one capsule · thirteen wet cells · no crossbar
The Catapult
Under the Fern
The 13-cell annulus measured in Polypodium aureum stores elastic energy as water leaves, cavitates near -100 ± 14 bar, and recoils in about 30 microseconds. Then a roughly 5-millisecond poroelastic relaxation supplies the missing crossbar. Operate both time scales and watch why the trigger alone is not enough.
Start with the water. Pull its pressure down through the marked median cavitation threshold. This run treats that 50% point as the trigger so that the mechanics can be repeated. A real sporangium cavitates probabilistically, not on command.
Load the ring until the water breaks
The drawing is slowed and enlarged. Its angle follows the normalized two-mode response stated below; it is not traced from a specimen video.
Drag right. The demonstration fires at the published 50% cavitation pressure, -100 bar, equal to -10.0 MPa.
Only the pore-flow time changes. The starting bend, fast recoil time, and normalized stored energy stay fixed.
Loaded. Pull past -100 bar to cavitate.
The annulus is bent backward; the 13 cell walls hold the elastic load.
What just happened
The bubble is a trigger, not the trick
Evaporation lowers cell volume and bends the annulus backward. Negative pressure in the cell water balances that elastic load until bubbles break the continuous water columns. The walls then recoil. The 2016 measurements place the 50% cavitation point at a pressure magnitude of 100 ± 14 bar, which is 10.0 ± 1.4 MPa.
The spores have no miniature release catch. They leave when the annulus changes speed sharply after its first movement. With the measured hydraulic resistance, the inertial motion finishes while most of the remaining closure is still waiting on water moving through the cell wall. Collapse that delay toward the inertial time and the two motions merge. The normalized model then has no distinct arrest from which to throw.
Depth layer · remove the crossbar
How far apart must two clocks be?
A drying spring is not yet a useful catapult. Llorens and colleagues state the design condition as an ordering: the inertial recoil must be much faster than pore flow, and pore flow must remain much faster than the roughly 100-second opening time.
Move the pore-flow clock. The green judgment uses the paper's explicit lower criterion, at least two orders of magnitude between inertial recoil and hydraulic relaxation. It does not invent an upper boundary inside this slider.
Timescale bench
Same fast period: 28.4 μs. Only the pore-flow relaxation moves.
The scale is logarithmic so the 30-microsecond and millisecond clocks can share one rail.
Measured means. The rounded 30 μs and 5000 μs figures give 166.7×; the paper describes the design separation as about 200.
The animated angle is a normalized reduction, with a disclosed 40% fast component and 60% pore-flow component:
The 40:60 split is a visualization choice, guided by the earlier report of 30 to 40% closure in the fast phase. The published full model is a damped inertial term plus two exponential relaxations. No angle or launch speed is inferred from this normalized curve.
The check
Measured anchors on one side, independent mechanics on the other, then two poisoned inputs that must be rejected.
| assertion | published anchor | independent route | result |
|---|
The fast-period route uses beam geometry and stiffness, not the measured period. The pore-time route uses viscosity, wall thickness, permeability, and Young's modulus, not the measured pore time. A checker with teeth must also reject wrong mechanics, so both corruptions are printed above. Re-run offline with node research/the-catapult-under-the-fern/verify-the-catapult-under-the-fern.mjs.
Measured, and species-specific
The 13-cell count, geometry, -100 ± 14 bar pressure, 28.4 ± 9 μs inertial period, 5.3 ± 3.5 ms hydraulic relaxation, and speed up to 10 m/s come from work on Polypodium aureum. Leptosporangiate fern annuli vary. These figures are not universal means.
Free choices, plainly named
- The median cavitation pressure is used as a repeatable trigger, though cavitation is probabilistic.
- The drawing is slowed, enlarged, and uses a normalized 40:60 response.
- The useful boundary is the paper's stated ratio of at least 100, not a fitted launch threshold.
- The no-brake button sets τ to 0.03 ms. That is a counterfactual, not a measured fern.