Home
Search
Collections
Journals
About
Contact us
My IOPscience
Leading edge vortices in lesser long-nosed bats occurring at slow but not fast flight speeds
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Bioinspir. Biomim. 9 025006 (http://iopscience.iop.org/1748-3190/9/2/025006) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 46.7.197.38 This content was downloaded on 25/05/2014 at 06:14
Please note that terms and conditions apply.
Bioinspiration & Biomimetics Bioinspir. Biomim. 9 (2014) 025006 (9pp)
doi:10.1088/1748-3182/9/2/025006
Leading edge vortices in lesser long-nosed bats occurring at slow but not fast flight speeds Florian T Muijres1,2, L Christoffer Johansson1, York Winter3 and Anders Hedenström1 1
Department of Biology, Lund University, Ecology Building, SE-223 62 Lund University, Sweden Department of Biology, Box 351800, 24 Kincaid Hall, University of Washington, Seattle, WA 98195-1800, USA 3 Cognitive Neurobiology, Humboldt University, Berlin, Germany 2
E-mail: [email protected] Received 8 November 2013, revised 23 April 2014 Accepted for publication 23 April 2014 Published 22 May 2014 Abstract
Slow and hovering animal flight creates high demands on the lift production of animal wings. Steady state aerodynamics is unable to explain the forces required and the most commonly used mechanism to enhance the lift production is a leading edge vortex (LEV). Although LEVs increase the lift, they come at the cost of high drag. Here we determine the flow above the wing of lesser long-nosed bats at slow and cruising speed using particle image velocimetry (PIV). We find that a prominent LEV is present during the downstroke at slow speed, but not at cruising speed. Comparison with previously published LEV data from a robotic flapper inspired by lesser long-nosed bats suggests that bats should be able to generate LEVs at cruising speeds, but that they avoid doing so, probably to increase flight efficiency. In addition, at slow flight speeds we find LEVs of opposite spin at the inner and outer wing during the upstroke, potentially providing a control challenge to the animal. We also note that the LEV stays attached to the wing throughout the downstoke and does not show the complex structures found in insects. This suggests that bats are able to control the development of the LEV and potential control mechanisms are discussed. S Online supplementary data available from stacks.iop.org/BB/9/025006/mmedia Keywords: aerodynamics, leading edge vortex, bat flight, control, delayed stall Introduction
obtaining the lift can be made from L = ρΓUb,
According to steady state aerodynamics the lift of a wing is given by L=
1 2 ρU SCL , 2
where Γ is the bound circulation and b is the wing span. By combining equations (1) and (2) and noting that S = bc, where c is the mean chord, we get that
(1)
CL = 2Γ Uc .
where ρ is the air density, U is the speed relative to the air, S is the wing area and CL is the lift coefficient. The lift coefficient is a composite variable that describes the capability of the wing to generate lift, related to factors such as angle of attack, shape and camber. The lift is also determined by the circulation about the wing, and an alternative way of 1748-3182/14/025006+09$33.00
(2)
(3)
showing the direct connection between circulation and the lift coefficient. As mentioned, the lift coefficient depends on the angle of attack and increases with increasing angle of attack until it reaches a point where a further increase in the angle of attack results in the flow separating from the wing surface and stall 1
© 2014 IOP Publishing Ltd Printed in the UK
F T Muijres et al
Bioinspir. Biomim. 9 (2014) 025006
Table 1. Studies on the leading edge vortices by means of mechanical models (flappers) dynamically scaled to mimic animal flight or direct studies involving real animals, with speed U and Reynolds number Re.
