphere. Part I: Modelling of forces and torque, and theoretical prospects,” Mathematical Methods in the Applied Sciences, 14, 447-460 (1991)
··· Fuchs, P. M., “Physical model. Theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical angular frequency and applications,” Mathematical Methods in the Applied Sciences, 14, No. 7, 461-481 (1991)
··· Ireson, G., “Beckham as physicist?” Physics Education, 36, 10-13 (2001)
· Wesson, J., “Football physics,” Physics World, 15, No. 5, 41-44 (May 2002)
··· Carre, M. J., T. Asai, T. Akatsuka, and S. J. Haake, “The curve kick of a football II: flight through the air,” Sports Engineering, 5, 193-200 (2002)
··· Bray, K., and D. G. Kerwin, “Modelling the flight of a soccer ball in a direct free kick,” Journal of Sports Sciences, 21, No. 2, 75-85 (2003)
··· Borg, K. I., L. H. Soderholm, and H. Essen, “Force on a spinning sphere moving in a rarefied gas,” Physics of Fluids, 15, No. 3, 736-741 (March 2003)
· Dubinsky, A., and T. Elperin, “Comment on ‘Force on a spinning sphere moving in a rarefied gas’ [Physics of Fluids, 15, 736 (2003)] and ‘On the inverse Magnus effect in free molecular flow’ [Phys. Fluids 16, L9 (2004)],” Physics of Fluids, 16, No. 10, 3832 (October 2004)
··· Weidman, P. D., and A. Herczynski, “On the inverse Magnus effect in free molecular flow,” Physics of Fluids, 16, No. 2, L9-L12 (February 2004)
· Craig, C. M., E. Berton, G. Rao, L. Fernandez, and R. J. Bootsma, “Judging where a ball will go: the case of the curved free kick in football,” Naturwissenschaften, 93, 97-101 (2006)
··· Goff, J. E., and M. J. Carre, “Trajectory analysis of a soccer ball,” American Journal of Physics, 77, No. 11, 1020-1026 (November 2009)
·· Goff, J. E., and M. J. Carre, “Soccer ball lift coefficients via trajectory analysis,” European Journal of Physics, 31, 775-784 (2010)

2.15  Golf ball dimples
Jearl Walker
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 break-away point occurs well before the air reaches the point on the rear that is opposite the impact point on the front.
    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.  golf ball (go down to the photos showing smoke tracers moving past a tennis ball)

·  Aoki, K., A. Ohike, K. Yamaguchi, and Y. Nakayama, “Flying characteristics and flow pattern of a sphere with dimples,” Journal of Visualization, 6, No. 1, 67-76 (2003)
· · ·  Penner, A. R., “The physics of golf,” Report on Progress in Physics, 66, 131-171 (2003)
· Won, S. Youl, Q. Zhang, and P. M. Ligrani, “Comparisons of flow structure above dimpled surfaces with different dimple depths in a channel,” Physics of Fluids, 17, article # 045105 (2005)
·  Choi, J., W.-P. Jeon, and H. Choi, “Mechanism of drag reduction by dimples on a sphere,” Physics of Fluids, 18, article # 041702 (4 pages) (2006)
· · 
Libii, J. N., “Dimples and drag: Experimental demonstration of the aerodynamics of golf balls,” American Journal of Physics, 75, No. 8, 764-767 (August 2007)

Want more references? Use the link at the top of this page.


2.18  Birds flying in V formation
Jearl Walker
June 2012  When a flock of birds must fly a long distance, as during migration, many elect to fly in a flat V formation. One reason is that there can be a considerable savings in the energy required by the birds.

When a bird flies by flapping its wings (instead of gliding), each downward push by a wing creates a vertical vortex (swirl) in the air trailing the bird. The vortex circulates downward on the bird side, outward on its bottom side, upward on its far side, and inward on its top side. If a trailing bird positions itself in the up-flow part of the vortex, it receives a free lift. It still must flap to stay aloft, but it does not have to flap quite as hard, and thus its energy expenditure is not quite as much. The savings can be significant over a long journey.

To be in the upflow, a trailing bird should be off to one side of a leading bird, and a V formation is one of the best formations for placing the birds properly. It also allows them visual contact. However, birds are rarely in exactly the best position for saving energy, and the spacing within a V formation is often uneven, suggesting that flying in formation is actually quite difficult.

Although the front bird experiences some of the upflow from the birds just to the left and right of it, the lead position is usually the most tiring. Presumably, many of the birds in a flock take turns as leader. The birds could, instead, fly in a flattened V or a straight line and then the lead position would not be so tiring.

