Honeybees use their wings for water
surface locomotion
Chris Roh
a,1
and Morteza Gharib
a,1
a
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125
Edited by Howard A. Stone, Princeton University, Princeton, NJ, and approved October 11, 2019 (received for review June 4, 2019)
Honeybees display a unique biolocomotion strategy at the air
–
water interface. When water
’
s adhesive force traps them on the
surface, their wetted wings lose ability to generate aerodynamic
thrust. However, they adequately locomote, reaching a speed up
to 3 body lengths
·
s
−
1
. Honeybees use their wetted wings as hy-
drofoils for their water surface propulsion. Their locomotion im-
parts hydrodynamic momentum to the surrounding water in the
form of asymmetric waves and a deeper water jet stream, gener-
ating
∼
20-
μ
N average thrust. The wing kinematics show that the
wing
’
s stroke plane is skewed, and the wing supinates and pro-
nates during its power and recovery strokes, respectively. The
flow under a mechanical model wing mimicking the motion of a
bee
’
s wing further shows that nonzero net horizontal momentum
is imparted to the water, demonstrating net thrust. Moreover, a
periodic acceleration and deceleration of water are observed,
which provides additional forward movement by
“
recoil locomo-
tion.
”
Their water surface locomotion by hydrofoiling is kinemat-
ically and dynamically distinct from surface skimming [J. H. Marden,
M. G. Kramer, Science 266, 427
–
430 (1994)], water walking [J. W. M. Bush,
D. L. Hu, Annu. Rev. Fluid Mech. 38, 339
–
369 (2006)], and drag-
based propulsion [J. Voise, J. Casas, J. R. Soc. Interface 7, 343
–
352
(2010)]. It is postulated that the ability to self-propel on a water
surface may increase the water-foraging honeybee
’
s survival
chances when they fall on the water.
Apis mellifera
|
hydrofoil
|
semiaquatic locomotion
|
honeybee
|
biofluid
mechanics
I
t is difficult for insects to retain the aerodynamic function of
their wings when they contact a water surface. The large-
amplitude wing motion required for producing thrust demands
hydrophobic wing surface or enough clearance between the wing
and the water to prevent wetting. Insects that satisfy 1 of these 2
conditions can perform nonflying aerodynamic locomotion on
the water surface, known as surface skimming (1
–
3) (e.g.,
stoneflies, mayflies, and water lily beetles). Other insects whose
wings touch the water surface and continue to be bounded, lose
their ability to generate aerodynamic thrust. In this condition, it
is unclear whether the insects are still capable of propelling with
their wetted wings.
Water-collecting honeybees fly close to a water surface. When
they fall on the water, they lose their aerodynamic ability. While
their buoyant bodies provide flotation, the ventral side of the
body and wings get wetted. They are not able to free their wings
from the water surface, likely due to the relatively high wetta-
bility of their wings requiring large energy input for detachment
(4). The contact angle (a quantitative measure of wettability) of
the honeybee
’
s wing is 85° to 102° (5, 6) compared to 118° to 125°
for the stonefly
’
s wing (5), which can be detached from the
surface (1, 7). However, upon beating their wetted wings, hon-
eybees display forward locomotion while producing a distinct
wave and flow pattern on the water surface (Fig. 1 and
Movies
S1
–
S3). Here, we report that honeybees fallen on a water surface
use their wetted wings as hydrofoils, generating positive thrust
by transporting momentum to the water underneath the wing.
Hydrofoiling highlights the versatility of their flapping-wing systems,
which are capable of generating propulsion with fluids whose
densities span 3 orders of magnitude.
Results
Our data were obtained with honeybees (
Apis mellifera
) collected
from a garden in Pasadena, California. To simulate its accidental
fall, a honeybee placed in a plastic tube (1-inch-diameter open-
ing) was gently tapped with the opening facing the water surface.
The bees were flight capable before contacting the water surface.
The temperature of the water was kept above 20 °C. Note that
another factor that may contribute to a honeybee
’
s inability to
detach its wings from the water surface could be the lowered
temperature of its flight muscles, which operate optimally at a
temperature much higher than the experimentally set water
temperature (8). The depth of the water was maintained at 2.5 to
5 cm, which is much longer than the width of their wing (
∼
4 mm)
and the wavelength of the water wave (
∼
5 mm) generated by the
bee. The honeybees that fell dorsal side facing up were used to
collect data. The bees that fell ventral side facing up were ex-
cluded from data collection. These bees were not able to upright
themselves but still showed the capability to propel.