LEV (% weight support)
Species
Condition
Method
U (m s−1)
Manduca sexta
Tether
Smoke rake
0.4–5.7
Manduca sexta
Model
Smoke rake
0.4
Increasing with U LEV, 65%
Manduca sexta Vanessa atalanta
Tether Free flight (take off) Tether Tether Model
DPIV Smoke rake
1.2, 3.5 1.5
10%, 35-65% LEV
DPIV DPIV
0.42 0.42 0
LEV LEV LEV, 45%
Model
DPIV
0
120–1400
Model
PIV
0
160 (100–250)
0
Model
Colour-coded DPIV Air bubbles
0
110–14 000
Free flight
DPIV
1–2
1000–1400
Smoke rake Smoke rake
1.2 (−1.5–1.8)
2500
Dragonfly
Free flight Tether, free flight Model
Dye, DPIV
0
160–3200
Selasphorua rufus Hummingbird Ficedula hypoleuca Apus apus Goose
Free flight Model Free flight Model Model
DPIV SPI PIV PIV PIV
LEV, 16% LEV LEV, 49% LEV LEV
Glossophaga soricina Leptonycteris yerbabuenae
Free flight
PIV
0 hover 920–5070 1 11 (swept wing) 37 500 56 000 (28 000 −113 000) 1 5000
Free flight
PIV
1, 5
12 000, 18 000
Leptonycteris yerbabuenae
Model
PIV
1–7
8800–29 000
LEV (@1 m s−1 / no LEV (@1 m s−1) LEV
Cynthia cardui Idea leuconoe Drosophila melanogaster Drosophila melanogaster Drosophila melanogaster Drosophila melanogaster Drosophila melanogaster Macroglossum stellatarum
Bombus terrestris Dragonflies spp
Re
Ellington et al 1996 Van den Berg et al 1997 Bomphrey et al 2005 Srygley and Thomas 2002 Fuchiwaki et al 2013 Fuchiwaki et al 2013 Dickinson et al 1999 Birch et al 2004
LEV LEV
occurs. Stall results in a strong increase in drag without a corresponding increase in lift, which results in a reduction of the lift to drag ratio (L/D), i.e. a reduction of the efficiency of lift production. The propensity of flow separation depends on the ratio between viscous and inertial forces, which is described by the Reynolds number, Re = Uc/ν, where ν is the kinematic viscosity. The maximum steady-state lift coefficient, and hence the maximum lift capacity of a fixed wing, at the relatively low Re relevant for animal flight is about 1.6 (Laitone 1997), but in many cases of animal wings the maximum steady-state CL is lower still (Spedding 1992). The maximum steady-state CL has in many cases been shown to
Source
LEV, 38–39% inner wing, 132–145% outer wing LEV LEV LEV
LEV, 42%
Birch and Dickinson 2001 Pick and Lehmann 2009 Lentink and Dickinson, 2009 Johansson et al 2013
Bomphrey et al 2009 Thomas et al 2004 Lu et al 2006, Lu and Shen 2008 Warrick et al 2009 Swanton et al 2010 Muijres et al 2012 Videler et al 2004 Hubel and Tropea 2010 Muijres et al 2008 This study
Koekkoek et al 2012
be insufficient to explain the lift required to support the weight of animals, especially in hovering flight (WeisFogh 1973, 1975, Ellington 1984, Sane 2003, Norberg 1975a, 1975b, Hedenström et al 2007, Rosén et al 2007) suggesting the use of unsteady mechanisms. Unsteady, time-dependent, aerodynamic mechanisms have in the past mainly been studied and discussed with respect to insect flight. A number of unsteady mechanisms have been suggested and confirmed in insect flight, i.e. clapand-fling, rotational lift, wake capture and dynamic stall with a leading edge vortex (LEV) (Ellington et al 1996, Dickinson et al 1999, Lehmann 2008). However, the utility of LEVs to 2
F T Muijres et al
Bioinspir. Biomim. 9 (2014) 025006
enhance lift seems universal in flying animals since small bats (Muijres et al 2008), hummingbirds (Warrick et al 2009) and flycatchers (Muijres et al 2012) also use LEVs to enhance their lift production during slow flight (table 1). In fact, LEVs may be universal in biological systems since they have also been discovered in winged plant seeds (Lentink et al 2009) and have been suggested to improve swimming performance in fish (Lauder et al 2007, Borazjani and Daghooghi 2013) and birds (Johansson and Norberg 2003). In flying animals the LEV stays attached to the wing throughout the downstroke and contributes 15–60% of the total lift (table 1), suggesting that it is of significant importance for flight at slow speeds and hovering. Despite the clear relevance of LEVs to lift production in biological systems, the exact mechanism of the LEV is still a focus of research (Pitt Ford and Babinsky 2013). However, using LEVs to increase the force production is associated with a cost since LEVs generate increased drag, and thus relatively low L/D (Dickinson et al 1999). This would suggest that animals should only use LEVs when absolutely necessary, e.g. during slow flight and manoeuvring, and avoid using LEVs at cruising flight, where the relatively high forward flight velocity reduces the necessity for high CL. Studies based on animal inspired models and mechanical flappers have indicated that birds and bats may be capable of using LEVs through a range of flight speeds (Videler et al 2004, Hubel and Tropea 2010, Koekkoek et al 2012). However, to the best of our knowledge, it has never been tested whether freely flying birds and bats use LEVs or not at cruising speed. In this paper we present data on LEV properties in the lesser long-nosed bat (Leptonycteris yerbabuenae), studied during free flight in a wind tunnel during both slow and cruising flight speed. These results are compared with equivalent data from a robotic flapper, inspired by the morphology and kinematics of a lesser long-nosed bat wing (Koekkoek et al 2012). In addition to new information about the LEV in bats, we also review studies of LEVs in live animals or models with animal-like morphology and kinematics.
