This adorable example of everyday physics took me entirely by surprise. We’ve all seen a sweet little floating parade in the springtime at our local river or pond, with a mumma duck or goose followed closely by a line of babies paddling quickly to keep up. But I never really noticed that the spacings of each duckling is quite consistent down the line. Or that the formation tends to be single file much more than other possible arrangements. Why? It’s all about the wave pattern generated by the duck in the lead position and how the wakes of the other ducklings in line interact with that pattern. Scientists have recently concluded that these sweet little fuzzballs find the exact right position in line every time so that they can surf along with a boost of energy to keep them moving with ease.
It honestly makes me smile to think that I have witnessed a fantastic example of wave interference countless times without realizing it. The only reason I now understand what’s happening is because I stumbled across a lovely little paper in the Journal of Fluid Mechanics a month or so ago by a collaboration from the University of Strathclyde (Glasgow, Scotland) & Jiangsu University of Science & Technology (Jiangsu, China). This team set about modelling the fluid dynamics both mathematically and numerically, discovering that these wee fluffs are both cute and smart: when they swim at the ‘sweet spots’ behind mumma, they instinctively choose positions that correspond to dips in the overall wave pattern. For ducklings in positions 1, 2, and 3, riding the crest of a wave (just under their little butts) gives enough of a boost that it is energetically favorable for them to swim there. The model found that ducklings in positions beyond #3 don’t gain in energy, but there is also no energy loss to drag in the water – a delicate dynamic equilibrium is established. Plus, ducklings have been observed to switch up their order in line, which might be an egalitarian approach to sharing the surfing boost among sibs.
It honestly blows my mind a little that math and physics can explain why ducklings swim in single file and can even predict the positions they will choose behind mumma; this article by Yuan and team was a lovely discovery. Their paper also led me to an equally delightful experimental study in which biologist Frank E. Fish from West Chester University measured the mechanical effort exerted by ducklings swimming in formation, with and without the presence of a mumma generating a wake for them to swim in. Dr. Fish imprinted his subjects to a decoy and then had the babies swim behind the decoy in a tank in which the flow rate they swam against was controlled. The decoy was always visible in front of the ducklings, but it could be raised slightly above the water so that it didn’t create a wake.
Instinctively, the ducklings self-organized into single-file formation behind the decoy. Dr. Fish then analyzed video recordings from the side of the clear tank, calculating the arc length of the foot stroke taken by a duckling as a measure of the effort exerted. Mumma’s wake, when she was lowered into the tank, resulted in a reduction in effort for all the ducklings studied – more so for the younger babies (3 days old) than the older ones (14 days old). Consistent with the mathematical modelling from Yuan et al, by swimming in the sweet spots, the ducklings take advantage of wave interference to expend less energy to paddle along behind their mumma.
Even though I wasn’t actually wondering why in this instance, now I know the physics behind the formation! So next spring, when I see this amazing example of fluid dynamics in action, I’ll be smiling at both the spectacle and the science.
Wave-riding and wave-passing by ducklings in formation swimming, Zhi-Ming Yuan et al, Journal Fluid Mechanics (2021) vol 928 R2 doi:10.1017/jfm.2021.820
Kinematics of ducklings swimming in formation: consequences of position, Frank E. Fish, Journal of Experimental Zoology (1995) 273 1-11
Ducklings swimming behind mumma – Shutterstock.com ID 1381730477
Video of Canada geese family – taken by the author, May 2021, Rockwood, ON
Mathematical model results of the wave pattern and the coefficient of drag (CDR) for mumma duck and 6 babies – Figure 4 from Yuan, Z., Chen, M., Jia, L., Ji, C., & Incecik, A. (2021). Wave-riding and wave-passing by ducklings in formation swimming. Journal of Fluid Mechanics, 928, R2. doi:10.1017/jfm.2021.820 (Huge thank you to Cambridge University Press for believing in Open Access publishing!)
Close up of ducklings swimming behind mumma – same Shutterstock image as the opening file with red lines indicating wave crests in the overall pattern added by the author
Sketch of the experimental setup of Dr. Fish, Figure 1 from the Journal of Experimental Zoology (1995) 273: 1-11, Copyright Wiley-Liss Inc.