Natural and human-made stingers follow universal design principles

Plants and animals of all shapes and sizes have evolved sharp, pointed outgrowths. Their uses vary widely, from injuring predators and delivering poison to providing buoyancy and adhesion. Despite their apparent diversity, stingers have inherent similarities. According to Kaare Jensen and colleagues at the Technical University of Denmark, natural stingers exist at the threshold of stability; they’re just strong enough to penetrate their targets without buckling. For straight, rigid stingers, the researchers turned that stability criterion to a relationship between length L and base diameter d₀ that accurately describes more than 200 natural and human-made examples, including wasp stingers, cactus spines, hypodermic needles, and lances.

For a stinger to penetrate a target, the force F inserting the stinger must be large enough to overcome F_f, the frictional force resisting it. The force also shouldn’t be so strong that the stinger buckles, as illustrated in the diagram. The stinger’s tapered structure can be made more resistant to buckling by increasing d₀ or decreasing L, but that has a cost: A larger stinger requires more material, and a shorter one has a reduced range.

The most economical option, Jensen and colleagues argue, is for the frictional and insertion forces to be equal and for that value to be just below the buckling threshold. By starting from that assumption and plugging in expressions for the frictional force and buckling threshold on a tapered column, the researchers found that d₀ and L are linearly related. Their proportionality constant depends on the frictional force per unit area on the stinger, μp₀, and its Young’s modulus E.

The graph above shows data from the researchers’ experiments and from the literature plotted with the model’s prediction (black diagonal line). The data, which include stinger lengths ranging from 40 nm to 4.5 m, diameters from 3 nm to 13 cm, and moduli varying over six orders of magnitude, generally follow the linear prediction. However, nature is often more nuanced than a simple model. For example, some insect ovipositors, which insert eggs, are designed to bend slightly during insertion, and plant thorns can be hollow or have otherwise heterogeneous compositions that affect their buckling. Those features cause physical properties to deviate from the predicted values.

The current model leaves out a wide swath of geometries, including fangs, curved stingers, horns, and claws. Jensen and colleagues expect that their force criterion will still hold in those systems. Extending their model, however, will require expressions for frictional forces and buckling thresholds in each of those other geometries. (K. H. Jensen et al., Nat. Phys., 2020, doi:10.1038/s41567-020-0930-9 .)