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ResearchCite this article: Schunk C, Swartz SM, Breuer

KS. 2017 The influence of aspect ratio and

stroke pattern on force generation of a

bat-inspired membrane wing. Interface Focus

7: 20160083.

http://dx.doi.org/10.1098/rsfs.2016.0083

One contribution of 19 to a theme issue

‘Coevolving advances in animal flight and

aerial robotics’.

Subject Areas:biomimetics, biomechanics

Keywords:compliant wings, flapping flight,

micro air vehicles

Author for correspondence:Cosima Schunk

e-mail: cosima_schunk@brown.edu

& 2016 The Author(s) Published by the Royal Society. All rights reserved.

Electronic supplementary material is available

online at https://dx.doi.org/10.6084/m9.fig-

share.c.3576347.

The influence of aspect ratio and strokepattern on force generation of abat-inspired membrane wing

Cosima Schunk1, Sharon M. Swartz1,2 and Kenneth S. Breuer1,2

1School of Engineering, and 2Department of Ecology and Evolutionary Biology, Brown University, Providence,RI 02912, USA

CS, 0000-0002-2511-0746

Aspect ratio (AR) is one parameter used to predict the flight performance

of a bat species based on wing shape. Bats with high AR wings are

thought to have superior lift-to-drag ratios and are therefore predicted to

be able to fly faster or to sustain longer flights. By contrast, bats with

lower AR wings are usually thought to exhibit higher manoeuvrability.

However, the half-span ARs of most bat wings fall into a narrow range of

about 2.5–4.5. Furthermore, these predictions do not take into account

the wide variation in flapping motion observed in bats. To examine the

influence of different stroke patterns, we measured lift and drag of highly

compliant membrane wings with different bat-relevant ARs. A two degrees

of freedom shoulder joint allowed for independent control of flapping

amplitude and wing sweep. We tested five models with the same variations

of stroke patterns, flapping frequencies and wind speed velocities. Our

results suggest that within the relatively small AR range of bat wings,

AR has no clear effect on force generation. Instead, the generation of

lift by our simple model mostly depends on wingbeat frequency, flapp-

ing amplitude and freestream velocity; drag is mostly affected by the

flapping amplitude.

1. IntroductionOwing to the size of bats and their capabilities, such as hovering, highly man-

oeuvrable flight and the ability to carry substantial loads (bat mothers carry

their pups until they are almost fully grown [1,2]), these flying animals are a

source of inspiration for flapping-wing micro air vehicles (MAVs).

Bats fly with compliant membrane wings, and this feature sets them apart

from birds and insects with comparatively rigid wings. Insects control their

wingstroke at one joint at the root of the wing, and their wings twist passively

due to inertial and aerodynamic forces [3]. Birds have more active control over

wing shape and stroke kinematics. For example, a coupled movement of the

elbow and wrist executes wing retraction [4], and feathers can be spread to

control wing shape and permeability to air.

The control of movement and shape in bat wings is more complex. The skel-

eton incorporates the entire upper limb and most of the lower limb and, in some

species, the tail. Some of the joints of the skeleton move in functional groups,

but more than a dozen independent dimensions are needed to describe 95%

of the total wing motion [5]. Overall, bat wings possess more degrees of

freedom than those of birds or insects.

The surface of the bat wing is composed of a compliant membrane [6]. This

membrane is complex; elastin fibres embedded in a predominantly spanwise

orientation introduce anisotropy, and muscles, oriented primarily in a chord-

wise direction, actuate during the wingstroke and might control wing camber

during flight [7].

Like those of birds and insects, bat wings exhibit a variety of shapes and sizes.

For several decades, biologists have drawn conclusions about flight behaviour

50

40

30

20

10

0

aspect ratio (half-span)

freq

uenc

y (%

)

aspect ratio distribution

7.06.5 6.05.5 5.04.5 4.03.53.02.52.0

all batsevening batsfree-tailed bats

Figure 1. Half-span aspect ratio distribution of 215 bat species (data fromNorberg & Rayner [9]). The distribution for the entire species sample is shownin blue. Vespertilionidae, evening bats (n ¼ 75) in green, and Molossidaefree-tailed bats (n ¼ 17), in purple.

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and efficiency from easily measured parameters, and con-

nected those conclusions to flight ecology (e.g. [8–10]).

Such parameters are, for example, wingspan and wing area,

and body weight. In a principal components analysis of

wing shape and body size of more than 200 bat species,

Norberg & Rayner suggested that aspect ratio (AR,

wingspan/wing chord), and wing loading (body weight/

wing area) critically determine flight behaviour [9]. They con-

cluded that high AR-winged bats are more likely to fly in open

air, whereas low AR wings are more suitable for cluttered

habitats. Bats with low wing loading generally fly more

slowly than bats with high wing loading. However, the

range of ARs among bat species is rather limited compared

with the full diversity found in aircraft, birds or insects

(figure 1). Indeed, based on the species sample published by

Norberg & Rayner [9], more than two-thirds of bats species

have half-span ARs between 2.75 and 3.75. Species of the

family Molossidae or free-tailed bats are exceptional within

this distribution with ARs approximately twice those of

other bat species.

The idea that flight behaviour can be predicted by AR

derives from fixed wing aeromechanics for high Reynolds

numbers, specifically the contribution of induced to total

drag. Induced drag, Di, is an inherent consequence of lift

generation and the presence of tip vortices; as AR increases,

the relative influence of the tip vortex to overall drag

production declines

CDi¼ C2

L

peAR, ð1:1Þ

where CDi is the coefficient of induced drag, CL the coefficient

of lift and e the wingspan efficiency [11].

