The cost of flight in flocks

There are well-known aerodynamic and energetic benefits to flying in an orderly formation. By contrast, it seems that the flocking flight seen in pigeons is metabolically expensive. So why do they do it? See Letter p.494

Formation flight has long been known to confer aerodynamic advantages on appropriately spaced fixed-wing aircraft. Flying with a wing positioned in an updraft is a little like finding a free source of lift, which, in turn, reduces drag. Drag is directly related to fuel consumption, so formation flight in birds is seen as a way for these creatures to increase their migratory range or cut the costs of general commuting. All a bird must do to reap the rewards of formation flight is stay in formation. The potential benefits of the V-formation¹ or of certain more complex clusters² have been noted in idealized mathematical models. However, many bird flocks apparently lack the order and precision required to make such energy savings, and it is far from obvious how to formulate a tractable theoretical model for such complex patterns.

On page 494 of this issue, Usherwood et al.³ describe how they made the first measurements of body accelerations in individual birds involved in voluntary, loosely formed flocking flights. The reasonable inference from the assembled data is that such flights do not save energy, but rather come at a cost. Energy saving is not of overriding importance in such flight excursions, and the flocks must form for other reasons.

Forty years ago, Lissaman and Shollenberger¹ pointed out that the aerodynamic advantages of formation flight could be especially accessible to birds: local wing twist and wing flexibility allow these animals to configure their aerodynamic profile according to the local air-flow field. The positioning accuracy required seemed reasonable, and the stable and preferred shape of V-formations was explained as the best configuration for evening out the drag distribution in a flock. Planar V-shaped formations, as observed in migrating geese for example (Fig. 1), could increase migratory range by as much as 70%; similar energetic advantages have been proposed for fish schooling4. And the potential cost savings in full-scale aircraft5, and in fleets or swarms of unmanned autonomous vehicles in the air or underwater, are topics of renewed interest.

Figure 1: Flight formations and clusters.

Canada geese migrate in a characteristic V-formation (left); such an orderly, planar arrangement can reduce drag, resulting in energy savings. Complex swirls and flocks of organisms, such as those of pigeons (right), have less apparent order, and in their research with pigeons Usherwood et al.³ find that flocking flight patterns are energetically costly. Group travel in flocks (birds), schools (fish) and herds (large vertebrates) is common, but there are probably several, often overlapping, reasons for such behaviours.

Noting that bird flocks are not always in neat, linear arrays, Higdon and Corrsin² analysed a more general cluster formation. In contrast to Lissaman and Shollenberger¹, they ignored details of the air-flow distribution on the wing, and replaced each bird with a mathematically convenient function, with almost identical far-field properties. They showed that, in three-dimensional flocks, drag savings could be either positive or negative, depending on the spanwise or vertical positions of the flock members. Their tentative conclusion was that “improved flight efficiency is not an important reason for migration in large, three-dimensional flocks”.

There are many possible reasons for flying in a flock, which may include mutual observation, collective guidance and navigation, enhanced security as a result of greater numbers of individuals or of eyes, fitness display, and assessment of group numbers. Energy saving may be of paramount, or little, importance. Even if energy saving is not an explicit goal, then avoiding excessive energy cost may at least be a consideration.

Usherwood et al.³ measured the wing-beat frequency and body accelerations of 18 trained racing pigeons when they left their home loft in voluntary excursions, which involved quite irregular clusters with varying densities and flight paths. Quite often the cluster would circulate in a tight circle or spiral. Backpacks containing Global Positioning System equipment relayed data back at rates sufficient to correlate wing-beat and body accelerations with flock position and density.

Several interesting observations followed. First, sharp turning manoeuvres, with centrifugal accelerations comparable to gravitational acceleration, are themselves costly. Second, pigeons flap their wings faster when in a cluster than when flying alone. Third, the flapping frequency correlates strongly with the proximity of neighbouring birds. The authors³ argue that the average aerodynamic downdrafts are probably comparatively small, and propose that the high-frequency flapping is more likely to be an adaptation to increased demands on flight control and collision avoidance. Regardless of the cause, because the flapping frequency can be very roughly used as a surrogate for power consumption, the implication is that flying in such a flock is more costly than flying alone.

The dynamics (social and physical) of flying in flocks is not easy to simplify. Even in seemingly orderly flocks of pelicans or geese, the measured precision in wingtip–wingtip spacing is often quite far from the mathematical ideal^6,7. This study³, like most others, ignores the effect of the complex wake disturbances that are undoubtedly generated by each pair of flapping wings. Yet the empirical evidence suggests that, because energetic savings are negative, in this instance we may have to search elsewhere for the reasons for flying in flocks. Perhaps the episodic flights of racing pigeons allow the birds to test and exercise their locomotory and control machinery. As with many problems in biology, it is quite possible that more than one reason conspires to create any given bird flock.