# The Aerodynamic Mechanisms of the Formation Flight of Migratory Birds: A Narrative Review
## 3 Results  
### Theoretical and Experimental Studies  
In 1969, [PERSON] [27] presented a study on the mechanics of flight in migratory birds, covering topics such as the power required to fly and the effects of altitude, which he expressed algebraically. His study, rooted in the classical aeronautical theory, was considered fundamentally reliable, despite some simplifications. The text also provided mathematical models for calculating the performance estimates of different bird species. However, [PERSON] pointed out that the accuracy of these estimates depended both on the theory and on the accuracy of the experimental data, which were scarce at the time of the study's publication. The text emphasized the imperative of accumulating experimental measurements for different types of flying animals in order to improve the accuracy of performance estimates. The study that has truly been considered a pioneer in the study of the aerodynamics of migratory birds flying in formation is that of [PERSON] and [PERSON] [28]. Their study was the first to theorize the aerodynamic advantages of formation flying, particularly those of V-formation (see Figure 1). Their theoretical model provided an estimate of the aerodynamic drag induced by birds flying in formation, concluding that V-formation was aerodynamically advantageous and generated substantial energy saving for birds following the leader. The authors developed a theoretical aerodynamic model that considered the optimal positioning of birds side by side in a V formation. This model described how optimal positioning could reduce induced power, i.e., the power required  
Figure 2: PRISMA flow diagram. to maintain sufficient lift and overcome gravity for each bird in the group. Their study was based on the idea that as wingtip spacing decreases, the induced power required also decreases, as the next bird now flies into an increasingly strong upward vortex from the vortices generated by its neighbor (Figure 3). Similarly, beyond a critical wingtip spacing, as the V-formation becomes tighter, the following bird begins to fly in the wake generated by the preceding bird, resulting in increased energy costs rather than energy saving (Figure 3). Thus, optimal wingtip spacing should exist that maximizes the benefits of formation flight while minimizing the potential costs resulting from the wake. [PERSON] and [PERSON] expressed their analysis by comparing formation flight with solo flight. Specifically, the induced power of a single bird in formation was expressed as the ratio of the induced drag of a bird flying in formation to that of a bird flying alone. At the time of its publication, [PERSON] and [PERSON]'s 1970 paper was essentially theoretical, mainly due to the lack of appropriate technology to experimentally study the dynamic flight of birds within a V-formation. This article has been a source of inspiration for many researchers, who have continued the work based on their preliminary results and theories. Although the authors omitted to present the calculations and formulas leading to their conclusions, this study remains a pioneer in the field. Based on the hypothesis of [PERSON] and [PERSON] [28], [PERSON] and [PERSON] [29] used the simplest stationary aerodynamic theory to model the induced drag of birds flying alone or in formation. The results of their study suggested that flying directly behind another bird would be detrimental in terms of aerodynamics. One of [PERSON] and [PERSON]'s mathematical models was based on the horseshoe vortex model, a major drawback being the assumption that wake vortices extend to infinity, whereas in reality vortex trails dissipate gradually. The authors raised the question of whether a \"drafting\" effect, now well known in the field of sport [30; 31; 32], could offset the adverse wake effect induced when one bird flies directly behind another.