Researchers at Cornell University have developed a 3D computational model that decodes the complex physics behind how insects and birds maintain stable flight. 

This research provides the missing link between how animals evolved to fly and how we can finally build robots that do the same. 

Particularly, the team identified five key physical dimensions of “passive stability” that could redefine both biology and robotics.

Dimensions of flight

It was long believed that most insects were inherently unstable and required constant neural corrections to stay airborne. 

However, this new model revealed an anti-resonance state — a mathematical “sweet spot” where the coupling of wing inertia and body motion allows an animal to remain stable automatically, even during air turbulence. It suggests that passive stability is far more common in nature than previously realized.

The new model overcame the limitations of previous ones that only mimicked real-world insects. It allows the exploration of a wide range of theoretical wing-and-body configurations. 

To simplify the complex dynamics of flight, researchers condensed their 3D simulations into a streamlined model focused on five core variables: the wing-to-body mass ratio, wing loading, hinge placement, stroke frequency, and flap amplitude. 

These parameters define a “five-dimensional space” that captures the essential interplay between a flyer’s physical shape and its movement.

“The power of this model is to give us something much more explicit than what we had before. We knew the fundamental physics. By capturing the essential physics in the new model, we can understand each piece conceptually as well as facilitate computation to explore a large parameter space,” said Z. Jane Wang, professor of physics and mechanical and aerospace engineering in the College of Arts and Sciences and Cornell Duffield College of Engineering.

Future robots

Analyzing flight data across five dimensions yielded two formulas that define a sweet spot for stability known as anti-resonance. This state relies on a precise balance between wing inertia and body mass, allowing animals to achieve passive stability. 

By mastering this interplay of frequency and physical proportions, fliers can automatically counteract air turbulence and maintain steady flight without constant active correction.

“All of a sudden, we found that many forms of flapping flight have passive stability, which surprised us initially, because work so far showed that most insects, except one or two, are passively unstable, hence the necessity for neural circuitry to control them,” Wang said.

“But when we expanded the morphological space, we realized that what we studied before are but a few dots in this new view,” the lead researcher added. 

Engineers can now design flapping-wing robots that are pre-tuned for stability. This reduces the need for complex, heavy feedback sensors and processors, simplifying the design of agile micro-drones.

Beyond robotics, this streamlined model offers a faster computational method for classifying winged species and charting the evolutionary path of flight traits in nature. It could help understand why certain wing shapes or frequencies were selected over millions of years.

“During evolution, various traits are selected, but we don’t have much idea about what they are, let alone understand why they are being selected and how they evolve, apart from a very few examples, such as an eye,” Wang said.

The study provides a quantitative framework for solving the biggest puzzles in biological evolution and robotic engineering.

The study was published in Proceedings of the National Academy of Sciences.