Parametric and Statistical Study of the Wing Geometry of 75 Species of Odonata

applied sciences

Article Parametric and Statistical Study of the Wing Geometry of 75 Species of Odonata

Nasim Chitsaz 1,*, Romeo Marian 1, Amirmasoud Chitsaz 2 and Javaan S. Chahl 1,3

1 School of Engineering, University of South Australia, Adelaide, SA 5095, Australia; [email protected] (R.M.); [email protected] (J.S.C.) 2 Faculty of Computer Engineering, Najafabad Branch, Azad University, Najafabad 8514143131, Iran; [email protected] 3 Joint and Operations Analysis Division, Defence Science and Technology Group, Edinburgh, SA 5111, Australia * Correspondence: [email protected]

Received: 18 June 2020; Accepted: 28 July 2020; Published: 4 August 2020

Abstract: The flight performance and maneuverability of Odonata depends on wing shape and aero-structural characteristics, including airfoil shape, wingspan, and chord. Despite the superficial similarity between Odonata planforms, the frequency with which they are portrayed artistically, and the research interest in their aerodynamics, those features that are stable and those that are labile between species have not been identified. Studies have been done on 2D aerodynamics over corrugated wings; however, there is limited comparative quantified data on the planforms of Odonata wings. This study was undertaken to explore the scale relationships between the geometrical parameters of photogrammetrically reconstructed wings of 75 Odonata species, 66 from Epiprocta, and 9 from Zygoptera. The wing semi-spans captured in the database range from 24 to 85 mm. By carrying out an extensive statistical analysis of data, we show that the geometrical parameters for the suborder Epiprocta (dragonflies) can be classified into scale-dependent and independent parameters using regression analysis. A number of close correlations were found between the wingspan and the size of other structures. We found that amongst the variables considered, the largest independent variations against the forewing span were found in the chord of the hindwing, and that hindwing properties were not reliably predicted by the Odonata family. We suggest that this indicates continuous evolutionary pressure on this structure.

Keywords: aerodynamics; dragonﬂy; micro air vehicle (MAV); Odonata; 3D reconstruction

1. Introduction There are various structural and aerodynamic demands related to the ecological niche of each species of Odonata that have influenced the characteristics of their wings through natural selection. An understanding of the aerodynamic performance of wings may inform considerations of metabolism, ecology, and evolutionary processes. Unlike many insects, Odonata wings have comparatively high aspect ratios [1], modest wing beat frequencies (30–40 Hz) [2–4], limited stroke angles (30◦–60◦)[5,6], and are used in gliding flight modes [7]. Some steady-state aerodynamic parameters are worth considering under these circumstances [8,9]. Odonata are categorized into the suborders Epiprocta (dragonflies) and Zygoptera (damselflies) [10]. The nodus size has been identified as an important parameter in the structure of a dragonfly wing, as illustrated in Figure1b. The nodus is the point where the camber of the leading edge spar inverts [ 11], which is believed to provide strength and flexibility in flight [12]. Zhang et al. studied the dynamics of the nodus and wing in gliding flight [13]. According to their experimental visualization analysis,

Appl. Sci. 2020, 10, 5389; doi:10.3390/app10155389 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 5389 2 of 17

Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 20 the nodus is an essential structural element of the wing, providing flexibility to the wing under aerodynamic loads [13]. The scanning electron microscopy (SEM) visualization and tensile testing havenodus shown and wing that thein gliding location flight of [13]. the nodusAccording is critical to their duringexperimental flight, visualization due to high analysis, tensile the stresses nodus [is14 ]. It alsoan essential provides structural the wings element with of shock-absorbing the wing, providing capability flexibility that to may the wing help under in dealing aerodynamic with any loads externally [13]. imposedThe scanning torsion electron or bending microscopy stress [11(SEM)]. During visualization the flight, and the tensile wings testing undergo have passiveshown that twist the that location is largely of dependentthe nodus on is critical the position during of flight, the nodusdue to [high15]. tensile The nodus stresses is located[14]. It also at the provides leading the edge wings at with the interfaceshock- absorbing capability that may help in dealing with any externally imposed torsion or bending stress [11]. of the second main vein and the leading edge of the wing where the orientation of the leading edge During the flight, the wings undergo passive twist that is largely dependent on the position of the nodus changes[15]. The [16 nodus,17], which is located is about at the 50%leading of wingspanedge at the frominterface the of root the [second18,19]. main The othervein and prominent the leading structure edge is theof the pterostigma. wing where It the is oftenorientation found of in the the leading outer partedge of changes the span [16,17], at the which leading is about edge 50% of Odonata of wingspan wings, andfrom is created the root by [18,19]. a blood-sinus The other duringprominent emergence structure [is15 the] (Figure pterostigma.1). Pterostigma It is often probablyfound in the plays outer a majorpart roleof inthe the span flight at the stability leading of edge Odonata. of Odonata The wings, concentrated and is created mass ofby the a blood pterostigma-sinus during is believed emergence to have [15] a counteracting(Figure 1). Pterostigma role during probably undesired plays a twisting major role of in the the wing flight instability the airflow of Odonata. [20]. The As concentrated shown in Figure mass 1, theof definition the pterostigma of chord is believed lines for to Odonata have a counteracting is different role compared during toundesired commercial twisting aircraft. of the Forwing Odonata, in the chordairflow lines [20]. are As defined shown toin haveFigure an 1, angle the definitionα to the of reference chord lines body for line, Odonata where is αdifferentis the anglecompared between to a perpendicularcommercial aircraft. line For to the Odonata, reference chord body lines line are anddefined the to perpendicular have an angle lineα to the to thereference chord. body However, line, where α is the angle between a perpendicular line to the reference body line and the perpendicular line to for aircraft, chord lines are defined parallel to a fuselage [21]. the chord. However, for aircraft, chord lines are defined parallel to a fuselage [21].

Pterostigma Body line Nodus

α Pterostigma size

Chord

Nodus chord

(a) (b)

FigureFigure 1. 1. DragonflyDragonfly wing wing geometry geometry definition: definition: geometrical geometrical parameters parameters (a) and dragonfly (a) and dragonflywing geometry wing geometrydefinitions definitions nodus and nodus pterostigma and pterostigma (b). (b).

OdonataOdonata appear appear to to have have a a characteristic characteristic arrangementarrangement of of wings wings and and overall overall planform planform common common to toall all species,species, but but with with parameter parameter variations. variations. TheThe purposepurpose of our study was was to to explore explore how how non non-dimensional-dimensional parameters might vary between species and scales of dragonflies for the next generation of the bio-inspired parameters might vary between species and scales of dragonflies for the next generation of the micro air vehicle. Our collection of 75 solid models of Odonata wings was measured to extract descriptive bio-inspiredwing parameters. micro airThe vehicle. main parameters Our collection of Odonata of 75 wings solid modelsinclude offorewing Odonata (FW) wings and washindwing measured (HW) to extractspan, descriptiveminimum and wing maximum parameters. chord length, The main and parameterslocation (these of parameters Odonata wings play an include important forewing role to (FW)an andoptimum hindwing for (HW)the lift span, distribution minimum over and the maximumwing) [22],chord nodus length, location and and location length, (thesepterostigma parameters size, and play andistance important from role the to nodus. an optimum These parameters for the lift together distribution describe over the the key wing) features [22 ],of nodusan Odonata location wing and that length, are pterostigmarelevant to size,flight andperformance. distance fromSpan and the nodus.chord measurements These parameters have a togethersignificant describe role [23] thein establishing key features ofthe an Odonatabasic performance wing that characteristics are relevant of to fixed flight-wing performance. aircraft, and Span are likely and chord to be measurementsequally important have to a significantunderstanding role [23 the] inaerodynamic establishing performance the basic performance of Odonata. characteristicsThis paper presents of fixed-wing the essential aircraft, geometrical and are likelyparameters to be equally of Odonata important wings toand understanding explores the trends the aerodynamic apparent in the performance dataset. The of database Odonata. and This analysis paper procedure may be suitable for studies of ecology and evolution, as well as for advancing the design of small presents the essential geometrical parameters of Odonata wings and explores the trends apparent in technological aircraft. the dataset. The database and analysis procedure may be suitable for studies of ecology and evolution, as2. well Materials as for advancingand Methods the design of small technological aircraft.