downwind direction and blocked laser reflections from intersecting the eyes of the bats. Before and after each experimental session, the weight of each bat was measured using an electronic balance. The average body mass and wing morphological data for both bats are presented in table 2. The PIV system consisted of two synchronized, double frame, CMOS cameras (HighSpeedStar3; 1024 × 1024 pixels) in stereo setup and a 200 Hz double pulsed 50 mJ Laser (Litron LPY732 series, Nd:YAG, 532 nm), controlled by the LaVision PIV software package DaVis (LaVision, DaVis 7.2.2.110). For the PIV experiments the air was seeded by filling the wind tunnel with fog (particle size 1 μm). These fog particles were illuminated by the laser sheet. For each measurement, 100 pairwise images (1/2 s at 200 Hz, image size ∼20 × 20 cm and dt = 200–270 ms) of the illuminated particles were recorded by each CMOS camera and stored on a computer. Simultaneously, a high-speed (250 Hz) digital video camera captured the animal to monitor its movement. The laser sheet was positioned vertically in the streamwise direction. By repositioning the feeder relative to the PIV measurement plane, the airflow around different wing sections was sampled. The PIV image pairs used for the PIV analysis were selected manually. Image pairs were assessed as good when the fluid section above the wing surface was not blocked by the wing or any part of the animal in the background. The selected PIV images were pre-processed to reduce errors in the PIV calculations. Background noise was filtered out using a high-pass filter (medfilt2, Matlab 7.7.0.471, R2008b, boxsize 15 × 15), and a mask was created over the part of the image where the bat was visible. The PIV images were analysed using the Lavision PIV software package DaVis (LaVision, DaVis 7.2.2.110) using a multi-pass normalized cross-correlation (32 × 32 and 16 × 16, 50% overlap, Whittaker reconstruction), followed by smoothing {3 × 3}. Due to the fact of the wing blocking the view of the different cameras during different phases of the wing beat a stereo analysis was not always possible, in which case we performed a 2D analysis using the camera with a clear view of the flow above the wing. The resulting velocity fields {u, w} were imported into a custom-made PIV analysis program (Matlab 7.7.0.471, R2008b), in which the spanwise vorticity (ωy) field was calculated, and corresponding vortex circulation could be calculated. Vortex circulation was calculated by manually selecting the patch of high vorticity associated with each LEV. Within this patch, vorticity was integrated over all the PIV node points with vorticity values above the threshold |ω|min = 100 s−1. This threshold was chosen because it lay above the background vorticity level in an empty wind tunnel running at the maximum experimental speed of 5 m s−1. The vorticity distribution outside the |ω|min iso-line was assumed to have a normal Gaussian distribution, so the total circulation of a vortex was estimated as Γ = (1 + |ω|min/|ω|max) Γmeasured, where Γmeasured is the measured circulation above the threshold |ω|min, and |ω|max is the maximum absolute vorticity in the vortex area (see Spedding et al 2003, Hedenström et al 2006).
Methods One male and one female lesser long-nosed bat were trained to fly in the Lund university low-turbulence wind tunnel (Pennycuick et al 1997, Spedding et al 2009). For the experiments the wind tunnel was constantly running at the required speed of 1 m s−1 or 5 m s−1, while the bats were roosting on the mesh within the settling chamber. When the bats were hungry, they would fly into the experimental test section of the wind tunnel, make a u-turn and approach a feeder from the downwind direction. When the bat was feeding from the feeder, experimental measurements were performed. The airflow around the bat wing was measured using a high-speed (200 Hz) stereographic particle image velocimetry (PIV) system. The feeder consisted of a metal tube providing honey water, and a mask that forced the bats to feed from the 3
F T Muijres et al
Bioinspir. Biomim. 9 (2014) 025006
Figure 1. Velocity and vorticity fields about the wing at mid-downstroke, of a lesser long-nosed bat (A), (B) and of a mechanical flapper
inspired by a lesser long-nosed bat, the RoBat (C), (D), (F). At low flight speeds (U = 1 m s−1) the real bats generate an attached LEV during the mid-downstroke (A), while at a cruising flight speed (U = 5 m s−1) the LEV is absent (B). The RoBat generates very similar vorticity field patterns with flapping kinematics similar to that of a lesser long-nosed bat, at both equivalent flight speeds (Ueq = 1 m s−1 and Ueq = 5 m s−1 for (C) and (D), respectively; Ueq is the airspeed of the dynamically scaled RoBat equivalent to that of a real bat). Operating the RoBat at Ueq = 5 m s−1 with an angle-of-attack similar to that of a real bat at U = 1 m s−1 (55°) leads to the development of an attached but bursting LEV. The colour bar shows magnitude and spin direction of vorticity (range −700 s−1 to 700 s−1). Scale bars in the panels are 10 mm and scale vectors are 10 m s−1. Panel E shows an image of a lesser long-nosed bat flying slowly in the Lund wind tunnel. All RoBat data (C)–(F) are from Koekkoek et al (2012).