Body Kinematics.
The honeybee
’
s wing and body kinematics were
recorded with high-speed videography (500 to 1,000 frames
·
s
−
1
)
at various camera angles on constrained and free-moving bees.
Significance
We report the honeybee
’
s propulsion at the air
–
water in-
terface. Honeybees trapped on a water surface use their wings
as hydrofoils, which means their wings generate hydrodynamic
thrust. The surface wave and flow patterns generated around
the bee are the first indication that the wings are used as hy-
drofoils. Furthermore, the water flow measured under a me-
chanical wing model showed that both net and oscillatory
thrust contribute to their locomotion. Hydrofoiling highlights
the versatility of their flapping-wing systems that are capable
of generating propulsion with fluids whose densities span 3
orders of magnitude. This discovery inspires an aerial
–
aquatic
hybrid vehicle. Moreover, the findings may have biological
implications on the survival of water foragers and preflight
locomotion mechanisms.
Author contributions: C.R. and M.G. designed research, performed research, analyzed
data, and wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
Published under the
PNAS license
.
Data deposition: All data discussed in the paper will be made available to readers upon
request. The flow field data in Fig. 5 have been deposited at CaltechDATA,
https://data.
caltech.edu/records/1292
. MATLAB code developed during the current study are available
from the corresponding author upon reasonable request.
1
To whom correspondence may be addressed. Email: croh@caltech.edu or mgharib@
caltech.edu.
This article contains supporting information online at
https://www.pnas.org/lookup/suppl/
doi:10.1073/pnas.1908857116/-/DCSupplemental
.
First published November 18, 2019.
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In comparison to the wing kinematics during hovering flights (9)
and fanning (10), the amplitude and the frequency of the wing
beat at the water surface are noticeably reduced. Note that,
throughout the wing motion, the ventral sides are constantly in
contact with water, but the dorsal sides remain dry. The stroke
amplitude on a water surface is less than 10° as opposed to 90 to
120° in air. The wings beat symmetrically and synchronously at
frequencies ranging from 40 to 290 Hz (mean, 100 Hz;
n
=
33
bees; SD, 61 Hz). Twenty-five out of 33 bees had wing-beat
frequencies less than 100 Hz (mean, 71.6 Hz;
n
=
25, SD,
14 Hz), substantially lower than the 200 to 250 Hz during flight (9)
and
∼
170 Hz during fanning (10). The stroke amplitudes tend to
decrease as the wing-beat frequency increases (
SI Appendix
,Fig.
S1). The locomotion speed and acceleration oscillate at the wing-
beat frequency (Fig. 2). The time-averaged locomotion speeds
were 1.4 to 4.3 cm
·
s
−
1
(mean, 3.1 cm
·
s
−
1
;
n
=
18 bees; SD, 0.77
cm
·
s
−
1
) at steady state, corresponding to 1 to 4 body length
·
s
−
1
[2 orders of magnitude slower than their free-flight speeds (11)].
Reynolds number (
Re
) based on the average speed is
O
(100). The
time-averaged acceleration is approximately zero at steady state.
Force Generation.
For the bees to maintain locomotion speed,
their wings need to exert
∼
20-
μ
N average horizontal thrust to
overcome hydrodynamic drag (
SI Appendix
,
Detailed Calculations
I
and Fig. S3
). According to the law of momentum conservation,
an equal and opposite momentum should be imparted to the
surrounding fluid. If the necessary positive thrust can be traced
to the negative momentum imparted to the water, then the wings
are indeed used as hydrofoils rather than aerofoils. Note that, on
a water surface, momentum can be carried as a surface wave and
flow; therefore, we visualize using both shadowgraph and parti-
cle seeding (
SI Appendix
,
Materials and Methods
).
