(Credit: © Daniel Dunca - stock.adobe.com)
In a Nutshell
- Mathematical modeling shows a bird could, in principle, land at zero speed, but only after flying unrealistically far and fast.
- Without flapping their wings, birds landing on open ground can never fully reach zero touchdown speed, so their legs and muscles must absorb the leftover force of motion.
- Flapping the wings likely lets birds trade a glide’s huge looping approach for a shorter, tighter path into a perch, not simply a slower one.
A pigeon has the physics on its side to land as softly as a feather settling, coming to a dead stop the instant it reaches its perch. Pulling that off, though, would mean rushing in at 36 meters per second, more than double its normal cruising speed, then looping through a long, climbing detour to bleed all of it away. That is the odd result from a new model of how birds land without flapping, a maneuver so impractical that almost no bird ever tries it.
A team of engineers built a mathematical model of how birds glide to a landing, like when a hawk swoops onto a perch or a pigeon drops onto a ledge. Writing in Proceedings of the Royal Society A, they calculated the best way for a bird to angle its wings to land as slowly as possible. The result: a perfectly soft, zero-speed landing is no fantasy; it’s physically possible, but only if the bird first flies an unusually long, high approach. Most birds don’t fly that way, and that gap between what’s possible and what birds actually do points to the hidden trade-offs behind every landing.
Beyond the zero-speed puzzle, the research explains why birds landing on open ground can never pull off this trick at all, and why hawks swoop into perches the way they do. Together, the findings offer a window into one of the most demanding moments in a bird’s life: the few seconds between flying and standing still.
How Scientists Modeled a Bird’s Final Seconds in the Air
Researchers built a simplified physics model that treats a landing bird as a single object moving through the air, held back by gravity and pushed around by the lift and drag its wings create. In this model, the only thing the bird can control is how much it tilts its wings against the oncoming air, since birds appear to have fine control over that tilt even when moving very slowly.
Rather than building the model around one species, the team designed it in general terms so it could describe landings for birds of nearly any size, pulling out rules that should apply broadly to gliding birds. From there, they used a mathematical approach that tests countless possible flight paths to find the single best one, calculating how a bird should angle its wings moment by moment to land at the slowest possible speed.
Zero-Speed Bird Landings Are Possible, But the Price Is Steep
Running the numbers produced a clean result: a zero-speed landing requires a flight path that curves upward into a near-vertical climb at the final instant, with the wings angled to squeeze every bit of lift from the air as the bird slows. In the model, a bird following this exact strategy from the right starting position and speed comes to a complete stop right at the landing site.
Applying the math to a pigeon-sized bird shows why this approach rarely works in practice. Reaching that near-vertical finish would require roughly 60 meters of horizontal travel and 20 meters of climbing, all at an approach speed more than double what a pigeon normally cruises at. For a bird moving through city streets or a crowded forest canopy, that much space simply isn’t there most of the time. Larger birds would need even more room, since these distances grow with body size.
This mismatch points to a reason birds flap their wings while landing that goes beyond simply slowing down. Flapping likely lets birds reduce the space a landing requires, trading a glide’s demand for huge looping distances for a shorter, tighter, more energy-costly approach. A steep climbing path could also make it harder for a bird to keep its eyes on the perch it’s aiming for, another possible reason birds skip the zero-speed strategy even when physics allows it.
Why Zero-Speed Landings Fail on Open Ground
Open ground presents its own problem: a bird obviously cannot dive below the surface it’s landing on. When the model only allowed flight paths that descend toward the ground rather than climb, a true zero-speed touchdown became impossible. Every unpowered ground landing, according to the math, leaves some leftover speed and motion that has to go somewhere.
That leftover energy has to be absorbed by the bird’s body, mainly through its legs. Birds landing on firm ground need strong enough legs to handle that impact safely, a requirement the researchers suggest could have shaped how bird legs and muscles evolved over time. Their model also offers a possible reason waterfowl like ducks, geese, and swans land differently on water than on solid ground: water can absorb far more leftover energy at touchdown, which may explain why some heavier birds favor splashdowns over ground landings.
Testing the Model Against Real Hawk Landings
To see whether the math actually explains bird behavior, researchers compared their model’s predictions to real flight data collected earlier from Harris hawks flying between two perches. These birds are known for a distinctive swooping path that dives low before curving back up to land. An earlier explanation for this dive suggested hawks were trying to minimize the total distance they covered while flying with stalled wings, the point where wings begin losing much of their lift.
Their new analysis found that explanation alone doesn’t fully capture what’s going on. Testing a strategy that minimizes only the time spent stalled, apart from distance, produced touchdown speeds fast enough to hurt a real bird. The best match to actual hawk flight paths came from a strategy that balanced two things at once: keeping touchdown speed low and limiting time spent in that wobbly, low-control stalled phase, with touchdown speed carrying somewhat more weight in shaping the swooping path. Diving down first, combined with wingbeats that add extra thrust, lets a hawk build enough speed to pull into the steep climb that produces a gentler landing.
None of this changes how a pigeon dropping onto a windowsill or a hawk settling onto a branch looks to an observer, but it explains why those landings happen the way they do. Perfectly soft landings aren’t off the table physically, they’re just impractical given the tight spaces birds actually fly through. On open ground, where a soft stop is mathematically out of reach, birds are stuck absorbing leftover energy with their legs, a built-in cost that may have nudged bird anatomy in a certain direction over millions of years.
Physics, then, is more than background detail. It has likely shaped how birds are built every time one comes in to land.
Paper Notes
Limitations
The study relies on a simplified point-mass model of flight dynamics that neglects rotational motion, assuming birds have near-ideal control over their body pitch, and does not explicitly model time-varying effects of wing flapping on aerodynamics within a single wingbeat. The lift and drag equations used are described as representative of bird wings across a broad range of conditions but are noted to underpredict and overpredict certain aerodynamic coefficients for some angles. Unsteady aerodynamic effects, such as those caused by rapid changes in wing angle, were explored only through a sensitivity analysis rather than being built directly into the core model. The comparison to real bird behavior drew on previously published experimental data on Harris hawks performing perching maneuvers between two perches, rather than new animal experiments conducted for this paper, and also used published morphological data for a pigeon to illustrate scaling examples.
Funding and Disclosures
The Biotechnology and Biological Sciences Research Council supported this work (grant no. BB/T008725/1). The authors declared no competing interests and stated that they did not use AI-assisted technologies to create the article.
Publication Details
Paper Title: “Flight dynamics and optimal control of unpowered avian landings”
Authors: Tom Rottier, Philippe Lavoie, and Ben Parslew, affiliated with the Mechanical and Aerospace Engineering Department at the University of Manchester and the Institute for Aerospace Studies at the University of Toronto. Corresponding author Tom Rottier can be reached at [email protected].
Journal: Proceedings of the Royal Society A, volume 482, article 20260103,
Supplementary material is available at https://doi.org/10.6084/m9.figshare.c.8693487







