Almost All of It Is Holes

Everything on the next eight spreads comes from one paper: C. Cummins, M. Seale, A. Macente, D. Certini, E. Mastropaolo, I. M. Viola & N. Nakayama, “A separated vortex ring underlies the flight of the dandelion,” Nature 562(7727), 414–418 (2018), doi:10.1038/s41586-018-0604-2.

How we read it, stated because it matters. Nature's own page answers with an authentication redirect, so this was read at full text from the peer-reviewed accepted author manuscript deposited in the University of Strathclyde's repository. Every figure and every quoted phrase in this zine comes from that copy. It is the accepted version rather than the version of record, so the wording of a caption could differ by a word from the printed article; none of the numbers used here sit in a caption.

“A very long way off” is the paper's own opening, and it is a citation rather than their measurement: Asteraceae seeds “routinely disperse over 30 km and occasionally even 150 km,” referenced to earlier work. The dandelion is Taraxacum officinale.

The count is real and it has an error bar. Using X-ray computed micro-tomography and light microscopy, the pappus was found to comprise “N = 100 [95, 106] (mean [95% Confidence Interval], n = 10) filaments… radiating out from a central point (pulvinus),” each 7.41 mm long and 16.3 µm across. So “about a hundred” is the honest way to say it to a child, and ten seed heads is the honest sample size to admit to.

“Thinner than a hair on your head” needs a caveat, because human hair is not one thickness. It runs roughly 17 to 180 µm, most commonly somewhere around 50 to 100. A filament at 16.3 µm is therefore finer than almost any human hair and several times finer than a typical one — but if you have very fine hair, they are close, and a child who says so is right.

The picture draws twenty-five, not a hundred, because a hundred at this size is a solid grey disc and the gaps are the entire point. The drawing is honest about the arrangement and deliberately not to scale in number; the number is in the label.

The measured figure is 0.916. The paper defines porosity precisely, and the definition is worth having, because it is narrower than “how empty it is”: “The porosity, defined as the ratio of the empty projected area to the plan area of the enclosing disk, of the pappus was measured using light microscopy, and was found to be 0.916 [0.907, 0.923] (mean [95% CI], n = 10).”

Projected area means the shadow, not the volume. This is the fraction of the flat circular outline the hairs fail to cover — what you would measure by photographing the plume against a light and counting pale pixels. It is the right quantity here, because it is the shadow the oncoming air meets.

91.6 becomes “about ninety-two” in the read-aloud layer, and the grid draws eight filled circles against ninety-two empty. Both roundings are toward the measurement rather than away from it.

The paper circle is the control, and the two halves of this demonstration only work done together, back to back, from the same height. Part two is on the next spread.

Two honest cautions, because this demonstration shows one thing and not another. First: a thumbnail-sized disc of ordinary printer paper weighs roughly twenty times what a dandelion seed weighs, so it comes down faster. This is a demonstration about the wobble, not the speed, and the read-aloud layer never claims otherwise. Second: it will not flutter identically every time. Drop it several times and watch the pattern rather than one go — the instability is the point, and an instability that repeated exactly would not be one.

Why a circle and not any old scrap. The paper's comparison is between a porous disc and a solid one of the same disc-like geometry. A torn scrap adds a shape difference on top of the porosity difference, and then the demonstration is showing two things at once.

This is the finding, at kitchen scale. The steadiness is not a side effect of the dandelion being light. It is a consequence of the porosity, and the paper separates the two by building plastic discs of varying porosity and dropping those as well. Spread nine has the number.

What this demonstration does not show. It does not show that the holey one falls more slowly — it does not, at these weights — and it does not show that porosity gives more drag, which would be false. Spread ten is the spread where that is said plainly, because a demonstration that quietly proves something other than what it claims is worse than no demonstration at all.

If your dandelion has gone over, a whole seed head kept dry indoors will hold for days. If it is the wrong season entirely, the parts of this zine that need the seed are these two spreads; the rest reads without it.