The wave field around the bee is bilaterally symmetric, but fore
–
aft asymmetric (Fig. 1
B
). A large-amplitude wave with an inter-
ference pattern forms at the rear of the bee, while the surface in
front lacks a strong (large-amp
litude) wave. The momentum
contained in a propagating wave scales as a square of the wave
amplitude (12); thus, the higher amplitude of the posteriorly
propagating wave suggests that the bee should be pushed forward.
The surface streaming flow generated by the bee has 3 out-
ward jets, 3 inward jets, and circulation regions between the jets
(Fig. 1
C
). Beneath this complex surface flow pattern, a simpler
flow is observed; of the 3 outward jets, only the backward flowing
central jet is present in deeper water (Fig. 1
D
and
SI Appendix
,
Fig. S7
). This jet
’
s penetration of deeper layers indicates its main
role as the momentum carrier. Therefore, the observed flow field
is also consistent with the forward thrust production.
More quantitative calculations of wave and flow momenta are
attempted with additional measurements and assumptions (
SI
Appendix
,
Detailed Calculations II
). With a wave amplitude
measurement, the average horizontal momentum per wing cycle
contained in the surface wave was calculated as 50
μ
N (over-
estimation is discussed in
SI Appendix
,
Detailed Calculations II
).
With a flow field measurement using digital particle image
velocimetry (13) (DPIV), the average flow momentum per wing
cycle was measured as 20
μ
N(
SI Appendix
,
Materials and Meth-
ods
and Fig. S7
). The magnitude of the hydrodynamically
imparted momentum and the thrust needed to overcome the
drag are the same order of magnitude. This shows that a bee
’
s
locomotion is sustained by imparting momentum to the water.
Note that these 2 measurements are not mutually exclusive, since
a traveling wave induces flow and vice versa. Previous studies on
water strider locomotion have shown that localized impulsive
forcing with a thin rod (i.e., leg) at the air
–
water interface results
in 1/3 and 2/3 partitioning of the imparted momentum to waves
Fig. 1.
Surface wave and flow visualization. (
A
) Honeybee
’
s locomotion on
a water surface. The ventral side of the wings and body are attached to the
water surface (
Movies S1
and S2 and
SI Appendix
, Fig. S1
). (
B
) Wave pattern
visualized using shadowgraph. The light and dark fringes indicate the wave
crests and troughs, respectively. Wing-beat frequency, 69 Hz (Scale bar,
1cm.)(
SI Appendix
,Fig.S4
and Movie S3
). (
C
) Surface streaming flow pattern
generated by a horizontally tethered bee. (
D
) Water flow at 2.0 mm below
the water surface generated by a constrained bee. Flow directions are
schematically shown in the
Bottom Left
corner for
C
and
D
.
Fig. 2.
Honeybee
’
s locomotion pattern. (
A
) Position change with time.
Wing-beat frequency, 60 Hz. (
B
) Forward locomotion speed. The dashed line
indicates the time-averaged speed (41 mm
·
s
−
1
). (
C
) Body acceleration. The
dashed line indicates the time-averaged acceleration (
−
0.0 m
·
s
−
2
). Also see
SI
Appendix
, Fig. S8
for mechanical model predicted body kinematics.
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and vortices, respectively (14)
. A similar study for sinusoidal
motion of a thin plate is necessary for distinguishing the measured
wave and flow momentum.
The net thrust generated by hydrofoiling,
O
(10
μ
N), is about 2
orders of magnitude smaller than the weight of the bee
O
(1,000
μ
N),
which is also the average aerodynamic lift force produced
during hovering flight (9). Interestingly, the peak thrust generated
during hydrofoiling (
SI Appendix
,Fig.S3
) and hovering are of the
same order of magnitude,
O
(1,000
μ
N). The small hydrofoiling net
thrust can be traced to the comparable magnitudes of positive and
negative thrust.
Flow Near the Wings.
The horizontal momentum
transport to water is
demonstrated more directly by an
alysis of the interaction between
the wing and the water underneath. To analyze, we first describe the
general features of wing kinematics (see Fig. 4 and
SI Appendix
,
Fig. S9
), and then show the flow generated by a mechanical wing
model mimicking the observed kinematics (see Fig. 5).
