Physicist Zhi-Ming Yuan and his colleagues at the University of Strathclyde are the recipients of this year’s Ig-Nobel prize in physics for their research into the reason ducklings swim in formation behind their mothers. It is hoped the research could be applied to explain the formations of other swimming birds, such as swans, as well as being used to make water transport more efficient.
The ideas behind duckling formation are similar to those behind surfing – the wave patterns on the water interact with the ducklings swimming on the surface pushing them forward. This makes it easier for the ducklings to swim.
Picture a duckling on a flat-level surface of water. The weight of the duckling acts vertically downwards, and the equal and opposite buoyant force acts upwards on the duck. If the duck is on a wave, then a component of the buoyant force is in the direction the duck is swimming. If the duck is in front of the wave, this acts in the same direction as the motion of the duck, making it easier to swim.
The problem gets a little more complicated when considering a group of ducks on the surface of the water, as they all produce wave patterns that interact with each other in a process called ‘interference’.
The team at the University of Strathclyde modelled the mother duck as a large ellipse and the ducklings as small ellipses following behind. They then simulated the positions of the ducks in the wave pattern that allowed them to use minimal energy to follow their mother.
They found that the ducklings should keep the same speed as their mother and that, unlike in the surfing case, the ducks should swim in the troughs (dips) of the wave pattern produced by the mother duck in order to be propelled by the waves. This is unlike the surfing case because the waves produced by the mother and the ducklings themselves interfere making this position in the wave favourable.
This simulation provides a physical motivation for the synchronised swimming formations seen in ducks, swans, and other birds. Beyond just following their mother, these formations allow the small ducklings to ‘ride’ the wave their mother creates, making it easier to swim.