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First published online March 31, 2007
Journal of Experimental Biology 210, 1413-1423 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02747
Take-off and landing forces and the evolution of controlled gliding in northern flying squirrels Glaucomys sabrinus
1 Centre for Biomimetic and Natural Technologies, Department of Mechanical
Engineering, University of Bath, Bath, BA2 7AY, UK
2 MS 6200, Department of Biology, Southeast Missouri State University, 1
University Plaza, Cape Girardeau, MO 63701, USA
* Author for correspondence (e-mail: K.E.Paskins{at}bath.ac.uk)
Accepted 12 February 2007
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Key words: flying squirrels, Glaucomys sabrinus, jumping, gliding, kinetics, substrate reaction forces, biomechanics
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) is that
gliding may have evolved as a means of reducing the energetic cost of
foraging. The squirrel can jump and glide from one tree to the next, enabling
it to cover greater distances within the canopy more quickly than would be
possible by climbing down and moving across the forest floor. An alternative
suggestion was that, rather than reducing cost of transport, gliding may offer
a means of foraging over a larger area in a certain time, making flying
squirrels better able to exploit a patchy food resource than non-gliders of
similar size (Scheibe et al.,
2006). The third hypothesis is that gliding evolved primarily as
an escape mechanism (Scheibe et al.,
1990; Keith et al.,
2000). Tree squirrels react to disturbances by moving to the
opposite side of their tree, whereas flying squirrels climb upwards and then
glide to another tree. However, this behaviour may increase susceptibility to
attack from their most likely predator, owls
(Scheibe and Robins, 1998). We
propose a fourth hypothesis: that the patagia, the flexible membranes that
squirrels stretch by fully extending their forelimbs and hindlimbs, evolved to
reduce or control landing forces. There is published evidence to support this
(Caple et al., 1983), where it
was calculated that increasing the amount of lift available to a body from 0
to 5% would not noticeably lengthen the jump nor allow much turning, but would
give the animal significantly improved control around the pitch and roll axes.
Of course, none of these four hypotheses are mutually exclusive.
This paper will investigate these hypotheses through experimental
determination of the performance and behaviour of these animals. By measuring
take-off and landing forces, we propose to quantify the advantage flying
squirrels can achieve as a result of their unique morphology. The outcome of
these measurements will be directly affected by substrate compliance. The
majority of previous studies measuring ground reaction forces used rigid force
measuring devices, while others investigated the effects of substrate
compliance on ground reaction forces
(Demes et al., 1999;
Bonser, 1999). Demes et al.
found that take-off forces were higher than landing forces when testing seven
primate species of varying body sizes using compliant apparatus, contradicting
previous studies based on rigid platforms
(Demes et al., 1999). Some of
the take-off force is used in bending the compliant branch before toe-off,
whereas the reaction force on landing is damped as the substrate yields in the
direction of motion, allowing more time for deceleration. Likewise, Bonser
showed that the magnitude of landing forces for starlings was lower than their
take-off forces (Bonser, 1999).
He proposed both that the birds used their wings to decelerate during landing,
and that additional energy is dissipated in deflecting their compliant perch
during take-off.
In arboreal locomotion, flying squirrels must generate higher take-off forces when jumping from narrow (and hence compliant) tree branches, and encounter their highest impact forces when landing on rigid tree trunks. Compliant substrates have been instrumented for this study, and so we expect take-off forces to exceed landing forces over short distances. At higher ranges, the squirrels will have accelerated due to gravity and their landing force will likely increase unless the squirrel can use its morphology to slow itself aerodynamically. Therefore our hypothesis that gliding in the squirrel evolved primarily to enable aerodynamic control of its landing speed can be rejected if measured landing forces continually rise at high ranges.
It is possible for animals to utilise stored elastic energy within a branch
by timing their take-off with its motion. However, primates do not seem to
take advantage of this (Demes et al.,
1995), which supports the proposition
(Alexander, 1991) that they
would not intentionally recover this energy. Therefore, we do not expect
flying squirrels to take advantage of the recoil of our instrumented branch
either. However, they have been observed using a bounding gait before
launching with both fore- and hind-feet together at the end of a platform just
before take-off (Keith et al.,
2000). It is probable that this bounding is used to maximise
take-off velocity and hence increase range.
