A. Additional perspective on the kamifusen pumping mechanism

Ichiro Fukumori

Jet Propulsion Laboratory, California Institute of Technology

In the January 2017 Quick Study “Kamifusen, the self-inflating Japanese paper balloon,” I explained why the balloon inflates when you bat it about with the palm of your hand. In brief, the kamifusen (紙風船) oscillates elastically, and during that process it spends a short amount of time in a high-pressure state in which air is expelled and a relatively longer period of time in a low-pressure state in which it sucks air in. Bernoulli’s principle guarantees that more air is sucked in than is expelled out. Detailed testing of the mechanism I described would require measurements of volume, pressure, airflow through the hole of the balloon, and the stress and strain of its paper skin. Nonetheless, some simple experiments can shed light on the mechanism I described.

Consider, for instance, a paper balloon in the shape of a cube instead of a sphere—a kakufusen (角風船). Traveling pharmacists called baiyaku-san (売薬さん) used to give out kakufusen (kaku means “angled”) as promotional items with ads printed on their sides, but nowadays kakufusen are less common than the round kamifusen. Like their spherical cousins, the kakufusen inflate by themselves when bounced on your palm. In particular, they inflate into convex forms with bulging faces and the maximum volume allowed by their construction. Because the fully self-inflated kakufusen is not cubic, the inflation is evidently not driven by the paper’s elastic tendency to return to its flat state. The bulging kakufusen is, however, consistent with the mechanism discussed in the Quick Study.

Further light on the nature of its inflationary mechanism comes from examining means that defeat the kamifusen’s inflation. For instance, poking an inflated kamifusen with a finger instead of bouncing it on a palm causes the balloon to deflate. The reason is that the small-scale finger poke produces a local plastic deformation that squirts air one way—out of the balloon—rather than an effective compression that generates the elastic oscillation fundamental to the balloon’s inflation. This poke response may also explain why most kamifusen are the size of a hand: Anything bigger would require something larger than a hand to keep it inflated and thus would not be well-suited as a toy.

A kamifusen also fails to inflate if its hole is too large, if it has too many holes, or if its paper skin is torn too much. In all those cases, too much air escapes from the balloon and an effective elastic oscillation never takes place. Kamifusen don’t inflate when they are softly caught and gently tossed instead of being bounced. That phenomenon, too, is consistent with the Quick Study’s explanation, in which the sudden impact of the bounce is essential to the balloon’s inflation. In general, kamifusen inflate more readily when they are bounced more sharply, provided, of course, that they do not rupture. When strongly batted, kamifusen also exhibit a jerky flight motion suggestive of air squirted in and out of the balloon due its elastic oscillation. According to the mechanism proposed in the Quick Study, a kamifusen would fail to inflate if it were bounced in a vacuum, because air fluctuation drives the inflation, not elastic rebounding of the balloon’s paper skin.

The mechanism described in the Quick Study implies that a kamifusen would deflate if it could be bounced from within or, equivalently, if it were to be suddenly expanded without a change in the quantity of air it contains. In that case, the low-pressure state would be the shorter-lived one, and Bernoulli’s principle would demand that more air be expelled than sucked in.

A sudden-expansion experiment would be an effective test of the ideas I proposed in the Quick Study. For now I leave that as a topic for future investigation. Plenty of room remains for a more rigorous analysis of the balloon’s behavior both experimentally and theoretically. Whether phenomena analogous to the kamifusen’s self-inflation exist elsewhere, particularly in the natural world, warrants examination. So do possible applications of the kamifusen mechanism.