Wing and body kinematics
This protocol is extracted from research article:
Biomechanics of hover performance in Neotropical hummingbirds versus bats
Sci Adv, Sep 26, 2018; DOI: 10.1126/sciadv.aat2980

The wingbeat kinematics of both hummingbirds and bats were analyzed in a similar way for fair comparison. First, the wing perimeter was extracted, and a midspan vector (from the wing tip through the center of wing planform) was calculated for each tracked frame. Then, the local coordinate system origin was placed at the best fit intersection of all midspan vectors over each wingbeat. The positive z axis was aligned up against the direction of gravity and calculated in easyWand5 (22) by dropping a small sphere through the volume. The positive x axis was aligned to the right of the animal (centered between maximum and minimum sweep angles, as shown in Fig. 3A), leaving the positive y axis pointing in front of the animal (when a bat’s left wing was tracked, kinematics were reflected to match a right wing). Next, the sweep angle (Fig. 3A) was defined as the angle of the wing tip with respect to the shoulder projected into the horizontal xy plane (normal to gravity). The wing motion in this horizontal plane shapes the (projected) actuator disk area associated with the vertical force (29). Similarly, the elevation angle was defined as the vertical elevation of the wing tip with respect to the shoulder (Fig. 3B). Finally, the instantaneous wing extension was defined as the distance from the shoulder to the wing tip, normalized by the maximum distance during the wingbeat (Fig. 3D).

We also measured and compared morphological and wingbeat-averaged variables. First, the wing length was defined as the distance from the wing tip to the shoulder (the shoulder was defined as the proximal tracked point on the leading edge; fig. S5C), while the wing area was calculated by summing the triangular patches (23 for hummingbirds and 4 for bats) that defined the wing surface (fig. S5F). Consequently, the mean chord length was defined as the wing area divided by the wing length (fig. S5D). Next, the aspect ratio was defined as the wing length divided by the mean chord length (fig. S5G). Finally, the swept area was calculated by projecting the wing outline to the horizontal plane over the whole wingbeat. The perimeter of this projected wing area was found using the alpha hull method with a 5-cm probe radius to account for concave features in the tracked points (fig. S5E). In addition to these standard kinematics variables, a 3D wing reconstruction was used to calculate the spanwise twist and angle of attack.

For each tracked frame, 50 equally spaced chord segments down the wing were calculated. Each chord intersected the leading and trailing edge but did not necessarily hold a constant length over the wingbeat (see movie S2). All chords were aligned perpendicular to the midspan vector, starting at the most proximal tracked point (on either the leading or trailing edge) and ending at the wing tip. First, the wing twist rate per meter of wingspan (degrees per meter) was found by calculating the angle of each chord relative to the root chord. A best fit twist rate down the wing’s span was calculated and multiplied by the wing’s length to get a measure of wing twist (Fig. 3C). Then, the angular velocity of each wing panel (single panel for hummingbird wing and five triangular panels for bat wing) with respect to the wing origin was numerically differentiated (38). Next, to find the local velocity of each chord, the position to each chord was vectorially crossed with the angular velocity of its closest panel. Then, the angle of attack of each chord segment was calculated by measuring the angle toward the wing’s leading edge relative to the component of the chord’s velocity perpendicular to the midspan (see movie S2 and Fig. 3E). The angle of attack was defined as negative when the wing was inverted on the upstroke. The angles of attack that we found are higher than in previous studies (4, 25) because we computed them more precisely based on the local chord velocities from wing root to wing tip (see movie S2). Next, the stroke-averaged angle of attack at each chord during the downstroke and upstroke (Figs. 3F and 6E) was averaged over the portion of the respective stroke when the wing tip speed exceeded the mean tip speed (see fig. S6). Finally, the wingbeat-resolved Reynolds number at the radius of gyration was calculated (fig. S1) using the average air density and dynamic viscosity.

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