The northern flying squirrel Glaucomys sabrinus is the larger of
two species of North American flying squirrel, although still much smaller
than some species found in SE Asia (Ando
and Shiraishi, 1993). Flight is made possible by the presence of
patagia, a morphological feature which has evolved independently several times
in vertebrates, the earliest known being from the Mesozoic era
(Meng et al., 2006). By
manipulating their limbs, flying squirrels are able to actively modify the
shape of this lift-generating surface during flight. The body proportions of
flying squirrels were compared with those of tree squirrels to determine what
morphological changes might be attributed to gliding
(Thorington and Heaney, 1981).
Increased leg length allows more energy to be expended during take-off,
offering superior horizontal range. In comparison with other similar-sized
squirrels, the forelimbs of flying squirrels are significantly longer, a trait
that has almost certainly evolved to improve aerodynamics during gliding
(Essner, 2002). This is
further improved by the styliform cartilage, which is a flexible projection
from the wrist held upward from the rest of the lift surface during gliding.
This combines with the manus (or hand, which points ventrally towards the
mid-line of the squirrel) to form a wing tip very similar to a NASA designed
winglet (Thorington et al.,
1998), who proposed that it reduces induced drag by diffusing and
directing vortices away from the patagia. Smaller flying squirrels tend to
have greater manoeuvrability and agility, whereas the larger species must
glide faster to achieve the same glide ratio.
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Apparatus
As flying squirrels often land on tree trunks, allowing vertical variation
in contact point, we used a vertical landing pole based on the design of Demes
et al. (Demes et al., 1995;
Demes et al., 1996;
Demes et al., 1999). The
squirrels were acclimated to it for several months prior to experimentation
and used it regularly. It was constructed in two pieces: a 1.52 m long PVC
tube (114 mm o.d.) covered in carpet and marked at 10 cm intervals (for
calibration and image analysis), mounted 80 cm of the way up a 2.41 m long
galvanised steel tube (23 mm o.d.). A concrete base secured this steel tube,
which had four strain gauges (FLA-2-11-3L, TML, Tokyo, Japan) equally spaced
around its circumference and aligned vertically
(Fig. 1). A half-bridge circuit
was used for each tension/compression pair so that force parallel and
perpendicular to the squirrel's direction of motion could be determined. The
compliance of the pole was measured to be 1.5 mm N–1 at the
free end, gradually decreasing down the pole, reducing to 0.2 mm
N–1 close to the fixed end and the resonant frequency was 2.2
Hz.
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). Four standard
linear strain gauges (CEA-13-240UZ-120, Vishay, Basingstoke, UK) were mounted
in two pairs, 50 mm from the fixed end of the 10 mm square aluminium bar
(Fig. 1) and connected in a
half-bridge circuit. Alignment was simplified because the chosen gauge width
was almost as large as the 10 mm width of the aluminium bar, but not critical
because any cross-talk was eliminated during calibration. The aluminium branch
was covered by tightly wound rope to simulate the surface of a tree branch.
The strain gauges were protected using polystyrene foam, which was itself
covered by plastic. A length of 4 cmx9 cm timber was fixed vertically to
the wall, and drilled with mounting holes every 10 cm to allow height
adjustment of the launch branch. The design of the branch was such that the
compliance was similar to that of the landing pole, measured to be 1.9 mm
N–1 at the free end and decreasing as would be expected
towards 0.0 mm N–1 at the fixed end. The resonant frequency
of the take-off branch was 17.3 Hz. The signal outputs from the strain gauges
on both instruments were amplified using AD524 chips or equivalent and the
sampling rate was 250 Hz. There was no need to acclimatise the squirrels to
the take-off pole as, unlike the landing pole, they had no choice over whether
or not to use it.
Experimental design
The take-off branch was raised as the experimental range increased such
that the angle between the tip of the branch and the base of the landing pole
remained consistent at approximately 55°. This configuration was chosen
because it was not possible with our equipment, and in the locations
available, to set up short jumps at high altitudes, and the squirrels were
unable to reach the landing pole unless given sufficient starting height.
Animals were released individually on the instrumented branch and responded by
running along the branch, usually pausing and then leaping to the instrumented
landing pole. The horizontal range was increased progressively from a low
distance of 0.5 m, to capture the leap-to-glide transition point, below which
squirrels merely leap around, and above which the flying squirrels achieve
aerodynamic advantage over other types of squirrel. Analysing this range of
arboreal locomotion was considered to be more critical for investigating the
initial divergence of flying squirrels.