All this has been known for many types of birds, such as geese. However, a recent study has shown that for pigeons, flying in a flock is actually considerably less efficient that flying alone. The frequency at which they flap their wings measurably increases when the pigeons are in a flock. Presumably the birds flap faster either because of aerodynamics due to nearby birds or because they need more control to avoid collisions.

Thus, we might say that geese have worked out the calculus of efficient flying but pigeons have not even done the arithmetic.

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
· Spedding, G., “The cost of flight in flocks,” Nature, 474, 458-459 (23 June 2011)
·· Usherwood, J. R., M. Stavrous, J. C. Lowe, K. Roskilly, and A. M. Wilson, “Flying in a flock comes at a cost in pigeons,” Nature, 747, 494-497 (23 June 2011)

For many more references, go to the pdf file

and scroll down to item 2.18.

2.23  Large bathtub-like vortexes
Jearl Walker
May 2013 You are familiar with the vortex that can form when water drains from a bathtub. The direction of swirling is set by the pre-existing (but probably imperceptible) swirling in the water, due to the initial pouring of water into the tub or by your motion while bathing. As water flows toward the drain, the vortex builds up until it can be appreciable. The water going down the middle of the vortex comes from the surface.

Here is the same type of vortex but on a larger scale, with far more energy. Water drains through pipes from one lock to another so that a boat might be able to move up or downstream on a river. As the water rushes into a pipe, a large vortex forms with a noticeable hollow center.

Here are two vortexes in water draining from a flooded field. There has to be a drain pipe beneath each.

And here is a vigorous vortex in what appears to be a river. Here again there must be a drain below the vortex but I do not know if it is a pipe. The other possibility is that the water has broken through the top of a cavern and water is now pouring into the cavern. same video

That type of nightmare situation occurred in 1980 in Lake Peigneur in southern Louisiana. A long-established salt mine stretched out beneath the lake, where salt was carried out from a large salt dome that had long ago been pushed upward by the surrounding rock bed. That bed also had oil deposits, and in November, 1980 an oil company began exploratory drilling to locate the oil. According to the company’s calculations, the drilling site was well away from the salt mine. However, someone made an error in the location because the drill pierced the roof of one stretch of the salt mine. The engineers knew something was wrong because the drill bit seized up with salt, and yet there supposedly was no salt in the way. When the drill bit was pulled up, water began to pour from the lake into the hole and into the salt mine.

All of the salt miners managed to escape before the water dissolved the salt walls and filled the mine. The entire drilling rig disappeared into the vortex that formed over the hole. The vortex also captured several barges and one tug boat, sinking them or pulling them down into the widening hole. As water poured into the mine, it rammed the air in the mine up and out of the mine, creating a 400-foot high geyser. The lake did not go dry only because the water flow through an adjacent canal reversed itself, bringing water from the Gulf of Mexico into the lake. Water drained into the mine for two days. Here is a documentary about the disaster:

So, the next you watch the soap bubbles disappear into the vortex over a bathtub drain, think about how much destruction a lake-size vortex can do.

2.26  Meandering rivers
Jearl Walker
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 should flow 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 River meander images  

· · ·  Edwards, B. F., and D. H. Smith, “River meandering dynamics,” Physical Review E, 65, article # 046303 (12 pages) (2002)
·  Hooke, J., “River meander behaviour and instability: a framework for analysis,” Transactions of the Institute of British Geographers, 28, No. 2, 238-253 (2003)
·  Hooke, J. M., “Cutoffs galore!: occurrence and causes of multiple cutoffs on a meandering river,” Geomorphology, 61, 225-238 (2004)
· · ·  Camporeale, C., and L. Ridolfi, “Convective nature of the planimetric instability in meandering river dynamics,” Physical Review E, 73, article # 026311 (7 pages) (2006)
·  Hayes, B., “Up a lazy river,” American Scientist, 94, No. 6, 490-494 (November-December 2006)
· · ·  Seminara, G., “Meanders,” Journal of Fluid Mechanics, 554, 271-297 (2006)
· · · Constantine, J. A., and T. Dunne, “Meander cutoff and the controls on the production of oxbow lakes,” Geology, 36, No. 1, 23-26 (January 2008)

Want more references? Use the link at the top of this page.

2.30  Canal effect
Jearl Walker
October 2013   When a large, long ship moves along a narrow channel, the water level alongside the bow noticeably dips, which seems wrong. Surely it should rise as water is forced from the front of the ship, alongside the ship, and then to the rear of the ship. Here is a figure from my textbook Fundamentals of Physics where I show the water action from an overhead view (top drawing) and then from a side view. In the figure, the ship is stationary and the water flows from right to left. The figure still applies if the ship moves from left to right through initially stationary water. Notice the water-level dip near the ship’s bow (at the right-hand end).