For fixed wings, efficiency has some dependency on AR

[12–16]. The wake of a fixed wing in steady flow can be

described as a horseshoe vortex system with the bound

vortex around the aerofoil and the tip vortices being the

only prominent vortex structures. However, in flapping

flight, wing motion during the wingbeat cycle and pressure

and velocity gradients along the wingspan can cause highly

unsteady flow conditions. Limited validity of quasi-steady

assumptions to explain force generation in flapping flight

was first demonstrated over 30 years ago [17]. Several

unsteady aerodynamic effects that cannot be predicted with

traditional aeromechanics have been identified, such as the

presence of stable leading edge vortices, wing-wake inter-

actions, and clap-and-fling [18–20]. Wakes of flapping

wings are considerably more complex than those of fixed

wings in steady flow, and factors other than the induced

drag of the tip vortices influence a wing’s efficiency. AR

thus might have less effect on force generation and flight

power than does the pattern of flapping motion. Although

few experimental studies have investigated flapping, highly

compliant membrane wings, available data suggest that

force generation and power demands depend strongly on

stroke pattern [21,22].

Here, we explore the relative roles of AR, wingbeat fre-

quency, wingbeat amplitude, sweep angle and downstroke

ratio on aerodynamic force generation. We hypothesize that

wingstroke kinematics have a stronger effect on overall

wing performance than AR. We test this idea with a robotic

flapper employing mechanical wings with ARs in a bat-rel-

evant range, 2.5 , AR , 4.5. We designed the wings based

on the vespertilionid Eptesicus fuscus, the big brown bat.

The shoulder joint of the model allowed for independent con-

trol of flapping and sweep amplitude, and thus testing of a

wide range of kinematic parameters.

2. Material and methods2.1. ModelsThe principal design and driving mechanism of our mechanical

flapping wing was adopted directly from previous work [23] in

which a full-scale wind tunnel model was designed based on the

wing geometry of the dog-faced fruit bat, Cynopterus brachyotis,

and fabricated using three-dimensional-printed parts. That

model had three degrees of freedom: flapping (up-down), sweep

(fore-aft) and folding, and was actuated by means of push–pull

cables that connected the skeletal joints to servo motors mounted

outside the wind tunnel test section.

We simplified the mechanics of our model by omitting wing

folding and keeping only the two motors that allow for flapping

and sweep motion of the wing. We built five models that encom-

pass wing shape variation. The baseline model, AR3.5bl, is based

on E. fuscus in size and general shape. It has an AR of 3.5, a half-

span of b ¼ 13 cm and a wing area of S ¼ 48 cm2. For ease of com-

parison and to reduce possible influences on force generation from

other sources such as scalloping of the trailing edge and tapering of

the wing, we simplified the geometry of the wing planform. The

armwing consists of a rectangle in which the membrane runs

between the body and what would be digit V in a bat. The mem-

brane is supported by a simple upper and forearm skeleton. The

handwing consists of two triangles that are formed by a total of

three digits (figure 2a). We used a ratio of handwing to armwing

area of 0.6, and of handwing to armwing span of 1.15, both charac-

teristic of E. fuscus [9]. The ratios of handwing to armwing area and

span were preserved.

The AR for non-rectangular wings is usually described as

AR ¼ b2/S. AR can therefore be easily modified by changing

wing area while keeping wingspan constant. The local spanwise

velocities introduced along the wingspan by flapping motion

remain constant among all models of a given wingspan. Alterna-

tively, wing area may be kept constant, and wingspan was

changed. Using these considerations, we built five models with

three ARs of 2.5, 3.5 and 4.5. Three of the models share the

same wing area, and three models share the same wingspan

(figure 2a). All five wings have a built-in static angle of attack

of ao ¼ 68, and 9% camber at 1/4 chord.

(a)

(d)(c)(b)

AR2.5csS = 67.2 cm2

b = 13.0 cm

AR3.5blS = 48.0 cm2

b = 13.0 cm

AR4.5csS = 37.3 cm2

b = 13.0 cm

AR2.5caS = 48.0 cm2

b = 11.0 cm

AR4.5caS = 48.0 cm2

b = 14.7 cm

sweep angle(top view)

flapping angle(back view)

built-in AoA 6°9% camber at ¼ chord

a

b q

shoulder

arm

Figure 2. (a) Skeleton of the five wings tested. The baseline model, AR3.5bl is shown in the middle. The aspect ratio of the models to its left and right is varied bychanging the wingspan, b, keeping the area, S, constant. The aspect ratio of the models below and above it is changed by changing the wing area, keeping the spanconstant. All wings have a built-in angle of attack of 68, and 9% camber at 1/4 chord. (b) Perspective view of the wing assembly. The shoulder part rotated alongthe long axis of the model to allow for the flapping motion, the arm rotated about its pivot point at the centre of the shoulder piece to allow for the sweep motion.(c) Top view of the model to illustrate the sweep motion of the arm rotation. (d ) Back view of the model to illustrate the flapping motion of the shoulder rotation.

