Lead the Ducklings
Gather the ducklings, keep the line tight, get home before sunset. Back to the game
How to play
You are a mama duck on a pond painted on notebook paper. Your ducklings have paddled off in every direction, and the sun is going down. Press and hold anywhere on the pond (or drag your finger) and mama swims toward that spot; let go and she glides to a stop. On a keyboard, steer with the arrow keys or W A S D. Swim close to a duckling and it imprints on you and joins the end of a wobbly single-file line. Press Quack (or Space or Q, or tap mama) to call any lost duckling nearby, and it paddles over to you. Bring the line into the reed nest marked home; when every duckling is tucked in before sunset, the whole family snuggles down for the night. R restarts a pond, and Ponds lets you pick any pond you have unlocked.
The eight ponds add more ducklings, a stream that pushes everyone downstream, drifting logs, a hungry pike shadow that circles under the water, and lily-pad mazes. Nobody ever gets hurt: if the pike passes a duckling that has fallen out of line, the duckling just gets a fright and scatters, and you have to go back for it. Finish with plenty of daylight left for three stars.
The real science: the Kelvin wake
Look behind mama as she swims and you will see a V of ripples drawn in ink. That V is a Kelvin wake, and its angle is one of the neatest results in physics. In deep water, anything moving steadily across the surface, from a duckling to a supertanker, makes a wake whose edges sit at 19.47° either side of its path, an angle of arcsin(1/3). It does not depend on speed. Lord Kelvin worked it out in 1887: water waves of different lengths travel at different speeds, and their energy moves at only half the speed of the crests, which pins the edge of the pattern to that fixed angle. Inside the V you can see two families of waves: curved transverse crests that run across the track, and short divergent wavelets feathering off the arms. In the game the pattern is attached to mama and moves with her, just as a real wake is.
Why ducklings swim in a line
For a long time people assumed ducklings follow their mother in single file for safety. In 2021, Zhi-Ming Yuan and colleagues calculated the wave drag on ducklings swimming behind a mother duck (Journal of Fluid Mechanics, volume 928). A duckling at the right spot just behind its mother can ride her wake: the waves push it forward instead of holding it back. Further down the line the effect is passed on (they called it wave-passing), and from the third duckling onward the wave drag on each one is close to zero. In the game, ducklings sitting in the wave just behind the one ahead glow blue, and the more of them that ride the wake, the faster the whole family can swim, up to 35 percent faster. Sharp turns break the line, so smooth, gentle curves are quickest.
Imprinting, and why ducks stay dry
Newly hatched ducklings and goslings follow the first moving thing they see. Konrad Lorenz made this famous in the 1930s when greylag goslings imprinted on him and followed him around in a line. Later experiments with mallard ducklings found the sensitive window peaks around 13 to 16 hours after hatching and has almost closed by about 36 hours. Ducks float high because their down and feathers trap a thick layer of air, which makes the bird far less dense than water. Oil from the preen gland at the base of the tail, spread with the beak, together with the fine, hooked structure of the feathers, keeps water from soaking in.
Tips
- Swim at a steady pace in long, gentle curves. Ducklings riding the wake keep up easily; ducklings that fall out of it slow down.
- Quack early: a call brings in every lost duckling within a few duck lengths, so you do not have to visit each one.
- Cross a stream by aiming upstream of where you want to land.
- You can drop off part of the family at the nest and go back for the rest.
- Around the pike, a short, tight line is a safe line.
Love animals moving together? Watch thousands of starlings in ../murmuration/, or lay a scent trail in ../follow-the-ants/.
Questions people ask
- Is Lead the Ducklings free?
- Yes. It runs in your browser on phones, tablets and computers, with no download and no account.
- What angle does a duck’s wake make?
- In deep water the edges of the wake sit about 19.47 degrees either side of the duck’s path (arcsin 1/3), whatever its speed. This is the Kelvin wake pattern, and ships make the same one.
- Why do ducklings swim in a line behind their mother?
- Riding in the waves just behind their mother lets them swim with less effort. Yuan and colleagues (Journal of Fluid Mechanics, 2021) showed a duckling at the sweet spot is pushed forward by her waves, and from the third duckling on the wave drag is close to zero.
- Can the pike eat the ducklings?
- No. It is a cosy game: if the pike passes a duckling that has fallen out of line, the duckling only gets a fright and scatters, and you can gather it up again.
- How do I play with a keyboard?
- Arrow keys or W A S D swim, Space or Q quacks to call nearby ducklings, and R restarts the pond. Enter or Space chooses the highlighted button on the end card.