Three digital video cameras (Canon GL2, Sony TRV 108, and Panasonic NV-DS55B) were used to film jumps. The first was positioned to capture take-off angle, the second to capture lateral landing angle and the third to capture a ventral view of landing. In the large squirrel barn it was not possible to mount a camera level horizontally with the take-off branch, so the resultant images represent frames perpendicular from the known camera angle. A minor trigonometric correction was therefore necessary to adjust all vertical distances measured from this take-off footage.
Calibration
With strain gauges, large changes in the external environment are
potentially significant, so a record of temperature was kept using two
I-buttons (Maxim Integrated Products, Sunnyvale, CA, USA), fixed to the top
and bottom of the 4 cmx9 cm timber stud, respectively. These recorded
temperature every hour. This daily verification of calibration was
particularly important because testing was carried out in two contrasting
environments; a temperature-controlled laboratory, and a hot and humid metal
barn.
Only the landing forces were measured by converting the output from strain gauges into force, for which a static calibration was performed daily by applying forces to different points along the pole. Resultant steady signals were used to draw calibration graphs that established the force constant, k, where F=kx; F is force (N) and x is the measured strain signal (V). Forces equivalent to between 1 and 10 body weight units (bw) were applied, producing good linearity across the full range of marking points on the pole. (On average, the square of the Pearson product moment correlation coefficient r2 = 1.00 in line and 0.99 transverse to the expected direction of motion.) Position of the animal along the instrumented poles was taken into account and a linear equation allowed the correct calibration to be used at any point. The cross-talk magnitudes were 13% and 17%, respectively, for parallel and transverse forces. Cross talk, in this context, is the unwanted output signal measured on one pair of strain gauges for a force applied perpendicularly. The frequency response of our equipment is sufficient to measure impulses generated by the squirrels. The effect of temperature on the calibration was found to be unimportant, as although it varied considerably between the two test areas, calibration graphs remained consistent throughout the study.
Results processing
Although both could measure force in two directions, neither the take-off
branch nor the landing pole were capable of measuring forces along their long
axes. To overcome this limitation, video footage from laterally positioned
cameras was recorded to determine the angle of action of the force, which
allowed the force vector to be resolved in 3D from the two measured force
components. This was an acceptable procedure for the landing forces because
the squirrels were arriving at angles perpendicular to the pole. For the
median data point at medium range, 1.5 m, a trigonometric calculation showed
that a 5° shift in measured landing angle would cause a 10% change in the
resultant force. During take-off the squirrels were consistent in their
behaviour, always choosing to move towards the free end of the branch and jump
away in the same direction. However, the resulting shallow take-off angles
mean that a 5° measurement error leads to an unacceptable 39% change to
the median resultant force at 1.5 m. Hence, resultant take-off forces had to
be calculated by integrating the output from the strain gauges with respect to
time, so that measured take-off velocity could be used to determine the
acceleration. This was multiplied by the known mass of each flying squirrel
for all jumps to calculate the resultant force. The frame rate of the lateral
take-off camera was 30 frames s–1 so an estimate of velocity
between the first two consecutive frames after toe-off could be obtained by
measuring the change in position of the centre of mass. The resultant force
calculated by this method is the total force required to accelerate the
squirrel to its actual take-off velocity based on its known acceleration
profile. This method does not take into account losses caused by deforming the
branch, but is completely independent of the accuracy in measurement of
take-off angle.
The video records were digitised using edge-detection software, which tracked the outline of the squirrel in each frame of a sequence of images from the laterally positioned camera (LabView – National Instruments, Austin, TX, USA). The tail was deliberately excluded from this outline, because it constitutes only a small percentage of the total weight of the animal and was often dorsally flattened and moving at high velocity outside the plane of the images. The centre of the region enclosed by the lateral outline of the squirrel was used as an approximation for its centre of mass and could be tracked from frame to frame, enabling both the landing point on the pole, and the angle of impact to be determined. Hence the resultant reaction force for each landing squirrel could be calculated.
To measure the take-off angle of the squirrel, principal components analysis was applied in the LabView squirrel tracking program to find the best-fitting ellipse to the outline detected in each frame. The take-off angle was taken to be the angle between the major axis of this ellipse and the axis of the branch in the final frame before toe-off. This program was also used to estimate the change in pitch during the landing sequence shown in Fig. 2C. Another program was written in NI Labview to determine the wing span and wing area of each squirrel from ventral images of a glide. Lateral images were used in conjunction with these to ensure that only frames in which the squirrels were in plane with a calibration bar were used for these measurements.