2. Materials and Methods For this study, 75 wing geometries of various Odonata were captured from the collection of the South Australia Museum. Figure2 shows the number of species of each family of Odonata species in the dataset. As shown in Figure2, 50% are from the Libellulidae and Aeshnidae families that contain a large number of species with a wide range of sizes [24,25]. The 75 Odonata families and species are included from the Libellulidae family (Libellula Pulchella, Libellula Murica Drury, Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 20

Appl. Sci. 2020, 10, 5389 3 of 17 For this study, 75 wing geometries of various Odonata were captured from the collection of the South Australia Museum. Figure 2 shows the number of species of each family of Odonata species in the dataset. AsLibellula shown in Indica, Figure Libellula2, 50% are Saturata, from the Libellulidae Lyriothemis and Meyeri, Aeshnidae Nesoxenia families that Mysis, contain Neurothemis a large number Stig Matizansof speciesBramina, with Neurothemis a wide range Oligoneura, of sizes [24,25] Orthetrum. The 75 Caledonicum, Odonata families Orthetrum and Glaucum,species are Orthetrum included from Villosovittatum, the Libellulidae family (Libellula Pulchella, Libellula Murica Drury, Libellula Indica, Libellula Saturata, Lyriothemis Pantala Flave Scens, Lathrecista Asiatica, Protorthemis Coronata, Plathemis Lydia, Rhodothernis, Phyothemis Meyeri, Nesoxenia Mysis, Neurothemis Stig Matizans Bramina, Neurothemis Oligoneura, Orthetrum Caledonicum, Graphipters, Phyothemis Phyllis, Phyothemis Princeps, Tholymis Tillarga, Tramea Loewii, Zyxomma Sp, Huonia Orthetrum Glaucum, Orthetrum Villosovittatum, Pantala Flave Scens, Lathrecista Asiatica, Protorthemis Coronata, PlathemisThalassophila, Lydia, Rhodothernis, Crocothemis Nigrifrons,Phyothemis Graphipters, Diplacina Phoebe, Phyothemis Camacinia Phyllis, Othello, Phyothemis Agrionopters Princeps, Tholymis Longitudinalis, Tillarga,Agrionoptera Tramea Loewii, Insignis, Zyxomma Celithemis Sp, Huonia Eponina), Thalassophila, Aeshnidae Crocothemisfamily (Adversaechna, Nigrifrons, Diplacina Anax Phoebe, Guttatus, Camacinia Anax Junius, Othello,Austroaeschna Agrionopters Multipunctata, Longitudinalis, Austroaeschna Agrionoptera Parvistigma,Insignis, Celithemis Gynacantha Eponina Kirbyi,), Aeshnidae Gynacantha famil Mocsaryi,y (Adversaechna,Dendroaeschna Anax Conspersa, Guttatus, Hemianax, Anax Junius, Notoaeschna Austroaeschna Sagittata, Multipunctata, Telephlebia Gode Austroaeschnaﬀroyi, Accessions), Parvistigma, Corduliidae Gynacanthafamily (Epicordulia Kirbyi, Gynacantha Princeps, HemicorduliaMocsaryi, Dendroaeschna Australiae, Hemicordulia,Conspersa, Hemianax, Procordulia, Notoaeschna Procordulia Sagittata, Jacksoniensis, TelephlebiaProcordulia), Godeffroyi, Gomphidae Accessions),family (GomphusCorduliidae Crassus,family Accessions,(Epicordulia DromogomphusPrinceps, Hemicordulia Spoliatus, Australiae, Hemigomphus Hemicordulia,Gouldii, Austrogomphus Procordulia, Procordulia Prasinus, IctinogomphusJacksoniensis, Procordulia), Australis), CalopterygidaeGomphidae familyfamily (Gomphus(Neurobasis Crassus, Australis, Accessions, Dromogomphus Spoliatus, Hemigomphus Gouldii, Austrogomphus Prasinus, Ictinogomphus Australis), Hetaerina Americana, Calopteryx Maculata, Playcypha, Papuagrion Occipitale), Macromiidae family (Macromia Calopterygidae family (Neurobasis Australis, Hetaerina Americana, Calopteryx Maculata, Playcypha, Papuagrion Tillyardi, Macromia Illinoiensis, Macromia Taeniolata), Petaluridae family (Petalura Ingentissima, Petalura Occipitale), Macromiidae family (Macromia Tillyardi, Macromia Illinoiensis, Macromia Taeniolata), Petaluridae familyGigantea, (Petalura Uropetala Ingentissima, Carovei Petalura), and Synthemistidae Gigantea, Uropetalafamily Carovei (Eusynthemis), and Synthemistidae Brevistyla, Choristhemis family (Eusynthemis Flavoterminate, Brevistyla,Archaeosynthemis Choristhemis Orientalis Flavoterminate,). Archaeosynthemis Orientalis).

6 6 4 3 3 3 Measured species number

FigureFigure 2. 2.NumberNumber of each of each genus genus of Odonata, of Odonata, according according to their tospecies. their species.

TheThe dataset, dataset, including including complete complete three-dimensional three-dimensional models, are available models, in the are Dryad available repository in the[26], Dryad withrepository the original [26], withphotographs the original from photographs which the frommodels which were the constructed. models were 3DF constructed. Zephyr Pro 3DF for Zephyr photogrammetryPro for photogrammetry and SolidWorks and software SolidWorks for conversion software forof the conversion point cloud of to the a solid point model cloud were to aused solid to model reconstructwere used the to wings reconstruct [27,28]. theFigure wings 3 shows [26,27 the]. 3D Figure reconstru3 showscted the hindwing 3D reconstructed of a Petalura hindwingIngentissima of from a Petalura Ingentissima from the dataset. The dimensions of the wing and geometrical parameters were measured for both FW and HW from the projected files. All specimens were from a publicly available Odonata collection in the South Australian Museum. Unfortunately, the entire collection has been classified by species, but has not been classified by sex. Furthermore, the collection specimens could not be accessed ventrally to establish their sex. The labeling of typical specimens is shown in the AppendixA. This is unquestionably a significant problem for some possible uses of this dataset, given the important role that sex might play in behavior, and thus functional demands on the flight apparatus. Considering further the implications of this limitation, we have studied many species with few individuals per species. We have considered wing shape, Appl. Sci. 2020, 10, 5389 4 of 17 not the remainder of the anatomy. There are known sex-specific features in Odonata [28], albeit more subtle than in some species, such as butterflies [29,30]. Sex in dragonflies is established from ventral thoracic structures [31] rather than wing features. However, examining the spread of the data, there are no superficial indications of a bimodal distribution. This could only be expected if male andAppl. female Sci. 2020 Odonata, 10, x FOR PEER had REVIEW systematic differences that were large compared to variations4 of 20 between species. One implicit assumption in our study that results from this limitation is that the variations of non-dimensionalthe dataset. The dimensions parameters of between the wingspecies and geometrical are greater parameters than the were variations measured between for both sexes. FW and HW from the projected files.