Based on the wing movement, which was visible in the PIV images, the normalized time stamp τ for each PIV frame was determined by identifying each PIV frame with the highest wingtip position (τ = 0 for the start of the downstroke, and τ = 1 for the end of the upstroke), and the PIV frame with the lowest wingtip position (at U = 1 m s−1, τ = Rds = 0.42,
where Rds is the downstroke ratio (von Busse et al 2012). For the PIV frames in between, the normalized time stamp was linearly interpolated. For each measured LEV, its spanwise location was measured, as well as the local wing velocity. The relative spanwise location of the LEV was defined as b* = l/bw, where 4
F T Muijres et al
Bioinspir. Biomim. 9 (2014) 025006
Table 2. Flight morphology for the bat specimens (Leptonycteris yerbabuenae) used in the experiments, with body mass M, wing span b, wing surface area S, mean chord c (=S/b), aspect ratio AR (=b2/S) and wing loading Q (=Mg/S), where g is acceleration due to gravity.
male female
M (kg)
b (m)
S (m2)
c (m)
AR
Q (N m−2)
0.0213 0.0214
0.335 0.323
0.015 76 0.015 29
0.047 0.047
7.1 6.8
13.3 13.7
l is the distance between the leading edge−laser intersect and the wing root and bw is the distance between the wingtip and wing root, measured within the calibrated PIV images. The wing velocity was estimated by manual tracking the leading edge-laser intersection throughout the PIV image sequence. Ueff was determined as the vector sum of the resulting leading edge velocity and the forward flight speed U. The resulting wingbeat average effective velocity U¯eff and the mean wing cord were used to normalize LEV circulation by Γ U¯eff c . To account for the repeated measures setup, the mean strength and error of the mean of the positive and negative LEVs were estimated from a mixed model with normalized circulation as the dependent variable and individual and sequence (nested within individual) as random variables (JMP v11, SAS Institute Inc.). In addition, we tested whether the circulation of the LEV increases from the beginning of the downstroke (τ = 0) to the middle of the downstroke (τ = 0.25), using a mixed linear model with normalized circulation as the dependent variable, τ as the independent variable and the individual and sequence (nested within the individual) as random variables.
upwards directed aerodynamic force with the ventral wing surface facing upwards (Helversen 1986, Hedenström et al 2007). The outer part of the wing also generates a LEV during the upstroke (figure 2(B), see also supplementary movie 2, available at stacks.iop.org/BB/9/025006/mmedia), but the circulation is positive (anti-clockwise). The inner part of the wing does not move backwards faster than the forward flight speed resulting in the inner wing functioning in a similar way as during the downstroke and, at least during the initial part of the upstroke, we find a LEV of negative circulation at the inner wing (figure 2(A)). The experimental setup prevents us from determining if the LEV at the inner wing also exists during later phases of the upstroke. Quantitative measurements of circulation in the LEV at different locations along the wing and at different times of the wingbeat period are shown in figure 3(A). Normalized circulation (Γ U¯eff c , where U¯eff = 3.7 m s−1 and c = 0.047 m) of the LEV present during the downstroke and well into the upstroke (negative circulation) was −0.61 ± 0.030 (mean ± standard error) (figure 3(B)). At the outer wing, the opposite spinning LEV occurs from about τ ≈ 0.75 and is present towards the end of the upstroke (figure 3(A), see also supplementary movie 2, available at stacks.iop.org/BB/9/025006/ mmedia). The mean normalised circulation of the outer wing LEV was Γ U¯eff c = 0.60 ± 0.045. Our results show that the lesser long-nosed bat develops a LEV in slow (1 m s−1) forward flight at high angle of attack (∼55°, von Busse et al 2012), while it is absent at a faster forward flight speed (5 m s−1) and a moderate angle of attack (
Search
Collections
Journals
About
Contact us
My IOPscience
Leading edge vortices in lesser long-nosed bats occurring at slow but not fast flight speeds
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Bioinspir. Biomim. 9 025006 (http://iopscience.iop.org/1748-3190/9/2/025006) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 46.7.197.38 This content was downloaded on 25/05/2014 at 06:14
Please note that terms and conditions apply.