If a side branch is connected to the water channel along which the ship moves, the water level in the side branch can be dramatically changed by the water-level dip alongside the ship. Here is a video example in which a 300 m freighter travels quickly along the St. Clair river, which connects Lake Huron and Lake St. Clair along the US–Canada border. We see the effect on the water in a narrow canal that branches off from the river. Watch how the ship’s passage first drains the canal and then, with a rush, refills it. same video

The rapid draining and refilling of the canal has so damaged it that fish no longer live there. The water flow also erodes the banks and damages any structures along them. Also, the rush of water refilling the canal brings in silt and debris that begin to fill in the canal.

The draining and refilling of the canal are caused by the water-level dip along the ship’s bow. As the ship moves along the water channel, water in front of the ship must be pulled through the narrow open space alongside the ship to end up behind the ship. That water motion is accomplished by a continuous dip in the water at the bow. Because the water pressure is lower in the dip, the dip effectively pulls water from the front of the ship and sends it to the side of the ship, an action dubbed drawdown. Thus, as the ship advances, the water dips along the side of the water channel in what is called the canal effect.

The resulting variation in water pressure and flow rate along the side of the boat can make navigation of a water way tricky because the pressure reduction on one side of the ship may be higher than on the other side, tending to move the ship sideways. What we are seeing in the video is the effect on a side canal: As the drawdown passes the opening to the side canal, the pressure reduction sucks water from the canal. As the ship then passes and clears the opening to the side canal, water from the river rushes back into the canal to refill it. The damage to the canal and the aquatic life there could easily be reduced if the ships would just slow down. Then the drawdown would produce only a moderate pressure reduction alongside the ship.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
· Morrison, G., and Dalrymple-Smith, B., (letters) “Waterfall” in “The Last Word,” New Scientist, 161, No. 2175, page 93 (inside back cover) (27 February 1999); available at where you search under keyword “riverboat”
· Widden, M., (letter) “Waterfall,” in “The Last Word,” New Scientist, 161, No. 2179, page 105 (inside back cover) (27 March 1999); available at where you search under keyword “riverboat”
··· Stockstill, R. L., and R. C. Berger, “Simulating barge drawdown and currents in channel and backwater areas,” Journal of Waterway, Port, Coastal, and Ocean Engineering, 127, No. 5, 290-298 (September/October 2001)
·· Maynord, S., “Ship effects at the bankline of navigation channels,” Maritime Engineering. Proceedings of the Institutue of Civil Engineers, 157, No. 2, 93-100 (June 2004)
··· Wolter, C., R. Arlinghaus, A. Sukhodolov, and C. Engelhardt, “A model of navigation-induced currents in inland waterways and implications for juvenile fish displacement,” Environmental Management, 34, No. 5, 656-668 (November 2004)

2.35  Swimming in dead water
Jearl Walker
July 2009    Dead water refers to a peculiar sea condition in which a ship is hardly able to move, even at full power. In The Flying Circus of Physics book I describe one of the earliest accounts of dead water. While on a polar expedition in August 1893, the ship Fram encountered dead water on the northern coast of Siberia. The ship was capable of traveling 6 or 7 knots but in the dead water it could manage only 1.5 knots, even though both the water and the weather were calm. Moreover, control of the ship was marginal; in fact, the captain was forced to travel in loops to escape the dead-water region. The water was not visibly different from any other stretch of ocean water.

Dead water occurs when a layer of relatively fresh water overlies salt water, which can happen when a river empties onto ocean water or where an iceberg melts onto ocean water. Two interfaces play a role: the air–fresh water interface and the fresh water–salt water interface. Normally, much of the energy of a ship engine creates waves along the first of those interfaces—think of the wave production as a form of drag on the ship. In dead water, however, the ship produces two sets of waves, one along each interface, and so the drag is significantly more. The faster the ship tries to go, the faster its energy drains to the internal waves, as they are called, on the fresh water–salt water interface.

The ship’s bow is located above the first crest in the internal wave. The water just below that crest moves in the direction opposite the ship, opposing the ship’s motion. The Fram’s length was such that the rudder was also above a crest of the internal wave, and so the rudder was of little use in maneuvering the ship.

This video shows a toy boat moving over dead water, with the bottom salty layer dyed so that you can visibly distinguish the two layers. The boat is too small for the alignment of bow or rudder with the internal wave but you can see how the internal wave is created. Part of the boat’s energy goes into producing that wave. video from New Scientist

Recently a group of researchers (Sander P. M. Ganzevles, Fons S. W. van Nuland, Leo R. M. Maas, and Huub M. Toussaint) from The Netherlands investigated whether dead water can interfere with swimming. That is, if you swim through a region of dead water, is your progress slowed?

