Lest We Forget the Pioneer: Ottokar Tumlirz and His Early Demo of the Coriolis Effect

Two years ago I wrote an article about The Myth of the Toilet Flush, comparing the angular rotation caused by the earth’s rotation to the typical rotation in experiments with garden hoses that make it easy to observe the Coriolis effect. There are several orders of magnitude in difference, and the effect can only be observed in an experiment done extremely carefully, not in the bathtub sink or toilet flush.

Now two awesome science geeks have finally done such a careful experimenteven a time-synchronized one, observing vortices on either hemisphere!

The effect has been demonstrated in a similarly careful experiment in 1908. It had been done on the Northern hemisphere only, but if it can attributed it to the Coriolis effect by ruling out other disturbances, the different senses of rotations are straight-forward.

Austrian physicist Ottokar Tumlirz had published a German  paper called “New physical evidence on the axis of rotation of the earth”. I had created this ugly sketch of his setup:

Tumlirz-1908-Coriolis-Experimental-Setup

Rough sketch based on the abstract of Tumlirz’ paper, not showing the vessel containing these components [*]

A cylindrical vessel (not shown in my drawing) is filled with water, and two glass plates are placed into it. The bottom plate has a hole, as well as the vessel. Both holes are connected by a glass tube that has many small holes. The space between the two plates is filled with water and water slowly flows out – from the bulk of the vessel through the the tiny holes into the tube. These radial red lines are bent very slightly due to the Coriolis force, and the Tumlirz added a die to make them visible. He took a photo 24 hours after starting the experiment, and the water must not flow out faster than 1 mm per minute.

Ernst Mach has given an account of Tumlirz’ experiment, quoted in an article titled Inventors I Have Met – anecdotes by a physicist approached by ‘outsider scientists’, once called paradoxers, today often called crackpots. I learned about Ernst Mach’s article from the reference and re-print of the article on this history of physics website.

Mach refers to Tumlirz’ experiment as an example of an idea that seems to belong in the same category at first glance, but is actually correct:

To be sure, Professor Tumlirz has recently performed an experiment which, while externally similar to this, is correct. By this experiment the rotation of the earth can be imitated, if the utmost care is taken, by the direction of the current of water flowing axially out of a cylindrical vessel. Further details are to be found in an article by Tumlirz in the Sitzungsberichte der Wiener Akademie, Vol. 117, 1908. I happened to know the origin of the thought that gave rise to this invention. Tumlirz noticed that the water flowing somewhat unsymmetrically in a glass funnel assumed a swift rotation in the neck of the funnel so that it formed a whirl of air in the axis of the flowing jet. This put it in his mind to increase the slight angular velocity of the water at rest with reference to the earth, by contraction in the axis.

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Comment on the German abstract: It seems one line or sentence got lost or mangled when processing the original as this does not make sense: so bendet sich das Wasser zwischen den beiden Glasscheiben [here something is missing] nach dem Rohrchen durch die kleinen Öffnungen.

I have not managed to find the full version of the old paper and the figures and photos online. I would be grateful for pointers.

Edit 2017: The link to the abstract used in 2015 is now dead, but I found a full-text version of the paper. Formulas are scrambled though.

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Update added August 2016: C. Schiller quotes this historical experiment in vol. 1 of his free physics textbook Motion Mountain (p. 135):

Only in 1962, after several attempts by other researchers, Asher Shapiro was the first to verify that the Coriolis effect has a tiny influence on the direction of the vortex flowing out of the bathtub.

Ref: A. H. SHAPIRO, Bath-tub vortex, Nature 196, pp. 1080-1081, 1962

The Twisted Garden Hose and the Myth of the Toilet Flush

If you have wrapped your head around why and how the U-shaped tube in the flow meter (described in my previous post) is twisted by the Coriolis force – here is a video of a simple experiment brought to my attention by the author of the quoted article on gyroscope physics:

You could also test it yourself using a garden hose:

Accidentally you can observe this phenomenon so clearly because the typical angular frequencies of manual rotation result in a rather strong Coriolis force – in contrast to other every day phenomena that are falsely attributed to the Coriolis force associated with the rotation of the earth.