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A calculation was performed to determine the percentage of body weight
supported during each measured glide, relative to the equivalent ballistic
trajectory (that is the trajectory of an object with the same take-off
velocity and angle subject to no drag or lift). For a simple free-falling
mass, the gravitational force acting downwards is opposed by any lift
generated. The resultant force acting on the body is hence:
 | (1) |
, velocity, v (m
s–1), and jump duration, t (s), are sufficient to
calculate the vertical drop, y (m), from the resultant acceleration
using the standard kinematic equation below:
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 | (3) |
Jumps observed, general mixed model, and other statistics
We measured 79 take-offs and 53 corresponding landings with the number of
jumps of each animal at each range specified in
Table 1. No landing force data
were obtained for the shortest range jumps of 0.5 m, but with this exception,
all measured take-off forces have a corresponding landing force. Only one
squirrel, young female 1, performed in the barn but it did not leap to the
force pole at distances greater than 2.5 m, landing instead on the ground
beyond the instrumented pole. This was the only animal to perform at all
ranges tested. Unfortunately, young female 2 only cooperated at 0.5, 1 and 1.5
m and the young male at 0.5 and 1 m. Owing to the number of missing data
points, the typical multivariate ANOVA could not be applied to our data, and
so a general mixed model (Krueger and
Tian, 2004) was applied to both take-off and landing forces, with
range as a fixed factor and squirrel ID a random factor. Unless otherwise
stated, all correlation statistics use Pearson's product moment
correlation.
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In the barn, the squirrels tended to have a steeper approach and did not pitch up very much prior to landing. The head still tilted backwards but the tail was rotated forwards towards the vertical. As a consequence of the lower angle of attack, the forelimbs contacted the pole first, causing the body to rotate around rapidly onto the hindlimbs due to the conversion of linear to angular momentum. Occasionally the tail was cambered such that the inside of the curve faced the landing pole. In some jumps, the squirrels were clearly banking or turning in the penultimate frames to correct misalignment with the pole and in one instance, a subject landed on the side of the pole. As it was simple to calculate the forces for these jumps too, these results were included in our analysis.
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The general mixed model introduced above provides statistical verification that normalised take-off forces were significantly dependent on range (F5,11.5=45.182, P<0.001) but not squirrel identity (P=0.602). Likewise, landing forces were dependent on range (F4,9.5=409.341, P<0.001) but independent of the particular squirrel (P=0.548). The means and 95% confidence intervals produced by the mixed model are plotted in Fig. 4.
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Landing force is positively correlated with angle of descent (r=0.740, P<0.001).
The outputs from all strain gauges were recorded simultaneously, enabling the duration of each glide to be measured. There is, unsurprisingly, a strong positive correlation (r=0.923, P<0.001) between glide distance and glide duration. Mean glide velocity based on the linear distance from take-off to landing position and not the actual trajectory, was strongly positively correlated (r=0.951, P<0.001) with horizontal range. This reached 4.5 m s–1 across a horizontal range of 2.5 m.
Average take-off angle for each squirrel at each distance was negatively correlated with range (r=–0.684, P<0.001) (Fig. 5).
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Glide angles increased steeply with horizontal range until they reached approximately 45° beyond 2.5 m (Fig. 7), the angle at which gliding is distinguished from parachuting, after which they gradually improve as seen by a strong, negative correlation between the 17 longest jumps (r=–0.816, P<0.001). At this point, only one animal was still performing but it did not land on the pole, and instead glided past it and landed on the floor.
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Take-off, landing and gliding performance are discussed separately.
Take-off
Flying squirrels generated take-off forces ranging from 1.08 to 9.57 bw.
The amount of force was proportional to the distance the animal travelled
(Fig. 3). It is logical that
squirrels generate a larger take-off force to go further, as ballistic theory
dictates they require a higher velocity in order to cover the distance.
However, there must be a maximum force the squirrel can generate. Our results
suggest this might be approximately 10 bw, which is equivalent to occasional
high jump forces at shorter ranges. (These occasional jumps support the idea
that flying squirrels jump more forcefully when startled, incidentally.)
