First published online January 31, 2006
Journal of Experimental Biology 209, 689-701 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02062
The relationship between 3-D kinematics and gliding performance in the southern flying squirrel, Glaucomys volans
Kristin L. Bishop
Department of Ecology and Evolutionary Biology, Brown University,
Providence, RI 02912, USA
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Fig. 1. Relationship between lift-to-drag ratio and glide angle. M, mass
of the animal; g, acceleration due to gravity; R,
resultant aerodynamic force vector; L, lift; D, drag;
 , glide angle.
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Fig. 2. Diagram of markers applied to the squirrels. The chord line is the line
connecting the wrist and ankle markers; the body axis is a line connecting the
sternum and pelvis markers.
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Fig. 3. Schematic of experimental setup at Brown University (Arena 1). As the
squirrels glided through the calibrated volume (box), they were filmed from
below by two digital cameras set at approximately 70° to one another. The
setup at Concord Field Station (Arena 2) was similar, but the landing pole was
positioned further away or was absent to allow the possibility of a longer
horizontal glide distance.
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Fig. 4. Angle of attack ( ) is defined as the angle between the chord line
and the velocity vector of the oncoming air flow. Angle of attack was computed
by subtracting the angle between the chord line and the horizontal from the
angle between x-y velocity of the center of mass and the
horizontal (equal to the glide angle).
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Fig. 5. Computation of camber. h, camber height; ap, anterior patagium
length; , leading edge angle.
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Fig. 6. Force diagram for unsteady (accelerating) glides. The resultant aerodynamic
force is inclined forward because of the horizontal acceleration. A downward
acceleration indicates that the vertical component of the resultant
aerodynamic force has a smaller magnitude than the weight. M, mass of
the animal; g, acceleration due to gravity; R,
resultant aerodynamic force vector; L, lift; D, drag;
 , reference angle between negative velocity (drag) and resultant
aerodynamic force vector.
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Fig. 7. Frequency distribution of the correlation coefficients at a time lag of
zero for a cross-correlation analysis of limb position with pitch angle. In
the majority of trials, chord angle with respect to the body axis was
negatively correlated with pitch angle, such that limb movements that tend to
increase angle of attack are associated with nose-down pitching moments and
vice versa.
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Fig. 8. (A) Pitch angle and chord angle (the angle between the chord line and the
body axis, a measure of active adjustment of limb positions relative to the
body) for one glide sequence. Values for pitch angle are positive when the
sternum marker is higher than the pelvis marker and negative when the sternum
marker is lower than the pelvis marker. The chord angle is positive when the
wrist marker is higher than the ankle marker with respect to the body axis and
negative when the ankle marker is higher than the wrist marker with respect to
the body axis. Note that as the pitch angle increases, the chord angle
decreases and vice versa. (B) Cross-correlogram for the same trial as
in A, showing maximum negative correlation between changes in pitch angle and
limb position at zero time lag. Lines represent 95% confidence interval.
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Fig. 9. (A) Coefficient of lift, coefficient of drag and lift-to-drag ratio
vs angle of attack. Lift coefficient
(y=0.0617x+4.7421) and lift-to-drag ratio
(y=-0.107x+6.8044) have a significant negative correlation
with angle of attack, whereas drag is positively correlated with angle of
attack (y=0.0209x+0.0925). (B) Coefficient of lift,
coefficient of drag and lift-to-drag ratio vs relative camber. Only
lift coefficient (y=11.391x+0.4127) and lift-to-drag ratio
(y=20.279x-0.5755) have a significant correlation with
relative camber.
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© The Company of Biologists Ltd 2006