To see, a “swimmer” lay on a carriage that was gradually pulled over the top of a tank of water while he reached down into the water and pulled backward with a common swimming stroke. This was done several times first with the tank containing only fresh water and then the tank containing a layer of fresh water overlying very salty water. During the stroke, the swimmer’s hands would come near the interface between the two layers of water.

With both arrangements, the researchers monitored the hand and body motions and measured the speed of the carriage. They found that in the dead-water arrangement, propulsion of the carriage was significantly less, suggesting that significant energy from the stroke was being diverted to internal waves along the interface between the two layers of water.

The researchers also measured the speed of swimmers for a front-crawl swim of 5 meters, both in the fresh-water and dead-water arrangements. They reported that the average speed was about 15% less in the dead-water arrangement.

Less pronounced layering of water can occur in a fresh water lake due to temperature variations with depth (rather than salinity), especially in calm conditions when there not much overturning of the water. The researchers speculate that you might sense something strange about swimming in such lake if your strokes carry your hands down to an interface that separates significantly cooler water from overlaying water that has been warmed by sunshine. If your energy is diverted to internal waves along such an interface, you may grow tired surprisingly early in your swim.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Bascom, W., Waves and Beaches, Anchor Books, 1980, pages 139-140
· Jelley, J. V., “Sea waves: their nature, behaviour, and practical importance,” Endeavour, 13, No. 4, 148-156 (1989)
· Walker, J. M., “Farthest north, dead water and the Ekman spiral. Part 2: Invisible waves and a new direction in current theory,” Weather, 46, 158-164 (1991 )
·· Harleman, D. R. F., “Keulegan legacy: saline wedges,” Journal of Hydraulic Engineering, ASCE, 117, No. 12, 1616-1625 (December 1991)
··· Motygin, O. V., and N. G. Kuznetsov, “The wave resistance of a two-dimensional body moving forward in a two-layer fluid,” Journal of Engineering Mathematics, 32, 53-72 (1997)
· Ganzevles, S. P. M., G. S. W. van Nuland, L. R. M. Maas, and H. M. Toussaint, “Swimming obstructed by dead-water,” Naturwissenschaften, 96, 449-456 (2009)

2.36  Being inside (yes, actually inside) a tornado
Jearl Walker
Dec 2011  Tornados are those giant, swirling funnels that move like vacuum cleaners along the ground, ripping up buildings, cars, trees, and almost anything else in their paths. The stories you may have heard about the wind driving splitters into tree trucks are likely true (such penetration has been duplicated in labs). A tornado is an awesome monster.

I always wanted to see one, even as a child. Alas, every time there was chance for a tornado near my home in Texas, my parents would hurry me down into a storm cellar to hide. The danger is clear: With debris flying around at high speeds, you can be shredded within seconds. And even if you avoid that shrapnel, cars and building materials can slam into you. So, hiding is probably a really good plan.

However, there have been some recent videos taken within a tornado. Here are three in which storm chasers purposely came close to a tornado or even parked in its path.

The storm chasers may have known enough about tornados to recognize a relatively weak one, so that they minimized the danger. Still, parking inside a tornado seems to me to be a dangerous stunt simply for bravado, and you should not even consider repeating it.

In one of the videos a person talks about his ears popping. That was due to the decrease in air pressure as the tornado passed. Long ago people were advised to open windows when a tornado approached, so that when the air pressure outside a building suddenly dropped, the pressure inside the building could also. Otherwise, it was thought, the pressure difference could push building walls outward. These days we realize that the pressure difference is not the danger and someone in the path of a tornado should not take the time to open windows. Hiding is far more important.

Here are two more videos, but with the video operators accidently in the path of a tornado. scroll down

Here is my favorite: As a tornado heads directly toward him, passing within walking distance, a man calmly describes the tornado on his cell phone:

The primary dangers of a tornado are the flying debris and the possibility of a wall or roof falling on you. Such failure of building sections is largely due to the wind. Typically, the wind can catch the edge of a roof and peel it off the house, and then the house will disintegrate. Here are videos showing such destruction. tornado lifting a house tornado rips up house, piece by piece

Here is footage showing how devastating the wind pressure can be. A security camcorder shows us the rear cars on a train as the train drives into a tornado. The wind blows the middle part of the train over and then the forward momentum of the rear cars carry them into the front cars.

