Experiment: Push the drawing board from the side so that it is moving in more or less a straight line, left to right from the perspective of where we normally stand as explainers (we’ll call this the y direction). Take the cap off and watch the pattern evolve.
Results: The line will gradually become an oval that’s higher on the left side and lower on the right (again from the perspective of the explainer with the pen arm). As the oval gets smaller it becomes more and more circular and more and more tilted, taking on significantly more motion in the x direction than it started with. Even if the original swing is a bit off, the pattern always looks the same and tilts in the same direction.
Hypothesis: This is because of the Coriolis Effect.
Explanation: One of my favorite things to do at the museum recently is to be baffled about drawing board, often very verbally, and so many people have posited this hypothesis, and stuck to it vehemently despite my protests that the Coriolis Effect is not that strong, that I thought I would research it.
Sidenote: Remember hearing that the Coriolis Effect causes sinks and bathtubs to drain counterclockwise in the Northern Hemisphere and the opposite direction in the Southern Hemisphere? If you do and you haven’t tried it yet, you should go check all the sinks you can find.
Calculations: This exhibit basically behaves like a giant pendulum. The turning movement of a really big pendulum was actually the first way the spinning of the Earth was directly measured. This is called a Foucault pendulum, and the line along which it swings rotates at a rate of 360° sin(a) per day, where a is the latitude. The Exploratorium is at latitude 37° 48’14”, exactly, so a free pendulum there will rotate about 220° a day. Now if one color on drawing board takes about 2 minutes, that means the Coriolis Effect will cause the board to rotate about 18’ clockwise before friction stops it. That’s about a third of a degree, or 1/1200th of a complete circle, not even enough to observe.
New Hypothesis: Something is off in the construction of the structure. Perhaps a cord is twisted, one side of the board is slightly lower, or the hooks that hold it together cause uneven friction. Look at this picture from the Exploratorium website. Drawing board no longer makes patterns that look quite like that. What changed? Is there some way to make drawing board more precise? What if we snuck in at night, took it apart, and put everything back together again. Would that change it?
Private Note: Dear Daniel, I was right about the Coriolis Effect. You owe me a beer.
Did you look in the exhibit files about this?
i am as yet unconvinced. and, still have 2 days left to refute you. i did some thinking about it and actually equationally solved out (for homework, not out of excess of free time) a 2D version of the system and i think i’ve got some ideas on it:
First: I haven’t solved out for a 2D rectangle as the pendulum yet, but for a 1D swinging rod the frequency of the twisting should be about sqrt(3) times the frequency of the swinging. From the moments of intertia of a rentangle (which I found here: http://www.efunda.com/math/areas/rectangle.cfm) the drawing board should behave the same way. So I’m wondering how you said they managed to get it to be twice the frequency. (note: as far as I can tell these frequency relations are independent of actual dimensions and mass. however, if the mass is not evenly distributed – the big weight – it could be different…)
Secondly: i don’t believe the coriolis effect is what is turning the board. the effect is very weak and random noise swamps it, as you were saying. however, random noise is random noise and the only persistant un-cancelled out effect i can think of is the coriolis effect. so, while other influences should have an effect and move it more, they should over time have no net effect and the should not consistently twist the board in the same direction.
Secondly(A): so, my current thinking is that the coriolis effect is what drives the twist to consistently be in the same direction but that some other instability increases the amplitude of this effect (i.e. it offshifts more than the few degree seconds the coriolis effect alone would cause.
Secondly (A’): this would make sense since for a rectangle the X moment of inertia is the middle one (i.e. the Z moment is larger and the Y moment is smaller), meaning that that any spin around that axis is unstable and will degrade into spins around the other axes. meaning that when you send it swinging in the Y direction there is a slight X twisiting (the side farther from you rising a little above the side closest to you as it swings away, then vice versa on the way back). I think this should cause the spin to want to shift towards being around the Y axis, but since everything is symmetrical (even when taking noise into account, since by definition noise generally sums to zero net) the only force that could determine which direction the board should consistently twist in is the coriolis effect.
[you could possibly easily prove me wrong by experimenting/calculating and seeing if the coriolis force is in the opposite direction than the board is twisting, but i’ve got a hunch it won’t be. ;-)
Summary: chew on that.
further thoughts:
that picture does look really cool though and we never seemed to be able to make pictures that cool. so yeah, the whole rig probably has shifted since it was built.
so…. maybe there is something that could make it spin in one direction, but i have no idea. the only thing i can think of that is assymetrical left to right as well as front to back would be if one string in one corner was slightly shorter than the rest. this might get the whole thing to twist.
so if you could do some experimenting and see if slightly shortening one string (or multiple strings) can consistently change the twisting, even possibly in a predictable direction, i would be very interested.
hooray for geeking out. i will fight for that beer till my last dying breath!
New experiment: Give the board a push forward and to the right at about a 45° angle (from the perspective of the explainer).
Results: The line gets smaller and smaller and does not twist or change directions.
Hypothesis: The Coriolis effect has nothing to do with any of this.
New Information: According to Anne this is actually the second drawing board. She posited the idea that perhaps the twisting is intentional. Without this effect a kid that pushes the board in one direction will end up with just a really dark line, and possibly be really disappointed.
I will conduct some further research and experiments and report back.
Wahooo!! I was right!! I posted this prediction on http://explainers.wordpress.com/2007/11/13/drawing-board/#comment-2135
It would be a lot easier to explain why this is the case in person as you should see force diagrams and such. Hmm maybe I could stop by one morning, or if I have more time I will try to write out a description. Basically, What you found at 45 degrees is a stable axis. Because the center of mass is in not in the center of the board the tension in each cable is not equal. The tension is greatest in the cable closest to the center of mass. When the board is displaced it is the sideways component of the cable tension that pulls it back to the center. Because the sideways components of the tension are not equal in each cable, there’s a net torque about the table. The magnitude and direction of this torque depends on which direction the table is displaced. What you found is a direction in which the torque is zero.
touché