Bioinspiration & Biomimetics Bioinspir. Biomim. 9 (2014) 025006 (9pp)
doi:10.1088/1748-3182/9/2/025006
Leading edge vortices in lesser long-nosed bats occurring at slow but not fast flight speeds Florian T Muijres1,2, L Christoffer Johansson1, York Winter3 and Anders Hedenström1 1
Department of Biology, Lund University, Ecology Building, SE-223 62 Lund University, Sweden Department of Biology, Box 351800, 24 Kincaid Hall, University of Washington, Seattle, WA 98195-1800, USA 3 Cognitive Neurobiology, Humboldt University, Berlin, Germany 2
E-mail: [email protected] Received 8 November 2013, revised 23 April 2014 Accepted for publication 23 April 2014 Published 22 May 2014 Abstract
Slow and hovering animal flight creates high demands on the lift production of animal wings. Steady state aerodynamics is unable to explain the forces required and the most commonly used mechanism to enhance the lift production is a leading edge vortex (LEV). Although LEVs increase the lift, they come at the cost of high drag. Here we determine the flow above the wing of lesser long-nosed bats at slow and cruising speed using particle image velocimetry (PIV). We find that a prominent LEV is present during the downstroke at slow speed, but not at cruising speed. Comparison with previously published LEV data from a robotic flapper inspired by lesser long-nosed bats suggests that bats should be able to generate LEVs at cruising speeds, but that they avoid doing so, probably to increase flight efficiency. In addition, at slow flight speeds we find LEVs of opposite spin at the inner and outer wing during the upstroke, potentially providing a control challenge to the animal. We also note that the LEV stays attached to the wing throughout the downstoke and does not show the complex structures found in insects. This suggests that bats are able to control the development of the LEV and potential control mechanisms are discussed. S Online supplementary data available from stacks.iop.org/BB/9/025006/mmedia Keywords: aerodynamics, leading edge vortex, bat flight, control, delayed stall Introduction
obtaining the lift can be made from L = ρΓUb,
According to steady state aerodynamics the lift of a wing is given by L=
1 2 ρU SCL , 2
where Γ is the bound circulation and b is the wing span. By combining equations (1) and (2) and noting that S = bc, where c is the mean chord, we get that
(1)
CL = 2Γ Uc .
where ρ is the air density, U is the speed relative to the air, S is the wing area and CL is the lift coefficient. The lift coefficient is a composite variable that describes the capability of the wing to generate lift, related to factors such as angle of attack, shape and camber. The lift is also determined by the circulation about the wing, and an alternative way of 1748-3182/14/025006+09$33.00
(2)
(3)
showing the direct connection between circulation and the lift coefficient. As mentioned, the lift coefficient depends on the angle of attack and increases with increasing angle of attack until it reaches a point where a further increase in the angle of attack results in the flow separating from the wing surface and stall 1
© 2014 IOP Publishing Ltd Printed in the UK
F T Muijres et al
Bioinspir. Biomim. 9 (2014) 025006
Table 1. Studies on the leading edge vortices by means of mechanical models (flappers) dynamically scaled to mimic animal flight or direct studies involving real animals, with speed U and Reynolds number Re.