FigureFigure 3. Three 3. Three dimensional dimensional reconstructed reconstructed of of a a PetaluraPetalura Ingentissima Ingentissima hindwing.hindwing.

TheAll precisionspecimens ofwere the from reconstruction a publicly available of the Odonata wings in collection both surface in the South dimensions Australian and Museum. depth of anglesUnfortunately,/corrugation the patternsentire collection was evaluated has been againstclassified a by measured species, but transparent has not been ﬂat classified model wing by sex. and Furthermore, the collection specimens could not be accessed ventrally to establish their sex. The labeling Micro-CT, respectively, with good agreement between results (Figure4). The method and validation Appl.of typ Sci.ical 2020 specimens, 10, x FOR PEER is shown REVIEW in the Appendix A. This is unquestionably a significant problem5 of for 20 some arepossible documented uses of inthis Chitsaz dataset, et given al. [26 the]. important role that sex might play in behavior, and thus functional demands on the flight apparatus. Considering further the implications of this limitation, we have studied

many species with few individuals per species. We have considered wing shape, not the remainder of the anatomy. There are known sex-specific features in Odonata [29], albeit more subtle than in some species, such as butterflies [30,31]. Sex in dragonflies is established from ventral thoracic structures [32] rather than wing features. However, examining the spread of the data, there are no superficial indications of a bimodal

distribution. This could only be expectedX- rayif Detectormale and female Odonata had systematic differences that were

large compared to variations between species. One implicit assumption in our study that results from this limitation is that the variations of non-dimensional parameters between species are greater than the

variations between sexes.

The precision of theRotating reconstruction sample of the wings in both surface dimensions and depth of

angles/corrugation patterns was evaluated against a measured transparent flat model wing and Micro-CT, respectively, with good agreement between results (Figure 4). The method and validation are documented in Chitsaz et al. [28].

X-ray Generator

Micro-CT, Xradia MicroXCT 400 Micro Photogrammetry, Nikon D610 Tomography system AF-S macro Nikkor 105 mm) Resolution: 16μm Resolution: 4016×6016 pixel

FigureFigure 4. Schematic4. Schematic view view ofof photogrammetryphotogrammetry and and Micro Micro-CT-CT process. process.

Wing Geometry and Parameter Definition In this section, the measured wing geometry parameters are presented. We have defined wing geometry to be consistent with standard aeronautical definitions where possible [33,34]. However, due to the additional features of Odonata wings compared to aircraft and the tandem configuration [35], there are some additional definitions presented for the nodus and pterostigma. Figure 1 shows a schematic of dragonfly wing geometry and defined parameters [36]. The definition of the chord is the same as in aeronautics; chord refers to the imaginary straight line joining the leading edge (LE) and trailing edge (TE) of an airfoil that comes from the projected area of the reconstructed 3D wings and is perpendicular to the span. 2 is wing semi-span (half wingtip-to-wingtip span). Maximum chord (Cmax) is the longest straight line from wing LE to TE [9,37]. 𝑏𝑏⁄ The other defining feature of the wing is the pterostigma (pigmented area), which is located close to the LE, which has a higher density than the rest of the wing [38]. This feature is also believed to be key to increasing critical speed in glide [20]. These eight parameters that describe the Odonata wings in our dataset are illustratively presented in the next section, and include wing semi-span, maximum chord, maximum chord location, mean chord, nodus chord, nodus chord location, pterostigma length, and location.

Appl. Sci. 2020, 10, 5389 5 of 17

Wing Geometry and Parameter Definition In this section, the measured wing geometry parameters are presented. We have defined wing geometry to be consistent with standard aeronautical definitions where possible [32,33]. However, due to the additional features of Odonata wings compared to aircraft and the tandem configuration [34], there are some additional definitions presented for the nodus and pterostigma. Figure1 shows a schematic of dragonfly wing geometry and defined parameters [35]. The definition of the chord is the same as in aeronautics; chord refers to the imaginary straight line joining the leading edge (LE) and trailing edge (TE) of an airfoil that comes from the projected area of the reconstructed 3D wings and is perpendicular to the span. b/2 is wing semi-span (half wingtip-to-wingtip span). Maximum chord (Cmax) is the longest straight line from wing LE to TE [9,36]. The other defining feature of the wing is the pterostigma (pigmented area), which is located close to the LE, which has a higher density than the rest of the wing [37]. This feature is also believed to be key to increasing critical speed in glide [20]. These eight parameters that describe the Odonata wings in our dataset are illustratively presented in the next section, and include wing semi-span, maximum chord, maximum chord location, mean chord, nodus chord, nodus chord location, pterostigma length, and location.

3. Results The results include the geometrical parameters of wings from a total of 75 species from 15 families of Odonata that were measured from the projected area of the 3D digitized wings. The measured wing planform parameters include wing semi-span (b/2), maximum chord (Cmax), location of the maximum chord (Cmax,L), mean chord length of the wing (Cmean), nodus chord (Cnodus), which is the straight distance from LE to TE at the nodus, its location from the span coordinate of dragonﬂy body (Cnodus,L), length of pterostigma (Spterostigma), and distance of nodus to pterostigma (D) for both FW and HW. All parameter dimensions are in millimeters.

3.1. Database Analysis In order to get a better understanding of the range in the processed data, initial results are shown with the probability (area under the curve) and fitted normal distributions. Since it is possible that no subsequent large study will be undertaken of dragonfly species’ wings, we have treated the sample as if it were randomly selected. In a collection, there is every likelihood that this is not the case for the most superficially obvious parameters, such as size, and other hidden indirect considerations leading to ease of capture of specimens. We assumed that derived measures and ratios were less likely to be biased by the process of sampling. Equation (1) shows the formula for calculating the probability of normal distribution. (x µ)ˆ2 2 1 − f ( x µ, σ ) = e− 2σˆ2 (1) √2πσˆ2 where µ, σ, and σˆ2 are the mean, standard deviation, and variance, respectively, and x is the desired measured parameter [38]. Figure5 shows the range of half-span of HW and FW across the collection, according to their families. In this study, the species with the smallest wingspan was Huonia thalassophila, with dimensions of 47.32 and 46.50 mm. The largest wingspan was 168.84 and 169.54 mm, of Petalura ingentissima (PI), the giant petaltail [39]. The maximum chord length was 16.24 mm and 20.92 mm for FW and HW, respectively. As shown in Figure5, it is evident that the wingspan length of the Odonata wings can vary from 47 mm to 169 mm. Thus, in order to find a proper trend between the geometrical parameters of the wings, all of the studied parameters of each wing were non-dimensionalized with the semi-span length (b/2) of that wing. This is a useful approach to design an applicable micro air vehicle (MAV), in both aerodynamics and flight performance aspects, which is similar to general airplanes. Figure6 shows Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 20

3. Results The results include the geometrical parameters of wings from a total of 75 species from 15 families of Odonata that were measured from the projected area of the 3D digitized wings. The measured wing planform parameters include wing semi-span (b/2), maximum chord (Cmax), location of the maximum chord (Cmax,L), mean chord length of the wing (Cmean), nodus chord (Cnodus), which is the straight distance from LE to TE at the nodus, its location from the span coordinate of dragonfly body (Cnodus,L), length of pterostigma (Spterostigma), and distance of nodus to pterostigma (D) for both FW and HW. All parameter dimensions are in millimeters.