The highest take-off angle recorded was 35° and this occurred at the shortest range of 0.5 m, which was short enough that landing position was often higher than take-off position. Take-off angle decreased as range of the jump increased (Fig. 5) but this may have been influenced by a confounding factor, the height of the branch. With sufficient height the animal can afford a shallower take-off angle, allowing it to generate a higher horizontal velocity.
Overall velocities of the squirrels increased with range. The animals usually ran and jumped immediately after release onto the branch, but occasionally it was necessary to startle them. It is unknown if the apparent levelling off of glide angle that we observed for longer jumps is a general trend because we did not obtain results for longer leaps.
Gliding performance
Squirrels used lower glide angles in the lab, but angles near 45°
(parachuting) for the longer ranges of 2 m and above in the barn. This may
have been a behavioural change due to unfamiliarity, and is based on only one
squirrel at these ranges. In a study describing the kinematics of two southern
flying squirrels Glaucomys volans, glides from both animals were
shorter and significantly steeper after moving to a new test arena
(Bishop, 2006). However, our
measured glide angles improved with increasing range
(Fig. 7) and are comparable
with similar distance results from two field studies of northern flying
squirrels (Vernes, 2001;
Scheibe et al., 2006), so it
is more likely a consequence of the need for this species (the larger of the
two North American species) to reach a higher velocity before it is able to
exhibit superior aerodynamic performance. Average glide velocities measured in
this study increased with range as would be expected. Observations of the
Japanese giant flying squirrel on long glides
(Ando and Shiraishi, 1993)
sometimes showed an initial steep descent with the glide angle decreasing with
increasing velocity, until both became constant. Likewise, northern flying
squirrels dropped steeply prior to gliding, and often even managed to gain
altitude slightly, just before landing
(Vernes, 2001). The squirrels
in this study may have initiated a similar behaviour, but the possible ranges
were too short for the effect to be noticed. This would help to explain why
field observations of northern flying squirrels have reported significantly
better glide ratios. In Alaska, USA, Scheibe et al. evaluated 168 glides from
82 different squirrels with mean glide distances of 12.46 m and 14.39 m in
successive years, and corresponding mean glide angles were 41.31° and
36.31° (Scheibe et al.,
2006). Vernes reports a mean angle of descent of just 26.8°
for glides which were longer, averaging 16.4 m
(Vernes, 2001). Gliding
behaviour is therefore likely to be optimised for significantly longer ranges
than were possible in this study.
Flying squirrels use their patagium as a low-aspect-ratio wing, which has
good aerodynamic stability at the relatively low speeds involved, generating
lift at high angles of attack of up around 40° without stalling
(Torres and Mueller, 2004).
This shape allows the squirrel to overcome any detrimental rotational momentum
that it might have generated during take-off. In the present study, full
gliding posture was always initiated before the hindlimbs left the substrate,
allowing the angular momentum produced by forelimb abduction to be transmitted
directly to the branch, even over the shortest leaps of just 0.5 m. It has
been argued (Essner, 2000)
that this behaviour enabled the squirrel to begin gliding earlier, resulting
in a flatter trajectory with more immediate manoeuvrability and control. We
quantified the gliding performance of each squirrel by calculating the
percentage of its bodyweight supported during each glide and showed that
flying squirrels exploited their unique morphology to generate lift at ranges
greater than 1.5 m (Fig. 6).
However, these values were negative over 0.5 m, implying that the squirrels
generated down-force. It could be that the combination of steep take-off
angles with immediate initiation of gliding results in their large patagial
surface area working against the squirrels on these steeper take-off angles.
Alternatively our estimate for the percentage body weight supported could be
slightly conservative. In any case, we have established that the transition
from leaping to gliding occurs at a horizontal range of 1.5 m for northern
flying squirrels. They are not able to benefit from gliding over distances of
less than 1 m, so although the resultant glide angles may appear to be
superior at these ranges, this is only a consequence of the higher take-off
angles and limited time in the air.
Landing
Landing forces varied between 3.01 and 9.52 times body weight. The impact
force on the landing pole was proportional to the range of the leap. This is
expected because the measured gliding velocity increased with horizontal
distance, reflecting the effects of gravitational acceleration.
