We’ve been thinking about Coriolis deflection a lot recently (see links at the end of this post). But this weekend, at Phaenomenta Flensburg, I came across a so-called “Coriolis fountain”. A fountain that you can put into spin and that then changes shape like so:
Uta, remember we talked about this a couple of years ago? Nice puzzle for anyone interested in fluid dynamics…
So how do we teach about the Coriolis force? The following is a shortened version of an article that Pierre de Wet and I wrote when I was still in Bergen, check it out here.
The Coriolis demonstration
A demonstration observing a body on a rotating table from within and from outside the rotating system was run as part of the practical experimentation component of the “Introduction to Oceanography” semester course. Students were in the second year of their Bachelors in meteorology and oceanography at the Geophysical Institute of the University of Bergen, Norway. Similar experiments are run at many universities as part of their oceanography or geophysical fluid dynamics instruction.
Rotating table with a co-rotating video camera (See Figure 1. For simpler and less expensive setups, please refer to “Possible modifications of the activity”)
Screen where images from the camera can be displayed
Solid metal spheres
Ramp to launch the spheres from
Tape to mark positions on the floor
About 45 minutes to one hour per student group. The groups should be sufficiently small so as to ensure active participation of every student. In our small lab space, five has proven to be the upper limit on the number of students per group.
In the demonstration, a metal ball is launched from a ramp on a rotating table (Figure 1A,B). Students simultaneously observe the motion from two vantage points: where they are standing in the room, i.e. outside of the rotating system of the table; and, on a screen that displays the table, as captured by a co-rotating camera mounted above it. They are subsequently asked to:
trace the trajectory seen on the screen on a transparency (Figure 1C),
measure the radius of this drawn trajectory; and
compare the trajectory’s radius to the theorized value.
The latter is calculated from the measured rotation rate of the table and the linear velocity of the ball, determined by launching the ball along a straight line on the floor.
In years prior to 2012, the course had been run along the conventional lines of instruction in an undergraduate physics lab: the students read the instructions, conduct the experiment and write a report.
In 2012, we decided to include an elicit-confront-resolve approach to help students realize and understand the seemingly conflicting observations made from inside versus outside of the rotating system (Figure 2). The three steps we employed are described in detail below.
Elicit the lingering misconception
1.a The general function of the “elicit” step
The goal of this first step is to make students aware of their beliefs of what will happen in a given situation, no matter what those beliefs might be. By discussing what students anticipate to observe under different physical conditions before the actual experiment is conducted, the students’ insights are put to the test. Sketching different scenarios (Fan (2015), Ainsworth et al. (2011)) and trying to answer questions before observing experiments are important steps in the learning process since students are usually unaware of their premises and assumptions. These need to be explicated and verbalized before they can be tested, and either be built on, or, if necessary, overcome.
1.b What the “elicit” step means in the context of our experiment
Students have been taught in introductory lectures that in a counter-clockwise rotating system (i.e. in the Northern Hemisphere) a moving object will be deflected to the right. They are also aware that the extent to which the object is deflected depends on its velocity and the rotational speed of the reference frame.
A typical laboratory session would progress as follows: students are asked to observe the path of a ball being launched from the perimeter of the circular, not-yet rotating table by a student standing at a marked position next to the table, the “launch position”. The ball is observed to be rolling radially towards and over the center point of the table, dropping off the table diametrically opposite from the position from which it was launched. So far nothing surprising. A second student – the catcher – is asked to stand at the position where the ball dropped off the table’s edge so as to catch the ball in the non-rotating case. The position is also marked on the floor with insulation tape.
The students are now asked to predict the behavior of the ball once the table is put into slow rotation. At this point, students typically enquire about the direction of rotation and, when assured that “Northern Hemisphere” counter-clockwise rotation is being applied, their default prediction is that the ball will be deflected to the right. When asked whether the catcher should alter their position, the students commonly answer that the catcher should move some arbitrary angle, but typically less than 90 degrees, clockwise around the table. The question of the influence of an increase in the rotational rate of the table on the catcher’s placement is now posed. “Still further clockwise”, is the usual answer. This then leads to the instructor’s asking whether a rotational speed exists at which the student launching the ball, will also be able to catch it him/herself. Ordinarily the students confirm that such a situation is indeed possible.
Confronting the misconception
2.a The general function of the “confront” step
For those cases in which the “elicit” step brought to light assumptions or beliefs that are different from the instructor’s, the “confront” step serves to show the students the discrepancy between what they stated to be true, and what they observe to be true.
