Marius Comper

An experiment about empty space

The
dandelion
and the
ring in the air

The seed’s pappus is barely there: 91.6% of its enclosing disk is empty projected area. Flow through those gaps maintains a stable, separated vortex ring that slows the fall.

91.6% is the empty area seen in projection, divided by the plan area of the enclosing disk. It is not the percentage of air by volume.

Follow the air

Vertical wind tunnel

interactive diagram
A dandelion seed and the airflow around it Air rises through the filament crown. A coral vortex ring sits downstream, separated from the pappus. separated, stable ring pappus Ø 13.8 mm falling seed relative air ↑
The flow is shown schematically from the study’s observations and models. This is not a CFD simulation.

Measured pappus: 91.6% empty projected area. In the experiment, flow through the filaments maintained a stable, separated ring.

The 0%, 33%, 55%, 75% and 89% stops come from the study’s porous disks. The ring’s drawn position between the endpoints shows the trend and does not mark a measured threshold.

How the pappus works

The gaps are part of the mechanism.

Air passes between the filaments. A region of slowed air forms around each one, and neighbouring filaments sit close enough for those regions to interact. The spread-out crown therefore behaves as a coherent aerodynamic object.

At filament scale, the measured Reynolds number was 0.422. The study estimates a mean spacing of roughly 41 filament diameters; the influence of neighbouring filaments might only become negligible beyond about 47.

Layers of slowed air around the filaments Five thin filaments are surrounded by regions of slowed air which meet and interact. ≈41 × filament diameter slowed air around each filament
Schematic section through five filaments. Dimensions are not to scale.
Filaments
≈100 95% CI: 95–106
Pappus diameter
13.8 mm 95% CI: 13.2–14.3
Terminal speed
39.1 cm/s 95% CI: 34.9–43.0

The speed was measured in still air across ten samples. It does not predict how far a seed will travel in wind.

The same measured force

The same force, far less material.

By the definition used in the study’s comparison, the pappus and the solid reference disk produce the same total drag at the same speed. The disk’s calculated diameter is 8.6 mm. Substituting the authors’ values in SI units gives an area of 57.7 mm²; the filaments add up to 12.6 mm².

solid diskpappus> 4× / mm²
Total drag is the same in this comparison. “More than four times” refers strictly to drag per unit projected area.

Where the comparison ends

A small-scale mechanism.

The result applies to the tested seeds and porous models. A human parachute operates at a different scale and in a different aerodynamic regime, so this ratio cannot be transferred directly.

What the authors measured

The team combined free-fall tests, a vertical wind tunnel, particle image velocimetry and microfabricated porous disks. The ten biological samples supplied the means and confidence intervals shown here.

How to read the drawing

The animation shows the mechanism schematically through an original drawing. It does not reconstruct the authors’ velocity field, identify a detachment threshold or predict a seed’s trajectory.

Reproduce the area ratio

The reference disk is defined by the same weight, the same speed and the solid disk’s drag coefficient:

Ddisk = √[8mg ÷ (CDρπU²)] = 8.57 mm

Substituting the authors’ values in SI units gives a disk area of 57.67 mm² and a filament projected area of 12.56 mm²:

57.67 mm² ÷ 12.56 mm² = 4.59 > 4

The paper states “more than four times”. The values in the prose are rounded and should not be divided to claim extra precision.

Primary evidence

Where the data came from

  1. Cummins et al., A separated vortex ring underlies the flight of the dandelion, Nature 562 (2018) The primary paper, DOI 10.1038/s41586-018-0604-2.
  2. Full accepted manuscript Paper text, methods, extended figures and confidence intervals.
  3. The authors’ MATLAB scripts Edinburgh DataShare, CC BY 4.0, DOI 10.7488/ds/2362.
  4. The authors’ video data Videos of the 75% porous disk, Edinburgh DataShare, CC BY 4.0, DOI 10.7488/ds/2363.

Sources checked on 23 August 2026. The illustrations and calculations on this page are original; experimental values are attributed to the study’s authors.