It is often stated – and I even found this in lecture notes and text books – that the Coriolis force is accountable for the unambiguously different sense of rotation of vortices in water flowing down the sink of your bathtub or toilet: In the Northern hemisphere water should spin anti-clockwise, in the Southern hemisphere clockwise. Numerous articles debunk this as an urban legend – I pick a random one.

On principle the statement on the sense of rotation is correct as the rotation of hurricanes is impacted by the Coriolis force. But for toilet flushes and the like the effect is negligible compared to other random factors impacting the flow of water. As pointed out in this article the momentum of leaves thrown into a bowl of water at a location near the equator of the earth (often used in demonstrations of entertain tourists) do have more impact than the Coriolis force.

Near the equator the Coriolis force is nearly zero, or more precisely: Since it is both perpendicular to the velocity and the axis of rotation the Coriolis force would be directed perpendicular to the surface of the earth – but there is no component of the Coriolis force that would allow water to flow North-South or East-West. Thus very near the equator the force is infinitesimally small – much smaller than the forces acting on, say, middle European or Austrian bathtubs. And even with those the Coriolis force does not determine the spin of rotation unambiguously.

How to estimate this impact – and why can we observe the twist in the garden hose experiment?

The size of the acceleration due to the Coriolis force is

2 times (angular frequency [rad/s]) times (component of the velocity [m/s] perpendicular to the axis of rotation)

The angular frequency in radians per second is 2 Pi times the number of rotations per second. Thus the angular frequency of the rotation of the earth is about 0,0000727 radians per second. The frequency of the motion of the garden hose was rather several turns per second, thus about 1 radians per second.

Imagine a slice or volume element of water flowing in a sink or a garden hose: Assuming a similar speed with an order of magnitude of 1 meter per second. The Coriolis force differs by several orders of magnitude

  • Bathtub vortex: 0,00015 m/s2
  • Garden hose: 2 m/s2

On the other hand, the acceleration due to gravity is equal to 9,81 m/s2.

The garden hose in the video moves under the influence of gravity – like a swing or pendulum – and the Coriolis force (The additional force due to motion of the hands of the experimenter is required to overcome friction). Since the Coriolis force is of the same order of magnitude as gravity you would expect some significant impact as the resulting force on every slice or volume element of water is the vector sum of the two.

It is also important to keep track of the origins of the components of the velocity:

The radial flow velocity (assumed to be about 1 m/s) in the hose is constant and simply dictated the by the pressure in the water line. There is no tangential flow velocity unless caused by the Coriolis force.

In case of the bath tub the assumed 1 m/s do not refer to the velocity of the tangential motion in the vortex, but to the radial velocity of the water flowing “down” the sink. The tangential velocity is what would be caused by the Coriolis force – ideally.

Any initial velocity is is subject to the initial conditions applied to the experiment.

Any random tangential component of the flow velocity in the vortex increases when the water flows down:

If there is a small initial rotation – a small velocity directed perpendicular to the symmetry axis of the flush – pronounced vortices will develop due to the conservation of angular momentum: As the radius of rotation decreases – dictated by the shape of the bathtub or toilet – angular frequency needs to increase to keep the angular momentum constant. Thus in your typical flush you see how a random and small disturbance is “amplified”.

However, if you would conduct such experiment very carefully and wait long enough for any disturbance to die out, you would actually see the vortices due to Coriolis force only.[*] I have now learned from Wikipedia that it was an Austrian physicist who published the first paper on this in 1908 – Ottokar Tumlirz. Here is the full-text of his German paper: Ein neuer physikalischer Beweis für die Achsendrehung der Erde.  (Link edited in 2017. In 2013 I haven’t found the full text but only the abstract).

Tumlirz calculated the vortices’ velocity of rotation and used the following setup to confirm his findings:

Tumlirz-1908-Coriolis-Experimental-Setup

My sketch of the experimental setup Ottokar Tumlirz used in 1908 as it is described in the abstract of his German paper “New physical evidence on the axis of rotation of the earth”. The space between the two plates is filled with water, and the glass tube is open at the bottom. Water (red) flows radially to the tube. The red lines are bent very slightly due to the Coriolis force.

Holes in a cylindrical tube – which is open at the bottom – allow water to enter the tube radially. This is not your standard flush, but a setup built for preventing the amplification of tangential components in the flow. Due to the Coriolis force the flow lines are not straight lines, but slightly bent.

