spill-proof coffee carrier

It all started decades ago when I saw a short item in Scientific American about a “spill-proof coffee carrier” (SPCC). It was in one of those small text boxes they reserve for those extra tidbits of information that don’t quite belong in the main article, or need special highlighting. I’m not sure I even read the whole thing because I remember being rushed and making a mental note to refer back to it later.

The gist of it was that some engineers at NASA had used their knowledge of physics to invent (and possibly market) a spill-proof coffee system for carrying your coffee back to the office. The only detail I remember from the blurb is some engineer quoted as saying, “First you measure the slosh velocity of the coffee,” or something like that. Oh, one other thing. I either knew at the time or somehow found out later (it seems to me I actually saw the SPCC being advertised in one of those gift catalogs somewhere along the way) that the carrier was a sling-type affair in which the coffee cup sat on a cradle supported by three chains that were joined to a “carrying” ring at the top.

I never did get back to the article, but I always remembered that, according to those guys at NASA, there was a way of carrying your coffee without spilling it, and it was accessible to anyone with a sufficient knowledge of physics. (Or you could buy one of those spill-proof coffee carriers, if you could find one anywhere.)

Years passed, until one Christmas vacation period a few years ago, when the whole family was home. I started talking about the SPCC with David, who was beginning his career as a science teacher. Soon, we were browsing through my old high school (or was it college) physics book, looking through pendulum formulae. The idea was to design an SPCC with a natural frequency (or period) that would interfere with the slosh frequency (or period) of the coffee.

First, like the NASA man said, we had to measure the slosh frequency of the coffee. We made the usual simplifying assumption that coffee is essentially water and, after filling a “standard” cup, started measuring the number of sloshes per minute. We asked other family members to count too, so we could average the results. I still have the calculation sheet. We counted the number of sloshes in 15-30 second intervals and came up with an average of 180 “swings” per minute, or a slosh period (T) of 1/3 second.

We knew that different cups would give slightly different answers, and that mom adding more sugar to the coffee would change the density and viscosity of the coffee slightly. We also figured that, as is the case with most engineering projects, these small variations wouldn’t matter. We would design the SPCC so that its natural frequency would interfere with the slosh frequency we measured. If there were some exotic cup or beverage out there for which it didn’t work, we’d live with it.

We started with the equation for simple harmonic motion (of a pendulum with length L):

(T/2pi)^2 = L/g

We then calculated the theoretical length of a pendulum with a period of 1/3 seconabout an inch. I don’t remember why. Then my calculations show something I no longer understand. It involved the formula, d = L sin x = A cos wt. We multiplied by some numbers and then picked a number between two other numbers (I think to find a frequency for our “big” SPCC pendulum that would interfere with the “small” coffee pendulum). Anyway, the design length we picked for the SPCC was about 12.5 inches.

Satisfied that we had solved the puzzle, David and I went downstairs to the “laboratory” and constructed the pilot SPCC using a paint can lid, a coat hanger, and some string. When we eagerly set a cup filled with water on the can lid, we were elated to find that it worked perfectly! The water in the cup didn’t show the slightest ripple as we swung the SPCC wildly. Ecstatic with the pure joy of scientific discovery, we went upstairs to show the family.

We went prancing through the family room, showing everyone how well it worked, shouting phrases like, “Science works, baby” and “physics rules.” Things were going pretty well unti

Patrick, erstwhile physics student, asked to see the SPCC. He didn’t say anything else, but in a few minutes, he could be seen off in a corner, grabbing the strings part way down to investigate the effect of reducing the length. The effect was exactly nothing. The SPCC worked at any length. Moments earlier, Dave and I had been convinced that changing the length by as much as a fraction of an inch would have rendered the device worthless. Now, Patrick had shown us that all the calculations had been for naught. Just string something together that feels comfortable and you too can make an SPCC.

We still don’t know why it works. I suspect that the large difference in period between the SPCC and the coffee cup makes it impossible to impart any sloshing into the cup. Anyway, this episode also exemplifies the importance of experimentation as well as calculation in science.

DadExplanations/Observations/Stories11/25/04 5 comments


Dad • 11/26/04 11:04 AM:

I forgot to mention the postscript to the story. After finding out that size didn’t matter, we decided to try and make a coffee carrier that would be “spill prone.” This could be done, we reasoned, by putting the cup on a pendulum with a length of 1 inch. This we did by creating a wooden ring (like a ping pong paddle with a large hole in it) under which we supported a platform (for the cup) on three one-inch strings. It worked! It was very difficult to carry the cup on this new device without spilling its contents.

Patrick • 11/30/04 2:58 AM:

No that it matters much, but my memory of this event is that we were still in the basement when I fiddled with the lengths to determine that they didn’t matter much. And then Tommy came bounding down the stairs and jumped right through the space between the coffee cup and the strings!

Seriously, though (the part about being in the basement really is how I remember it), that was a great day for bullheaded experimentation. Thanks, Dad, for reminding us here.

Dad • 11/30/04 9:53 AM:

We definitely came upstairs first to show off the invention. Had you been downstairs, you would have burst our bubble before we had a chance to gloat. It was after we had triumphantly walked through several upstairs rooms that you asked to see it.

By the way, I have no doubt my curiosity about the preciseness of the calculation would have led me to try shortening the strings myself had you not wrested the device from my hands.

David • 12/05/04 10:39 PM:

Dad is correct. We did come upstairs after four straight days in the dungeon/basement to show off our revolutionary invention (ranking a close third in Madden history behind 1. Toilet-seat-holder-upper and 2. Flag-pole putter-upper). We didn’t even eat or drink or use the bathroom. We were absolutely pumped. It must’ve been how Mendeleyev, Roentgen, Fleming, and Newton felt. Only thing is, the apple’s effect was soon supplanted by the sledgehammer of Pat’s tampering. Long live science!

David • 11/21/05 11:56 AM:

Has anyone seen that marvelous toilet-seat-holder-upper lately? I know the Smithsonian was borrowing it for a recent exhibit titled, “The Best Inventions in the History of the Universe”, but I thought they had returned it. Maybe we can look for it over Christmas break while we’re all re-cleaning out all our drawers, cleaning the basement, and while Dan is organizing the crawl-space.

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