Only until recently, with the widespread use of portable video recorders, has such close-up and personal videos of tornadoes been possible. Previously, we had to rely on photographs and written accounts. Because I consider tornadoes to be both intriguing and horribly threatening, my favorite written story was published by a man who not only was in a tornado but actually was able to look up a long way into its interior, which happened to be hollow. Here is the description as I have it in The Flying Circus of Physics:

A few people have survived the experience of looking up into the funnel of a tornado. The most thorough description on record is by Captain Roy S. Hall whose house was attacked by a tornado in May 1948. After the roof had been taken and some of the walls pushed in by the wind, Hall was able to see his neighbor’s house and was relieved that his house was not flying through the air as he had momentarily feared. However, he then saw something horrible: About 20 meters away something descended to about 6 meters above the ground and hovered with a slow vertical oscillation. That something was curved with a concave surface facing him. With shock he realized that this hovering thing was the inside surface of the tornado funnel, and so he was inside the funnel!

As he looked up into the funnel, it seemed to stretch for 1000 feet, swaying and gradually bending. It contained a bright central region that glowed like a fluorescent light fixture. As the funnel bent over, rings formed along its length. Hall saw nothing being pulled up through the funnel’s interior, had no trouble breathing (so the air pressure could not have been noticeably low), and marveled at the complete silence (in contrast to the dramatic noise during the tornado’s approach). Suddenly the funnel moved away, and Hall’s family came out of hiding to find him. stationary tornado, man walks up to it very fast turning tornado ripping apart buildings security cams inside store near a tornado tornado and bank

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Jackson, R., and S. G. Bigler, “Inside the Kansas City tornado,” Weatherwise, 11, 88-90 (1958)
· Hall, R. S., “Inside a Texas tornado,” Weatherwise, 4, 72-75 (April 1987)
· Keller, B., “Looking a tornado in the eye,” Weatherwise, 44, 30 (June 1991)
· Cosgrove, D., (letter) “Inside an F0 tornado,” Weatherwise, 45, No. 3, 6 + 50 (June/July 1992)
· Hall, R. S., “Inside a Texas tornado,” Weatherwise, 51, 16-20 (January/February 1998); also see the excerpt by Snyder, C. H., “Looking at tornado in the eye” on page 19
· Snyder, C. H., “Looking a tornado in the eye,” Weatherwise, 51, 19 (1998); originally published in Monthly Weather Review (May 1930)
· Bluestein, H., Tornado Alley, Oxford University Press, 1999, pages 3-4

2.36  Tornado versus house
Jearl Walker
Nov 2012 One of the disappointments of my childhood in Texas was that I never saw a tornado. However, I did spend a number of nights sleeping in a storm cellar when my grandparents feared that a tornado might appear. If such a monster were to come down the street, we quite definitely did not want to be in the house.

The danger is two-fold: (1) The swirling, gusty, high-speed winds can collapse a house. (2) The high-speed projectiles can penetrate the windows and even the walls of a house, killing anyone inside and collapsing the house. In this video, notice that the wind is very strong and that it shifts directions. Then watch how the roof is peeled off the walls; then the walls collapse and everything is blown away.

Similar destruction occurs in these next two videos:

In this one, notice the hail, which is sometimes a precursor of a tornado. After about 2 minutes, we see a house ripped apart and then lifted up.

In this video, a schoolhouse explodes.

Houses can be built to meet a tornado but not perfectly. The weak points are where the roof is attached to the walls and where the walls are attached to the concrete slab on the ground. Without special attachments, the wind can leverage the roof off a wall or a wall off the concrete slab, and then the whole structure is wiped out.

The only way to stop the high-speed projectiles is to build the walls especially thick. To do so for the full house is probably too expensive, so people living in a tornado prone area have an interior “safe room” with very thick walls. In the most powerful tornados, projectiles can penetrate even those walls.

In you are in a vehicle such as a car or truck, you have almost no protection against either the winds or the projectiles. Here is a video shot from within a school bus as a tornado passes it. The broad side of the bus easily allows the winds to topple the bus.

Similarly, the tractor-trailer has such a wide side that it is easily turned over and then ripped apart.

Even a heavy train can be pushed over, though it will not be ripped apart. Here is a video of a tornado that passes over part of a train, pushing it over. The coupling between that toppled section and the trailing section broke. The trailing section still had momentum and, as you see in the video, it comes slamming into the front section.

When a tornado is possible, one place you definitely do not want to be is in a traditional mobile home. Those homes are built to be lightweight so that they can easily be towed or driven between cities or campgrounds. Because they must fit into a single road lane, they must be fairly long to provide enough living area. Being both lightweight and long with a broad side, they are easily pushed over, crumpled, and ripped apart by high-speed winds and projectiles.

Better built “pre-manufactured homes” are reinforced with stronger materials and might be able to withstand the high winds. Here is a curious video in which the backwash of an airplane is used to show how strong a pre-manufactured house can be. .

