Kinetic energy is key to a successful strike

Getting bitten, clawed or stung is never a pleasant experience.But a trio of researchers in the US firing arrows into cubes of gelatin have uncovered a fundamental predictor of how well a fang or claw or sting will puncture flesh.

The work, led by Philip Anderson at the University of Illinois at Urbana-Champaign and colleagues, shows a projectile’s kinetic energy – that is, energy due to its motion – is a better indicator of piercing ability than its mass.

It follows the equation governing kinetic energy, which is equal to half of the mass multiplied by velocity squared. “This means that one potential way for small animals to puncture and get through tough materials, even with a low mass, is to increase their speed,” Anderson says.

And when you look at animals equipped with piercing equipment, this rings true. A snake can strike at three metres per second – a blink of an eye to us. But a jellyfish’s stinging cells, nematocysts, are almost seven orders of magnitude smaller than a fang and propel at a blistering 38 metres per second.

To emulate a puncturing animal, Anderson and his colleagues fired carbon fibre archery arrows of identical shape but varied mass and speed into cubes of ballistic gelatin from 90 centimetres. The gelatin, which simulates the density of human flesh, was photoelastic, meaning light travelling through it was bent as it warped and strained.

The whole experiment was filmed with two cameras set to 40,000 frames per second.

Over the course of 20 arrow shots, they noticed a pattern. Stress waves peeled off and propagated from the front and sides of the impact point as the surface pushed in. After three or four milliseconds following impact, the gelatin tore.

Once the arrow stopped moving forward, the elastic energy stored in the compressed gelatin in front of it forced it backwards. In nine of the 20 arrow shots, the arrow was spat back out again.

High-velocity impacts, they write, maximise the efficiency of the projectile, and ensure more of the kinetic energy is transferred into the tearing the “skin” surface rather than simply deforming it, as happens in steady, slow impacts.

Indeed, firing an arrow at high speed reduced the amount of time the gelatin surface “pushed in”.

As animals get smaller, particularly down to the micrometre range, the mass of their piercing weapons also decreases, which reduces their kinetic energy. This is why, to compensate, they increase projectile speed.

The researchers acknowledge that their study doesn’t take the projectile morphology into account – just mass and velocity – nor does it test how different “flesh” reacts to puncture.

But, they say, it’s the first step to understanding how nature has developed firing mechanisms to best use teeth, claws and tentacles to hunt or protect itself.

The work was published in Interface Focus.