This is the paper's central claim, and it is stated as a hypothesis they then tested: “We hypothesized that the circular disk-like geometry and the porosity of the pappus are the key design features that enable the formation of the separated vortex ring.”

How they tested it is the part worth having, because it is what turns a nice story into a result: “The porosity gradient was surveyed using microfabricated disks, and a disk with a similar porosity was found able to recapitulate the flow behaviour of the real pappus.” They built plastic discs with holes in, across a range of porosities, and a disc matched to the dandelion's porosity behaved like a dandelion. That is how you know it is the holes and not something else about being a seed.

“Design features” is their phrase and it does not mean designed. It is standard engineering usage for the properties of a structure. Spread eleven refuses the other reading explicitly.

It is called a separated vortex ring, and separated is the load-bearing word: the ring is detached from the body rather than attached to its surface, which is what makes it unusual. The paper's own words: “Here we visualized the flow around dandelion seeds, uncovering an extraordinary type of vortex. This vortex is a ring of recirculating fluid, which is detached owing to the flow passing through the pappus.”

Two figures for it. The ring runs about one pappus diameter in length, and the flow inside it moves at roughly a tenth of the speed of the surrounding air. It was visualised in a vertical wind tunnel with long-exposure imaging of the flow.

“Nobody had ever properly seen” is defensible and worth checking. The paper says in its abstract that “the physics underpinning pappus-mediated flight remains unresolved,” and closes by saying the discovery “signals the existence of a new class of fluid behaviour.” People had watched dandelion seeds fly for as long as there have been people. What was new in 2018 was seeing what the air was doing while they did it.

The number is a critical Reynolds number — the speed-and-size threshold past which the ring stops being steady and starts shedding, which is the wobble. Measured: 149 ± 2 for an impervious disc, against 429 [415, 440] for real dandelion seeds. And a porous disc built to the dandelion's own porosity came out at 457 ± 5, which is the control that makes the claim about porosity rather than about seeds.

Verbatim, and the reason the read-aloud says every single one: “All of the dandelion samples tested flew at a Re below Re_c.” Their conclusion, also verbatim: “This suggests that evolution has tuned the pappus porosity to eliminate vortex shedding as the seed flies.”

“Tuned” is their word and it needs its caveat, which is why the read-aloud layer answers it in the same breath with nobody chose that. Tuned here describes an outcome selection produced over a very long time. It is not an intention, and there is no tuner.

What your paper circle has to do with any of this is our arithmetic, not theirs: a thumbnail-sized disc of printer paper falls fast enough to be far above 149, which is why it flutters. The paper measured discs in a controlled drop; we are extrapolating their threshold to a kitchen, and saying so.

Verbatim: “the filamentous design of plumed seeds confers two major advantages compared with a membranous one: a four-fold increase in the loading and enhancement of the flight stability. This makes the plumed design far more efficient at flying than a membrane (i.e. a circular disk) for lightweight seeds.” Loading is weight carried per unit of material.

Now the correction this zine owes you, because it is the thing an adult will get wrong first. It is tempting to conclude that a solid disc would be worse in every way. It would not, and the paper does the arithmetic against itself. For a solid disc to supply the same drag as the pappus at the same falling speed, its diameter “is given by D = 8.6 mm, which is 38% smaller than” the real pappus, which measures 13.8 mm across. Per unit of width, a solid disc is the better brake. What porosity buys is load per unit of material, and freedom from fluttering — not more drag.

This is why spreads five and six are about the wobble and not the speed. A same-size paper circle is much heavier and comes down faster, and a demonstration built on “the holey one falls slower” would have handed a child the opposite of the promised result. Which is the failure this collection names on its own face: an imperative a child follows and gets nothing from teaches them that the book was wrong.

And the open end, in their words: the discovery “signals the existence of a new class of fluid behaviour around fluid-immersed bodies that may underlie locomotion, weight reduction and particle retention in biological and manmade structures.” May underlie is a proposal about where else to look, and it has not been settled.