As you might notice in the comments below the video, the demonstration might not be entirely convincing because the wind from the airplane was fairly steady whereas the winds in a tornado are swirling and gusting. The counter to that argument was that the house in the video had already survived a tornado.

If I lived in a tornado-prone area, I think I would follow the example of my grandparents and build a storm cellar out in the yard where I could hide underground. If the sky turned green or if a tornado warning was broadcast, I would dive into that cellar. Well, actually I would wait for just a bit, in case I could see the tornado, as I always wanted to as a child. tornado over car, buildings torn apart, “We’re in the tornado.” hiding from tornado, ceiling was ripped off tornado hits house cell phone inside or near tornado

Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
· Schmidlin, T. W., P. S. King, B. O. Hammer, and Y. Ono, “Behavior of vehicles during tornado winds,” Journal of Safety Research, 29, No. 3, 181-186 (1998)
· Pinelli, J-P., C. Subramanian, and M. Plamondon, “Wind effects on emergency vehicles,” Journal of Wind Engineering, 92, 663-685 (2004)
·· Hu, H., Z. Yang, P. Sarkar, and F. Haan, “Characterization of the wind loads and flow fields around a gable-roof building model in tornado-like winds,” Experiments in Fluids, 51, 835-851 (2011)
·· McPeak, B. G., and A. Ertas, “The good, the bad, and the ugly facts of tornado survival,” natural Hazards, 60, 915-935 (2012)

2.39  Dust devil core
Jearl Walker
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. Huge dust devil, with people on bikes riding through it and the camera operator walking through it Wal-Mart dust devil Big dust devil develops at a baseball game Dust devil (vortex) produced by a fire Driving through a dust devil Whirlwind coming off a bonfire More bonfire vortices, really good More of the bonfire vortices Big dust devil at camping ground Paragliders picked up a whirlwind Whirlwinds from a brush fire

The photo here is by ninevoltheart.

· · ·  Kurgansky, M. V., “Steady-state properties and statistical distribution of atmospheric dust devils,” Geophysical Research Letters, 33, article # L19S06 (4 pages) (2006)
· · ·  Balme, M., and A. Hagermann, “Particle lifting at the soil-air interface by atmospheric pressure excursions in dust devils,” Geophysical Research Letters, 33, article #L19S01 (5 pages) (2006)
· · ·  Gu, Z., Y. Zhao, Y. Li, Y. Yu, and X. Feng, “Numberical simulation of dust lifting within dust devils---simulation of an intense vortex,” Journal of the Atmospheric Sciences, 63, 2630-2641 (October 2006)
·  Oke, A. M. C., D. Dunkerley, and N. J. Tapper, “Willy-willies in the Australian landscape: The role of key meteorological variables and surface conditions in defining frequency and spatial characteristics,” Journal of Arid Environments, 71, 201-215 (2007)
· Oke, A. M. C., D. Dunkerley, and N. J. Tapper, “Willy-willies in the Australian landscape: Sediment transport characteristics,” Journal of Arid Environments, 71, 216-228 (2007)

Want more references? Use the link at the top of this page.

2.39  Martian dust devils
Jearl Walker
April 2007
     Some of the Martian dust devils (whirlwinds) are so tall that they can be seen from a satellite orbiting Mars. In fact, the satellite can even see their shadows on the Martian surface. In addition, the Martian rovers have captured images and even “movies” of Martian dust devils from the ground level. Check out the URLs listed below.
     Dust devils on Earth are often charged because when dust, sand, and other debris are airborne, they tend to exchange electrons as they collide with another and the ground. As result, a dust devil can flash and pop as pockets of negative charge suddenly spark to pockets of positive charge. The Martian dust devils are likely to be highly charged, and because the air pressure there is much lower than on Earth, the sparking could be widespread.
     Just image that you are one of the first explorers put down on the Martian surface and have the bad luck of being in the path of a large dust devil. It would not be like the playful dust devils found in the American Southwest. Rather it would be a kilometer high and several hundred meters wide. And the winds may be up to 30 meters per second, more than enough to scour your viewing visor and the rest of your spacesuit with a continuous flow of airborne sand. As you wait out the passage, you are surrounded by a continuous play of sparks, as if you are at a celebration and somehow ended up having the celebration fireworks go off on your body. As your visor is scrubbed until it is opaque and sand is driven into every crevice of your spacesuit, you suddenly worry about what all that sparking might do to the microelectronics of your communications gear and the thermal control of your spacesuit. Oh, yes, there is also the oxygen control.
    Martian dust devils will not be playful to explorers. The rovers already there have been lucky to have avoided the big ones.
URLs: Movies and other images of Martian dust devils   Several photos run as a video.