3.1. Database Analysis In order to get a better understanding of the range in the processed data, initial results are shown with the probability (area under the curve) and fitted normal distributions. Since it is possible that no subsequent large study will be undertaken of dragonfly species’ wings, we have treated the sample as if it were randomly selected. In a collection, there is every likelihood that this is not the case for the most superficially obvious parameters, such as size, and other hidden indirect considerations leading to ease of capture of Appl.specimens. Sci. 2020, 10We, 5389 assumed that derived measures and ratios were less likely to be biased by the process6 of of 17 sampling. Equation (1) shows the formula for calculating the probability of normal distribution. 1 ( µ)^ the non-dimensional maximum chord( µ and, ) its= location and non-dimensional^ mean chord(1 normal) 𝑥𝑥− 2 2 ^2 − distribution and probability density function2 (PDF) for both FW2𝜎𝜎 and2 HW. Results show that the average where µ, σ, and σ^2 are the mean, standard𝑓𝑓 𝑥𝑥⃓ 𝜎𝜎 deviation, and 𝑒𝑒variance, respectively, and x is the desired mean and maximum chord length of the HW is around√ 𝜋𝜋𝜋𝜋 25% larger than corresponding measurements measured parameter [39]. from the FW. The average value for Cmax/Cmean parameter is 1.4 for both HW and HW. The location Figure 5 shows the range of half-span of HW and FW across the collection, according to their families. of Cmax is also an interesting parameter in the overall shape of the wing. C is the deterministic In this study, the species with the smallest wingspan was Huonia thalassophila, withmax,L dimensions of 47.32 parameterand 46.50 formm. spanwise The largest lift wingspan and drag was distribution 168.84 and across 169.54 themm, wing. of Petalura Results ingentissima show that (PI) C, max,Lthe giant/b has highpetaltail scatter, [40] with. standard deviation of around 0.1.

Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 20

chord and its location and non-dimensional mean chord normal distribution and probability density function (PDF) for both FW and HW. Results show that the average mean and maximum chord length of the HW is around 25% larger(a) than corresponding measurements from the( b FW.) The average value for Cmax/Cmean parameter is 1.4 for both HW and HW. The location of Cmax is also an interesting parameter Figure 5. Semi-span distribution for both FW (a) and HW (b). in the overall shape ofFigure the wing. 5. Semi-span Cmax,L is the distribution deterministic for parameter both FW for (a) spanwise and HW lift (b). and drag distribution across the wing. Results show that Cmax,L/b has high scatter, with standard deviation of around 0.1. The maximum chord length was 16.24 mm and 20.92 mm for FW and HW, respectively. As shown in Figure 5, it is evident that the wingspan length of the Odonata wings can vary from 47 mm to 169 mm. Thus, in order to find a proper trend between the geometrical parameters of the wings, all of the studied parameters of each wing were non-dimensionalized with the semi-span length (b/2) of that wing. This is a useful approach to design an applicable micro air vehicle (MAV), in both aerodynamics and flight performance aspects, which is similar to general airplanes. Figure 6 shows the non-dimensional maximum

(a) (b)

(e) (f)

FigureFigure 6. Probability 6. Probabilitydensity density function function (PDF) (PDF) and andfitted ﬁttednormal normal distribution distribution of forewing of (FW) forewing max chord (FW) (a), max hindwing (HW) max chord (b), FW max chord location (c), HW max chord location (d), and FW mean chord chord (a), hindwing (HW) max chord (b), FW max chord location (c), HW max chord location (d), (e) and FW mean chord (f). and FW mean chord (e) and FW mean chord (f). The PDF and normal distribution of nodus and pterostigma parameters from the sample, which are Thebelieved PDF to and be normal functional distribution features of ofOdonata nodus wings and pterostigma [20], were calcul parametersated. Figure from 7 shows the sample, the non which- are believeddimensional to benormal functional distribution features of nodus of Odonatachord length, wings pterostigma [20], were size, calculated.and their locations Figure for7 FW shows and the HW. As shown below, the ratio of nodus to pterostigma location is 1.7 and 1.9 for FW and HW. The results show that the size of the pterostigma has a relatively high scatter. Calopterygidae and Chlorocyphidae do not have pterostigma. Also, it is found that for Petalura Ingentissima, 2 × pterostigma, L/b is between 0.6–0.7.

Appl. Sci. 2020, 10, 5389 7 of 17

non-dimensional normal distribution of nodus chord length, pterostigma size, and their locations for FW and HW. As shown below, the ratio of nodus to pterostigma location is 1.7 and 1.9 for FW and HW. The results show that the size of the pterostigma has a relatively high scatter. Calopterygidae and Chlorocyphidae do not have pterostigma. Also, it is found that for Petalura Ingentissima, 2 pterostigma, Appl. Sci. 2020, 10, x FOR PEER REVIEW × 8 of 20 L/b is between 0.6–0.7.

(a) (b)

(e) (f)

(g) (h)

FigureFigure 7. PDF 7. PDF and and fitted ﬁtted normal normal distribution distribution of FW of FWnodus nodus chord chord (a), (HWa), HW nodus nodus chord chord (b), ( bFW), FW nodus nodus chord locationchord (c location), HW nodus (c), HW chord nodus location chord (d), location FW pterostigma (d), FW pterostigma size (e), HW sizepterostigma (e), HW size pterostigma (f), FW pterostigma size (f), locationFW pterostigma (g) and HW location pterostigma (g) and location HW pterostigma (h). location (h).

TheThe non non-dimensional-dimensional normal normal distribution distribution of max of chord, max max chord, chord max location, chord mean location, chord mean nodus chord chord, nodusnodus chord chord, location, nodus pterostigma chord location, size, pterostigmaand pterostigma size, location and pterostigma for both FW location and HW for bothfor the FW same and species HW of twofor thefamilies same of species Aeshnidae of twoand familiesLibellulidae of areAeshnidae illustratedand inLibellulidae Figures 8 andare 9. illustrated These two in figures Figures were8 and plotted9. to compareThese two two ﬁgures families were of plotted Aeshnidae to compare and Libellulidae, two families as they of Aeshnidae are nearlyand 50%Libellulidae of the dataset,, as they and are tend nearly to be larger. By comparing two families, it is found that some parameters are dependent, such as Cmax,L, and some are non-dependant, such as Cmax. Also, for HW, the standard deviation differs between Aeshnidae and Libellulidae, compared with FW. Appl. Sci. 2020, 10, 5389 8 of 17

50% of the dataset, and tend to be larger. By comparing two families, it is found that some parameters

Appl.are Sci. dependent, 2020, 10, x FOR such PEER as C REVIEWmax,L, and some are non-dependant, such as Cmax. Also, for HW, the standard9 of 20 deviation diﬀers between Aeshnidae and Libellulidae, compared with FW.