2.b What the “confront” step means in the context of our experiment
The students’ predictions are subsequently put to the test by starting with the simple, non-rotating case: the ball is launched and the nominated catcher, positioned diametrically across from the launch position, seizes the ball as it falls off the table’s surface right in front of them. As in the discussion beforehand, the table is then put into rotation at incrementally increasing rates, with the ball being launched from the same position for each of the different rotational speeds. It becomes clear that the catcher need not adjust their position, but can remain standing diametrically opposite to the student launching the ball – the point where the ball drops to the floor. Hence students realize that the movement of the ball relative to the non-rotating laboratory is unaffected by the table’s rotation rate.
This observation appears counterintuitive, since the camera, rotating with the system, shows the curved trajectories the students had expected; circles with radii decreasing as the rotation rate is increased. Furthermore, to add to their confusion, when observed from their positions around the rotating table, the path of the ball on the rotating table appears to show a deflection, too. This is due to the observer’s eye being fooled by focusing on features of the table, e.g. cross hairs drawn on the table’s surface or the bars of the camera scaffold, relative to which the ball does, indeed, follow a curved trajectory. To overcome this latter trickery of the mind, the instructor may ask the students to crouch, diametrically across from the launcher, so that their line of sight is aligned with the table’s surface, i.e. at a zero zenith angle of observation. From this vantage point the ball is observed to indeed be moving in a straight line towards the observer, irrespective of the rate of rotation of the table.
To further cement the concept, the table may again be set into rotation. The launcher and the catcher are now asked to pass the ball to one another by throwing it across the table without it physically making contact with the table’s surface. As expected, the ball moves in a straight line between the launcher and the catcher, who are both observing from an inert frame of reference. However, when viewing the playback of the co-rotating camera, which represents the view from the rotating frame of reference, the trajectory is observed as curved.
Resolving the misconception
3.a The general function of the “resolve” step
Misconceptions that were brought to light during the “elicit” step, and whose discrepancy with observations was made clear during the “confront” step, are finally corrected in the “resolve” step. While this sounds very easy, in practice it is anything but. The final step of the elicit-confront-resolve instructional approach thus presents the opportunity for the instructor to aid students in reflecting upon and reassessing previous knowledge, and for learning to take place.
3.b What the “resolve” step means in the context of our experiment
The instructor should by now be able to point out and dispel any remaining implicit assumptions, making it clear that the discrepant trajectories are undoubtedly the product of viewing the motion from different frames of reference. Despite the students’ observations and their participation in the experiment this is not a given, nor does it happen instantaneously. Oftentimes further, detailed discussion is required. Frequently students have to re-run the experiment themselves in different roles (i.e. as launcher as well as catcher) and explicitly state what they are noticing before they trust their observations.
Possible modifications of the activity:
We used the described activity to introduce the laboratory activity, after which the students had to carry out the exercise and write a report about it. Follow-up experiments that are often conducted usually include rotating water tanks to visualize the effect of the Coriolis force on the large-scale circulation of the ocean or atmosphere, for example on vortices, fronts, ocean gyres, Ekman layers, Rossby waves, the General circulation and many other phenomena (see for example Marshall and Plumb (2007)).
Despite their popularity in geophysical fluid dynamics instruction at the authors’ current and previous institutions, rotating tables might not be readily available everywhere. Good instructions for building a rotating table can, for example, be found on the “weather in a tank” website, where there is also the contact information to a supplier given: http://paoc.mit.edu/labguide/apparatus.html. A less expensive setup can be created from old disk players or even Lazy Susans. In many cases, setting the exact rotation rate is not as important as having a qualitative difference between “fast” and “slow” rotation, which is very easy to realize. In cases where a co-rotating camera is not available, by dipping the ball in either dye or chalk dust (or by simply running a pen in a straight line across the rotating surface), the trajectory in the rotating system can be visualized. The method described in this manuscript is easily adapted to such a setup.
Lastly we suggest using an elicit-confront-resolve approach even when the demonstration is not run on an actual rotating table. Even if the demonstration is only virtually conducted, for example using Urbano & Houghton (2006)’s Coriolis force simulation, the approach is beneficial to increasing conceptual understanding.
Another neat experiment in the collection I’ve recently been talking about is measuring pressure at different points on a wing profile. It’s not terribly surprising that – as long as the wing is oriented in the correct way in the flow – pressure is high below the wing and low above it. Kinda the whole point of having a wing profile. Yet, it’s nice to actually measure it.
