Why do birds fly in a V formation?

For two reasons that work together: aerodynamic efficiency and staying in visual contact.

The aerodynamics are genuine and measurable. A flying bird's wings generate vortices of air spinning off the wingtips. Directly behind the bird this creates downwash, which is unhelpful, but slightly behind and to the side there is upwash — air moving upward. A bird positioned in that upwash gets free lift and can reduce its own effort.

Studies fitting data loggers to migrating birds have confirmed this in remarkable detail. Work with northern bald ibises found that birds positioned themselves accurately in the optimal spot and, more strikingly, timed their wingbeats to match the rising air left by the bird ahead. When flying directly behind another bird, they reversed the phasing to avoid the downwash. That degree of precision suggests active management rather than coincidence.

Estimates of the energy saved vary by species and conditions, but reductions in heart rate and wingbeat frequency have been measured directly.

The lead bird gets no benefit, which is why formations rotate. In several species the front position is swapped regularly, and studies of ibises found birds took turns almost equitably — one of the clearer examples of reciprocal cooperation in animals.

Visual contact is the second function. A V lets every bird see the others and the direction of travel without obstruction, which helps keep a flock together over long distances.

Not all flocking birds use it. It appears mainly in large birds on long migrations — geese, swans, cranes, pelicans, ibises. Small birds flock in dense, shifting clouds instead, where the aerodynamic benefit is negligible and predator confusion is the likelier purpose.