40 40 Libellulidae Nondimensional Max Chord Libellulidae Nondimensional Max Chord Normal Distribution Normal Distribution Aeshnidae Nondimensional Max Chord 30 Aeshnidae Nondimensional Max Chord 30 Normal Distribution Normal Distribution

=0.27715 20 20 =0.016308 Density =0.21892 Density =0.30708 =0.012441 10 10 =0.047128 =0.22166

=0.019154

0 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

FW Nondimensional Max Chord (2*Cmax/b) HW Nondimensional Max Chord (2*Cmax/b)

(a) (b) 12 12 Libellulidae Nondimensional Max Chord Location LibellulidaeAeshnidae Nondimensional Nondimensional Max Max Chord Chord Location Location NormalNormal DistributionDistribution 10 Normal Distribution 10 Aeshnidae Nondimensional Max Chord Location Aeshnidae Nondimensional Max Chord Location Normal Distribution Normal Distribution 8 8

6 6 Density Density 4 =0.61421 4 =0.36992 =0.037728 =0.11089 2 =0.57894 2 =0.26631 =0.13234 =0.13148 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 FW Nondimensional Max Chord Location HW Nondimensional Max Chord Location(2*Cmax,L/b)

(c) (d ) 50 50 Libellulidae Nondimensional Mean Chord Libellulidae Nondimensional Mean Chord Normal Distribution Normal Distribution 40 40 Aeshnidae Nondimensional Mean Chord Aeshnidae Nondimensional Mean Chord Normal Distribution Normal Distribution 30 30

20 20 =0.20104 Density Density =0.15548 =0.014028 =0.017978 10 10 =0.22478 =0.16528 =0.033521 =0.014283 0 0 0.1 0.15 0.2 0.25 0.3 0.1 0.15 0.2 0.25 0.3 0.35 FW Nondimensional Mean Chord(2*Cmean/b) HW Nondimensional Mean Chord(2*Cmean/b)

( e) (f)

FigureFigure 8. 8.ProbabilityProbability density density function function and and fitted ﬁtted normal normal distribution distribution of of non non-dimensional-dimensional parameters: FW maxFW chord max chord(a), HW (a), max HW chord max chord (b), FW (b), max FW maxchord chord location location (c), (HWc), HW max max chord chord location location (d), (d HW), HW mean mean chord (e)chord and HW (e) and mean HW chord mean (f) chord of the ( ftwo) of families the two familiesof Aeshnidae of Aeshnidae and Libellulidae.and Libellulidae .

Appl.Appl. Sci. 20 Sci.202020, 10,, x10 FOR, 5389 PEER REVIEW 10 of 920 of 17

(a) (b)

(e) (f)

(g) (h)

FigureFigure 9. Probability 9. Probability density density function function and and fitted ﬁtted normal normal distribution distribution of ofnon non-dimensional-dimensional parameters: parameters: FW nodusFW chord nodus ( chorda), HW (a ),nodus HW nodus chord chord (b), FW (b), nodus FW nodus chord chord location location (c), ( HWc), HW nodus nodus chord chord location location (d (),d ),FW pterostigmaFW pterostigma size (e), sizeHW (pterostigmae), HW pterostigma size (f), FW size pterostigma (f), FW pterostigma location location(g) and HW (g) andpterostigma HW pterostigma location (h) for locationboth FW (andh) for HW both of FWtwo and families HW of twoAeshnidae familiesand of Libellulidae.Aeshnidae and Libellulidae.

3.2.3.2. Regression Regression Analysis Analysis TheThe species species studied studied included included small small species species with with a span a span length length of 46 of mm 46 mm up upto large to large ones ones with with a span a lengthspan of length 170 mm.of 170 In mm. this In section, this section, both both linear linear and and polynomial polynomial regression regression is is presented presented for for the the seven seven measuredmeasured parameters, parameters, including including b/2, Cb/max2,, C Cmaxmean,C, Cmeannodus,C, Cnodus,Lnodus,,C pterostigmanodus,L, pterostigma size, and location. size, and A location. P-value of A p-value of less than 0.05 is the criteria for accepting the regression equation [40]. Note that the objective of this section is to identify trends, particularly with respect to scale. Figure 10 shows the wing semi-span (b/2) length versus the maximum chord of the FW with the minimum and maximum lengths of 5 mm and 16 mm, respectively. Both polynomial (y1) and Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 20 less than 0.05 is the criteria for accepting the regression equation [41]. Note that the objective of this section is toAppl. identify Sci. 2020 trends,, 10, 5389 particularly with respect to scale. 10 of 17 Figure 10 shows the wing semi-span (푏/2) length versus the maximum chord of the FW with the minimum and maximum lengths of 5 mm and 16 mm, respectively. Both polynomial (y1) and linear (y2) linear (y ) regressions were found to be a satisfactory fit to find the C vs. b/2 for both FW and HW. regressions2 were found to be a satisfactory fit to find the Cmax vs. b/2 for maxboth FW and HW. In the following figures,In the the following red dots figures, correspond the red to dots Zygoptera correspond (damselfly) to Zygoptera order,(damselfly) while the order,black dots while relate the black to Epiprocta dots (dragonfly)relate to Epiproctaorder, and(dragonfly) both are order,suborders and bothof Odonata. are suborders Petalura of Odonata.IngentissimaPetalura is a large Ingentissima dragonfly,is a largebut is a singledragonfly, sample butvery is far a single from samplethe other very dragonflies far from thein scale, other so dragonflies we have excluded in scale, soit and we havethe Zygoptera excluded from it regressionand the fittingZygoptera in thefrom following. regression fitting in the following.

25 25 25

PI 20 20 PI

15 15

10 10 2 2

y1 = -0.0003x2 + 0.2157x + 0.692 y1 = -0.0007x2 + 0.2664x + 1.7429

FW Max FW Max Chord (mm)

HW Max Max HW Chord (mm) FW Max FW Max Chord (mm) R² = 0.858 Max HW Chord (mm) R² = 0.63 5 5 y2 = 0.1965x + 0.9362 y2 = 0.2109x + 2.8472 R² = 0.8966 R² = 0.6293 Max Chord Poly. (Max Chord) Linear (Max Chord) Max Chord Poly. (Max Chord) Linear (Max Chord) 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Half Span- b/2 (mm) Half Span b/2 (mm) (a) (b)

FigureFigure 10. 10.MaximumMaximum chord chord versus versus wing wing semi semi-span-span of the of theforewings forewings (a) of (a) dragonflies, of dragonﬂies, and and maximum maximum chord versuschord wing versus semi wing-span semi-span of the hindwings of the hindwings (b) of dragonflies. (b) of dragonﬂies.

FigureFigure 11 11illustrates illustrates wingspan wingspan versus versus the themean mean chord chord of FW of FW and and HW, HW, respectively. respectively. Similarly, Similarly, both polynomialboth polynomial (y1) and(y linear1) and (y linear2) regressions (y2) regressions predict predictthe relationship the relationship between between the mean the chord mean chordand the and half- spanthe fo half-spanr both FW for and both HW. FW and HW.

20 20

y1 = -0.0024x2 + 0.3159x - 2.2886 y1 = -0.0013x2 + 0.2562x + 0.1312 y1 = -0.0024x + 0.3159x - 2.2886 y1 = -0.0013x + 0.2562x + 0.1312 PI R² = 0.761 R² = 0.5615 15 15 y2 = 0.1441x + 2.3623 y2 = 0.1159x + 1.7237 PI PI R² = 0.5565 R² = 0.7207

10 10

FW Mean FW Mean Chord (mm) FW Mean FW Mean Chord (mm) 5 HW Mean Chord (mm) 5 HW Mean Chord (mm) 5

Mean Chord Poly. (Mean Chord) Linear (Mean Chord) Mean Chord Poly. (Mean Chord) Linear (Mean Chord) Mean Chord Poly. (Mean Chord) Linear (Mean Chord) 0 0 0 20 40 60 80 100 0 0 20 40 60 80 100 0 20 40 60 80 100 Half Span b/2 (mm) Half Span b/2 (mm) (a) (b)

FigureFigure 11. 11.MeanMean chord chord versus versus wingspan wingspan of of the the forewings forewings ( (aa)) of of dragonﬂies, dragonflies, and and mean mean chord chord versus versus wingspanwingspan of the of thehindwings hindwings (b) (ofb) dragonflies. of dragonﬂies.