LEV (% weight support)
Species
Condition
Method
U (m s−1)
Manduca sexta
Tether
Smoke rake
0.4–5.7
Manduca sexta
Model
Smoke rake
0.4
Increasing with U LEV, 65%
Manduca sexta Vanessa atalanta
Tether Free flight (take off) Tether Tether Model
DPIV Smoke rake
1.2, 3.5 1.5
10%, 35-65% LEV
DPIV DPIV
0.42 0.42 0
LEV LEV LEV, 45%
Model
DPIV
0
120–1400
Model
PIV
0
160 (100–250)
0
Model
Colour-coded DPIV Air bubbles
0
110–14 000
Free flight
DPIV
1–2
1000–1400
Smoke rake Smoke rake
1.2 (−1.5–1.8)
2500
Dragonfly
Free flight Tether, free flight Model
Dye, DPIV
0
160–3200
Selasphorua rufus Hummingbird Ficedula hypoleuca Apus apus Goose
Free flight Model Free flight Model Model
DPIV SPI PIV PIV PIV
LEV, 16% LEV LEV, 49% LEV LEV
Glossophaga soricina Leptonycteris yerbabuenae
Free flight
PIV
0 hover 920–5070 1 11 (swept wing) 37 500 56 000 (28 000 −113 000) 1 5000
Free flight
PIV
1, 5
12 000, 18 000
Leptonycteris yerbabuenae
Model
PIV
1–7
8800–29 000
LEV (@1 m s−1 / no LEV (@1 m s−1) LEV
Cynthia cardui Idea leuconoe Drosophila melanogaster Drosophila melanogaster Drosophila melanogaster Drosophila melanogaster Drosophila melanogaster Macroglossum stellatarum
Bombus terrestris Dragonflies spp
Re
Ellington et al 1996 Van den Berg et al 1997 Bomphrey et al 2005 Srygley and Thomas 2002 Fuchiwaki et al 2013 Fuchiwaki et al 2013 Dickinson et al 1999 Birch et al 2004
LEV LEV
occurs. Stall results in a strong increase in drag without a corresponding increase in lift, which results in a reduction of the lift to drag ratio (L/D), i.e. a reduction of the efficiency of lift production. The propensity of flow separation depends on the ratio between viscous and inertial forces, which is described by the Reynolds number, Re = Uc/ν, where ν is the kinematic viscosity. The maximum steady-state lift coefficient, and hence the maximum lift capacity of a fixed wing, at the relatively low Re relevant for animal flight is about 1.6 (Laitone 1997), but in many cases of animal wings the maximum steady-state CL is lower still (Spedding 1992). The maximum steady-state CL has in many cases been shown to
Source
LEV, 38–39% inner wing, 132–145% outer wing LEV LEV LEV
LEV, 42%
Birch and Dickinson 2001 Pick and Lehmann 2009 Lentink and Dickinson, 2009 Johansson et al 2013
Bomphrey et al 2009 Thomas et al 2004 Lu et al 2006, Lu and Shen 2008 Warrick et al 2009 Swanton et al 2010 Muijres et al 2012 Videler et al 2004 Hubel and Tropea 2010 Muijres et al 2008 This study
Koekkoek et al 2012
be insufficient to explain the lift required to support the weight of animals, especially in hovering flight (WeisFogh 1973, 1975, Ellington 1984, Sane 2003, Norberg 1975a, 1975b, Hedenström et al 2007, Rosén et al 2007) suggesting the use of unsteady mechanisms. Unsteady, time-dependent, aerodynamic mechanisms have in the past mainly been studied and discussed with respect to insect flight. A number of unsteady mechanisms have been suggested and confirmed in insect flight, i.e. clapand-fling, rotational lift, wake capture and dynamic stall with a leading edge vortex (LEV) (Ellington et al 1996, Dickinson et al 1999, Lehmann 2008). However, the utility of LEVs to 2
F T Muijres et al
Bioinspir. Biomim. 9 (2014) 025006
enhance lift seems universal in flying animals since small bats (Muijres et al 2008), hummingbirds (Warrick et al 2009) and flycatchers (Muijres et al 2012) also use LEVs to enhance their lift production during slow flight (table 1). In fact, LEVs may be universal in biological systems since they have also been discovered in winged plant seeds (Lentink et al 2009) and have been suggested to improve swimming performance in fish (Lauder et al 2007, Borazjani and Daghooghi 2013) and birds (Johansson and Norberg 2003). In flying animals the LEV stays attached to the wing throughout the downstroke and contributes 15–60% of the total lift (table 1), suggesting that it is of significant importance for flight at slow speeds and hovering. Despite the clear relevance of LEVs to lift production in biological systems, the exact mechanism of the LEV is still a focus of research (Pitt Ford and Babinsky 2013). However, using LEVs to increase the force production is associated with a cost since LEVs generate increased drag, and thus relatively low L/D (Dickinson et al 1999). This would suggest that animals should only use LEVs when absolutely necessary, e.g. during slow flight and manoeuvring, and avoid using LEVs at cruising flight, where the relatively high forward flight velocity reduces the necessity for high CL. Studies based on animal inspired models and mechanical flappers have indicated that birds and bats may be capable of using LEVs through a range of flight speeds (Videler et al 2004, Hubel and Tropea 2010, Koekkoek et al 2012). However, to the best of our knowledge, it has never been tested whether freely flying birds and bats use LEVs or not at cruising speed. In this paper we present data on LEV properties in the lesser long-nosed bat (Leptonycteris yerbabuenae), studied during free flight in a wind tunnel during both slow and cruising flight speed. These results are compared with equivalent data from a robotic flapper, inspired by the morphology and kinematics of a lesser long-nosed bat wing (Koekkoek et al 2012). In addition to new information about the LEV in bats, we also review studies of LEVs in live animals or models with animal-like morphology and kinematics.
