My class this term is a “Scholars Research Seminar” with the title “A Brief History of Timekeeping,” looking at the science and technology of timekeeping from prehistory through modern atomic clocks. This is nominally an introduction to “research methods,” though the class operates under a lot of constraints that fully justify the scare quotes, at least for scientists. As I am a scientist, though, I want the class to include at least one original measurement and the reporting thereof, so I’ve been thinking of really simple measurements that I can have them do independently and write up. I’ve previously blogged about some measurements using cheap timers and the NIST web site, that I did as a preliminary for this class.
In poking around a bit, I stumbled across this European Journal of Physics paper on the physics of a sand glass (thanks to a passing mention of it in The Physics Book), which is a really nice piece that we’ll be going over in detail in class. This suggested another possible cheap and easy measurement, though, so I bought a pack of cheap sand timers from Amazon, and intend to hand them out (along with digital timers from our teaching labs and the NIST time URL) as another possible measurement.
Because it would be the height of foolishness to assign students to make a measurement that I haven’t done myself, I pulled one out of the pack (shown at right), and tested it myself. The testing protocol was extremely simple: I fired up the stopwatch app on my Android phone, and measured the time required for the timer to empty, flipping it back and forth until I had 32 total measurements (these were spread over the course of a couple of days, in intervals when SteelyKid was watching tv or otherwise distracted). Averaging together all 32 measurements, I come up with an average emptying time of 177.5+/-0.6 s, where the uncertainty is the standard deviation of the mean of the 32 measurements (which were rounded to the nearest second).
That by itself is better than I expect for cheap plastic timers that sell for less than $1 each– the uncertainty in the time is about 0.3% of the time, which is pretty darn good. But it’s actually much more interesting than that, if you dig into the data a little. Here’s a histogram of the emptying time for the various measurements, with the height of the bars indicating the number of trials falling in each 1-s bin:
Pretty striking, isn’t it? This is a classic example of a bimodal distribution– the average of all the trials is 177s, but there were basically no runs that gave a time of 177s. Instead, there was a big clump at around 174s, and another big clump at 180s.
What’s going on here? Well, as you can tell from the bar coloring, the two different groups correspond to the two different orientations of the timer. One end has a “made in China” sticker on it, and when that end is up, the emptying time was 174.7+/-0.4 s (mean and standard deviation of the mean for 16 trials). When the sticker was down, the emptying time was 180.3+/-0.3 s (mean and standard deviation of the mean for 16 trials). That’s a difference of 14 standard deviations, which even a particle physicist would accept as a significant separation.
So, what accounts for the difference between the two? I think it’s the cheapness of the timers. Specifically, the plastic end caps on the tube containing the glass bulbs– one of them is not on quite straight (the one without the sticker), and as a result, the tube is slightly tilted in one orientation relative to the other. Weirdly, the orientation that, by eye, appears to be tilted from the vertical is the one that empties faster; I would’ve expected the more vertical of the two to be faster, but maybe the dynamics of the sand flow process are a little counterintuitive in this respect. (For the record, tilting it more dramatically (by propping it on the handle of a spoon) did significantly slow the emptying time, as expected.) Or maybe it’s just really difficult to judge the verticality of the timer.
This does, of course, suggest another possible experiment, which wasn’t included in the otherwise fairly exhaustive EJP paper, namely measuring the effect of the tilt on the emptying time. I’ll leave that for an interested student to try out, though, and just note that when you start looking closely at the physics of things, even cheap plastic made-in-China crap holds some surprises…