It has previously been proposed that the nodus plays an essential role in wing structural ﬂexibility, which has led to a nodus structured wing being used in an MAV [19]. The deﬁnition of the nodus chord (Cnodus) for FW and HW is demonstrated in Figure 12. The position and size of the pterostigma are believed to be important in dynamically regulating wing pitch angle by harnessing inertial forces [20]. Figure 13a,b graphs b/2 versus nodus chord location and pterostigma location (Lpterostigma) of FW and HW, respectively, with polynomial and linear trends for the distribution. It is apparent that the FW nodus location to mid-span is almost similar Appl. Sci. 2020, 10, 5389 11 of 17

Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 20 compared to the HW. However, 90% of both FW and HW nodus are concentrated between 20% and 60%It has of wing previously semi-span. been Strongproposed correlation that the is nodus found plays between an essential wingspan role and in pterostigma wing structural size forflexibility, both whichFW has and led HW to in a Figurenodus structured13c. The red wing and being green used dots in are an related MAV to[19].Zygoptera The definitionfamily forof the FW nodus and HW, chord respectively. (Cnodus) for FW and HW is demonstrated in Figure 12.

25 25

PI 20 20 y1 = 0.0013x2 + 0.1023x + 4.237 PI R² = 0.7449 y1 = 0.0022x2 + 0.0072x + 4.4219 15 R² = 0.8724 15 y2 = 0.2045x + 2.2546 y2 = 0.1835x + 1.0179 R² = 0.743 R² = 0.8631

10 10

HW NodusHW Chord (mm) FW FW Nodus Chord (mm) 5 5 Nodus Chord Nodus Chord Poly. (Nodus Chord) Poly. (Nodus Chord) Linear (Nodus Chord) Linear (Nodus Chord) 0 0 0 20 4060 80 100 0 2040 6080 100 Half Span b/2 (mm) Half Span b/2 (mm) (a) (b)

FigureFigure 12. 12.NodusNodus chord chord versus versus wing wingsemi- semi-spanspan of forewings of forewings (a), and (a ),nodus and noduschord versus chord versuswing semi wing-span Appl. Sci.of hindwings 20semi-span20, 10, x FOR ( ofb). hindwings PEER REVIEW (b). 13 of 20

The position and size of the pterostigma are believed to be important in dynamically regulating wing 60 60 pitch angle by harnessing inertial forces [20].PI Figure 13a,b graphs 푏/2 versusy2 = 0.7889xnodus - 1.2082 chordPI location and y1 = -0.0047x2 + 1.0849x - 2.7311 R² = 0.9035 pterostigma50 location (Lpterostigma)R² of= 0.9465 FW and HW, respectively,50 with polynomialy1 = -0.0058x 2and+ 1.2587x linear - 10.081 trends for the distribution. It is apparent that the FW nodus location to mid-span is almost similarR² = 0.9078 compared to the PI 40 40 2 y2 = 0.6927x + 4.9515 y1 = -0.0042x + 0.7659x - 7.1971 HW. However, 90% of both FW and HW nodus are concentrated between 20% and 60% of wingPI semi-span. R² = 0.9293 R² = 0.9068 Strong correlationy2 = 0.447x +is 2.4104 found between wingspan and pterostigmay2 = 0.4289x size - 0.6642 for both FW and HW in Figure 13c. 30 30 R² = 0.9009 The red and greenR² = 0.8269 dots are related to Zygoptera family for FW and HW, respectively.

2 20 y1 = -0.0029x + 0.6823x - 2.1325 20 Cnodus,L R² = 0.8296 L Pterostigma Poly. (Cnodus,L) 10 10 Poly. (L Pterostigma)

Cnodus,L L Pterostigma HW Cnodus,L Cnodus,L HW Pterostigma & L (mm) FW Cnodus,L FW Cnodus,L & Pterostigma L (mm) Poly. (Cnodus,L) Poly. (L Pterostigma) Linear (L Pterostigma) Linear (L Pterostigma) Linear (Cnodus,L) Linear (Cnodus,L) 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Half Span b/2 (mm) Half Span b/2 (mm) (a) (b) 18 HW PI 16

14 FW PI FW Pterostigma Size y1 = 0.0035x2 - 0.1505x + 3.5408 HW Pterostigma Size 12 Poly. (FW Pterostigma Size) R² = 0.7023 Poly. (HW Pterostigma Size) y2 = 0.1044x - 0.8748 10 Linear (HW Pterostigma Size) R² = 0.3158 Linear (FW Pterostigma Size) 8 y1 = -0.0021x2 + 0.2632x - 3.4173 6 R² = 0.2586

y2 = 0.0833x + 0.1896 Pterostigma Pterostigma Size (mm) 4 R² = 0.2378

0 0 20 40 60 80 100 Half Span b/2 (mm) (c)

FigureFigure 13. 13.(a) (Nodusa) Nodus chord chord and and pterostigma pterostigma location location versus wingwing semi-spansemi-span of of the the forewing, forewing, (b )( nodusb) nodus chordchord and and pterostigma pterostigma location location versus versus wing wing semi semi-span-span of thethe hindwing,hindwing, and and (c )(c pterostigma) pterostigma size size versus versus wingwing semi semi-span-span of the of theforewings forewings and and hindwings. hindwings.

To better understand the correlation between the nodus and pterostigma, the nodus chord, nodus location, and pterostigma size and its location were normalized to wing semi-span. In the following, the non-dimensional parameters of nodus chord vs. pterostigma location (Figure 14a,b), nodus chord location vs. pterostigma location (Figure 14c,d), and pterostigma location vs. size (Figure 14e,f) for FW and HW are presented (Figure 14). The graph shows that nodus and pterostigma of FW and HW are still well-correlated for both families. Correlation is found for chord nodus vs. pterostigma for Epiprocta, being 40% to 60% of nodus chord, while for Zygoptera, it varies (Figure 14a,b). Appl. Sci. 2020, 10, 5389 12 of 17

Appl.nodus Sci. 2020 vs., 10 pterostigma, x FOR PEER REVIEW for Epiprocta , being 40% to 60% of nodus chord, while for Zygoptera14, it of varies 20 (Figure 14a,b).