And yes – next time I set up that manometer I’m gonna make sure that it’s a little easier to get a good reading!
Another one of those awesome hydrodynamics toys: A Pitot tube!
This is what it looks like:
What you can’t see here is the little hole at the tip of the tube that is pointing downwards in the picture. What the Pitot tube measures is the pressure difference between that hole (the stagnation pressure since it’s the stagnation point) and the vents some 3.5 cm above (the static pressure), from which you can calculate the dynamic pressure, hence air speed of a plane (if the Pitot tube was mounted on said plane) or, in our case, the speed of air flow from a fan relative to a stationary Pitot tube.
Again, I’m sadly too lazy to calculate anything, but you can take the measurements from the movie below and do it yourself if you so desire! :-)
On Monday I posted about playing with Venturi tubes. Guess what: We are going to play more today! Because today the Venturi tubes are connected to a “proper” manometer:
Now, if I wasn’t so lazy this would be a great opportunity to get good readings of the pressure differences caused by different flow rates. However, I’ll just let the images speak for themselves. Enjoy!
A Venturi tube is one of the things one hears about in hydrodynamics class all the time, but one never gets to see them for real. And even though I just said on Friday that the thing that I found most fascinating in the aerodynamics collection I got to borrow recently was to see how the flow reversed downstream of a paddle I might have to take that back, because the hands-down most exciting thing was to play with a Venturi tube!
So what is all the fuss about? This is what a Venturi tube looks like:
Basically, it is a tube, open at both ends, that gets thinner in the middle and wider again. All the rest you see in the picture is props: The mouth of the fan in the top right, and then three U-tubes filled with dyed water below the Venturi tube.
The Venturi tube is so famous because it nicely demonstrates the Venturi effect, namely the reduction in pressure that occurs when a flow is accelerated. In the case of the Venturi tube, the flow is accelerated in the thin section of the tube, where – for continuity reasons – it has to go faster than in the wider sections. So what happens when we turn on the fan?
Yep! The levels in the three U-tubes change. And most importantly, the pressure for the middle U-tube drops, as demonstrated by the red water being “sucked up” on the side of the U-tube that is connected to the Venturi tube.
One of the things that fascinated me most when playing with the huge fan we used to look at the flow downstream of a paddle was how the flow direction reverses.
Unfortunately (alas, it was to be expected) we didn’t really see this on the paper towel stream line test I did the other day.
But here is another way to visualize it: using a propeller!
Depending on the direction the air flows at the propeller, its direction changes. So as we move it towards and away from the paddle, when the flow direction changes, so does the direction of rotation of the propeller, too.
Whenever I’m in a canoe or kayak, I love watching the two eddies that form behind the paddle when you pull it through the water. It looks kinda like this:
Instead of pulling a paddle through more or less stagnant water, we could also use a stationary paddle in a flow. And that is the setup I want to discuss today: A stationary, round paddle perpendicular to an air flow.
A very cool feature of the paddle – which we know has to exist from the sketch above – is shown below: There is a point somewhere downstream of the paddle, where the direction of the air flow changes and a return flow towards the paddle starts. You can see that the threads on the stick I am placing in the return flow go partly towards, partly away from the paddle. So clearly the stick is in the right spot!
Another visualization that my dad came up with below: Threads are pulled back towards the paddle in the return flow.
Doesn’t it look awesome?
Another way to visualize the change in flow direction is to take a rotor and move it from far downstream of the paddle towards the paddle and back.
All of this is shown in the movie:
Don’t you wish you had all this stuff to play with? :-)
(And do you now understand why I was so excited about the diving duck? :-))
One of the reasons I have been wanting to do the vortex street experiment I wrote about on Monday is that it is pretty difficult to visualize flow fields (especially if you neither want to pollute running water somewhere in nature, nor want to waste a lot of water by setting up the flow yourself). As a first order approximation, pulling an object through a stagnant water body is the same as the water body moving past a stationary object.
At the Thinktank Birmingham, they do have a small channel with water constantly running through, and a couple of objects that you can place in the current. Unfortunately, what you see is the wave field that is caused by the obstacle, not the current field.
It is still pretty cool to play with it, though!
But neither of the setups (the channel discussed above or the vortex streets on a plate thing from Monday) is really optimally suited to teaching students the way a flow field will react to an obstacle. How amazing would it be if we had a flow field that could be modified to suit our needs? Stay tuned – I might have a solution for you on Friday! :-)