Three-dimensional geometry of the wing of Megatypus schucherti (Odonatoptera: Meeganeuridae)

by Roy J. Beckemeyer (Johnston Geology Museum, Emporia State University, Emporia, Kansas, USA) 

Last updated 4 April 2005

A paper based on the presentation made at the FossilsX3 Congress in Pretoria, South Africa, February, 2005

  Abstract / INTRODUCTION / MATERIALS & METHODS: Materials 

 Methodology: Measurement of Two-Dimensional Geometry / Measurement of Wing Relief 

 RESULTS: Wing Planform / Wing Relief / Taphonomic Effects 

DISCUSSIONS & CONCLUSIONS / ACKNOWLEDGEMENTS / REFERENCES

Abstract:  

Wings of palaeopterous insects are often characterized by fluting or corrugation wherein the longitudinal veins are alternately convex or concave, thus providing structural stiffening to the wing membrane.  Of the extant insects, the Odonata are perhaps the best examples of this type of wing construction.  Corrugated surfaces are also often preserved in the fossil wings of Palaeozoic Odonatoptera.  Particularly well-preserved hind wings of a large (195 mm wing length) Permian meganeurid (Megatypus schucherti Tillyard, from the Elmo, Kansas North American fossil beds) were measured and the three-dimensional relief quantitatively characterized.  Although some flattening of the wing surface obviously occurred during the preservation of the fossils, a comparison with the relief of the wing of an extant dragonfly shows that the corrugation relief, when non-dimensionalized by the local wing chord, is roughly comparable.

Key Words:  dragonfly, Meganeuridae, Odonatoptera, three-dimensional relief, wing corrugation, wing geometry

INTRODUCTION

Insect wings are basically two-dimensional structures.  In the palaeopterous insects such as the Odonatoptera, the major longitudinal veins are alternately located in the dorsal or ventral surfaces of the wing, thus resulting in a three-dimensional corrugation or fluting of the wing surface that is particularly prominent in the anterio-basal portion of the wing.  Although the veins provide for blood flow and contain tracheae and  nerves, they also provide much of the functional structure of the wing.  The location of the longitudinal veins on the wing, their cross sectional area, the spacing, shape and size of cross veins, and the nature of the cross to longitudinal vein joints can also affect the wing stiffness, but in this paper we will focus on the corrugation geometry alone.  In the case of the Palaeoptera, this three-dimensional relief provides significant flexural (Wootton, 1981, Newman, 1982, Newman & Wootton, 1986) and torsional (Sunada et al, 1998) rigidity.

Newman (1982) documented the cross-sectional geometry of a number of extant Odonata taxa, but to date surveys of fossil insect functional morphology have dealt either with two-dimensional geometry factors or with qualitative evaluations of wing structural characteristics (e.g., Edmunds & Traver, 1954, Wootton & Kukalová-Peck, 2000).  Although some insect compression fossils may be little more than carbonized images of wings, there are also fossils with significant three-dimensionality preserved in the wings.  In the case of  meganeurids this is likely due in part to their large size and robust structure.  Samuel Hubbard Scudder was one of the first scientists to report on the three-dimensionality of a fossil “dragonfly” wing.  In his description of Paralogus aeschnoides from the Rhode Island Coal Fields (1893), he included a twice-life size drawing (by J. Henry Blake) of the fossil, shaded to indicate the relief of the wing, together with a cross-section giving an indication of the depth of the wing corrugations (Fig. 1).  I have not had the opportunity to measure this specimen, but the cross-section appears to be to scale.

Figure 1.  Drawing of Paralogus aeschnoides from the Rhode Island Coal Fields as it appeared in S. H. Scudder’s original type description, published in 1893 in the Bulletin of the United States Geological Survey (No. 101: Plate I).  The original drawing was by J. Henry Blake.  The cross-section depicted the corrugation of the wing surface caused by the alternating dorsal and ventral location of the major longitudinal veins.

I have begun to measure the planform geometry and vertical relief of the veins of extant and fossil dragonfly wings in the hope that knowledge of the structural characteristics and of the flight-related deformations of extant insects (Kesel et al, 1998, Wootton et al, 2003) might be used to infer possible flight characteristics of extinct insects from their structural geometry.  I have begun with a species of Meganisoptera: Meganeuridae for which there are a number of especially well-preserved fossil specimens: Megatypus schucherti  Tillyard 1925, a large meganeurid with a wing length of 195 mm.  There are at least two fine specimens, each comprising both part and counterpart, of this species.  I have been able to work with 3 of these 4 fossils to date.  I have also measured the three-dimensional wing geometry of an extant North American dragonfly, Anisoptera: Aeshnidae: Anax junius, and I here compare the non-dimensional relief of the hind wings of these two insects.