At the onset of the wing beat (Fig. 3
B
,t
=
t1; Fig. 4
C
,t
=
0),
the bee diagonally lifts the leading edges backward (Fig. 3
B
,t1to
t3; Fig. 4
C
,t
=
0mstot
=
6 ms;
θ
2
=
stroke plane angle
∼
30°,
θ
2
defined in Fig. 4
C
). Simultaneously, the wings supinate, and the
trailing edges are pushed down (Fig. 4). The bee
’
s body accel-
erates during this phase (Figs. 3
A
and 4
A
and
B
, shaded area),
thus hereinafter this phase is referred to as
“
power stroke
”
phase. Following the power stroke, the bee diagonally pushes
down the leading edges forward (Fig. 3
B
, t3 to t5; Fig. 4
C
,t
=
7ms
to t
=
16 ms). As the leading edges move down, the wings
pronate, and the trailing edges move up (Fig. 4). The bee de-
celerates during this phase; thus, hereinafter, this phase is re-
ferredtoas
“
recovery stroke
”
phase (Figs. 3
A
and 4
A
and
B
,
nonshaded area).
Throughout the honeybee
’
s wing kinematics, the ventral side
of the wing does not detach from the water surface. Thus, the
described wing kinematics continually interact with the water.
During the power stroke, the water underneath the wing is lifted
(Movie S1
). During the subsequent recovery stroke, the wing
pushes down on the lifted water sending ripples around the wing.
The response of the water surface to the bee
’
s wing motion is
clearly shown in
Movie S1
; however, the free surface visualiza-
tion alone is not enough to estimate the momentum transport.
Instead, a proper calculation of the momentum exerted by the
wing motion requires flow measurement.
To accomplish this, a mechanical wing model was constructed
(
Materials and Methods
and
SI Appendix
, Fig. S8
), and the flow
directly under the mechanical wing was measured using DPIV
(
SI Appendix
,
Materials and Methods
). This model was necessary
to measure the flow because of the unpredictable movement of
honeybees. We ensured that the mechanical wing replicates
general features of the honeybee
’
s wing kinematics (compare
Fig. 4
A
and
B
with Fig. 5
A
and
B
; also compare
SI Appendix
,
Fig. S8
C
with
SI Appendix
, Fig. S8
D
) and the free surface re-
sponse (compare
Movie S1
with
Movie S4
). A time-resolved
body motion calculated from the measured flow field (
SI Ap-
pendix
, Fig. S8
E
–
G
)
also resembles the body motion of the
honeybee (Fig. 2
A
–
C
). One main difference is that the me-
chanical wing is only passively supinated and pronated by its
flexibility, whereas the bee
’
s wing rotation can be effected both
actively and passively. The flow generated by the model wing
actuated at 30 Hz is shown in Fig. 5 (
Movie S5
) (15).
The flow averaged over a period shows that negative hori-
zontal momentum is imparted to the water underneath the wing
(Fig. 5
C
). This clearly shows that the mechanical wing motion
mimicking the honeybee
’
s wing kinematics results in nonzero
horizontal thrust. In addition, a periodically oscillating momen-
tum is observed (Fig. 5
D
and Movie S5
). Based on the order of
magnitude analysis of the different hydrodynamic forces in-
volved, the only force that can account for this oscillation is
unsteady inertial force (added mass) associated with the wing
Fig. 3.
Body acceleration and wing kinematics. (
A
) Leading-edge vertical
position and acceleration of the bee
’
s body. Wing-beat frequency, 44 Hz.
Blue
−
○
line indicates the leading edge vertical position. Red
−
×
line indi-
cates the acceleration. Shaded regions, power stroke phase. Nonshaded re-
gion, recovery stroke phase. (
B
) The wing position corresponding to each
time point marked on
A
;t1
–
t5,
Top
to
Bottom
.
Fig. 4.
Honeybee wing kinematics. (
A
) Leading edge position. Wing-beat
frequency, 63 Hz. Shaded regions, power stroke phase. Nonshaded region,
recovery stroke phase. Left corner wing indicates the measurement location,
where red circle indicates leading edge. (
B
) Supination and pronation angle.
(
C
) Approximated wing motion. The wing motion was estimated with
straight line.
θ
1
=
pronation and supination angle.
θ
2
=
stroke plane angle.