Tumlirz noted that the water must not flow with a speed not higher than about 1 mm per minute.

Edit, Oct 2, 2013: See Ernst Mach’s original account of Tumlirz’ experiment (who was Mach’s student)

Edit, June 3, 2015: Actually somebody did that careful experiment now – and observed the tiny effect just due to the Coriolis force, as Tumlirz. Follow-up post here.

Edit, Augist 2016: Stumbled upon another reference to an experiment done in 1962 and published in Nature (and filmed) – link added to the post from 2015.

Intuition and the Magic of the Gyroscope – Reloaded

I am baffled by the fact that my article The Spinning Gyroscope and Intuition in Physics is the top article on this blog so far.

So I believe I owe you, dear readers, an update.

In the previous article I have summarized the textbook explanation, some more intuitive comments in Feynman’s Physics Lectures, and a new paper by Eugene Butikov.

But there is an explanation of the gyroscope’s motion that might become my new favorite:

Gyroscope Physics by Cleon Teunissen

It is not an accident that Cleon is also the main author of the Wikipedia article on the Coriolis flow meter, as his ingenious take on explaining the gyroscope’s precession is closely related to his explanation of the flow meter.

The Coriolis force is a so-called pseudo-force you “feel” in a rotating frame of reference: Imagine yourself walking across a rotating disk, or rolling a ball soaked in white color rolling across a black disk and watch its trace. In the center of the rotating disk, there is no centrifugal force. But you would still feel being dragged to the right if the disk is rotating counter-clockwise (viewed from the top).

This force dragging you to the right or making the path of the ball bend even in the center – this is the Coriolis force. It also makes tubes bend in the following way when a liquid flows through them and allows for determining the flow velocity from the extent of bending:

Vibration pattern of the tubes during mass flow. Credits: Cleon Teunissen.

Vibration pattern of the tubes during mass flow. Credits: Cleon Teunissen – Coriolis flow meter

The “loop” formed by the tubes rotates about an axis which is parallel to the direction of the flow whose speed should be measured (though not the full 360°). Now the Coriolis force always drags a moving particle “to the right” – same with the volume elements in the liquid. Note that the force is always directed perpendicular to the axis of rotation and perpendicular to the velocity of the flowing volume element (mind the example of the rolling ball).

In the flow meter, the liquid moves away from the axis in one arm, but to the axis in the other arm. Thus the forces acting on each arm are antiparallel to each other and a torque is exerted on the “loop” that consists of the two arms. The loop is flexible and thus bent by the torque in the way shown in the figure above.

Now imagine a gyroscope:

Gyroscope with Coriolis force per quadrant indicated. Credits: Cleon Teunissen.

Gyroscope with Coriolis force per quadrant indicated. Credits: Cleon Teunissen – Gyroscope Physics

Gravity (acting on the weight mounted on the gyroscope’s axis) tries to make the gyroscope pitch. Cleon now shows why precession results in an “upward pitch” that compensates for that downward pitch and thus finally keeps the gyroscope stable.

The clue is to consider the 4 quadrants the gyroscope wheel consist of separately – in a way similar to evaluating the Coriolis force acting on each of the arms of the flow meter:

The tangential velocity associated with the rotation about the symmetry axis of the gyroscope (“roll”, spinning of the wheel) is equivalent to the velocity of the flowing liquid. In each quadrant, mass is moving – “flowing” – away from or to the “swivel axis” – the axis of precession (indicated in black, parallel to gravity).

The per-quadrant Coriolis force is again perpendicular to the swivel axis and perpendicular to the “flow velocity”. Imaging yourself sitting on the blue wheel and looking into the direction of the tangential velocity: Again you are “dragged to the right” if precession in counter-clockwise. As right is defined in relation to the tangential velocity, the direction of the force is reversed in the two lower quadrants.

A torque tries to pitch the wheel “upward”.

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If you want to play with gyroscopes yourself: I have stumped upon a nice shop selling gyroscopes – incl. a steampunk version, miniature Stirling engines, combustion engines (… and strange materials such as ferrofluids).

This is a gyroscope that is subject to precession – due to the counter weight:

Gyroscope gimbals kit with counter weight. Credits: www.gyroscope.com