·  Stanzel, C., M. Patzold, R. Greeley, E. Hauber, and G. Neukum, “Dust devil on Mars observed by the High Resolution Stereo Camera,” Geophysical Research Letters, 33, article # L11202 (5 pages) (10 June 2006)
· Drake, N. B., L. K. Tamppari, R. D. Baker, B. A. Cantor, and A. S. Hale, “Dust devil tracks and wind streaks in the North Polar Region of Mars: A study of the 2007 Phoenix Mars Lander Sites,” Geophysical Research Letters, 33, article #L19S02 (4 pages) (2006)

Want more references? Use the link at the top of this page.
2.40 Vortex rings --- from hookahs to powerful air cannons
Jearl Walker
September 2010  A smoke ring is blown with a strong puff from a mouth filled with smoke, as you can see in this video of a smoker with a hookah.

As the smoke and air leave through the rounded opening of the mouth, the flow near the lips is slowed by friction, and so the flow through the center of the opening tends to outrun it. This tendency causes the flow to curl outward around the lips, thus starting the vortex motion.


When blown correctly, the air swirls around as if it circles a solid circular ring --- moving away from the smoker on the inside of the ring and moving toward the smoker on the outside. Here is a cross section of the ring seen from the side.

The ring itself gradually moves away from the smoker, generally growing somewhat larger in diameter. The structure is called a ring vortex (or a vortex ring). The smoke merely acts as a tracer, making the air motion visible.

If a smoke ring approaches a wall, the friction on the airflow from the wall causes the ring to expand. The rate at which the air swirls decrease, somewhat like the rate at which an ice-skater spins on point decreases when arms are extended outward. The ring can also be controlled by moving a nearby hand toward it, thus pushing air against the ring. Here is a link that shows a young man forcing a ring to descend around the neck of a beer bottle.


Air Cannons
Larger vortex rings can be formed with an air cannon, which is a box with a circular opening at the front and a flexible covering (such as a plastic garbage bag) fitted across the otherwise open back. When the flexible covering is pulled to the rear and released, it pushes a stream of air through the circular opening. Just as with a blown smoke ring, the flow forms a ring vortex but without the benefit of a tracer. With an air cannon, you can startle someone across the room with a large ring vortex that approaches with no warning.

Here is link that shows a moderate size air cannon. In one part of the video, notice how a trailing but faster-moving vortex ring shoots through the leading vortex ring. In a laboratory situation, we would probably see that as the trailing vortex approaches the leading vortex, the trailing one shrinks and rotates faster while the leading one expands and rotates slower. “Big smoke gun”


Here is another large air cannon but without the smoke. “Candle cannon: behind the scenes”, head-on view of the vortex

Here is an air cannon that is large enough to require several people to generate the rings. “Giant vortex box: 20 meter test”


Powerful air cannon
Here is my favorite, one that resembles the big, bad wolf in the story of the three little pigs, a favorite in the English language. In the fable, the wolf blows down the straw house of the first pig and then the wood house of the second pig, but he cannot blow down the strong brick house of the third pig. However, in front of the air cannon powered by an explosion of acetylene and air, not even a brick wall stands a chance. Vortex cannon” from “Bang! Goes the theory” television show


Smoke rings can also be produced by large explosions, as in this video. “Coffee can fireball (5 Charcoal Cremora)”

(Obviously, this is very dangerous, so leave this to the experts.) So much thermal energy is transferred to the air at the center of the explosion that the hot air quickly rises in a channel. However, because it encounters drag from the cooler air surrounding the channel, it tends to curl over like the smoke being blown by the hookah smoker. If everything goes right, the hot air forms a vortex ring, with the smoke from the explosion acting as a tracer.


More links:
ttp:// “Rauchringkanone” living room vortex cannon from a drum set “Huge smoke ring generator” “Paper cup air cannon”, MacDonald’s cup backyard vortex cannon “Big smoke ring”, smoke ring from an explosion


Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
··· Maxworthy, T., “The structure and stability of vortex rings,” Journal of Fluid Mechanics, 51, part 1, 15-32 (1972)
··· Maxworth, T., “Some experimental studies of vortex rings,” Journal of Fluid Mechanics, 81, part 3, 465-495 (1977)
· Jenkins, D. C., “A Thanksgiving turkey shoot---physics style,” Physics Teacher, 26, 516-517 (November 1988)
· Bouffard, K., “The vortex cannon,” Physics Teacher, 38, No. 1, 18 (January 2000)
··· Niemi, A. J., “Exotic statistics of leapfrogging vortex rings,” Physics Review Letters, 94, article # 124502 (4 pages) (1 April 2005)
· Bouffard, K., “The vortex cannon,” Physics Teacher, 38, No. 1, 18 (January 2000)


2.41  Pub trick --- sucking liquid up a straw
Jearl Walker
October 2012 Common pub drinking straws range in length from a few centimeters (for mixed drinks) to about 12 centimeters (for pop and other flavored carbonated drinks). For either, sucking the liquid up into the mouth requires little effort. Of course, if you had longer straws, more effort would be required.

