Modelling bird formations using fuzzy logic

This paper is the outcome of a long work trying to model bird formations, in particular line formations. In the scientific literature, there are several attempts to model flock of birds flying in a cluster (as for example those wonderful flocks of starling that look like dancing in the sky). However, about birds flying in line formation there is little as it is rather challenging to collect data.

In a collaborative project led by the Waldrappteam (, we tracked a flock of Northern Bald Ibis (Geronticus eremita) during the human-guided migration south (read here to discover how we did it) and collected data on line formation.

Once the data was collected, we needed to classify when a bird was flying in the wake of another individual and when not. But first: what does it mean to “fly in the wake”? When a bird flies and flaps its wings, it produces vortexes of air behind itself: a downwash behind the body and two upwashes, in correspondence of the wingtips. If another bird position itself in order to catch the upwash, then it is flying in the wake of the other bird. It does so because it can gain lift and save some energy while flying. However, it is not so easy to determine where exactly these upwashes lie, how they develop, and their extent or limits because they do not have crisp boundaries, but fuzzy ones. Therefore, it is difficult to determine when a bird is exploiting the upwash and when not.

We decided to model these vortexes using fuzzy logic, which helps to model vague and uncertain concepts. In addition, the model allows to classify the bird as being in the wake (if it is exploiting any upwash) of another bird or not.

To the best of our knowledge, this is the first attempt in the scientific literature that tries to model line formations. Further steps will be to apply the model to investigate if birds that are flying in the wake are saving energy, to unveil pattern of movements while flying in formation, and to study social interactions and their influence during flight formation.

If you are interested in reading more on the model, check out the paper published in Journal of the Royal Society Interface “Characterization of bird formations using fuzzy modelling” , and stay tuned for updates!

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