Time stamp at the corner corresponds to time axis on
A
and
B
. The blue
dashed line represents undisturbed air
–
water interface.
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movement (
SI Appendix
,
Detailed Calculations III
). While this
reactive force does not impart net thrust, it can move the body,
which is known as recoil locomotion (16, 17). This unsteady force
also explains the oscillatory body velocity and acceleration seen
in the body kinematics of the honeybee (Fig. 2).
One question that remains is how the wing kinematics are able
to generate positive thrust. From the time-varying flow field and
the corresponding wing kinematics, we suggest a potential mech-
anism of net negative horizontal momentum generation. By the
end of the power stroke, the diagonally lifting wing has accelerated
water upward and backward (Fig. 5
D
,t
=
13.3 ms). In transitioning
to the recovery stroke, the wing pronates, progressively flattening its
conformation (Fig. 5
B
and
D
). The decreased wing angle would
reduce the wing
’
s interaction with the horizontal flow during the
recovery stroke, which would sustain a portion of the horizontal
momentum produced by the power stroke. Hence, over a period of
wing motion, the wing would impart net negative horizontal mo-
mentum to the water. As the wing resets to the initial position, the
excess water momentum would be shed at the trailing edge as the
surface wave and wake.
The current analysis of a bee
’
s hydrofoiling capability lacks
certain considerations. Here, only general features of the wing
kinematics are described. In the future, more detailed wing ki-
nematics need to be studied. One feature that has not been
discussed is the apparent wing bending resulting from its com-
pliance. The interaction between a compliant wing and hydro-
dynamic forces would result in a transient solid
–
fluid wave. This
wave is a dynamic phenomenon, which introduces a timescale to
the well-studied quasistatic interaction between flexible sheet
and hydrostatic forces (18, 19). The wave motion on the wing
would be governed by the bending stiffness of the wing and the
added mass of the water. If the mass of the thin elastic sheet is
negligible compared to the accelerating water mass, the wave
speed,
c
, should scale as
c
2
∼
k
2
×
(bending stiffness)/(added
mass), where
k
is the wave number. The shape of the wing de-
formation would correspond to the sections of the traveling solid
–
fluid wave form.
Moreover, we did not discuss the effect of surface tension and
gravitational force. The surface tension and gravitational force
are an order of magnitude smaller than the added mass force
(added mass number
=
added mass force/steady inertial force
∼
20;
Weber number
=
steady inertial force/surface tension
∼
1, Froude
number
=
steady inertial force/gravitational force
∼
3;
SI Appendix
,
Detailed Calculations III
). Although these forces are relatively
small, they may be important in determining the boundary con-
ditions at the leading and trailing edges of the wing. For instance,
the shedding of surface wave and wake might be determined by the
impedance mismatch at the trailing edge (the impedance of the
elastic sheet region would be water density times the wave speed
described above; the impedance of the water surface region would
be water density times the wave speed governed by the surface
tension and gravitational force). The mismatched impedance
would determine how much of the propagating solid
–
fluid wave
would be transmitted and reflected at the trailing edge.
Discussion
Comparison with Other Water Surface Locomotion.
The hydrofoiling
of the honeybee is a form of biolocomotion that has not pre-
viously been characterized. Most semiaquatic insects utilize thin
hydrophobic legs for their propulsion, known as water walking
(20
–
22). Water walking relies on the surface tension rather than the
inertia of water, characterized by a small Weber number
<<
O
(
1
).
The honeybee
’
s hydrofoiling involves the unsteady inertial
force (i.e., added mass) as the dominant hydrodynamic force.
Furthermore, whereas the power stroke of the water walker
strikes down on the water surface, the bee
’
s power stroke lifts the
water surface. Thus, the 2 locomotion strategies are dynamically,
kinematically, and morphologically distinct.
Fig. 5.
Mechanical wing kinematics and resulting flow. (
A
) Leading edge position. Wing-beat frequency, 30 Hz. Shaded regions, power stroke phase.
Nonshaded region, recovery stroke phase. The left corner wing indicates the measurement location, where red circle indicates leading edge. (
B
) Supination
and pronation angle. (
C
) Time-averaged horizontal velocity over 3 periods. (
D
) Velocity field under the wing. The black line above the velocity field is the
cross-section of the wing. Time stamp at the corner corresponds to the time axis on
A
and
B
.See
Movie S5
for a full sequence. The red
“
o
”
and
“
x
”
mark the
leading and trailing edges, respectively. An angle that the red dotted line makes with a horizontal axis is the supination/pronation angle.
