I sat on the edge of a ball pit at Chuck E. Cheeses, calipers in hand, measuring the diameters of a random sampling of plastic balls within the pit.
I suppose I stood out, an officious-looking adult wielding a precision instrument in a place designed for fun. So much so that a father attending his child asked me what I was doing.
I was measuring the ball sizes. I explained that if the balls were too small, and a child became covered with them, then the void space around the balls, the contorted empty volumes that represented places where air can be exchanged, would be too small, making breathing difficult. That made sense to the father, and he seemed pleased that I was looking after his child’s safety.
Contrary to the way it seemed, I was not a corporate inspector for Chuck E. Cheeses. I was also not a government inspector. But I was curious, gaining information for ideas I was developing about the breathing resistance imposed by particles of various sizes. I was acting, as it were, as a freelance scientist investigating flow through porous beds.
Consider the circumstance where a person is forced to breathe through a mass of balls, as in the illustration below. You can see, better than in the case of the ball pit, that if the balls become too small, or smaller balls fill in the void spaces between larger balls, then the person would be at risk for suffocation.
Advertisements for balls sold for ball pits point out the safety advantage of larger balls for children under age 3. The smaller children are obviously more susceptible to tunneling deeper into a pit of balls, some of which may be piled to two feet or deeper depths.
Balls of 3.1 in. diameter are touted as being ideal for three-year-olds, whereas other popular sizes [2.5 in. (65 mm), 2.75 in. (70 mm)] are not. The 3.1 in. ball is almost twice as large, in terms of actual volume, as the 2.5 in. balls.
A problem awaits a child if the ball pit has poorly sorted ball sizes, especially a mixture of larger and small balls. As shown in the figure to the right, well-sorted balls provide a porosity (airspace for breathing) of over 32%, whereas a mixture with balls fitting into the void spaces between larger balls can reduce void space down to about 12%. That would not be a good plan for a ball pit.
It also is not a good plan for the Namib mole.
The Namib Golden Mole is found in one region of Namibia because of the peculiar characteristics of the sand in that area. The sand grains are surprisingly homogeneous in size, and as the illustration to the right shows, similarly sized particles have a relatively large porosity. For the mole that means that when they burrow deep into the sand to escape blistering noonday heat, they will not suffocate. They can breathe through the sand.
If the sand were of mixed grain sizes, which is more typical of sand dunes, then porosity would be low and the mole would not be able to burrow deep enough to avoid the African heat without suffocating.
So, quite unexpectedly there is a connection between the uniform size of plastic balls in a ball pit and the survival of a mole in a faraway African desert.
You never know where scientific curiosity will lead you.
As will be shown in an upcoming blog post, the topic of breathing through porosities in packed beds is relevant to diving with rebreathers or breathing through chemical absorbent cartridges in gas masks.