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The wing skeletons were designed in SolidWorksw 2012 x64

(Dassault Systemes SOLIDWORKS Corp., Waltham, MA, USA),

and three-dimensionally-printed (Dimension 1200es, Stratasys,

Eden Prairie, MN, USA) with ABS plastic (acrylonitrile butadiene

styrene). We applied a coating of superglue (M60 Advanced

performance instant adhesive, Adhesive Systems Inc., Frankfort,

IL, USA) to all digits to strengthen them. To reduce some of the

strain on the membrane, the attachment site on the body was

modified from previous versions of the flapper [23]. The mem-

brane was glued to an appendix of the shoulder piece and

follows the shoulder rotation during the flapping motion

(figure 2b–d ). Our membranes were made of a highly elastic sili-

cone rubber, Dragon Skinw (Smooth-On Inc., Macungie, PA,

USA). This material has a reported shore-A durometer value of

10 (Young’s modulus of about 0.7 MPa). We adjusted the com-

ponent A : B mix ratio to 3 : 1, which enabled us to produce

thinner membranes.

To fabricate the thin membrane, we poured the uncured mix-

ture onto a Teflon-covered aluminium plate. This was covered

with a second plate that was treated with mould-release and

weighted, for a combined load of about 8 kg. The resulting mem-

branes had a thickness of about 0.2 mm. The membrane was

glued directly to the skeleton and the reinforcement structures

with silicone epoxy (Sil-poxy, Smooth-On, Inc., Easton, PA,

USA) with the wing in its neutral gliding position (figure 2b).

We reinforced the entire leading edge and trailing edge

between the fingers with 0.25 mm thin elastic (Stretchrite

sewing thread, Jo-Ann Stores, Inc.) [23]. The remainder of the

trailing edge was reinforced with a 0.5 cm wide strip of

Dragon Skin membrane glued to the skeleton at the trailing

edge, and a second strip added at a distance of about 1 cm

further from the trailing edge. Those two strips were glued on

with the wing placed in its most swept-back position.

The flapping and sweep motions were driven by two brush-

less servo motors with integrated encoders (BE163CJ-NFON,

Parker Hannfin Corp., Rohnert Park, CA, USA) and controlled

by a servo controller (Accelera DMC-4060, Galil Motion Control,

Rocklin, CA, USA) with integrated amplifiers (AMP-43040, Galil

Motion Control). A MATLAB script translated the inputs for flap-

ping frequency, flapping amplitude angle, sweep angle and

downstroke-to-upstroke ratio into PVT (position, velocity and

time) commands that were sent to the servo controller.

2.2. Experimental set-upA custom-made force plate was mounted to the floor panel of the

test section of a closed-circuit wind tunnel at Brown University

(test section dimensions: 3.8 � 0.6 � 0.82 m3). The force plate is

a flexure based system that allows for independent displacement

in two perpendicular directions (lift and drag axes) of the centre

wing inside test section

sweep motor

drag sensor

flapping motor

lift sensor

force plate

Figure 3. Computer-aided-design rendering of the experimental set-up. The force plate is mounted below the test section with the wing extending vertically intothe air flow. Two motors outside the test section control the sweep and flapping motion of the wing.

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section which serves as mount for the experimental model. A

rack to mount the motors and models was attached to the

force plate, allowing the wings to extend into the test section

through the floor of the wind tunnel, and the motors remained

accessible from outside the test section (figure 3). Displacement

of the test plate was measured using two optical displacement

sensors (D64, 20 kHz resolution, Philtec Inc., Annapolis, MD,

USA) and recorded using a data acquisition board (NI USB-

6210, National Instruments Corporation, Austin, TX, USA) at

1024 Hz using a customized MATLAB script. The Scope tool of

the GalilTools software (GalilTools 1.6.4.576, Galil Motion

Control Inc., Rocklin, CA, USA) was used to record the voltage,

current and position of the servo motors, along with the trigger

signal, all at 512 Hz.

2.3. Wing stroke kinematicsTo investigate the effect of wing stroke kinematics, we chose two

baseline stroke patterns about which to carry out a series of vari-

ations. The first pattern was based on kinematics of E. fuscus [24].

A second stroke pattern was based on the kinematics of Tadaridabrasiliensis (Brazilian free-tailed bat) [25], a member of the Molos-

sidae, a family of bats characterized by high AR wings (figure 1).

The E. fuscus pattern is characterized by higher flapping and

sweep amplitudes, and an equal duration of up- and downstroke

(table 1). For all stroke patterns the flapping and sweep motion

are in phase resulting in a straight-line trajectory input signal.

In general, the stroke plane is close to vertical when the

sweep angle is small, and the angle between stroke plane and

the horizontal decreases with increasing sweep motion.

We performed parameter sweeps over all variables based on

these two baseline stroke patterns (table 1). The two baseline

strokes and the 17 combination strokes that arise from varying

one parameter at a time were tested at wind speeds of U1 ¼

5.0 and 7.5 m s21 for all five wings (Reynolds number range

based on mean chord 10 000 , Rec , 26 000).

2.4. Data collectionEach flapping trial started with the wing in a gliding position

(figure 3). The wing was then moved to a position representing the

top of the downstroke and through 50 complete wingbeat cycles

before moving back to the neutral gliding position. Force data

were collected throughout the flapping and terminal gliding phase.

2.5. Data processingTo ensure that a steady state condition was achieved, the first 10

and last five wingbeat cycles of the 50 recorded cycles were

excluded from analysis. The flexure-supported force plate acts as

a mass-spring-damper subjected to the unsteady periodic forcing

due to the flapping wing, F(t). Note that this force comprises both

aerodynamic and inertial forces associated with the wing motion.

