# The Aerodynamic Mechanisms of the Formation Flight of Migratory Birds: A Narrative Review
## 3 Results
### Theoretical and Experimental Studies
He also noted that in low-level formation flights of geese, the birds are extremely sensitive to disturbances from the ground, making it unlikely to find phase relationships between wingbeats. The first theoretical studies [28] were often carried out with simplifications, as the experimental facilities of the time were unable to quantify the forces exerted on the birds' wings, or to obtain precise information on the relative positions of the birds in relation to each other. It was only with the development of biologgers, capable of measuring energy expenditure, body movements (accelerometers), and individual positioning (GPS), that many of the key ideas could be tested [44; 45; 46]. One study, also considered pioneering for its experimental approach conducted with birds in flight, was carried out by [PERSON] et al. [13]. In this study, the authors used wireless technologies and miniaturized sensors to train eight white pelicans (_Pelectanus oncrotalus_) to fly in a V formation behind a motorboat and an ultralight glider in Djoudj National Park, Senegal. Flight sessions were filmed and sensors were used to measure wingbeat frequency and heart rates and estimate the birds' energy expenditure in flight. Pelicans flying in V formation showed a significant reduction in heart rate compared to birds flying solo. The observed reduction in heart rate suggests that flying in formation enables the birds to increase their flight endurance. Although some pelicans had difficulty maintaining their position in formation, the energy savings were nevertheless significant. The study concludes that the main advantage of V-formation flight may lie in the pelicans' ability to glide for longer periods by flying in the vortex wake, thus achieving substantial energy savings. This strategy translates into energy saving of between 11.4% and 14.0%. These energy saving values, although lower than those estimated in the theoretical studies of geese [11; 28], should be considered significant because pelicans flap their wings more slowly and glide for longer periods. Formation flying offers birds the opportunity to extend their range on migratory flights or foraging expeditions. The difficulty of studying living birds has prompted most researchers to adopt a purely theoretical approach. This is the case of [PERSON] et al. [47], who theoretically analyzed the V-formation of migratory birds, testing the two main hypotheses: aerodynamic advantage and enhanced visual communication. In this study, each bird is assumed to fly at a constant speed, and each segment of the linear formation is modeled as a chain of (N + 1) birds. The authors drew on the work of [PERSON] [48] to estimate the forces acting on the birds. The motion of each bird was modeled using [PERSON]'s equations, and force generation was analyzed using a linear model. The results suggested that spacing control is difficult when a predecessor-following strategy is implemented. The dynamics of the linearized system showed that tracking errors are amplified, requiring higher accelerations for birds far from the leader. The study by [PERSON] et al. provides a better understanding of bird organization strategies within a V formation, and these results can also be applied to Unmanned Aerial Vehicle (UAV) control devices. [PERSON] [49] also adopted a mathematical approach to better understand how birds manage to maintain an aerodynamically efficient formation. In his study, he sought to understand the mechanisms behind energy conservation by examining the existence, stability and self-organization of the formation flight used by migratory birds. The author argues that, due to the low flight speed and high Reynolds number, it is appropriate to treat air as an inviscid, incompressible fluid. While modeling air with this approach may offer simplifications, it inherently carries risks of underestimating or overestimating actual aerodynamic forces and overlooking significant phenomena.