The correlation of measured landing force with the contact position of the animal on the pole is due to the compliance decreasing towards the fixed end. Higher forces were experienced by squirrels landing lower down on the pole, where it was relatively stiffer and did not deflect so far. This is inevitable because the kinetic energy of the squirrel becomes the product of reaction force and deceleration distance – proportional to the deflection of the pole given that leg length remains constant. This has an important implication for the use of compliant substrates when quantifying forces for comparison. Ideally, only forces measured at points of equal compliance should be compared directly, or there should be a random scattering of landing positions. This was the case for our results, with the exception of the 2 m range, at which the squirrel consistently landed at the base of the pole. The reason for this is unknown, because the angle between the base of the landing pole and the tip of the take-off branch was consistent at 55° for all ranges. However, by removing the data from the 2 m range (7 data points out of 53), a strong linear relationship can be observed between the means of the other 46 jumps where more compliance was available (Fig. 4). The square of the Pearson product moment correlation coefficient (the r2 value) improves from 0.61 to 0.99 when the 2 m data is ignored. Such a good linear fit means that the flying squirrels adopt a consistent landing technique. On stiffer substrates, we would expect a similar, but steeper, linear increase in landing force with range.
Over short leaping distances, take-off forces are not significantly
different from landing forces (Fig.
3; t-test). This fits with the expectation (see
Introduction) that landing forces would not be higher than take-off forces on
compliant substrates, as they are on rigid platforms
(Demes et al., 1995).
Landing force was correlated with angle of descent, suggesting the
squirrels are better able to absorb landing impacts with a flatter approach.
Some of the impact force is likely absorbed as a result of the consistent
landing posture observed, which it seems the squirrels were unable to
accomplish with steeper approaches. During shallower glides the squirrels are
able to increase their drag force by transforming the patagia and distichous
tail from a cambered surface with low angle of attack, high lift and low drag,
to a more parachute-like surface orientated against the direction of motion.
Additionally, this posture enabled the squirrel to absorb the remaining impact
forces more evenly over its four extended limbs on contact. Aerodynamically,
the flying squirrel has a low aspect ratio (close to 1) and glides at low
speed so an angle of attack in excess of 40° would be required for it to
stall in flight (Torres and Mueller,
2004). The squirrel has additional aerodynamic implications
associated with its morphology, such as its fur, so it is not possible to
measure whether or not they are actually stalling from our video footage.
However, it is clear from the example landing sequence shown in
Fig. 2C that the pitch angle of
the body has increased to effectively 90° immediately prior to landing,
supporting the theory that they deliberately stall themselves
(Alexander, 1995).
Caple et al. stated that the vector sum of angular momentum must be
conserved during any mid-air movement of a body with no lift or drag
(Caple et al., 1983). Although
flying squirrels will also be able to generate some external force from their
patagium, this could help explain the origin of some of the consistent landing
movements observed. For example, the rotations of the head and tail backwards
would directly counteract the thrusting of the limbs ventrally, although it is
equally likely that the head tilt may be for defence against accidental
impact. A falling cat also uses counter-rotations in order to right itself
when falling from an upside-down position
(McDonald, 1960). Caple's
calculations (Caple et al.,
1983) also show that some of the morphological features of flying
squirrels, such as long forelimbs with dense, distally located mass (hands and
feet) and a lightweight tail that can produce lift, are optimisations for
controlling pitch and roll. We show that the squirrels were able to reduce
landing forces by pitching upwards as they approach, and it is this behaviour
which may have applied selective pressure to these morphological features
rather than glide range, which increases negligibly in comparison. Increasing
forelimb length allows the landing energy to be absorbed over a larger
distance. Likewise, the flexed back on impact should further reduce the peak
landing force. A falling cat also tries to land with its back arched and all
four limbs outstretched towards the ground
(McDonald, 1960).
Unfortunately the squirrels could not be persuaded to land on the pole
above the relatively small horizontal range of 2.5 m, compared to their normal
arboreal glide distances (Vernes,
2001; Scheibe et al.,
2006), choosing instead to deliberately manoeuvre past the landing
pole and land on the floor. It is possible that the squirrels may have a sense
for a maximum speed at which they can safely or comfortably land on a stiff or
unknown substrate for a given approach angle. Glide angles achieved at ranges
between 3 and 6 m exceeded 45° (Fig.
