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Stingers Have Achieved Optimal Pointiness, Physicists Show:

The spines of a cactus, the proboscis of a mosquito, the quills of a porcupine: straight, pointed objects serve a plethora of functions in nature. Yet no matter the size, from bacteriophages' nanometer-scale tail fibers to narwhals' two- or three-meter-long tusk, these structures tend to be long and slender cones whose base diameter is much smaller than their length. Now researchers have used physics to explain why this narrow shape is optimal for stingers and other piercing objects—including human-made tools such as hypodermic needles.

A stingerlike object's dimensions are limited by two opposing constraints. To puncture its target, it must apply a force large enough to overcome the pressure created by friction. At the same time, this force must be smaller than the "critical load," the maximum force that the structure can support without bending or breaking. A large range of geometries, from long and narrow to short and wide, satisfy both constraints. Yet living organisms do not exhibit all the possible variability. Instead nature seems to prefer narrow designs with a base-diameter-to-length ratio of around 0.06.

[...] Jensen and his graduate student Anneline Christensen devised a simple theoretical model for a solid conical stinger at the edge of stability. Their calculations predicted that the optimal base diameter depended on only three factors: the object's length, the stiffness of its material and the friction from the pressure of the target tissue. The dependence on stiffness and pressure was weak: doubling the stiffness would allow the base diameter to decrease by only 21 percent, for instance. It was primarily the relationship between diameter and length that intrigued the duo.

[...] To see if a linear relationship held in the natural world, Jensen's team compiled the dimensions of nearly 140 stingers, spikes and spines in living organisms. Vertebrates and invertebrates, land and sea creatures, and plants, algae and viruses all had structures that matched the new model. Almost 100 human-made "stingers" such as needles, nails and arrows also aligned with the researchers' predictions. "It's always nice when you do some kind of theoretical work, and then you see it applies to something in real life," Christensen says. "It's not just an equation on a piece of paper."

Journal Reference:
Kaare H. Jensen, Jan Knoblauch, Anneline H. Christensen, et al. Universal elastic mechanism for stinger design, Nature Physics (DOI: 10.1038/s41567-020-0930-9)

Original Submission