0.8 0.8 y1 = -9.8188x2 + 5.3273x - 0.3707 0.7 0.7 R² = 0.0585 0.6 0.6

y2 = -0.0347x + 0.3543

0.5 0.5 R² = 0.0005 0.4 0.4

0.3 y1 = 11.992x2 - 5.7519x + 0.9883 0.3 D D FW/(b 0.2 R² = 0.0872 D HW/(b 0.2 PI PI 0.1 y2 = -0.8241x + 0.4882 0.1 R² = 0.1089 0 0 00.050.10.150.20.250.3 0 0.10.20.30.4 C nodus FW/(b 2) C nodus HW/(b 2) (a) (b) 0.8 0.8 y1 = -2.7137x2 + 2.3543x - 0.1629 0.7 0.7 R² = 0.0319 0.6 0.6

y2 = 0.1881x + 0.2676

2) 2)

0.5 0.5 R² = 0.0177

0.4 0.4 0.3

D D FW/(b 0.3

y1 = 2.9461x2 - 3.5759x + 1.3685 D D HW/(b 0.2 R² = 0.7807 PI 0.2 PI 0.1 y2 = -0.4933x + 0.5666 0.1 R² = 0.1818 0 0 00.10.20.30.40.50.60.7 00.10.20.30.40.5 0.6 C nodus, L FW/(b 2) C nodus, L HW/(b 2) (c) (d) 0.2 0.2 2 y1 = 1.0495x2 - 1.0966x + 0.3351

0.18 PI y1 = 1.3913x - 1.2455x + 0.3421 0.18 PI 2) 2) R² = 0.3556

R² = 0.3157 0.16 0.16 0.14 y2 = -0.2964x + 0.1834 0.14 y2 = -0.3355x + 0.1988 0.12 R² = 0.2381 0.12 R² = 0.3029 0.1 0.1 0.08 0.08 0.06 0.06

0.04 0.04 S S Pterostigma FW/(b 0.02 S Pterostigma HW/(b 0.02 0 0 0 0.20.40.60.8 0 0.20.40.60.8 D FW/(b 2) D HW/(b 2) (e) (f)

FigureFigure 14. Nodus 14. Nodus chord chord and pterostigma and pterostigma location location versus versus wing semi wing-span semi-span of the forewings of the forewings (a) and hindwings (a) and (b), hindwingsnodus chord (b), location nodus chord and pterostigma location and location pterostigma versus location wing versussemi-span wing of semi-span the forewings of the (c forewings) hindwings (d),( andc) hindwings pterostigma (d), size and versus pterostigma wing semi size versus-span of wing the semi-spanforewings of(e) the and forewings hindwings (e) (andf). hindwings (f).

3.3.3.3. Design Design Approach Approach TableTable 1 presents1 presents the the essential essential parameters parameters extracted fromfrom regression regression for for all all studied studied Odonata Odonata wings, wings, includingincluding damselflies damselﬂies and and dragonflies. dragonﬂies. Normalizing Normalizing against against wingspan wingspan makes makes it possible it possible to export to exportthe other parametersthe other of parameters the wing and of the compare wing and wing compare shape chara wingcteristics, shape characteristics, despite scale despitevariations. scale For variations. instance, it hasFor been instance, shown itthat has the been pterostigma shown thatis thelocated pterostigma at 81% of is the located FW and at 81% 76% of of the HW FW. and 76% of HW.

Table 1. Essential wing geometrical parameters exported from the graphs.

Wing Geometry Parameter R2 Cmax FW = 0.219 × (b/2) 0.86 Cmax HW = 0.276 × (b/2) 0.70 Cmax,L FW = 0.58 × (b/2) 0.62 Cmax,L HW = 0.37 × (b/2) 0.27 Cmean FW = 0.16 × (b/2) 0.73 Cmean HW = 0.20 × (b/2) 0.63 b FW/HW = 1 - Cnodus,L FW = 0.489 × (b/2) 0.78 Appl. Sci. 2020, 10, 5389 13 of 17

Table 1. Essential wing geometrical parameters exported from the graphs.

Wing Geometry Parameter R2

Cmax FW = 0.219 (b/2) 0.86 × Cmax HW = 0.276 (b/2) 0.70 × C FW = 0.58 (b/2) 0.62 max,L × C HW = 0.37 (b/2) 0.27 max,L × Cmean FW = 0.16 (b/2) 0.73 × Cmean HW = 0.20 (b/2) 0.63 × b FW/HW = 1 - C FW = 0.489 (b/2) 0.78 nodus,L × C HW = 0.404 (b/2) 0.91 nodus,L × C FW = 0.811 (b/2) 0.95 pterostigma,L × C HW = 0.756 (b/2) 0.91 pterostigma,L ×

These parameters were derived from our sample of specimens of many species and are independent of wing size. There is consistency and low deviation from the trend for some geometrical parameters, like the maximum chord for the whole species, which means that these parameters are independent of wing size and species. On the other hand, having a large deviation shows that the actual parameters for a species (Figures8 and9) are driven by other factors. Table2 lists the nondependent and dependent variable parameters. For this case, it is assumed that the compiled results with R-squared correlation value of less than 0.7 are dependent parameters.

Table 2. List of family-dependent and nondependent geometric parameters of the dragonﬂy wing.

Nondependent Parameters (R2 > 0.7) Dependent Parameters (R2 < 0.7)

Cmax Cmax,L Cmean FW Pterostigma size Cnodus Cmean HW Cnodus,L - Lpterostigma -

The non-dimensional maximum, average, and minimum ratio of the dimension and location of the maximum chord, and also the nodus chord, for FW and HW are described in Table3.

Table 3. Maximum, minimum, and average ratio for FW and HW.

Forewing Hindwing Min. Ave. Max. Min. Ave. Max. 2 Cmax/b 0.17 0.22 0.32 0.17 0.27 0.40 × 2 C /b 0.33 0.59 0.79 0.10 0.37 0.74 × max L 2 Cmean/b 0.10 0.16 0.23 0.10 0.20 0.30 × 2 C /b 0.06 0.20 0.25 0.06 0.247 0.34 × nodus AR 8.74 12.68 19.30 6.77 10.37 19.20

4. Discussion Comparing average results, one can say that the dimension of the maximum chord is around 25% of the wing semi-span in the species measured. However, its location is closer to the body for the HW, which is 37% of the wing semi-span. Furthermore, the location of the maximum chord can be significantly different for different species. The minimum span location belongs to the HW of the Libellulidae family by a fraction of 0.1 of semi-span length. Among our dataset, the maximum chord is placed at approximately 79% of the FW semi-span. Figure 15 presents an illustrative example of the observed design criteria, regarding the minimum and maximum margins of the maximum chord and its location relative to the wing dimension (hatch-line areas). The hatch areas are the representative Appl. Sci. 2020, 10, 5389 14 of 17

of the estimation range for both max chord and its location. In other words, the length of the hatch areas is representative of the range of the location of the max chord, which can vary from 0.33 to 0.8 of

Appl.the Sci. semi-span2020, 10, x FOR length. PEER REVIEW On the other hand, the width of the hatch areas is representative of16 the of 20 max chord length, which can vary between 0.17 and 0.32 of the semi-span length.

FigureFigure 15. Non 15. Non-dimensional-dimensional estimation estimation range range of the of theFW FWmax max chord chord max, max, and and its location its location through through the thewing semiwing-span. semi-span.

