# The Aerodynamic Mechanisms of the Formation Flight of Migratory Birds: A Narrative Review
## 3 Results
### Theoretical and Experimental Studies
In line with theoretical studies by [PERSON] and [PERSON] [28], they pointed out that migratory birds such as geese, flying within a V-shaped formation, could save a significant amount of energy through mutual aerodynamic interaction. They also suggested that a tall, narrow flock would actually experience an increase in drag. They also tentatively concluded that improved flight efficiency was not a sufficient reason for migration in large, three-dimensional flocks. Their theoretical study did, however, make a significant contribution to the scientific literature of the time. A few years later, [PERSON] and [PERSON] [6] questioned the theory of formation flight and focused on the V-formation observed in Canadian geese. [PERSON] and [PERSON]'s measurements on Canadian geese initially cast doubt on the aerodynamic advantage of V-formation. This theory, originally proposed by [PERSON] and [PERSON] [28], suggested that birds could save energy by flying in a specific formation. However, an in-depth analysis, taking into account the spacing between the wingtips of birds in formation, confirmed that the theory was valid. The methodology employed in their study involved making videos of groups of Canadian geese, then measuring the V-angle and distance between birds flying in formation. The study highlighted the importance of considering non-aerodynamic factors  
Figure 3: Diagram of the vortex flow developing in the wake of a large bird gliding at high speeds. such as group cohesion and navigation parameters. The results showed variations in the apparent angle of V formations as birds moved along their flight path. Measurements taken from images of migratory bird groups determined that the average angle between the arms of the V-formation was 34\({}^{\circ}\), while [PERSON] and [PERSON] [28] estimated this angle at 120\({}^{\circ}\). Table 1 summarizes the range of apparent V-formation angles reported by various authors. The article by [PERSON] and [PERSON] [6] underlined the need for further studies with other species and taking into account various factors such as weather, wind, altitude, group size, season, etc... Thus, [PERSON] and [PERSON]'s study played a crucial role in empirically examining the validity of formation flight theory in migratory birds, contributing to a better understanding of bird flight behavior. A few years later, [PERSON] [33] continued the work of his predecessors, addressing various aspects of the dynamics and aerodynamics of migratory birds and the V-formation of Canadian geese (_Branta candensis_). [PERSON] [33] takes up the theories of [PERSON] and [PERSON] [28] and determines that the aerodynamic advantage for large birds of flying in formation is \"minimal\". He estimates the gain at around 10% compared with solitary flight, which nevertheless confirms the aerodynamic advantage of flying in a group. [PERSON] also suggests using depth to quantify the distance between birds measured along the flight path. A few years later, [PERSON] and [PERSON] [11] continued their research into V-flight in Canadian geese. In their study, they re-evaluated the data of [PERSON] and [PERSON] [6] using wingtip spacing instead of the distance between body centers to test the aerodynamic hypothesis of V-flight. They observed that several birds had wingtips that overlapped with the wingtips of the preceding bird, thus contradicting the hypothesis of [PERSON] and [PERSON] [28]. Completing the aerodynamic theory of V-flight, [PERSON] and [PERSON] [11] estimated that V-flying birds could save 51% energy compared with flying alone, whereas [PERSON] and [PERSON] [28] estimated an energy saving of 71%. Using the description of the velocity field induced by a finite wingspan in the case of formation flight, [PERSON] [36] demonstrated that each wing in formation flies within an upwash field generated by all the other wings in the formation, leading to a significant reduction in flight power demand.