For simplicity, we describe motion in the y direction, although the

following procedure applied to both the x and y directions. When

the plate is forced dynamically, the displacement of the plate sec-

tions can be written as

FðtÞ ¼ kyðtÞ þ b _yðtÞ þm€yðtÞ , ð2:1Þ

where y, _y and €y are the position, velocity and acceleration of the

system, respectively. The mass, m, spring constant, k, and damp-

ing coefficient, b, are known characteristics of the force plate,

measured previously from a dynamic calibration [24] (table 2).

The measured displacement, y(t), was fit to a Fourier series,

retaining terms associated with the driving frequency and

higher harmonics, up to the natural frequency of the force

plate. Velocity, _y, and acceleration, €y, were computed from the

Fourier series, and using the known characteristics of the force

plate, m, k and b, the driving force, F(t), was calculated using

equation (2.1). The inertial contribution to the force, measured

by recording the forces resulting from flapping the wing in still

air and without an attached membrane, was then subtracted,

leaving only the aerodynamic force for a particular kinematic

parameter combination.

Some kinematic parameter combinations seemed to be more

prone to measurement noise, leading to poor repeatability of

force measurements at these settings. Measurements that

obviously differed from all other traces of a parameter combi-

nation set were excluded from further analysis. Parameter

combinations with fewer than two valid trials were also excluded

from further analysis.

Table 1. Range of stroke kinematics tested. For comparison, the baseline values are also given, derived from Eptesicus fuscus, the bat species on which thephysical model is based [24], as well as for a second species with a markedly different wing stroke, Tadarida brasiliensis [25].

parameter E. fuscus T. brasiliensis min. max. increment

frequency, f (Hz) 9 9 2 10 2

flapping amplitude, u (8) 110 80 20 110 15

sweep amplitude, w (8) 55 15 15 55 10

downstroke ratio, DR 0.55 0.44 0.44 0.56 0.06

Table 2. Characteristics of the force plate in the lift and drag directions. The stiffness, k, was determined using a static calibration procedure, measuring thedisplacement versus applied force. The natural frequency, mass and damping were determined using a dynamic calibration, or ‘ring-down’ test. The sensingplate was moved away from its equilibrium position and then released. The oscillatory decay of the plate position was used, in conjunction with the stiffness, todetermine the natural frequency, fo; mass, m; and damping coefficient, b [24].

spring constant damping coefficient mass natural frequency

k (N m21) b (Ns m21) m (kg) f0 (Hz)

lift axis 224 500 6.5 3.3 35

drag axis 89 200 1.2 2.7 27

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2.6. Velocity scaling and dimensionless numbersThe force generated by each set of parameters depends on seven

input variables: wing half-span, b, wing area, S, flapping frequency,

f, flapping amplitude angle, u, sweep amplitude angle, w, down-

stroke ratio, DR, and freestream velocity, U1. To compare the force

generation for different stroke patterns and different wing models,

we characterized each trial by the dimensionless ratio of average rela-

tive horizontal to average vertical wind speed at mid span: Uv/Uh.

Note that the velocity ratio differs between downstroke and

upstroke. The time-resolved vertical velocity, Uv, can be expressed as

Uv ¼ �b2� sin

u

2

� �� sinðvtþ npÞ: ð2:2Þ

Similarly the horizontal velocity, Uh, is defined as

Uh ¼ U1 +b2� sin

w

2

� �� sinðvtþ npÞ, ð2:3Þ

where v ¼ fp/DR and n ¼ 0 for the downstroke, and v ¼ fp/(1 2

DR) and n ¼ 1 for the upstroke.

The combination of freestream velocity, flapping and sweep-

ing motion also affects the effective angle of attack, aeff, and the

effective air speed, Ueff, experienced by the wing during the

wingbeat cycle

aeff ¼ ao þ arctanUv

Uh

� �

and

Ueff ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU2

h þU2v

q,

(figure 4). Effective instantaneous angles of attack are more

extreme at the lower freestream velocities, especially during the

upstroke, largely because the relative contribution of the vertical

velocity component, induced by the flapping motion, decreases

as the wind speed increases. Flapping frequency and amplitude

produce the greatest changes in local flow conditions, leading to

substantial changes in angle of attack. The coefficients of lift and

drag are defined by the magnitude of the time-resolved velocity

vector described by Uv and Uh

CL ¼2 � L

r � S �U2eff

ð2:4Þ

and

CD ¼2 �D

r � S �U2eff

: ð2:5Þ

The choice of the instantaneous velocity for normalization

imposed certain limitations because it is based on quasi-steady

assumptions, but it also has considerable utility, particularly if

the wing speed is comparable to or even larger than the forward

flight speed.

2.7. StatisticsStatistical tests were performed using MATLAB’s Statistics and

Machine Learning toolbox. To compare force generation among

models, we performed an analysis of covariance (ANCOVA)

using aoctool on the wingstroke-averaged coefficients of lift and

drag. Data from separate data collection events were treated as

independent data points. We independently tested CL and CD

of up- and downstroke using linear regression. We grouped the

data into 15 bins, with a bin width of 1/15 the total velocity

ratio range of each test. This number of bins ensured a minimum

of two data points for every non-empty bin. Prior to the statistical

analysis, we excluded outliers in each bin. Data points that were

more than the mean+ s.d. different from all data in the bin were

excluded from the statistical analysis (electronic supplementary

material).

