Some of the best technology is the oldest. Sandbags have been used by armies to stop bullets since the Napoleonic Wars, because the granular medium is very efficient at absorbing the energy of the projectile and dissipating it as friction between grains.

Experiments on the shock-absorbing capabilities of granular materials generally show that a projectile penetrates only to a shallow depth before coming to rest. Military researchers hope to exploit this property in armour that might be considered a sort of 'advanced sandbag', with grains tailored for maximal stopping power — for example, arranged as tapered chains of gradually increasing or decreasing grain size, sandwiched between confining plates1.

But anyone who studies granular media knows well to take nothing for granted. For instance, they can switch between solid-like and fluid-like behaviour in response to vibration or shearing — a dangerous capability in the case of seismic hazard. Some lizards exploit that duality to actually swim through sand, using an undulatory motion to control the solid–fluid transition2.

Even bearing such subtleties in mind, a new observation of projectile motion in a granular medium by Pacheco-Vázquez and colleagues3 is remarkable. They find that an object penetrating into grains under gravity can, in some circumstances, acquire a finite terminal velocity — in other words, it never comes to rest, but penetrates to (in theory) an infinite depth.

The researchers demonstrated this experimentally by dropping heavy balls (ping-pong balls filled with small steel spheres) into a deep silo of expanded polystyrene beads a few millimetres in diameter. The beads are packed loosely by first blowing air through them: the packing fraction of 0.637 sounds rather close to the random close-packed fraction of 0.64, but in fact the bed is rather less than close-packed because of the polydispersity of bead sizes.

Balls of lighter mass come to rest within the column of grains, but above a certain mass threshold they sink all the way to the bottom. In the latter case the balls appear to reach a constant speed as they descend. This, Pacheco-Vázquez and colleagues argue, is a genuine terminal velocity.

As counter-intuitive as it might seem, the behaviour is not hard to rationalize. One of the striking properties of granular media is that, below a certain depth, the pressure reaches a constant value — in contrast to the case for ordinary liquids, where pressure continues to increase with depth. This pressure determines the friction experienced by a descending particle, and so it is possible for the drag to balance the downward force due to gravity, just as with an object falling at terminal velocity in a normal viscous fluid.

However, these situations are not identical. Resistance to the projectile's motion is caused by the temporary formation of chains of grains in contact. This means that the force of resistance fluctuates, so that descent proceeds in a jerky, stick–slip fashion — as the researchers' simulations confirm. They end with what sounds like a warning for military sandbag engineers: in certain circumstances, they say, “we believe that self-propelled intruders in static sand may also reach terminal speeds.”