7), which would normally be defined as parachuting rather than
gliding (Oliver, 1951), and we
speculate that this is likely to be the most difficult distance for northern
flying squirrels to land. The steeper approach angles inhibit their ability to
pitch up and absorb the landing across all four limbs simultaneously, and
there is more energy to dissipate due to the inevitable increase in velocity
with range. Velocity continues to increase above the proposed awkward range
but this also improves the flying squirrel's aerodynamic ability, allowing a
progressive improvement in approach angle and consequent landing posture. It
is likely that these animals would try to avoid making hard landings on tree
trunks at this unfavourable range. Vernes reported that in 21% of his 100
glides observed (Vernes,
2001), northern flying squirrels landed on the ground or in dense
undergrowth. The other landings were on trees and it should be noted that the
mean glide distance was much higher in the Vernes study than ours. Likewise,
Scheibe et al. noted that sometimes squirrels released onto a tree trunk at
breast height did not climb and glide, choosing instead to jump to the ground
and run to a nearby tree (Scheibe et al.,
2006). Future experimental designs should consider that northern
flying squirrels might be more likely to land on an instrumented pole
positioned at a high rather than medium horizontal distance from the take-off
position, but this would necessitate an arena allowing sufficient take-off
height.
The equation for the linear relationship between landing force and range on
the compliant part of the pole is shown on
Fig. 4 and can be used to
predict the landing force at longer ranges than we were able to measure.
However, the squirrels would not keep accelerating indefinitely during long
glides; rather their speed would stabilise as they approach terminal velocity.
Maximum glide velocities of close to 12 m s–1 have been
reported (Scheibe et al.,
2006), although the weighted means were 6.26 m
s–1 and 8.11 m s–1 in two consecutive years.
These values are much higher than our highest observed speed of 4.5 m
s–1, although this was measured across a relatively much
shorter horizontal glide distance. With more time in the air, squirrels must
be able to control their trajectories, otherwise they would be subject to
extremely high impact forces. Depending on substrate compliance, we can use
the equation from Fig. 4 to
calculate that squirrels trying to land from an ordinary 16 m glide would be
subject to impact forces of upwards of 28 bw if they did not slow themselves,
as we have shown, by pitching up and employing air braking.
Evolution of gliding
Hypothesis 1
Hypothesis 1 that gliding developed to reduce the energetic cost of
foraging supposes that the squirrels' primary objective should be to maximise
range in every jump while minimising the loss in altitude. Therefore, from
ballistic theory we would expect the squirrels to jump at close to the optimum
take-off angle of 45°, but they did not. As expected, the advantage gained
by gliding increases with range. This vertical advantage achieved relative to
the ballistic trajectory enables flying squirrels to reach trees beyond normal
jumping range, or reduces the amount of climbing required after a glide is
completed, thus saving energy. However, during this study flying squirrels did
not try to take off at 45°, which would be expected for maximising range,
and take-off angle decreased with range. However, the non-optimum take-off
angles and frequently observed range-reducing aerial manoeuvres are evidence
to suggest that energetic transport cost is not of primary importance to
flying squirrels.
Hypothesis 2
If gliding evolved to maximise the foraging area that could be reached in a
given time, as proposed by Hypothesis 2, then we would expect the squirrels to
glide at high velocities. We have shown that velocity increases with range,
and that flying squirrels can generate higher lift forces when travelling
further, so we cannot reject the hypothesis that gliding is an optimisation to
maximise speed and potential foraging area.
Hypothesis 3
Hypothesis 3 is that gliding evolved primarily to facilitate escape from
predation. One might expect that an escaping squirrel would jump horizontally,
or downwards given sufficient altitude, in order to ensure that it did not
decelerate due to gravity. Bonser and Rayner proposed that starlings may
deliberately vary take-off trajectory for predator avoidance
(Bonser and Rayner, 1996), but
we have shown a negative correlation of the take-off angle with range,
suggesting that during this experimentation at least, flying squirrels choose
a take-off trajectory to suit their intended destination. Caple et al. stated
that all gliders pre-select a landing site, which must be large enough to
allow some vertical variation in the contact point
(Caple et al., 1983). Vernes
also observed that flying squirrels appeared to think about their intended
flight path before launching and we saw no evidence to suggest otherwise
(Vernes, 2001). Given that the
squirrels seem to exhibit this behaviour even during the jumps that were
initiated by startling, it seems unlikely that gliding evolved primarily for
escape, at least not from high-speed chases.
The ability to make sudden aerial direction changes could potentially help
to lose a predator. However, their most likely aerial predator is the owl
(Scheibe et al., 1990), and it
is unlikely that such sophisticated fliers would be troubled by the relatively
clumsy swerving squirrel.