After identifying significant differences between the linear

regression of force versus velocity ratio, we compared the

results of the previous analysis using multcompare to determine

statistically significant differences among the models.

3. Results and discussion3.1. Change of forces with velocity ratioDuring gliding, lift and drag vary among models and, for

each model, vary with velocity. Gliding forces show no

trend in relation to AR (table 3). The coefficient of drag for

model AR2.5ca for the U1 ¼ 5.0 m s21 seems suspiciously

vary frequency

vary sweepamplitude

vary flappingamplitude

vary downstrokeratio

5

10

25 50 75 100 25 50 75 100

U• = 7.5 m s–1U• = 5.0 m s–1

Uef

fU

eff

Uef

fU

eff

wingbeat (%) wingbeat (%)

5

10

5

10

5

10

025 50 75 100 25 50 75 100

a eff

a eff

a eff

a eff

50(a) (b)

0

–50

50 q

j

q

j

0

–5050

0

–50

50

0

–50

wingbeat (%)wingbeat (%)

U• = 7.5 m s–1U• = 5.0 m s–1

50

0

–50

50

0

–5050

0

–50

50

0

–50

7.5

12.5

7.5

12.5

7.5

12.5

7.5

12.5

2.5

dr dr

f f

Figure 4. Summary of relative flow direction and strength during flapping. Effective angles of attack (a) and magnitude of flow (b) over the wingbeat cycle at thecentre of the handwing for different flapping frequencies, f, flapping and sweep amplitudes, u and w, and downstroke ratios, DR, for both freestream velocities.The black arrows show the direction of increasing parameter value. Changes in flapping frequency have the strongest effect on effective angle of attack and relativeflow velocity, whereas changes in sweep amplitude and downstroke ratio have only small effects.

Table 3. Summary of the coefficients of lift and drag for all models at both freestream velocities.

wing area half-spancoefficient of lift coefficient of drag

S (cm2) b (cm) 5.0 m s21 7.5 m s21 5.0 m s21 7.5 m s21

AR3.5bl 48.0 13.0 0.75 0.81 0.50 0.36

AR2.5ca 48.0 11.0 0.86 0.78 0.15 0.41

AR4.5ca 48.0 14.7 0.86 0.82 0.40 0.34

AR2.5cs 67.2 13.0 0.75 0.58 0.30 0.26

AR4.5cs 37.3 13.0 0.79 0.88 0.42 0.50

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low, and requires future confirmation, but is included here

for completeness.

The range of velocity ratios, Uv/Uh, is smaller for down-

stroke than upstroke (figure 5). The sweep motion of the wing

increases the horizontal velocity (denominator) during down-

stroke, when the wing moves forward, whereas the

backwards motion during upstroke decreases the relative

horizontal velocity.

All wings generate positive lift during downstroke and

negative lift during upstroke, but the magnitude of lift

depends strongly on the velocity ratio (figure 5). High vel-

ocity ratios, associated with larger wing motions, result in

higher forces. At low velocity ratios, the coefficient of lift is

lowest for stroke patterns with large flapping and sweep

angles during downstroke (figure 5, purple markers).

During the downstroke, the wing sweeps forward and the

combined motion results in increased effective angle of attack

and airspeed (figure 4). The opposite is true during the

upstroke. In addition, the compliance of the wing membrane

allows for auto-camber, which is influenced by flow direc-

tion. During upstroke, angle of attack is usually negative

(figure 4) and is likely to decrease the 9% built-in camber,

or even lead to reversed camber of the skin membrane in

the armwing region, where the membrane shape is not

reinforced by the digits. In such a case, the wing would

deflect airflow up, instead of downward, which may enhance

the opposing trends in lift coefficients of down- and upstroke.

With few exceptions, the magnitude of CL is larger during the

downstroke than during the upstroke and thus the wing

generates net lift over a complete cycle (figure 7 and §3.2).

The coefficient of drag shows only a weak dependence on

velocity ratio (figure 5). Many high sweep cases (blue and

purple symbols) generate relatively high drag. This phenom-

enon arises from the mechanical behaviour of the membrane

during flapping. At the beginning of the downstroke, when

the wing is in its most swept-back position, the membrane

bulges (figure 6, red arrow). As the wing sweeps forward,

the membrane stretches and forms a smooth surface until

mid-downstroke, when the wing starts to fold in towards

the body. The trailing edge reinforcement is too compliant

to take up the slack from the membrane and the bulge re-

appears. This effect is most pronounced when the freestream

velocity and the flapping amplitude angle are low, corre-

sponding to the parameter combinations in which the

higher drag values are observed. At higher freestream vel-

ocities and flapping amplitudes, the increased aerodynamic

pressure on the membrane subjects the membrane to greater

tension and probably reduces this bulging effect.

CL

CL

0

2

4downstroke

–4

–2

0

upstroke

Uv/Uh

CD

CD

0.50.10 0.80.1–1

1

2

0

2

4

Uv/Uh

0

15°

110°

20°

sweep angle

marker colour: wing movement

marker size: wind speed

5.0 m s–1

7.5 m s–1

marker style: downstroke ratio

0.440.500.56

flap

ping

ang

le

55°

Figure 5. Summary of the mean coefficients of lift and drag for the baseline model, AR3.5bl, separated into downstroke and upstroke. The freestream velocity isdesignated by marker size. The marker style designates the downstroke ratio. The colour coding represents the wing movement: more green colours indicate littlewing movement, and purple colours large wing movement. Blue is an indicator for wing movement dominated by the sweep motion, and red for an almost pureflapping motion. The speed ratio is the ratio of the relative horizontal to the relative vertical wind velocity over the wing.

