As I’ve said before, some of the best scientific demonstrations are things that can be put together with simple everyday components and exhibit surprising, even counter-intuitive, phenomena.

One of my all-time favorite demonstrations is of this form!  All one needs is a plastic garbage can, a plastic shower curtain, and a bungee cord that hooks snugly around the top of the can.  Optional but quite useful is a fog machine.

What happens?  We cut a roughly 4-5” diameter hole in the bottom of the garbage can, and use the bungee cord to seal the shower curtain to the other end.  Fill the garbage can with fog, strike the shower curtain and — voila! — smoke rings!

These are actually vortex rings — circulating masses of air (and fog) that can persist and travel over a surprisingly long distance.  They also carry enough “oomph” to knock over a stack of plastic cups or scare the heck out of one’s housepets*.

So how does this “vortex cannon” work, and what does it demonstrate?  There is a surprisingly amount of physics and history behind such vortices, and they can be a lot more powerful!

I first saw this phenomenon on the Ellen DeGeneres show, as demonstrated by Steve Spangler.  I quickly adopted it as a reliable and eye-catching effect for the UNC Charlotte Science and Technology Expo.

So what is the physics behind this eye-catching effect?  It is actually quite a complicated phenomenon, and any explanation almost necessarily raises as many questions as it answers!  Nevertheless, we take a stab at it here.

The smoke ring produced is in fact a circulating donut-shaped mass of air and smoke which is technically referred to as a toroidal vortex. An illustration of such a vortex is shown below.

The molecules within the ring circulate around it, swirling up and around it in the direction of motion.  This is the “vortex”: the ring is very much like a mini-tornado, if one takes the top and bottom ends of the tornado and connects them together.

This circulation traps the air (and smoke) within it, and the mass of air moves through the atmosphere and carries momentum, which allows it to knock over light objects at a distance.  More importantly, the circulation provides the vortex ring with its remarkable persistence.  The circulating ring carries angular momentum — momentum of rotation — and this angular momentum is resistant to dissipation, much like a spinning bicycle wheel is resistant to being tipped over.  (Though the vortex ring circulates much different from a bicycle wheel.)

So where does this circulation come from?  A simple way to think about it is that the air forced through the small opening “spills out” on the other side, spreading past the opening and wrapping around the edges, inducing the circulation.  The image below is adapted from a nice short article on vortex guns.

There clearly must be a bit more we can say about the phenomenon, however!  Another facet of the effect has to do with the viscosity of air.  When the air is forced through the small opening, the air near the edges of the opening experiences drag relative to the air flowing through the center.  The result is that the air is moving faster out through the center and slower at the edges.  Here is another picture of air exiting the opening where the arrow size now indicates the speed of air coming out (and the spreading of the stream is neglected).

This variation of speed actually induces what is referred to as shear vorticity in the fluid!

How can different straight line speeds induce a circulation in a field?  Let’s imagine that we put a trio of small little paddlewheels into the flow out of the garbage can at different points, and look at what happens to them.

All three paddlewheels are pushed away from the garbage can by the rush of air — they acquire linear momentum.  For paddlewheel A, that is the only effect: the left and right sides of the paddlewheel are pushed equally and it does not spin as it moves.  Paddlewheel B, however, is pushed harder on the bottom than on the top.  This imbalance sets it spinning in a counterclockwise manner; the opposite happens for paddlewheel C, which spins clockwise.  Broadly speaking, this shear vorticity, combined with associated pressure changes and other viscosity effects, sets the air mass spinning as a vortex ring.

Vortices in general, and vortex rings in particular, have a long, interesting, and sometimes dubious place in the history of science.  In the 1500s, the great Leonardo da Vinci (1452-1519) made sketches of vortex motion in water falling into a pool.  Though no “rings” are formed for obvious reasons, one can still see the circulation of water in opposite directions on either side of the waterfall.

In the mid-1800s, vortex rings played a truly unusual role: they became the inspiration and model for a new atomic theory!  In 1867, William Thomson (later to assume the title Lord Kelvin) gave a presentation to the Royal Society of Edinburgh** in which he proposed that atoms (whose inner structure and nature was at the time unknown) are in fact complicated vortex rings circulating in an aetherial “fluid”.   Just as water waves travel in water and sound waves travel in air, it was postulated that light waves propagated in a mysterious, undetected medium known as the aether.  The aether, introduced in the early 1800s, seemed to answer a lot of questions about the nature of light and matter, though as the century progressed it ended up causing as many problems as it seemed to solve.  In 1887, Michelson and Morely attempted to measure the motion of the Earth relative to the aether, but could not detect it — this, combined with Einstein’s 1905 special theory of relativity, ended up spelling the end of the aether in serious physics.