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The locomotion of the honeybee is also different from fully
submerged aquatic insects that swim near the water surface, such
as the whirligig beetle (23) and the water boatman (24). Both the
whirligig beetle and water boatman use drag-based propulsion
with their legs, which uses asymmetric power and recovery stroke
speed and propulsive area to create net thrust. The drag-based
propulsion relies on steady inertial force; however, unsteady in-
ertial force is dominant in the honeybee
’
s hydrofoiling.
Another interesting water surface locomotion strategy is a
Marangoni propulsion displayed by some hemipterans and rove
beetles (21, 22). These insects locally release a surfactant (a
chemical that lowers surface tension) to create uneven surface
tension around their bodies. The resulting surface tension gra-
dient provides forward thrust. The Marangoni propulsion mecha-
nism is different from the mechanically driven propulsion strategies
mentioned above, as it is driven chemically.
Perhaps most similar to the honeybee
’
s hydrofoiling locomo-
tion is a rowing locomotion of the stonefly (7). Rowing is one of
the stonefly
’
s locomotion modes that mixes both hydrodynamic
(drag-based) and aerodynamic (lift-based) propulsion. It is in-
teresting to note that this locomotion may also utilize added
mass (unsteady inertial force) as part of its propulsion. From the
video provided in the referenced paper, it appears that the
stonefly
’
s forewing supinated before detaching from the water.
Presumably, this wing kinematics produce similar acceleration of
the water mass underneath the lifting wing. The stonefly
’
s wing
motion appears to be more effective for propulsion, because
after wing detaches from the water surface, the wing no longer
interacts with the accelerated water mass.
Compared to water surface locomotion of other insects, nei-
ther the speed nor the efficiency achieved by the honeybee
’
s
hydrofoiling impresses. The 3 body length per s speed is much
slower than the top speed of water striders, whirligig beetles, and
water boatmen. Moreover, we have observed that honeybees can
sustain hydrofoiling for only about 2 to 5 min. The short duration
might indicate large consumption of energy or muscle fatigue,
most likely as the consequence of accelerating and decelerating a
fluid 1,000 times denser. Nevertheless, this duration gives hon-
eybees a range of approximately 5 to 10 m, which may be enough
to reach the shore. When bees were placed on the surface of a
local pond, they were able to locomote to the shore and pull
themselves out of the water. A similar observation was reported
in a previous study (25). Once out of the water, they dry them-
selves for a short time and fly away.
Applications to Robotics.
The hydrofoiling mechanism inspires an
aerial
–
aquatic hybrid vehicle. The honeybee
’
s propulsion with
wetted wings show that the flapping-wing system is a viable way
to generate thrust both in the air and on a water surface. As such,
this mechanism could provide flapping aerial vehicles with
swimming capability on water surfaces without imposing signifi-
cant changes to their morphologies. For successful implementa-
tion of the hydrofoiling mechanism in a robotic system, several
parameters need to be considered.
First, the scaling analysis suggests that the unsteady inertial
force is important for generating thrust. The unsteady inertial
force scales with amplitude and frequency of the wing motion (
SI
Appendix
,
Detailed Calculations III
); thus, increasing amplitude
and frequency can augment propulsion. Second, it is impor-
tant for the wing
’
s leading edge to move diagonally, rather than
vertically. This is so the wing generates a horizontal component of
thrust. Third, to take advantage of a passive supination and pro-
nation of the wing, it is important to consider the solid
–
fluid
interaction timescale, which is governed by the suggested wave
speed,
c
. The much weaker net force of hydrofoiling, compared to
that of flight, is due to the large deceleration of body speed during
the recovery stroke (Fig. 3). By timing the recovery stroke to more
precisely coincide with passive pronation, a flattened wing may
reduce the negative thrust generated and thus improve overall
thrust production. Last, wing surface microstructures and chem-
istry may provide another opportunity to bypass negative thrust
generation. The static and dynamic hydrophobicity of the water-
walking insect
’
s legs (26) and the wings of the stonefly (5) are
affected by hair and surface chemistry. If the hydrofoiling wing can
detach from the water surface following the power stroke, the
recovery stroke may be able to avoid adverse thrusting.
