PROVIDENCE, R.I. [Brown University] — Scientists have known for years that birds like geese and ibises get an aerodynamic advantage from flying in a “V” formation. Now, researchers from Brown University have provided new insights into the nature of that advantage.
In a study published in Proceedings of the National Academy of Sciences , Brown researchers Olivia Pomerenk and Kenny Breuer developed an aerodynamic model that simulates the forces at play when one flapping bird — specifically a northern bald ibis — follows another behind and off to the side, the classic V formation sweet spot. The model showed that birds in that position experience an 11% reduction in the mechanical power needed for flight. Those savings are driven largely by a reduction in the vertical distance of their wing flaps.
“The big change we see in this position is in the amplitude of flapping,” said Pomerenk, a postdoctoral researcher in Brown’s School of Engineering. “At least for this specific bird species, we're looking at an amplitude that is something like 70% of what it would be if the bird were flying alone. That’s a pretty dramatic change.”
Breuer, a professor of engineering and of ecology, evolution and organismal biology at Brown, has long been interested in animal flight. His lab at Brown, which is equipped with a custom-made wind tunnel festooned with high-speed cameras, has made numerous discoveries about the flight dynamics of both bats and birds. Experiments done with starlings in the wind tunnel a few years ago helped to confirm that the V formation does help trailing birds save energy — reducing the energetic cost of flight by 25% in wind tunnel flights.
The energetic benefit is likely linked in some way to wingtip vortices, tiny horizontal tornadoes that spin off the tips of each wing. The airflow from those vortices creates an area of aerodynamic “downwash” directly behind the bird, and an area of “upwash” off to the side. That upwash zone, Breuer and Pomerenk say, is the likely source of the aerodynamic advantage, but exactly how it translates into less work for a bird was a mystery. That’s what this new model attempts to reveal.
A major question is whether the upwash generates extra lift for the birds, or extra thrust.
“If I'm a flying bird, I have two problems to solve,” Pomerenk said. “I have to generate lift so I can counter gravity, and I have to generate thrust so I can fly forward. Those two problems both require energy to solve, but they might be affected differently by flying in another bird’s wake.”
Prior research has either oversimplified the problem or overcomplicated it, Pomerenk says. The simplest models treat birds much like fixed-wing aircraft. That eliminates the dynamics introduced by flapping, which are of obvious importance to bird flight. But the more complicated models and real-world experiments are problematic too, often burying important dynamics in a jumble of complexity.
The researchers’ new model breaks the problem down to the essentials. Using prior experimental research on northern bald ibises, Pomerenk and Breuer carefully modeled the wake produced by a single flapping bird, then added a second bird flying in that wake. Because the lead bird is flapping its wings, its wake undulates vertically with each flap. To capture the effects of that undulation on the trailing bird, the model breaks the action down into a series of snapshots over time.
“If I press freeze on the world, we’re left with a wake that’s in a certain position and a follower's wings in a certain position,” Pomerenk explained. “There are a bunch of fluid dynamics theorems that you can apply in sequence to arrive at the forces on the trailing bird at that moment in time.”
By adding those snapshots up, the model zeros in on the effects of the undulating wake. The work showed that a lead bird’s wake reduces the need for a trailing bird to generate thrust. That enables the bird to reduce the amplitude of its flaps, which in turn saves energy. All of the model findings are consistent with experimental observations but add a much-needed explanation for how exactly a leading bird’s wake translates into an easier ride for a trailing bird.
That explanation could be applied beyond avian flight.
“There are also implications for engineered systems,” Breuer said. “All of this can also be applied to understanding how to best operate swarms of drones used in agriculture or firefighting, for example.”
Pomerenk says she’s hopeful that the model of two-bird interaction can eventually be incorporated into a larger model of avian flight that includes social and behavioral dynamics. In that way, the work could prove an important step in understanding the formations and murmurations that have long fascinated birdwatchers and scientists alike.
The research was supported by the U.S. Office of Naval Research (N00014-21-1-2816) and the U.S. National Science Foundation (IOS-1930924).
Proceedings of the National Academy of Sciences
A minimal wake–vortex model explains formation flight of flapping birds
21-Jul-2026