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3.2. Influence of kinematics on force generationBecause changes in effective instantaneous angles of attack

are more extreme at the lower freestream velocities, especially

during the upstroke (figure 4), and because the flapping

frequency and amplitude produce the greatest changes in

the local flow conditions, the flapping frequency and ampli-

tude affect lift more than do sweep and downstroke ratio

(figure 7a,c), which had little net effect (figure 7b,d). Drag

decreases with flapping amplitude, but flapping frequency

has no strong effect other than a slight increase in lift at the

highest flapping frequency (figure 7a,c). Drag increases

with sweep amplitude (figure 7d ), probably because of mem-

brane bulging (see also above). By contrast, previous work,

using a similar model with a more robustly reinforced arm-

wing trailing edge, tested in the same wind tunnel, [22],

demonstrated a positive correlation between flapping angle,

flapping frequency and stroke plane angle for mean lift

and thrust. Differences in model design, specifically trailing

edge flutter and deformation of the compliant membrane

due to aerodynamic pressure may underlie these divergent

results. Our results agree well with those of Hu et al. [21],

who found a positive correlation between flapping frequency

and net lift with a membrane model tested over a range of 1

to 10 Hz in flapping frequency and 0 to 10 m s21. For freestream

velocities lower than 4 m s21, the compliant membrane wing

used in that study generated thrust as the frequency increased;

however, like our wings, their compliant membrane wing gen-

erated net drag instead of thrust at the higher freestream

velocities comparable with the velocities tested in our exper-

iments, and drag increased when the flapping frequency was

greater than 6 Hz.

3.3. Effects of aspect ratioAR does not influence lift or drag over the range of stroke

patterns tested (figure 8; electronic supplemental material).

Although the force coefficients, CL and CD, clearly increase

or decrease in relation to velocity ratio in many cases, they

exhibit substantial scatter, particularly in the case of CD

during upstroke, and we observe no statistically significant

trend that depends on the wing AR. Two wings, AR3.5bl

and AR4.5cs show no decrease in the coefficient of drag

with increasing velocity ratio, unlike the other three wings,

where CD decreased with increasing velocity ratio. However,

the slope of these five regression lines are statistically not sig-

nificantly different (probability a ¼ 5%). The slopes of the CL

versus velocity ratio regressions for the two models with the

same area but the highest and lowest AR, AR2.5ca and

AR4.5ca, differ only during the upstroke ( p , 0.05). The

dependence on velocity ratio of lift during the downstroke

and of drag during the entire wingbeat does not differ signifi-

cantly between those two wings ( p . 0.05) (electronic

supplemental material). The wing that differs the most

from all other wings with respect to lift generation is model

AR2.5cs; in relation to velocity ratio, this wing shows an

increase in lift during downstroke, and a decrease during

upstroke greater than that of other wings. However, its

drag regression slopes are most similar to the AR2.5ca and

AR4.5ca wings during downstroke ( p ¼ 1.00 and p ¼ 0.96,

respectively).

The lack of a significant change in CL and CD with AR

suggests that AR is a poor predictor of a species’ flight behav-

iour and ecology over the range of values observed in bats,

with the exception of molossids. In this study, we did not

test models with ARs as high as those common in this

family, although we did use one baseline stroke pattern

that was based on the wingbeat kinematics of the molossid,

T. brasiliensis. T. brasiliensis can fly at high altitudes and

achieve high peak speeds [26,27] and their higher AR might

allow for a higher lift to drag ratio compared with the low

AR models tested here. We did not investigate the effect of

AR on power consumption, but predict wings with the lar-

gest area or wing span require more power, because their

angular momentum is higher in the first case due to greater

downstroke

upstroke

cam

era

1ca

mer

a 2

cam

era

1ca

mer

a 2

Figure 6. Sequence of snapshots of one wingbeat cycle in quiescent air. The flapping amplitude is u ¼ 1108, sweep is b ¼ 558, and flapping frequency, f ¼ 9 Hz.Camera 1 is located in front and above the wing, looking at the top side of the wing in a mostly front view, camera 2 is slightly elevated as well showing the bottomside of the wing. The upper row shows the downstroke, the lower row the upstroke sequence. The red arrows show the membrane bulging when the wing isin a swept-back position. Our data indicate that the membrane bulging affects the force generation more when the freestream velocity is low and the flapping amplitudeis small.

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mass overall, and because of the larger radius (span) that

places some of the mass further away of the body, which

requires more torque from the motors to reverse the stroke

direction in the second. This effect might be balanced by

lower induced drag and therefore lower induced power

due to the larger wingspan, but because we did not observe

a significant influence of AR on drag, we do not expect a

strong impact.

We noted the greatest amount of wear on models

AR2.5cs, the wing with the largest wing area, and AR4.5ca,

the wing with the longest wingspan. We believe that this

arose directly from the loads they experienced. Overall, the

aerodynamic force experienced by the AR2.5cs model is

higher than for the other wings (comparable CL as the other

wings with a larger area indicates higher lift force). For the

AR4.5ca wing, inertial forces are higher than for the models

with shorter wingspans, which causes higher strain on the

skeleton at the rapid reversal of the wing stroke direction.

