In their daily lives, flying insects face a gauntlet of environmental challenges, from wind gusts to raindrop impacts. In this combined experimental and theoretical study, we use high-speed videography to film raindrop collisions upon both flying insects and dynamically scaled spherical mimics. We identify three outcomes of the collision based upon the insect's mass and characteristic size: drops push the insect while remaining intact, coat the insect, and splash. We present a mathematical model that predicts impact force and outcome consistent with those found in experiments. Small insects such as gnats and flies are pushed by raindrops that remain intact upon impact; conversely, large flyers such as locusts and micro-aerial vehicles cause drops to splash. We identify a critical mass of 0.3 g for which flyers achieve both peak acceleration (100 g) and applied force (104 dyn) from incoming raindrops; designs of similarly massed flying robots should be avoided.
REFERENCES
1.
R.
Wood
, “The first takeoff of a biologically inspired at-scale robotic insect
,” IEEE Trans. Robotics
24
, 341
–347
(2008
).2.
G.
De Croon
, K.
De Clercq
, R.
Ruijsink
, B.
Remes
, and C.
De Wagter
, “Design, aerodynamics, and vision-based control of the DelFly
,” Int. J. Micro Air Vehicles
1
, 71
–97
(2009
).3.
C.
Richter
and H.
Lipson
, “Untethered hovering flapping flight of a 3D-printed mechanical insect
,” Artif. Life
17
, 73
–86
(2011
).4.
F.
Van Breugel
, Z.
Teoh
, and H.
Lipson
, “A passively stable hovering flapping micro-air vehicle
,” Flying Insects and Robots
(Springer
, 2010
), pp. 171
–184
.5.
G. J.
Amador
, Y.
Yamada
, M.
McCurley
, and D. L.
Hu
, “Splash-cup plants accelerate raindrops to disperse seeds
,” J. R. Soc. Interface
10
, 0880
(2013
).6.
7.
E.
Reyssat
, F.
Chevy
, A.-L.
Biance
, L.
Petitjean
, and D.
Quéré
, “Shape and instability of free-falling liquid globules
,” Europhys. Lett.
80
, 34005
(2007
).8.
C.
Voigt
, K.
Schneeberger
, S.
Voigt-Heucke
, and D.
Lewanzik
, “Rain increases the energy cost of bat flight
,” Biol. Lett.
7
, 793
–795
(2011
).9.
V.
Ortega-Jimenez
and R.
Dudley
, “Aerial shaking performance of wet Anna's hummingbirds
,” J. R. Soc. Interface
9
, 1093
–1099
(2011
).10.
A. K.
Dickerson
, P. G.
Shankles
, N. M.
Madhavan
, and D. L.
Hu
, “Mosquitoes survive raindrop collisions by virtue of their low mass
,” Proc. Natl. Acad. Sci. U.S.A.
109
, 9822
–9827
(2012
).11.
T.
Weis-Fogh
, “Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production
,” J. Exp. Biol.
59
, 169
–230
(1973
).12.
A. R.
Ennos
, “The kinematics and aerodynamics of the free flight of some Diptera
,” J. Exp. Biol.
142
, 49
–85
(1989
).13.
S. N.
Fry
, R.
Sayaman
, and M. H.
Dickinson
, “The aerodynamics of hovering flight in Drosophila
,” J. Exp. Biol.
208
, 2303
–2318
(2005
).14.
C.
Ellington
, “The aerodynamics of hovering insect flight. III. Kinematics
,” Philos. Trans. R. Soc. London, Ser. B
305
, 41
–78
(1984
).15.
C.
Ellington
, “The aerodynamics of hovering insect flight. II. Morphological parameters
,” Philos. Trans. R. Soc. London, Ser. B
305
, 17
–40
(1984
).16.
Y.
Liu
and M.
Sun
, “Wing kinematics measurement and aerodynamics of hovering droneflies
,” J. Exp. Biol.
211
, 2014
–2025
(2008
).17.
R.
Dudley
, “Extraordinary flight performance of orchid bees (Apidae: Euglossini) hovering in heliox (80% He/20% O2)
,” J. Exp. Biol.
198
, 1065
–1070
(1995
).18.
R.
Dudley
and C.
Ellington
, “Mechanics of forward flight in bumblebees: I. Kinematics and morphology
,” J. Exp. Biol.
148
, 19
–52
(1990
).19.
A. P.
Willmott
and C. P.
Ellington
, “The mechanics of flight in the hawkmoth manduca sexta. II. Aerodynamic consequences of kinematic and morphological variation
,” J. Exp. Biol.
200
, 2723
–2745
(1997
).20.
A. P.
Willmott
and C. P.
Ellington
, “The mechanics of flight in the hawkmoth Manduca sexta. I. Kinematics of hovering and forward flight
,” J. Exp. Biol.
200
, 2705
–2722
(1997
).21.
P.
Chai
and D.
Millard
, “Flight and size constraints: Hovering performance of large hummingbirds under maximal loading
,” J. Exp. Biol.
200
, 2757
–2763
(1997
).22.
D.
