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First published online July 20, 2007
Journal of Experimental Biology 210, 2593-2606 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.002071

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Aerodynamic force generation, performance and control of body orientation during gliding in sugar gliders (Petaurus breviceps)

Kristin L. Bishop

Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02912, USA

View larger version (8K): [in this window] [in a new window]   Fig. 1. Experimental set-up, drawn to scale. Sugar gliders were trained to glide from a launching pole to a landing pole in an enclosed space. Two high-speed digital cameras were positioned beneath the glide path at approximately 90° to one another. The calibrated volume of space visible in both cameras is represented by the box surrounding the glider. The blue lines are computed trajectories of the sternum through the space for all glide sequences.

View larger version (10K): [in this window] [in a new window]   Fig. 2. Placement of reflective body markers. The chord line is the line connecting the wrist and ankle markers. The `mean hip' is the mean of the positions of the right and left hip.

View larger version (20K): [in this window] [in a new window]   Fig. 3. Force balance diagrams for gliding and computation of angle of attack and camber. (A) Steady (non-accelerating) glides. The resultant aerodynamic force is oriented vertically and is equal to mass x acceleration due to gravity. The angle between the resultant aerodynamic force vector and the lift vector is equal to the glide angle, so lift and drag can be computed as the magnitude of the resultant aerodynamic force x the cosine and sine, respectively, of the glide angle. The lift-to-drag ratio is equal to the cotangent of the glide angle, and is therefore inversely proportional to it. (B) Non-steady (accelerating) glides. Horizontal accelerations indicate that the resultant aerodynamic force is inclined with respect to the vertical and vertical accelerations indicate that the magnitude of the vertical component of the resultant aerodynamic force is not equal to mass times acceleration due to gravity. More complicated computations of lift and drag are required (see text) and there is no necessary relationship between lift-to-drag ratio and glide angle. Angle of attack is the angle between a line connecting the wrist and ankle and the direction of the whole body velocity. See text for details on calculations. Camber is computed as the perpendicular distance from the patagium marker to a line connecting the wrist and ankle. The 3D angle between the chord line and the line connecting the wrist and the patagium marker is computed as a reference. Camber height is estimated as the distance from the wrist to the patagium marker times the sine of the reference angle. V, velocity vector; V', direction of velocity vector; R, resultant aerodynamic force vector; M, mass of glider; g, acceleration due to gravity; L, lift; D, drag; , glide angle; , reference angle between drag and the resultant aerodynamic force; , angle of attack; h, camber height; ap, anterior patagium distance (between wrist and patagium markers); , reference angle between chord line and anterior patagium line.

View larger version (15K): [in this window] [in a new window]   Fig. 4. (A) Coefficient of lift, (B) coefficient of drag, and (C) lift-to-drag ratio vs angle of attack. The range of lift coefficients used by each glider is similar, although they used different ranges of angles of attack. No correlation was detected between lift coefficient and angle of attack. There appears to be no correlation between angle of attack and drag, but a multiple regression analysis detected a significant positive relationship. Multiple regression analysis detected a significant negative correlation between angle of attack and lift-to-drag ratio. Points represent averages over a glide sequence for 4 animals (Ind1–4).

View larger version (16K): [in this window] [in a new window]   Fig. 5. (A) Coefficient of lift, (B) coefficient of drag, and (C) lift-to-drag ratio vs relative camber. Individual gliders use different ranges of relative camber. There was no significant correlation between relative camber and lift coefficient. Although no correlation is apparent between drag coefficient and relative camber, multiple regression results detected a significant negative correlation. There is a significant positive correlation between lift-to-drag ratio and relative camber. Points represent averages over a glide sequence for 4 animals (Ind1–4).

View larger version (14K): [in this window] [in a new window]   Fig. 6. Limb positions vs time for separate representative glide sequences. Limb movements were ubiquitous throughout all glides and of magnitudes that far exceed the estimated digitizing error. The correlation between these movements and body rotations indicate that these movements function to control body orientation. (A) Chord angles tended to be fairly large and positive at the start of the sequences and decrease through the trial. Chord angles became negative in 14 of 49 trials. (B) Forelimb elevation angles tended to fluctuate between positive and negative, but usually remained fairly small. (C) Forelimb protraction angles were large and positive at all times in all glide sequences.

View larger version (16K): [in this window] [in a new window]   Fig. 7. Glide angle vs (A) coefficient of lift, (B) coefficient of drag, and (C) wing loading. There appears to be no relationship between glide angle and lift coefficient, but multiple regression detects a significant negative correlation. There is no correlation between drag coefficient and glide angle. There is a clear positive relationship between glide angle and wing loading. N=4 animals (Ind1–4).

View larger version (14K): [in this window] [in a new window]   Fig. 8. Velocity vs (A) coefficient of lift, (B) coefficient of drag, and (C) wing loading. Multiple regression detects a significant negative correlation between both lift and drag coefficients and velocity. Wing loading has a positive relationship with velocity. N=4 animals (Ind1–4).