Figure 3.
Position of the origin of the turn. (a) Absolute scalar product of the longest elongation axis unit vector I 3 with the unitary vector of the mean position relative to the barycentre d 0/d0 of the 10 top-ranked birds (data are given in the electronic supplementary material, table S1). The result does not change qualitatively for another number of top-ranked birds, as long as this number is small compared with the total number of birds in the flock N. (b) Scalar product 
where dmax is the maximal possible distance of the birds along the I 3 axis at the tip where the turn started. We show the results for d 0 calculated for the 10 top-ranked birds (blue bars), but also as a position of only the first bird that started the turn (red bars). For most events, the values are higher than 0.5, although not too close to 1 due to the sparseness of the flock at the very tips and particular orientations.