Biological Implications.
Hydrofoiling may also have important bio-
logical implications on the survival of water-collecting honeybees.
On a hot summer day, 10 to 14% of the foraging honeybees collect
water instead of nectar for hive thermoregulation (27). With in-
creased activity near the water, foragers may fall onto a water
surface more often. Although hydrofoiling with wetted wings is not
as effective as flying, when becalmed on a water surface, the ability
to self-propel to shore may increase the chance of survival.
More broadly, winged locomotion on a water surface could be
an evolutionarily important category of biolocomotion. One of
the hypotheses on the origin of insect flight is that flight evolved
from the locomotion on a water surface (7), on which the weight
of an organism is offset by either buoyancy or surface tension.
While it is unlikely that the honeybee
’
s flight evolved from their
water surface locomotion, the mechanism of hydrofoiling may
have biomechanical resemblances to early preflight locomotion.
Materials and Methods
Mechanical Wing Model.
The mechanical model was constructed to simulate
the wing kinematics of the bee (
SI Appendix
, Fig. S8
). The model was con-
structed from a magnetic actuator (Plantraco Microflight) and a wing frame
connected to a plastic platform. The magnetic actuator uses a magnetic field
generated by the electric current flowing through copper coil to torque the
lever with neodymium magnets. The wing frame was constructed by
bending a steel wire with 0.38-mm diameter. The wings were constructed
from a polyester film with 12.7-
μ
m thickness. The polyester film was cut into
a rectangle shape with 0.75-inch span length and 0.25-inch chord length.
The wing motion was generated by the magnetic actuator pulling on the 2
ends of the wing frame with a silk string. A function generator (HP 3314A)
was used to power and control the magnetic actuator with a square wave of
50% duty cycle at varying frequencies.
Data Availability Statement.
All data discussed in the paper will be made available
to readers upon request. The flow fie
ld data in Fig. 5 are available at
https://
data.caltech.edu/records/1292
. MATLAB code developed during the current
study are available from the correspond
ing author upon reasonable request.
ACKNOWLEDGMENTS.
We thank davidkremers, Cong Wang, and Jennifer
Han for their reviews and comments on the manuscript. We also thank
anonymous reviewers for their insights and comments. An IDT-OS3-S3 cam-
era was provided by IDT, for which we are grateful. We thank Editage for
their language-editing service. This material is based upon work supported
by the National Science Foundation under Grant CBET-1511414; additional
support was provided to C.R. by a National Science Foundation Graduate
Research Fellowship under Grant DGE-1144469. This work was partially sup-
ported by Charyk Bio-inspired Laboratory at California Institute of Technology.
1. J. H. Marden, M. G. Kramer, Surface-skimming stoneflies: A possible intermediate
stage in insect flight evolution.
Science
266
, 427
–
430 (1994).
2. H. Mukundarajan, T. C. Bardon, D. H. Kim, M. Prakash, Surface tension dominates
insect flight on fluid interfaces.
J. Exp. Biol.
219
, 752
–
766 (2016).
3. J. H. Marden, B. C. O
’
Donnell, M. A. Thomas, J. Y. Bye, Surface-skimming stoneflies
and mayflies: The taxonomic and mechanical diversity of two-dimensional aero-
dynamic locomotion.
Physiol. Biochem. Zool.
73
, 751
–
764 (2000).
4. D.-G. Lee, H.-Y. Kim, The role of superhydrophobicity in the adhesion of a floating
cylinder.
J. Fluid Mech.
624
,23
–
32 (2009).
5. T. Wagner, C. Neinhuis, W. Barthlott, Wettability and contaminability of in-
sect wings as a function of their surface sculptures.
Acta Zool.
77
,213
–
225
(1996).
6. Y. Liang, J. Zhao, S. Yan, Honeybees have hydrophobic wings that enable them to fly
through fog and dew.
J. Bionics Eng.
14
, 549
–
556 (2017).