Thomson’s vortex atom theory (of which I will have much more to say in a future post) was inspired by theoretical work of Hermann von Helmholtz on vortices in perfect fluids and demonstrations by Peter Guthrie Tait of — vortex smoke rings!

Why introduce a vortex atom at all?  As we have noted, the best model of the atom in Thomson’s time was little different than the ancient Greek concept of atoms consisting of rigid and indestructible spheres.  This theory could not account for the different species of atoms known, and it struggled with other simple experimental observations such as the compressibility of gases.  The interactions of multiple smoke rings — they can bounce off of each other, much like solid particles — indicated that they could serve as the fundamental elements of matter.  Thomson suggested that different atoms might consist of multiple vortex rings linked together, or possibly single rings tangled in knots of increasing complexity.

Tait took Thomson’s ideas and expanded them significantly, studying and categorizing the theoretical properties and structures of knots.  In fact, Tait’s study of knots played a pivotal role in the development of what is now known as knot theory in mathematics.

Thomson and Tait’s atomic vortex theory didn’t survive under experimental scrutiny, but others saw opportunity in the unusual vortex ring phenomenon.  In the August 1942 issue of Popular Science, for example, an article appeared titled, “Whirling smoke rings to free cities of soot”.

The article begins with what should now be a rather familiar description:

Dr. Philips Thomas, research engineer of the Westinghouse Electric & Manufacturing Company, picked up what appeared to be a small copper and brass drum with an aperture some two inches in diameter in its head.  By means of a tubular peep sight affixed to the top of the drum, he aimed the aperture at a row of one of lighted candles about ten feet away, and then tapped the back of the drum with a rubber hammer.  Instantly the candle was extinguished.

There is also an attached picture of Dr. Thomas working his “vortex gun”.

And what did Dr. Thomas hope to use vortex rings for?

Some of the experiments now under way are military secrets, but others deal with the possible use of vortex rings in peacetime.  The most promising of these applications so far has to do with the elimination of smoke from industrial areas.  Dr. Thomas suggests that it may prove feasible to trap the smoke of a manufacturing plant in huge vortex guns just above or below the roof.  Powerful automatic hammers would strike the guns at periodic intervals, and the smoke would be sent into the air in the form of vortex rings.  Then, instead of low-lying clouds of disagreeable smoke, the air above an industrial plant would be clean and pure, filled with gigantic smoke rings hurtling heavenward at terrific speed.

I can think of any number of reasons why this would be a rather impractical way of clearing industrial pollution, and to the best of my knowledge it was never implemented.

Speaking of “military secrets”, the United States Military has tested a vortex ring gun as a non-lethal weapon that could deliver chemicals into a crowd, disperse smoke or fog, or even knock down targets at a distance.  The early tests seem not to have been particularly successful, but vortex ring guns are still being developed and marketed.

Speaking of unsuccessful tests, another closely-related technology is the venerable hail cannon, which has been existence for at least 100 years and still used by farmers today.  Purportedly, when the cannon is used to fire vortex shockwaves into thunderclouds, it can disrupt potentially damaging hailstorms; however, the effectiveness of such cannons is doubtful.  (Other than their ability to annoy the neighbors.)

Vortex rings may still be a solution in search of a problem, but the fact that they have captured the imagination of scientists for over a century shows that they are definitely useful as a physics demonstration!

Postscript: So how powerful can a vortex ring really be?  In an episode of BBC’s “Bang Goes the Theory”, the host demonstrates that vortex rings can pack an incredible amount of punch!

UPDATE: Probably most people have noticed that the hardest to come by component of this demonstration is a smoke or fog machine!  Quite good ones can be purchased for surprisingly little money, however; I personally got a Mini-Fog Machine designed for DJs that was only $40.  Even cheaper ones designed for Halloween displays are out there.

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* Scaring the cats was kinda an accident the first time I tested the vortex cannon.

** W. Thomson, “On vortex atoms,” Proc. Roy. Soc. Edinburgh 6 (1866-69), 94-105.