ThisThis graph graph can be can extended be extended for the for other the parameters, other parameters, such as pterostigma such as pterostigma and nodus, and to provide nodus, a generalto provide mapping a general algorithm mapping for algorithm the preliminary for the preliminary design of a design flapping of a wingflapping drone wing aircraft. drone aircraft. Another parameterAnother shown parameter in Table shown 3 is inthe Table aspect3 is ratio the aspect(AR), which ratio (AR), is generally which isdefined generally as the defined ratio asof full the ratiospan to meanof chord full span [42] to. According mean chord to these [41]. Accordingdata, the average to these AR data, is 12.68 the averageand 10.37 AR for is FW 12.68 and and HW, 10.37 respectively. for FW Pterostigmaand HW, respectively.is the other significantPterostigma factor is the for other designing significant the factor bio-inspired for designing wing. the Possessing bio-inspired a favorable wing. aerodynamicPossessing function, a favorable the aerodynamic pterostigma function, is located the in pterostigma close proximity is located to in the close tip proximity of the wing to the as tipa dark, of thickenedthe wing membrane as a dark, structure thickened [14]. membrane The pterostigma structure changes [14]. The the pterostigma center of mass changes of the the wing center at of the mass leading of edge,the which wing leads at the to leading more stability edge, which in flapping leads to fli moreght [43] stability. The pterostigma in flapping flightis located [42]. near The the pterostigma wingtip; in Aeshnais located Juncea near(one the the wingtip; large species in Aeshna of hawker Juncea (one dragonflies the large from species the Aeshnidae of hawker family) dragonflies they from have the mass relativeAeshnidae to thefamily) FW and they HW have of around mass relative 9% and to the16% FW respectively and HW of [44] around. By comparing 9% and 16% the respectively results, it can [43]. be understoodBy comparing that the the location results, of itthe can pterostigma be understood of the that FW theto HW location ratio ofis 1.07. the pterostigma The size of the of thepterostigma FW to appearsHW ratio to be is weakly 1.07. The correlated size of the with pterostigma size and appears chord, which to be weakly might be correlated caused with by evolution size and chord,of flight performancewhich might and be conspecific caused by communication evolution of flight functions performance of the and pterostigma conspecific both communication driving this feature. functions of thePrevious pterostigma research both has driving shown this that feature. the wings of damselfly and dragonfly are different [45]. This is also shown byPrevious our data, research particularly has shown relating that to the the wings nodus of and damselfly pterostigma. and dragonfly In terms areof overall different dimensions [44]. This isand ratiosalso of shownwing geometry, by our data, the Zygoptera particularly and relating Epiprocta to are the statistically nodus and similar. pterostigma. In terms of overall dimensionsIn the methods and ratiossection, of winga limitation geometry, of the the underlZygopterayingand collectionEpiprocta of areanimals, statistically and thus similar. the study, was mentioned,In the which methods was that section, we could a limitation not determine of the underlyingthe sex of the collection specimens. of animals,It seems reasonable and thus the to study,surmise thatwas the mentioned,variations by which sex are was less that than we variations could not determinebetween orders, the sex and of thethis specimens. study aimed It seemsto find reasonable the range of parametersto surmise and that their the trends variations against by scale sex are for less the than order variations Odonata. between orders, and this study aimed to findThe the results range regarding of parameters the placement and their of trends the nodus against extend scale forthe thedata order available Odonata. in the literature [13], and reaffirm Thethat resultsthe nodus regarding is a significant the placement structure. of the nodus extend the data available in the literature [13], andThroughout reaffirm that the thedataset, nodus there is a is significant a trend of structure. non-dimensional HW parameters having lower correlation against theThroughout trend and thelarger dataset, variation there across is a trendthe dataset of non-dimensional than the FW, with HW species parameters not being having predictive lower of the correlationvariations. againstIt may theindicate trend andthat largermore variationrecent adaptations, across the datasetperhaps than cau thesed FW, by withvariations species in not habitat being or lifestyle, favor HW changes over FW changes. Appl. Sci. 2020, 10, 5389 15 of 17

predictive of the variations. It may indicate that more recent adaptations, perhaps caused by variations Appl.in Sci. habitat 2020, 10 or, x lifestyle, FOR PEER favor REVIEW HW changes over FW changes. 17 of 20

5. Conclusions 5. Conclusions In this study, a geometrical and basic planform study on the dragonfly wings from 75 samples ofIn 15 this diff study,erent Odonataa geometrical species and families basic planform was performed. study on the The dragonfly diversity wings of species from enabled75 samples us of to 15 differentdocument Odonata the geometry species families of the planformwas performed. of the wingsThe diversity from the of span species length enabled of 48 us mm to todocument 170 mm. the geometryThe measured of the planform parameters of the were wings taken from from the span the projectedlength of 48 area mm of to the 170 3D mm. reconstructed The measured models parameters of werethe taken wings. from The the measurements projected area wereof the taken 3D reconstructed over the eight models essential of the planform wings. The wing measurements parameters forwere takenboth over FW the and eight HW. essential These included planform wingspan wing parameters length, mean for both and FW maximum and HW. chord These length, included maximum wingspan length,chord mean location, and maximum nodus location, chord pterostigma length, maximum size, and chord location. location, An nodus extensive location, statistical pterostigma analysis size, of the and location.data was An performedextensive statistical to investigate analysis the of independence the data was performed of the measured to investigate parameters the independence from the families of the measuredof the Odonata. parameters In general,from the acrossfamilies the of species the Odonata. studied, In HWsgeneral, appear across to the have species the most studied, variation HWs in appear all to dimensions have the most measured variation compared in all dimensions to the FW, with measured family compared not being predictive to the FW, of with HW shape. family Further not being predictivework will of H tryW to shape. identify Further functional work will reasons try to for identify scale-related functional variations. reasons for In addition,scale-related the variations. shapes of In addition,Odonata the wings shapes are of notOdonata similar, wings and are this not is an similar, important and this parameter is an important requiring parameter further investigation requiring further in investigationthe future. in the future. Author Contributions: Conceptualization: N.C., R.M., and J.S.C.; methodology: N.C. and J.S.C.; software: N.C., R.M., Author Contributions: Conceptualization: N.C., R.M., and J.S.C.; methodology: N.C. and J.S.C.; software: N.C., A.C.,R.M., and A.C., J.S.C.; and validation: J.S.C.; validation: N.C., A.C., N.C., and A.C., J.S.C.; and formal J.S.C.; analysis: formal analysis: N.C. and N.C. A.C.; and investigation: A.C.; investigation: N.C., A.C., N.C., and A.C., J.S.C.; resources:and J.S.C.; R.M resources:. and J.S.C.; R.M. data and curation: J.S.C.;data N.C., curation: A.C., and N.C., J.S.C.; A.C., writing and J.S.C.;—original writing—original draft preparation: draft N.C.; preparation: writing— reviewN.C.; and writing—review editing: N.C., andR.M., editing: A.C., and N.C., J.S.C.; R.M., visualization: A.C., and J.S.C.; N.C. visualization: and J.S.C.; supervision: N.C. and J.S.C.; R.M. supervision: and J.S.C.; R.M.project administration:and J.S.C.; project N.C. administration:and J.S.C.; funding N.C. acquisition: and J.S.C.; fundingJ.S.C. All acquisition: authors have J.S.C. read All and authors agreed have to the read published and agreed version to of thethe manuscript. published version of the manuscript. Funding: This research received no external funding. Funding: This research received no external funding. Acknowledgments: We would like to thank the South Australian Museum, Adelaide, for granting access to their Acknowledgments:collection of dragonflies We would used inlike this to study. thank The the first South author Australian is the recipient Museum, of the Adelaide, William for T. Southcott granting Scholarshipaccess to their collectionfrom the of Universitydragonflies of used South in Australia. this study. The first author is the recipient of the William T. Southcott Scholarship fromConflicts the University of Interest: of SouthThe authorsAustralia. declare no conflicts of interest. Conflicts of Interest: The authors declare no conflicts of interest. Appendix A Appendix A

Figure A- Labeling of typical specimens at South Australian Museum Figure A1. Labeling of typical specimens at South Australian Museum. References Appl. Sci. 2020, 10, 5389 16 of 17

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