Journal: Journal of the Royal Society Interface

Article Title: The role of passive avian head stabilization in flapping flight

doi: 10.1098/rsif.2015.0508

Figure Lengend Snippet: A mass–spring–damper model predicts passive head stabilization in whooper swans. (a) The cropped video frame illustrates the tracked points used to reconstruct vertical head and body displacements. (b) The neck model stabilizes the motion of the head with mass, m, using a vertical spring with stiffness, k and damping constant, c. (c) Raw traces of the vertical displacement for the head and body of a whooper swan in the high-speed video. The vertical axis shows body displacement divided by average body amplitude, while the horizontal axis shows time divided by flap period. (d) Raw traces of the horizontal displacement for the head and body, using the same units as in (c), show that oscillatory displacement due to flapping is principally vertical. (e) High-pass filtered (HP) head and body traces are used to corroborate the neck transfer function that minimizes r.m.s.e. (yellow, measured; black, predicted). (f) Gain and phase of body, neck and head. Error bars indicate the standard deviation between flights. The body and neck have the same gain with opposite phase, which shows that the neck compensates for body motion; n = 5 flights.

Article Snippet: Using a parameter sweep, we minimized the r.m.s.e. between simulated and measured head displacement in response to the tracked body displacement (custom MATLAB R2013a script; for all five flights, A–E, r.m.s.e.

Techniques: Standard Deviation

Journal: Journal of the Royal Society Interface

Article Title: The role of passive avian head stabilization in flapping flight

doi: 10.1098/rsif.2015.0508

Figure Lengend Snippet: The different frequency and damping ratios for the five flights are connected in parameter space and give similar performance at the wingbeat frequency (displacement frequency ratio = 1). (a,b) Black dots indicate the predicted values for gain and phase at the wingbeat frequency, respectively, based on the calculated minimal r.m.s.e. damping and natural frequency ratios for all five flights. The ‘+’ symbol represents the point calculated for the average gain and phase over all five flights (the connecting dashed arrows between the box plots in (c,d) illustrate this). The colour map range represents ±2σ variation (σ = standard deviation) in the measured gain values (a) and phase values (b) shown in inset boxplots: (c,d) Predicted frequency response for gain (c) and phase (d, measured in flaps) outside the wingbeat frequency (displacement frequency ratio ≠ 1). We used corroborated gain and phase values for the plots, as they are not different from the measured ones (see text).

Article Snippet: Using a parameter sweep, we minimized the r.m.s.e. between simulated and measured head displacement in response to the tracked body displacement (custom MATLAB R2013a script; for all five flights, A–E, r.m.s.e.

Techniques: Standard Deviation

Journal: Journal of the Royal Society Interface

Article Title: The role of passive avian head stabilization in flapping flight

doi: 10.1098/rsif.2015.0508

Figure Lengend Snippet: Passive head stabilization is robust to mild gusts that perturb the swan. (a) Example of the effect of a mild (asterisk (*) symbol; 3.5 body amplitudes, eight flaps) versus a strong gust (plus (+) symbol; 11.1 body amplitudes, 4.12 flap) on head stabilization. (Head response, red; body oscillation, blue; gust displacement, black; inset shows a range of simulated gusts.) (b) The maximal neck amplitude response in a mild gust can stay within 2σ bounds for mild gusts (σ, measured standard deviation of vertical head displacement). Red and black shaded areas indicate physically unreasonable responses that require active avoidance. (c) The recovery time after a mild gust, measured in number of flaps needed to return within the measured 2σ range, is less than one wingbeat.

Article Snippet: Using a parameter sweep, we minimized the r.m.s.e. between simulated and measured head displacement in response to the tracked body displacement (custom MATLAB R2013a script; for all five flights, A–E, r.m.s.e.

Techniques: Standard Deviation