downwind direction and blocked laser reflections from intersecting the eyes of the bats. Before and after each experimental session, the weight of each bat was measured using an electronic balance. The average body mass and wing morphological data for both bats are presented in table 2. The PIV system consisted of two synchronized, double frame, CMOS cameras (HighSpeedStar3; 1024 × 1024 pixels) in stereo setup and a 200 Hz double pulsed 50 mJ Laser (Litron LPY732 series, Nd:YAG, 532 nm), controlled by the LaVision PIV software package DaVis (LaVision, DaVis 7.2.2.110). For the PIV experiments the air was seeded by filling the wind tunnel with fog (particle size 1 μm). These fog particles were illuminated by the laser sheet. For each measurement, 100 pairwise images (1/2 s at 200 Hz, image size ∼20 × 20 cm and dt = 200–270 ms) of the illuminated particles were recorded by each CMOS camera and stored on a computer. Simultaneously, a high-speed (250 Hz) digital video camera captured the animal to monitor its movement. The laser sheet was positioned vertically in the streamwise direction. By repositioning the feeder relative to the PIV measurement plane, the airflow around different wing sections was sampled. The PIV image pairs used for the PIV analysis were selected manually. Image pairs were assessed as good when the fluid section above the wing surface was not blocked by the wing or any part of the animal in the background. The selected PIV images were pre-processed to reduce errors in the PIV calculations. Background noise was filtered out using a high-pass filter (medfilt2, Matlab 7.7.0.471, R2008b, boxsize 15 × 15), and a mask was created over the part of the image where the bat was visible. The PIV images were analysed using the Lavision PIV software package DaVis (LaVision, DaVis 7.2.2.110) using a multi-pass normalized cross-correlation (32 × 32 and 16 × 16, 50% overlap, Whittaker reconstruction), followed by smoothing {3 × 3}. Due to the fact of the wing blocking the view of the different cameras during different phases of the wing beat a stereo analysis was not always possible, in which case we performed a 2D analysis using the camera with a clear view of the flow above the wing. The resulting velocity fields {u, w} were imported into a custom-made PIV analysis program (Matlab 7.7.0.471, R2008b), in which the spanwise vorticity (ωy) field was calculated, and corresponding vortex circulation could be calculated. Vortex circulation was calculated by manually selecting the patch of high vorticity associated with each LEV. Within this patch, vorticity was integrated over all the PIV node points with vorticity values above the threshold |ω|min = 100 s−1. This threshold was chosen because it lay above the background vorticity level in an empty wind tunnel running at the maximum experimental speed of 5 m s−1. The vorticity distribution outside the |ω|min iso-line was assumed to have a normal Gaussian distribution, so the total circulation of a vortex was estimated as Γ = (1 + |ω|min/|ω|max) Γmeasured, where Γmeasured is the measured circulation above the threshold |ω|min, and |ω|max is the maximum absolute vorticity in the vortex area (see Spedding et al 2003, Hedenström et al 2006).
Methods One male and one female lesser long-nosed bat were trained to fly in the Lund university low-turbulence wind tunnel (Pennycuick et al 1997, Spedding et al 2009). For the experiments the wind tunnel was constantly running at the required speed of 1 m s−1 or 5 m s−1, while the bats were roosting on the mesh within the settling chamber. When the bats were hungry, they would fly into the experimental test section of the wind tunnel, make a u-turn and approach a feeder from the downwind direction. When the bat was feeding from the feeder, experimental measurements were performed. The airflow around the bat wing was measured using a high-speed (200 Hz) stereographic particle image velocimetry (PIV) system. The feeder consisted of a metal tube providing honey water, and a mask that forced the bats to feed from the 3
F T Muijres et al
Bioinspir. Biomim. 9 (2014) 025006
Figure 1. Velocity and vorticity fields about the wing at mid-downstroke, of a lesser long-nosed bat (A), (B) and of a mechanical flapper
inspired by a lesser long-nosed bat, the RoBat (C), (D), (F). At low flight speeds (U = 1 m s−1) the real bats generate an attached LEV during the mid-downstroke (A), while at a cruising flight speed (U = 5 m s−1) the LEV is absent (B). The RoBat generates very similar vorticity field patterns with flapping kinematics similar to that of a lesser long-nosed bat, at both equivalent flight speeds (Ueq = 1 m s−1 and Ueq = 5 m s−1 for (C) and (D), respectively; Ueq is the airspeed of the dynamically scaled RoBat equivalent to that of a real bat). Operating the RoBat at Ueq = 5 m s−1 with an angle-of-attack similar to that of a real bat at U = 1 m s−1 (55°) leads to the development of an attached but bursting LEV. The colour bar shows magnitude and spin direction of vorticity (range −700 s−1 to 700 s−1). Scale bars in the panels are 10 mm and scale vectors are 10 m s−1. Panel E shows an image of a lesser long-nosed bat flying slowly in the Lund wind tunnel. All RoBat data (C)–(F) are from Koekkoek et al (2012).
