# The Aerodynamic Mechanisms of the Formation Flight of Migratory Birds: A Narrative Review
## 3 Results
### Theoretical and Experimental Studies
rating experimental data collected from birds in flight, is undoubtedly among the major contributions of the last decade. In 2015, [PERSON] et al. [53] used a similar research methodology to [PERSON] et al. [52] and [PERSON] et al. [13], training 14 young northern bald ibises (_Geronticus eemita_) to follow an ultralight paraplane in flight. The authors demonstrated a strong correlation between the duration during which a bird was leader of a formation and the time during which it had previously benefited from the wake of another bird. This temporal correlation suggests cooperation between birds directly taking turns to lead the formation. Interestingly, analyses revealed that these changes in pairs had a significant impact on the overall cohesion of the V formation. With the aim of better understanding the organization of birds within the group, [PERSON] et al. [54] used a mathematical method to investigate the intrinsic mechanism of V-formation. Using control-engineering principles, the authors incorporated visual communication constraints into a standard gradient-based control algorithm. Their simulation results show that the group of birds gradually converges towards a stable V-formation, which is consistent with flight phenomena observed in biology. This paper presents the development of a cost function aimed at achieving V-shape formation in bird groups, using control-engineering principles. This cost function incorporates visual communication constraints to ensure that each bird maintains a correct collision-free formation. In summary, the paper proposes a mathematical and control framework for achieving stable V-formation in bird flocks, balancing visual communication and collision avoidance through a carefully designed cost function and control algorithm. Using classical aerodynamic theory, [PERSON] and [PERSON] [55] theoretically investigated the aerodynamic advantages and energy efficiency of V-flight in Canadian  
Figure 7: The flapping of the wings creates a vortex that starts at the bird’s wingtips. A-A represents a virtual line that extends through the wingtips of the trailing bird (**a**). Vertical velocity can be plotted along this line A-A (**b**). From (**b**), we can see that the airflow at the center of this wake is directed downwards (downwash; in blue); in this area, the velocity is negative, while the area outside each wing represents an upwash region (in red), where the velocity is positive. A bird flying in the wake of the one preceding it can reduce its energy expenditure by taking advantage of the upwash in the wake of the leading bird (a, side view; b, front view). geese. The results of their study confirmed that the lead bird consumes the most energy, while subsequent birds benefit from reduced drag. They calculated the energy required for migration and the total drag of the flock, demonstrating the benefits of position rotation in increasing flight time and distance. Their study revealed that changing position within the flock can improve flight time and distance travelled by over 44.5%. This research highlights strategic formation and load balancing in migrating Canada geese, optimizing their energy consumption and flight efficiency through collaborative behaviors and aerodynamic advantages. Also theoretically, [PERSON] et al. [56] investigated the effects of wingtip spacing on total drag in a group of bald ibises. Using existing mathematical models [9; 40], the authors carried out an aerodynamic study on bald ibises in flocked flight. They determined the percentage drag reduction of individual ibises and showed that ibises can save energy by flying in formation. The results indicated that as the number of ibises in a group increases, the drag force of each individual ibis decreases. Depending on whether the number of birds is even or odd, there are always one or two ibises in the middle with the lowest drag value.