Understanding how animals navigate through space is crucial for many scientific fields. In particular, studying insects can aid engineers in the development of a new type of drone. For instance, research vehicles that can fly in narrow tunnels, hover in the air, and land on vertical and steep surfaces.
To address these issues, a team of Russian scientists has proposed a new computational model for mosquito flight. The work was published in Communications in Nonlinear Science and Numerical Simulation—an international academic journal dedicated to methods of mathematical modeling and analysis.
The researchers explained that the interest in studying mosquito flight stems from the fact that these insects possess one of the most unique techniques for generating lift. Their flight results from two oscillatory motions: twisting and flapping. A mosquito's wing undergoes frequent oscillatory movements with a small amplitude (around 400). Additionally, at the end of each upward and downward stroke, it slightly twists, creating additional vortices at the edge of the aerodynamic surface and increasing vertical thrust.
The proposed computational model is based on just six equations. This simplicity allows for significant savings in computational resources. At the same time, an exclusive algorithm was implemented in building the model, which accounts for the deformation of the computational grid considering the bending and flapping of the wings through a dynamic transformation method. This way, the researchers could take into account the movement of airflows created around the mosquito's body during flight.
“During our work, we constructed an accurate mathematical model of the insect's movement in the air. It allows us to calculate, roughly speaking, not only how a small creature flaps its wings but also what happens to the airflow around it. As a result, the algorithm enables the construction of the corresponding pressure fields and the calculation of lift,” explained the lead researcher, Viktor Kazantsev, head of the Neurobiomorphic Technologies Laboratory at MIPT and head of the Department of Neurotechnologies at NNSU.
In particular, thanks to the new model, the wingbeat frequency necessary for the insect to hover in the air was calculated. According to the researchers' findings, this value is between 800-820 cycles per second. The obtained data matched earlier experimental calculations, confirming the predictive accuracy of the proposed algorithms. Furthermore, the scientists determined that the increase in lift generated by the insect's wings is proportional to the square of the frequency of their oscillations.
“The mosquito's wing has a relatively simple shape. This allows us to use the calculations obtained as a basis for developing more complex models. For example, those that describe the flight of birds, whose forelimbs change their geometry while flapping,” said Viktor Kazantsev.
Additionally, according to the scientists, the proposed models could serve as a foundation for developing drones based on the principles of mosquito flight. Technologies for recreating the wing movements of such biomimetic devices with high-frequency oscillations already exist.