Based on the wing movement, which was visible in the PIV images, the normalized time stamp τ for each PIV frame was determined by identifying each PIV frame with the highest wingtip position (τ = 0 for the start of the downstroke, and τ = 1 for the end of the upstroke), and the PIV frame with the lowest wingtip position (at U = 1 m s−1, τ = Rds = 0.42,
where Rds is the downstroke ratio (von Busse et al 2012). For the PIV frames in between, the normalized time stamp was linearly interpolated. For each measured LEV, its spanwise location was measured, as well as the local wing velocity. The relative spanwise location of the LEV was defined as b* = l/bw, where 4
F T Muijres et al
Bioinspir. Biomim. 9 (2014) 025006
Table 2. Flight morphology for the bat specimens (Leptonycteris yerbabuenae) used in the experiments, with body mass M, wing span b, wing surface area S, mean chord c (=S/b), aspect ratio AR (=b2/S) and wing loading Q (=Mg/S), where g is acceleration due to gravity.
male female
M (kg)
b (m)
S (m2)
c (m)
AR
Q (N m−2)
0.0213 0.0214
0.335 0.323
0.015 76 0.015 29
0.047 0.047
7.1 6.8
13.3 13.7
l is the distance between the leading edge−laser intersect and the wing root and bw is the distance between the wingtip and wing root, measured within the calibrated PIV images. The wing velocity was estimated by manual tracking the leading edge-laser intersection throughout the PIV image sequence. Ueff was determined as the vector sum of the resulting leading edge velocity and the forward flight speed U. The resulting wingbeat average effective velocity U¯eff and the mean wing cord were used to normalize LEV circulation by Γ U¯eff c . To account for the repeated measures setup, the mean strength and error of the mean of the positive and negative LEVs were estimated from a mixed model with normalized circulation as the dependent variable and individual and sequence (nested within individual) as random variables (JMP v11, SAS Institute Inc.). In addition, we tested whether the circulation of the LEV increases from the beginning of the downstroke (τ = 0) to the middle of the downstroke (τ = 0.25), using a mixed linear model with normalized circulation as the dependent variable, τ as the independent variable and the individual and sequence (nested within the individual) as random variables.
upwards directed aerodynamic force with the ventral wing surface facing upwards (Helversen 1986, Hedenström et al 2007). The outer part of the wing also generates a LEV during the upstroke (figure 2(B), see also supplementary movie 2, available at stacks.iop.org/BB/9/025006/mmedia), but the circulation is positive (anti-clockwise). The inner part of the wing does not move backwards faster than the forward flight speed resulting in the inner wing functioning in a similar way as during the downstroke and, at least during the initial part of the upstroke, we find a LEV of negative circulation at the inner wing (figure 2(A)). The experimental setup prevents us from determining if the LEV at the inner wing also exists during later phases of the upstroke. Quantitative measurements of circulation in the LEV at different locations along the wing and at different times of the wingbeat period are shown in figure 3(A). Normalized circulation (Γ U¯eff c , where U¯eff = 3.7 m s−1 and c = 0.047 m) of the LEV present during the downstroke and well into the upstroke (negative circulation) was −0.61 ± 0.030 (mean ± standard error) (figure 3(B)). At the outer wing, the opposite spinning LEV occurs from about τ ≈ 0.75 and is present towards the end of the upstroke (figure 3(A), see also supplementary movie 2, available at stacks.iop.org/BB/9/025006/ mmedia). The mean normalised circulation of the outer wing LEV was Γ U¯eff c = 0.60 ± 0.045. Our results show that the lesser long-nosed bat develops a LEV in slow (1 m s−1) forward flight at high angle of attack (∼55°, von Busse et al 2012), while it is absent at a faster forward flight speed (5 m s−1) and a moderate angle of attack (