The physics is rather straight forward: By expanding your lungs, you reduce the air pressure in them, your mouth, and the air within the straw. Because the atmosphere pushes down on the exposed liquid surface in the liquid container, there is then a pressure difference between the lower end of the straw and the upper end. This pressure difference pushes liquid up the straw and into your mouth.

You could certainly manage all this with a straw that is twice as long as the standard pub straw. How about three times as long, or four times? How long can the straw be and still be useful? The two men in this video experimentally (and humorously) determine the limit: world’s longest straw

As the men explain, the upper limit to the straw’s length would be set if they could produce a vacuum at the upper end of the straw.

However, another effect reduces that limit. As I discuss in The Flying Circus of Physics book, if water is pulled up a straw, the water is said to be under tensile stress, because any portion of it is being pulled downward by gravitation and upward by the molecular attraction from the water just above it. Water can withstand tensile stress up to a certain limit, but beyond that limit, the water suddenly forms cavities and vaporizes into them. The water column then breaks and collapses. Such cavitation is less likely to occur in a narrower straw because the water molecules are also attracted to the nearby molecules of the straw and thus are better held in place. In a wider straw, the water molecules in the middle of a wider straw lack that attraction and stabilizing.

2.41  Chain siphon that rises into the air
Jearl Walker
August 2013  In a normal water siphon, water moves out of an open container by flowing through a flexible tube that is draped over the container’s edge. The siphoning is initiated by someone sucking on the tube’s hanging end, reducing the air pressure in the tube. Because the water surface in the container is under normal atmospheric pressure, the pressure difference between the surface and the tube’s interior pushes water up the tube, over the turn, and then down the hanging section. The siphoning continues as long as the hanging end is lower than the end submerged in the container. In that way, the weight of the water in the hanging section exceeds the weight of the water in rest of the tube. Because water molecules attract one another, that extra weight on one side of the siphon continuously pulls water up on the other side.

Here is a video of a similar siphon but with a long thin chain instead of water in a tube. The idea is about the same. Initially the chain is fully within the container. Then one end is pulled up and over the edge and allowed to fall. The falling chain drags more chain up out of the container and over the rim. But soon something strange happens.

Here is the video: video is also posted here

Just after the siphoning begins, the high point of the chain (where the chain makes the transition from moving upward to moving downward) shifts upward. The tube in a water siphon would never do that? What is different about the chain?

Well, when a section in the container is about to begin moving upward, it is actually yanked upward and thus becomes a projectile. When this action begins with only a little of the chain in motion, this yank is mild and the next bit of chain to start moving is barely pulled up and over the rim. As the length of hanging chain increases, so does the acceleration of the entire length of moving chain. When the free end of the chain reaches the floor, the acceleration stops but the chain is then moving quickly at an approximately constant speed. Each new section of chain pulled into motion must accelerate quickly from zero speed to this constant speed. Thus, each new section is yanked hard to get it into motion, and it is thrown higher than the container’s rim. However, this projectile motion differs from the common type such as a ball thrown into the air. Here the entire length of moving chain moves at a constant speed. A ball first slows until it reaches its maximum height and then speeds up as it descends.


Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
· Nokes, M. C., “The siphon,” School Science Review, 29, No. 108, 233-234 (March 1948)
·· Potter, A., and F. H. Barnes, “The siphon,” Physics Education, 6, 362-366 (September 1971)
··· Sedgewick, S. A., and D. H. Trevena, “An estimate of the ultimate tensile strength of water,” Journal of Physics D: Applied Physics, 9, L203-L205 (1976)
· Cortes-Comerer, N., “In search of the perfect flush,” Mechanical Engineering, 110, No. 2, 40-47 (February 1988)
·· Benenson, R. E., “The hyphenated siphon,” Physics Teacher, 29, 188 (March 1991)
· Hughes, S. W., “A practical example of a siphon at work,” Physics Education, 45, No. 2, 162-166 (March 2010)
· Planinsic, G., and J. Slisko, “The pulley analogy does not work for every siphon,” Physics Education, 45, No. 4, 356-361 (July 2010)
· Hughes, S. W., “The secret siphon,” Physics Education, 46, No. 3, 298-302 (May 2011)
· Binder, P-M, and A. Richert, “The explicit siphon,” Physics Education, 46, No. 6, 710-711 (November 2011)

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