Byun
et al., “Wetting characteristics of insect wing surfaces
,” J. Bionic Eng.
6
, 63
–70
(2009
).23.
Y.
Zheng
, X.
Gao
, and L.
Jiang
, “Directional adhesion of superhydrophobic butterfly wings
,” Soft Matter
3
, 178
–182
(2007
).24.
E.
Villermaux
, B.
Bossa
et al., “Drop fragmentation on impact
,” J. Fluid Mech.
668
, 412
–435
(2011
).25.
A.
Yarin
, “Drop impact dynamics: Splashing, spreading, receding, bouncing …
,” Annu. Rev. Fluid Mech.
38
, 159
–192
(2006
).26.
Y.
Jiang
, A.
Umemura
, and C.
Law
, “An experimental investigation on the collision behaviour of hydrocarbon droplets
,” J. Fluid Mech.
234
, 171
–190
(1992
).27.
M.
Orme
, “Experiments on droplet collisions, bounce, coalescence and disruption
,” Prog. Energy Combust. Sci.
23
, 65
–79
(1997
).28.
M.
Rein
, “Phenomena of liquid drop impact on solid and liquid surfaces
,” Fluid Dyn. Res.
12
, 61
–93
(1993
).29.
J.
Field
, J.
Dear
, and J.
Ogren
, “The effects of target compliance on liquid drop impact
,” J. Appl. Phys.
65
, 533
–540
(1989
).30.
S.
Bakshi
, I.
Roisman
, and C.
Tropea
, “Investigations on the impact of a drop onto a small spherical target
,” Phys. Fluids
19
, 032102
(2007
).31.
A.
Rozhkov
, B.
Prunet-Foch
, and M.
Vignes-Adler
, “Dynamics of a liquid lamella resulting from the impact of a water drop on a small target
,” Proc. R. Soc. London, Ser. A
460
, 2681
(2004
).32.
A.
Rozhkov
, B.
Prunet-Foch
, and M.
Vignes-Adler
, “Impact of water drops on small targets
,” Phys. Fluids
14
, 3485
(2002
).33.
M.
Bussmann
, J.
Mostaghimi
, and S.
Chandra
, “On a three-dimensional volume tracking model of droplet impact
,” Phys. Fluids
11
, 1406
(1999
).34.
S.
Chandra
and C.
Avedisian
, “On the collision of a droplet with a solid surface
,” Proc. Math. Phys. Sci.
432
, 13
–41
(1991
).35.
D.
Hauser
, P.
Amayenc
, B.
Nutten
, and P.
Waldteufel
, “A new optical instrument for simultaneous measurement of raindrop diameter and fall speed distributions
,” J. Atmos. Oceanic Technol.
1
, 256
–269
(1984
).36.
R.
Gunn
and G.
Kinzer
, “The terminal velocity of fall for water droplets in stagnant air
,” J. Meteorol.
6
, 243
–248
(1949
).37.
C.
Clanet
, C.
Béguin
, D.
Richard
, and D.
Quéré
, “Maximal deformation of an impacting drop
,” J. Fluid Mech.
517
, 199
–208
(2004
).38.
J. E.
McDonald
, “Collection and washout of airborne pollens and spores by raindrops
,” Science
135
, 435
–437
(1962
).39.
J. P.
Stapp
, “Effects of mechanical force on living tissues
,” J. Aviation Med.
26
, 268
(1955
).40.
H.
Bennet-Clark
and E.
Lucey
, “The jump of the flea: A study of the energetics and a model of the mechanism
,” J. Exp. Biol.
47
, 59
–76
(1967
).41.
M.
Pasandideh-Fard
, Y.
Qiao
, S.
Chandra
, and J.
Mostaghimi
, “Capillary effects during droplet impact on a solid surface
,” Phys. Fluids
8
, 650
(1996
).42.
C.
Mundo
, M.
Sommerfeld
, and C.
Tropea
, “Droplet-wall collisions: Experimental studies of the deformation and breakup process
,” Int. J. Multiphase Flow
21
, 151
–173
(1995
).43.
J.
Keller
, “Teapot effect
,” J. Appl. Phys.
28
, 859
–864
(1957
).44.
C.
Duez
, C.
Ybert
, C.
Clanet
, and L.
Bocquet
, “Wetting controls separation of inertial flows from solid surfaces
,” Phys. Rev. Lett.
104
, 084503
(2010
).45.
T. A.
McMahon
and J. T.
Bonner
, On Size and Life
(Scientific American Books
, New York, NY
, 1983
).46.
K.
Schmidt-Nielson
, Scaling
(Cambridge University Press
, New York, NY
, 1984
).47.
C.
Ellington
, “Limitations on animal flight performance
,” J. Exp. Biol.
160
, 71
–91
(1991
).48.
O.
Povarov
, O.
Nazarov
, L.
Ignat'evskaya
, and A.
Nikol'skii
, “Interaction of drops with boundary layer on rotating surface
,” J. Eng. Phys. Thermophys.
31
, 1453
–1456
(1976
).© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
You do not currently have access to this content.