4. Implications for robotic wing design4.1. The role of sweep on wing tensionUnlike many robotic models that use only wing flapping,

the model we employed here used both flapping and

sweeping motion. This additional degree of freedom pro-

vides some operational advantages; forward sweep at low

forward flight speeds can be used to maintain the magnitude

of the effective velocity while still controlling the effective

angle of attack. This might be useful for robotic devices

in which low speed operation with heavy payloads and

high coefficients of lift are required. However, the kinematics

of combined flapping and sweeping has its challenges: the

compliant membrane follows flapping actuation closely,

particularly where it attaches to the model’s body, but it

deviates more substantially from the theoretically dictated

sweep motion; specifically the area of the armwing decreases

when the wing is swept back and increases with forward

sweep. The membrane ‘bulging’ observed at high sweep

angles is symptomatic of this lack of precise control over

the membrane area and it leads to undesirable increases in

drag coefficients.

Bats have evolved active mechanisms to control the ten-

sion of the wing membrane, such as leg motion [28] and

active modulation of skin stiffness by muscles that attach to

the collagen and elastin connective tissue elements of the

skin [7,29]. In C. brachyotis, the length of the trailing edge

between the ankle and fifth digit increases during down-

stroke and decreases during upstroke due to this dynamic

control of the wing geometry [28]. Inspired by this, we are

developing a new version of our mechanical flapper with a

‘leg’, in which the wing attachment site on the body moves

in synchrony with the sweep motion of the arm skeleton.

When the wing sweeps fore and aft, the leg rotates with the

arm segment, and the body attachment plus arm, combined,

follows the rotation of the shoulder. This ensures that the

wing area does not vary as dramatically, and thus helps to

maintain tension in the armwing membrane. A second

improvement would be to develop a more hyperelastic

wing membrane material that, like the biological bat wing

membrane, can better accommodate a substantial range of

wing motion without excessive wrinkling or buckling.

4.2. Importance of wing twistAt high angles of attack, the airflow over a wing no longer

follows the wing’s profile and separates, leading to increased

drag and decreased lift, ultimately producing stall. Although

compliant wings are able to tolerate higher angles of attack

before stall than rigid wings because the wing’s camber can

self-adjust to balance the pressure difference between the

upper and lower surfaces of the wing [30,31], airflow still sep-

arates when the angle of attack becomes too extreme.

0

2

6

110

0

2

4

8065503520 95

4

0.560.500.44

0

2

6(a) (b)

(c) (d )

100

2

4

98642

4

5545352515sweep amplitude (°)

flapping frequency (Hz) downstroke ratio

flapping amplitude (°)

coef

fici

ent o

f lif

tco

effi

cien

t of

lift

coef

fici

ent o

f dr

agco

effi

cien

t of

drag

E. fuscus stroke

T. brasiliensis stroke

5.0 m s–1

7.5 m s–1

Figure 7. Summary of the effect of flapping frequency, downstroke ratio, flapping amplitude, and sweep amplitude on lift and drag during the downstroke. In eachplot, one parameter of the respective baseline stroke varies over the given range (table 1) and the other parameters are kept constant. Circles: E. fuscus baselinestroke pattern; crosses: T. brasiliensis stroke pattern; blue: 5 m s21 freestream velocity; orange: 7.5 m s21. Error bars indicate standard deviation of the means ofindependent trials. Baseline data thicker in all panels. (a) Flapping frequency, (b) downstroke ratio, (c) flapping amplitude and (d ) sweep amplitude.

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Kinematic patterns that encompass rapid and high amplitude

flapping motion produce unfavourably large effective angles

of attack, particularly at the outer portion of the wing, and at

mid-downstroke and mid-upstroke when the vertical speed is

greatest (figure 4a). These portions of the stroke cycle are thus

susceptible to separation and stall. Wing twist, in which the

effective angle of attack at the distal portions of the wing

can be reduced by reorienting the wing relative to the flow,

adjusting the pitch downward during downstroke and

upward during upstroke, can mitigate these problems.

Birds use of wing twist has long been recognized [32] and

there is evidence to suggest that bats also control the effective

angle of attack locally along the wingspan. The effective

angle of attack changes over the wingbeat cycle at different

flight speeds in Glossophaga soricina (Pallas’ long-tongued

bat) [33]. The relative angle of attack remains relatively

constant throughout the downstroke at higher flight speeds,

but becomes moderately negative during upstroke. This

suggests pitching of the handwing for better alignment

with the main flow direction [33]. Similar results have been

reported for Leptonycteris yerbabuenae (lesser long-nosed bat)

[34]. Similarly, pteropodid bats maintain a very small, or

even negative chord line at mid-downstroke [35]. In the big

brown bat, E. fuscus, we observe a clear pitch motion about

the wrist [24]. At mid-downstroke, the wing is oriented

with a very shallow or possibly slightly negative angle with

respect to the flight direction, but at mid-upstroke, the

handwing is pitched up, with the digits in an almost vertical

position (figure 9). Long-axis rotation of the forearm to allow

for pitch of the handwing is possible for the mechanical

1.0

1.5

2.0

2.5

3.0

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40–0.6

–0.4

–0.2

0

0.2

0.4

0.6

0.8

0.10 0.20 0.30 0.40 0.600.50–0.5

0

0.5

1.0

1.5

2.0–5

–4

–2

–3

–1

0

1co

effi

cien

t of

lift,

CL

downstroke upstroke

velocity ratio, Uv/Uh

coef

fici

ent o

f lif

t, C

L

coef

fici

ent o

f dr

ag, C

D

coef

fici

ent o

f dr

ag, C

D

velocity ratio, Uv/Uh

AR4.5ca AR4.5cs

AR2.5csAR2.5caAR3.5bl

Figure 8. Summary of results from statistical analysis. Separate linear regression line fits for all five models for coefficients of lift and drag, separated into down- andupstroke.

