# The Aerodynamic Mechanisms of the Formation Flight of Migratory Birds: A Narrative Review
## 3 Results
### Theoretical and Experimental Studies
For a group of 15 ibises, it was shown that drag is reduced by 34% for the lead and trailing ibises by changing the wingtip spacing, while the rest of the ibises see a drag reduction of 65 to 73%. Note that this level of drag reduction is close to the estimates of [PERSON] and [PERSON] [28] and well above the predictions of other authors (see Table 3). Building on their previous study [56], [PERSON] et al. [57] again investigated the effects of not only wingtip spacing but also wingspan on the individual drag of each ibis in the flock. An algorithm was applied for the replacement mechanism and load balancing of ibises during flight. In this replacement mechanism, ibises with the highest remaining energy value are iteratively replaced by ibises with the lowest energy. After four replacement stages, ibises with wingspans of 1.39 m and 1.37 m were found to have the lowest remaining energy. In addition, small birds were found to have a chance of taking the lead position during group flight. Still based on aerodynamic theory, the study by [PERSON] et al. [7] reaffirmed the effectiveness of V-formation in reducing induced drag. The [PERSON] et al. study [7] examines aerodynamic drag forces for individual Canada geese as well as for the overall group to understand how flock size affects drag and energy conservation. Theoretical modeling demonstrated a significant reduction in drag as group size increased. The study also explored the effects of wingtip spacing on total group drag. The results showed that by reducing wingtip spacing to a certain point, total group drag decreased. Their study provided information on optimizing energy consumption by repositioning leaders and followers, which could improve the range and flight endurance of these migratory birds by over 44.6%. Previous research had already confirmed the principle that birds exhibit cooperative behavior, taking turns at the front of formations to optimize energy use. Table 3 summarizes the theoretically estimated maximum energy savings that following birds \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Energy Savings** & **Bird Species** \\ \hline [PERSON] and [PERSON] [28] & 71\% & - \\ \hline [PERSON] and [PERSON] [11] & 51\% & Canada Geese \\ \hline [PERSON] [37] & 36\% & Canada Geese \\ \hline [PERSON] and Speakman [41] & 14\% & Pink Footed Geese \\ \hline [PERSON] and [PERSON] [42] & 26.5\% & Greylag Geese \\ \hline [PERSON] et al. [13] & 11.4–14\% & White pelicans \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy savings for a trailing bird in formation flight. The potential energy savings in formation flight are quantifiable by considering the ratio between the induced drag coefficient for solo flight and the average drag coefficient of a bird within the formation, as proposed by [PERSON] and [PERSON] [28]. could experience in a formation flight. Remarkably, the theoretically estimated energy savings decrease as predictive models evolve and become more refined over time. Over time, researchers have compiled information on the structure and spatial organization of migratory birds in formation flight. Based on existing data, [PERSON] and [PERSON] [58] studied the interaction rules of a limited sample of migratory bird species. Based on available flight data, they postulated that groups composed of larger shorebird species would show improved organization compared to those composed of smaller species, reflecting the tendency of larger birds to fly in well-structured V-formations. In addition, they anticipated that larger species would more regularly display aerodynamic formations. Contrary to expectations, all the species studied flew in a group structure that the researchers termed a \"composite V-formation\". [PERSON] and [PERSON]'s results are consistent with theoretical and empirical studies supporting the hypothesis that birds flying in simple V formations benefit from aerodynamic and energetic advantages. They proposed that these advantages might also explain why birds adopt the composite V formation.