Table 1. Intermediate calculations.

These formulae were used to determine the birds velocity, distance, and changes in flight trajectory at each frame using their x-, y-, and z- coordinates. These instantaneous values were then used to calculate the flight metrics described in Table 2.

Description	Formulae and notes
Instantaneous velocity (m/s) at frame n	$v_n=\sqrt{{\left(x_n-x_{n-1}\right)}^2+{\left(y_n-y_{n-1}\right)}^2+{\left(z_n-z_{n-1}\right)}^2}\ast 60$ The vector distance (m) between two consecutive positions is multiplied by the frame rate (60 fps) to achieve instantaneous velocity in m/s.
Distance (m) at frame n	(a)With respect to the obstacle atX=0 andY= 0 (excluding the Z plane, as the obstacle occupies all possible Z coordinates): $d_{n_{\text{obstacle}}}=\sqrt{x_n^2+y_n^2}$ (b)With respect to the speaker at X = 0, Y = 0, and Z = 0: $d_{n_{speaker}}=\sqrt{x_n^2+y_n^2+z_n^2}$
Change in flight trajectory at frame n	(a) Curvature (rad/m): $\kappa =\frac{\left|x^{{}^{\prime }}{z}^{{}^{\prime \prime }}-z^{{}^{\prime }}{x}^{{}^{\prime \prime }}\right|}{{x^{{}^{\prime }}}^2+{z^{{}^{\prime }}}^2}$ (b) Angle of inflection (rad): ${\Theta }_n={cos}^{-1}\frac{\left(x_{n+1_{expected}}-x_n\right)\ast \left(x_{n+1_{actual}}-x_n\right)+\left(z_{n+1_{expected}}-z_n\right)\ast \left(z_{n+1_{actual}}-z_n\right)}{\sqrt{{\left(x_{n+1_{expected}}-x_n\right)}^2+{\left(z_{n+1_{expected}}-z_n\right)}^2}\ast \sqrt{{\left(x_{n+1_{actual}}-x_n\right)}^2+{\left(z_{n+1_{actual}}-z_n\right)}^2}}$ , where xn+1expected = xn + (xn − xn−1) and zn+1expected = zn + (zn − zn−1) Both calculations exclude movement in the Y direction, which dilutes any meaningful changes in trajectory by including the bird’s forward motion. The greatest change of flight trajectory was determined as the frame during which both curvature and angle of inflection were maximized.