24450
|
www.pnas.org/cgi/doi/10.1073/pnas.1908857116
Roh and Gharib
Downloaded at California Institute of Technology on December 3, 2019
7. J. H. Marden, M. A. Thomas, Rowing locomotion by a stonefly that possesses the
ancestral pterygote condition of co-occurring wings and abdominal gills: Rowing by
an adult stonefly with gills.
Biol. J. Linn. Soc. Lond.
79
, 341
–
349 (2003).
8. H. Kovac, A. Stabentheiner, S. Schmaranzer, Thermoregulation of water foraging
honeybees
—
balancing of endothermic activity with radiative heat gain and functional
requirements.
J. Insect Physiol.
56
,1834
–
1845 (2010).
9. D. L. Altshuler, W. B. Dickson, J. T. Vance, S. P. Roberts, M. H. Dickinson, Short-
amplitude high-frequency wing strokes determine the aerodynamics of honeybee
flight.
Proc. Natl. Acad. Sci. U.S.A.
102
, 18213
–
18218 (2005).
10. J. M. Peters, N. Gravish, S. A. Combes, Wings as impellers: Honey bees co-opt flight system
to induce nest ventilation and disperse pheromones.
J. Exp. Biol.
220
, 2203
–
2209 (2017).
11. A. M. Wenner, The flight speed of honeybees: A quantitative approach.
J. Apic. Res.
2
,
25
–
32 (1963).
12. M. S. Longuet-Higgins, R. W. Stwert, Radiation stresses in water waves; a physical
discussion, with applications.
Deep-Sea Res.
11
, 529
–
562 (1964).
13. C. E. Willert, M. Gharib, Digital particle image velocimetry.
Exp. Fluids
10
, 181
–
193
(1991).
14. O. Bühler, Impulsive fluid forcing and water strider locomotion.
J. Fluid Mech.
573
,
211
–
236 (2007).
15. C. Roh, M. Gharib, Hydrofoiling honeybee velocity field data. CaltechDATA. https://
doi.org/10.22002/d1.1292. Deposited 8 October 2019.
16. P. G. Saffman, The self-propulsion of a deformable body in a perfect fluid.
J. Fluid
Mech.
28
, 385
–
389 (1967).
17. S. Childress,
“
The Eulerian realm: The inertial force
”
in
Mechanics of Swimming and
Flying
(Cambridge University Press, 1981), pp. 76
–
88.
18. E. Jambon-Puillet, D. Vella, S. Protière, The compression of a heavy floating elastic
film.
Soft Matter
12
, 9289
–
9296 (2016).
19. D. Vella, Floating versus sinking.
Annu. Rev. Fluid Mech.
47
, 115
–
135 (2015).
20. D. L. Hu, B. Chan, J. W. M. Bush, The hydrodynamics of water strider locomotion.
Nature
424
, 663
–
666 (2003).
21. J. W. M. Bush, D. L. Hu, Walking on water: Biolocomotion at the interface.
Annu. Rev.
Fluid Mech.
38
,
339
–
369 (2006).
22. D. L. Hu, J. W. M. Bush, The hydrodynamics of water-walking arthropods.
J. Fluid
Mech.
644
,5
–
33 (2010).
23. J. Voise, J. Casas, The management of fluid and wave resistances by whirligig beetles.
J. R. Soc. Interface
7
, 343
–
352 (2010).
24. V. Ngo, M. J. McHenry, The hydrodynamics of swimming at intermediate Reynolds
numbers in the water boatman (Corixidae).
J. Exp. Biol.
217
, 2740
–
2751 (2014).
25. J. O. Moffett, H. L. Morton, Surfactants in water drown honey bees.
Environ. Entomol.
2
, 227
–
231 (1973).
26. J. W. M. Bush, D. L. Hu, M. Prakash,
“
The integument of water-walking arthropods:
Form and function
”
in
Advances in Insect Physiology, Insect Mechanics and Control
,
J. Casas, S. J. Simpson, Eds. (Academic Press, 2007), pp. 117
–
192.
27. S. Kühnholz, T. D. Seeley, The control of water collection in honey bee colonies.
Behav.
Ecol. Sociobiol.
41
, 407
–
422 (1997).
Roh and Gharib
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|
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|
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|
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|
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