Hypothesis 4
Hypothesis 4 relates the development of flight to the control of landing.
Even at the relatively short ranges in this study, we observed direction
changes being introduced by rapid beating of the tail from side to side.
Additionally, last-second manoeuvres were observed, such as banking and using
the tail as a rudder, implying that flying squirrels are able to make precise
adjustments to improve their landing. As range increases, any error in
take-off trajectory would become more significant without aerial control; in
this case squirrels could face serious consequences for misjudging long leaps
at the top of the forest canopy.
Flying squirrels choose to initiate a full gliding posture even though they do not produce significant lift during glides of less than 1 m, suggesting that this behaviour is innate. It might be that the squirrel is simply throwing its arms out conveniently widely for rapid rotation of the joint in order to gain forward momentum during take off. They do exhibit a consistent landing behaviour at these distances, with the gliding posture enabling them to pitch upwards as they approach and spread the landing reaction force over all limbs. It is likely that the squirrels deliberately stall themselves by this quick increase of their angle of attack immediately prior to landing.
Landing control of pitch and roll improves much more rapidly than range for the same incremental improvements in forelimb length and tail surface area. Increasing forelimb length simultaneously reduces the landing force further by increasing the deceleration distance. Landing force was correlated with angle of descent, suggesting flying squirrels were unable to pitch up sufficiently to execute the evenly distributed four-limbed landings when approaching steeply, demonstrating the utility of aerial control in longer jumps. Given the reported values of terminal velocity for flying squirrels, and the measured landing forces on compliant substrates that increase with range, we know that if the squirrels could not slow themselves or improve landing posture aerodynamically prior to landing, they would have to sustain impact forces of upwards of 28 bw.
Evolution of gliding in flying squirrels has undoubtedly reduced their energetic cost of transport, while improving potential foraging area and response to predation, but we conclude that the selective pressure for their divergence from ground squirrels was the improvement of landing control.
Conclusions
Take-off and landing forces generated by northern flying squirrels are both
positively correlated with horizontal range, at least up to 2.5 m. The maximum
take-off force measured was 9.57 bodyweights, although the squirrels would
occasionally produce close to this force when jumping only short distances,
most likely a natural behavioural response to alarm. Take-off forces were not
significantly different to the corresponding landing forces on these similarly
compliant substrates. They are able gliders, abducting all limbs to create a
wing-like surface, which is held at a low angle of attack for maximum
lift/drag ratio. Glide angle increased rapidly with horizontal range up to
approximately 4 m, before progressively improving, suggesting that gliding in
northern flying squirrels is optimised for significantly longer ranges than
were possible in this study.
Any compliant force-measuring device will likely have some variation in its compliance along its length. In the case of a cantilever beam, this begins to behave more like a rigid instrument towards its fixed end. Valuable comparisons can only be made between forces measured at known points of equal compliance. If this is not possible, then sample sizes should be chosen to ensure a random scattering of landing positions.
It seems unlikely that gliding evolved in flying squirrels to reduce the energetic cost of transport even though the measured lift generated would lessen the amount of climbing required. Take-off angle decreased with range without getting close to 45°, the value for maximum ballistic range, and further height would be lost to the aerial manoeuvres occasionally observed. The flying squirrels in this study did not attempt to make either unplanned or deliberately unpredictable take offs, casting doubt on the theory that gliding might improve predatory escape response.
Gliding might have evolved to maximise the foraging area that could be reached in a given time. High glide speeds were measured and this velocity increases with range, but the development of improved landing control is a necessary consequence of faster flight. We provide evidence that if northern flying squirrels could not slow themselves aerodynamically from terminal velocity, prior to landing, they would have to try and sustain impact forces of upwards of 28 bw. Flying squirrels seem to innately adopt a gliding posture on take off, even during leaps of less than 1 m when no vertical advantage is gained, but this leaves them better prepared for aerial control. At these low distances, a consistent landing strategy was exhibited by flying squirrels, allowing the impact force to be spread over all four limbs and their arched back, thanks to a dramatic pitch upwards immediately prior to contact with the pole. This rapid increase of their angle of attack immediately prior to landing is likely a behaviour evolved to enable rapid deceleration by stalling, although this would have greater effect at high speeds. We conclude that at divergence, small glide producing surfaces were developing in flying squirrels allowing mid-air adjustments in pitch and roll, and improving their resilience during high-speed arboreal transport.
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