mid-downstroke mid-upstroke

(b)(a)

Figure 9. Two snapshots of E. fuscus in steady flight [24]; digit III highlighted in red. (a) Mid-downstroke; handwing is oriented in a shallow or slightly negativeangle with respect to the flight direction. (b) Mid-upstroke; handwing is pitched up, resulting in steep positive angle between wing and flight direction.

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wings. Numerical studies also demonstrate the importance of

wing twist, which appears to be necessary to increase lift

and generate thrust instead of drag in a compliant bat-like

wing [36,37].

These observations, combined with an analysis of the

differences between upstroke and downstroke, suggest that,

in a robotic wing model, force generation would benefit

significantly from an additional degree of freedom in pitch.

In a model of this kind, high wing pitch would be a key

mechanism by which to reduce both drag and negative lift

during upstroke.

4.3. Wing area and membrane propertiesIn addition to wing twist, modulating wing area during

upstroke is an effective means for controlling drag and

reducing inertial costs during the upstroke, and has been

observed in both small birds [38,39] and pteropodid bats

[40]. Birds are able to reduce wing area easily without incur-

ring negative side effects. Feathers can slide over each other

as they overlap with no disruption to the smooth lifting sur-

face. Bats, however, face a problem similar to that observed

with our model during sweep: reduction of the wing surface

can reduce the tension that keeps the membrane smooth,

leading to bulging or wrinkling. For bats, the solution to

this problem lies in skin composition: the membrane skin

of the bat wing is a fibre composite composed of a collage-

nous matrix with an imbedded network of pre-strained

elastin fibres [29]. This unique membrane construction

serves to corrugate the wing membrane as it folds, taking

out the excess length and preventing the wing from flapping

or bulging.

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The benefit of varying wing area has been successfully

demonstrated in a previous version of the mechanical flapper

employed here [22,23]. However, the challenge of accom-

modating excess membrane length during the retraction of

isotropic wings remains challenging. Attaching the mem-

brane to the wing at its most swept-back configuration

would prevent wrinkling, and keep tension in the membrane

as the wing sweeps forward during the downstroke.

However, this solution imposes high demands on actuators

(servo motors in this case) and high stresses on the wing

skeleton and body attachment site when ‘conventional’ elastic

membrane materials such as silicone are employed. This

stress leads to fatigue and a reduced operational life. Mimick-

ing the anisotropic, hyperelastic behaviour of the biological

membrane material would be a preferable approach, and

research in this direction is promising [41].

:20160083 5. Concluding remarksThe design, fabrication and testing of a robotic wing that cap-

tures several important characteristics of bats and also allows

experimental manipulation has demonstrated several valu-

able features of bioinspired wing design, and dispelled

some initial expectations regarding the role of AR. We con-

clude that wing stroke pattern has a stronger effect on

aerodynamic force generation than geometric AR. The gener-

ation of lift depends strongly on the ratio of relative vertical to

relative horizontal wind speed, with higher vertical velocities

resulting in more lift. The dependence of drag is less clear,

partly because drag values are lower and subject to greater

experimental uncertainty. Nevertheless, higher velocity

ratios decrease drag during the downstroke.

Whether our findings apply to larger bats that fly at a

higher Reynolds number regime, where quasi-steady aero-

dynamics become more applicable, remains uncertain.

Furthermore, we did not investigate the very high AR

range that is relatively rare among bats, but is characteristic

of Molossidae.

Based on insights gained during these experiments using

relatively simple models, we propose some desirable direc-

tions for wing design in future robotic wing experiments:

(i) incorporation of a wing-area reduction mechanism, using

elbow and wrist flexion during upstroke [23], (ii) mitigation

of membrane bulging at the swept-back position of the

wing, either by the use of a ‘leg’ attachment that follows

the sweep motion or by the use of anisotropic hyperelastic

materials that allow extreme spanwise stretch without

substantial chordwise elongation, and last, (iii) introduction

of long-axis rotation of the forearm to enable pitch of the

handwing and thus control the local angle of attack.

Data accessibility. Data are supplied as part of the electronic supplemen-tal material.

Authors’ contributions. C.S. contributed to the experimental design, datacollection, data analysis and manuscript preparation; K.S.B. andS.M.S. contributed to the experimental design, data analysis andmanuscript preparation.

Competing interests. We declare we have no competing interests.

Funding. This work was supported by AFOSR grant FA9550-12-1-0210,monitored by Doug Smith, and NSF-NRI grant CMMI 1426338.The support of the Ostrach Graduate Fellowship (C.S.) is gratefullyacknowledged.

Acknowledgements. We thank Dr Joseph Bahlman for the developmentof and training on the use of the original flapper. Many thanks toKristen Michaelson and Tristan Paine for their help with MATLAB pro-gramming for the motor control, and to Dr Nicolai Konow for hishelp with the statistical analysis.

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