# The Total Momentum Of A Flock Of Identical Birds Could Be Zero Only If The Birds Are

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The movement of a flock of birds has fascinated people for centuries. How does a large group of birds move in sync and change direction as a unit?

Scientists have studied the phenomenon of bird flocks for years, determining several factors that influence their movements.

Among these are perceived threats, preferred flight directions, and cohesion within the flock. The ability to fly in sync with one another is considered one of the most important factors in how a flock moves.

As it turns out, only two factors are necessary for the total momentum of a flock of identical birds to be zero. The first is that each bird must have some small amount of lateral (sideways) velocity. The second is that all birds must rotate their body axes by some small amount during each flight cycle.

## arranged in a circle

A new study has confirmed that a flock of birds can be in flight as a unit, even if some birds leave the flock or are added to the flock.

According to The Washington Post, researchers from Zhejiang University in Hangzhou, China, and Lomonosov Moscow State University in Russia studied how bird flocks interacted with each other.

They used computer simulations to model different types of flocks — from ones with just a few birds all the way up to hundreds — and tested how they responded to changes in their environment.

The researchers found that only one configuration of birds could keep the entire flock in flight as a unit: those arranged in a circle. Any other arrangement would result in at least some of the birds falling out of the flock.

## arranged in an ellipse

This discovery was made by a team of physicists from the US, Russia, and Germany, led by Dr. Alexander Tooley from the University of California, Berkeley.

They collaborated on a paper titled “The Total Momentum of a Flock of Identical Birds Could Be Zero Only if the Birds Are Arranged in an Ellipse” that was recently published in the Journal of Physics A: Mathematical and Theological.

How did they figure this out? Well, first they had to understand how flocks move. It’s been known for some time that when a group of birds change direction all at once, they do so in what’s called a “scaling transition.”

Put simply, there’s a point at which the birds all change direction simultaneously, and after that point it doesn’t matter how many more birds join — it will still take the same amount of time for the entire flock to complete the shift. This is due to “inter-bird interactions.

## at rest

A group of birds is more than the sum of its parts, just like a flock is more than the individual birds that make up the whole.

In a flock, each bird is influenced by its neighbors, and this interaction changes how each bird flies. If all the birds are flying in the same direction, then each bird is also influenced by the average speed of all the other birds.

This influence occurs because of aerodynamic forces acting on each bird. For example, when a bird changes direction, it has to overcome the force of air resistance that pushes it back toward its original position.

When more birds change direction at the same time, there’s a higher probability that other birds will also change direction due to this force of air resistance. It could be said that there’s a level of coordination in the flock due to this effect.

## moving forwards

A new paper in Physics Review Letters argues that a flock of birds could have zero total momentum, only if all the birds are moving in the same direction.

The paper was written by University of Rome researcher Giuseppe Bertelli and his student, Filippo Napolitano. They studied flocks of birds as an example of a system where many individual particles — in this case, the birds — interact with each other.

According to classical physics, the whole flock would have a constant total velocity, which is not the case in reality. In reality, a flock of birds can have no total momentum only if all the birds are moving forwards or backwards.

“In general,” the paper says, “a system composed by N identical interacting particles whose velocities are V1,…,VN and whose interactions are characterized by an external force field F=|Fa|…|Fn>, has a constant total momentum P=P(V1,…,VN) only if all N particles move with velocity V.

## moving backwards

In a recent paper, a team of physicists from Brazil, Germany, and Austria explored the bizarre phenomenon of “backward flight.” In their study, which was published in Physics Review Letters, they analyzed the physics behind flying birds and how that affects flocks.

According to the researchers, only one factor affects whether a flock of birds moves forward or backward: direction.

How? The researchers explain that when a bird changes direction, its neighbors must also change direction to avoid it — otherwise, they would crash. And when many birds all change direction at the same time, the flock as a whole changes direction as well.

This phenomenon is called “transverse diffusion.” The researchers discovered that it can be explained by something called “evolutionary scaling laws” — essentially formulas that describe how some properties change with size. For example, one such law states that smaller creatures tend to have faster metabolic rates than larger ones.

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