MATERIALS AND METHODS

Materials

The specimens of Megatypus schucherti studied here include the Holotype (part and counterpart), YPM1021a,b from the Yale Peabody Museum, and the Wenger-Holmes specimen from Kansas State University (I have not been able to measure the counterpart of the Wenger-Holmes specimen, which is in the Harvard Museum of Comparative Zoology).  The Wenger-Holmes specimen is a nearly complete hind wing; the holotype is roughly 2/3 of a complete hind wing, and the counterpart of the holotype comprises the basal quarter of the hind wing.  The extant dragonfly wing is a hind wing from a female Anax junius specimen collected by the author in 1998 in Sedgwick County, Kansas.  The specimens are shown in Figure 2.

 Figure 2.  Specimens used in this study.  a)  Wenger-Holmes specimen of Megatypus schucherti Tillyard 1925.  Hind wing.  Department of Entomology, Kansas State University.  b)  Holotype specimen YPM1021a.   c) Holotype (counterpart) specimen YPM1021b, of M. schucherti.  Hind wing.  Yale Peabody Museum.  d)  Hind wing of a female specimen of the extant Odonata: Aeshnidae: Anax junius (Drury) 1770, from the author’s collection, collected in Sedgwick County, Kansas, 1998.

Methodology

Measurement of Two-Dimensional Geometry

Wings (both extant and fossil) were scanned on a flat bed scanner at resolutions of 600 to 1200 pixels per inch.  This provides digital image files (TIF files were used) that can be measured accurately and can also be used for detailed specimen-to-specimen comparisons at various scales.  The scanned images are input to image processing software (Adobe Photoshop, NIH Image, and Sigma Scan Pro were used for this study) to digitize vein locations and other features (Figure 3).  The software can also be used to compute area and moments of area of the wings.  Vein planform geometry was stored in Microsoft Excel spreadsheets.  Figure 4 shows the wing vein two-dimensional geometry of M. schucherti as plotted using the spreadsheet graphing capabilities. 

Figure 3.  Computer screen showing software being used to digitize the wing vein two-dimensional geometry of Megatypus schucherti.

Figure 4.  Two-dimensional wing vein geometry of Megatypus schucherti as plotted from Microsoft Excel spreadsheet.

Measurement of Wing Relief

Béthoux et al (2004) reported on a laser-scanning method for automatically determining the three-dimensional geometry of fossil insect wings.  There are also three-dimensional stacked-image-montage approaches to generating fully in-focus images in microphotography that can be adapted to provide image geometric data.  However, economic considerations led me to use a more time-intensive but lower cost approach.  I used a measuring fixture and a very accurate digital depth gage (a Fowler Depthmatic Model EDG065i unit that was certified accurate to 0.001 mm) to measure the vein relief of the fossil wings.  The scanned image of the wing was used to orient the specimen and an RS-232 interface allowed data points to be transmitted directly into the Microsoft Excel spreadsheet that held the two-dimensional vein coordinates (Fig. 5).  This yielded a spreadsheet with three-dimensional coordinates of points along the major wing veins, and allowed me to generate cross-sections at various spanwise stations along the wing (Fig. 6).

Figure 5.  Depth gage and fixture used to measure three-dimensional relief of Megatypus schucherti wing specimens.  The Fowler Depthmatic was accurate to 0.001 mm.  Readings were sent directly to the spreadsheet through an RS-232 interface.

Figure 6.  Example of relief measurements of the Megatypus schucherti hind wing at various spanwise locations.

For the extant wing, the method used by Newman (1982) was adapted.  The wing was cast in transparent resin.  The casting was sectioned (Fig. 7) and the sections polished using carborundum.  They were then scanned at 1200 pixels per inch to yield accurate cross sectional images (Fig. 8) from which measurements of vein geometry could be made.  Fig. 9 illustrates cross sections for the extant dragonfly wing.  Note that this method can also provide information on wing vein cross-sectional areas, which will eventually be required for modeling wing stiffness.

Figure 7.  Wings of Anax junius cast in resin blocks shown before (right) and after (left) sectioning.  The sections provide data on relief and on cross-sectional area of major longitudinal veins.

Figure 8. An example of the cross-section of an Anax junius hind wing.

Figure 9.  Example of relief measurements of the Anax junius hind wing at various spanwise locations. 

RESULTS

Wing Planform

Wing planform parameters for Megatypus schucherti and Anax junius hind wings are listed in Table 1.  These are measures of the two-dimensional geometry of the wings, and include R, the wing length (cm), c_bar, the mean wing chord or width (cm), S/2, the area of a single hind wing (cm²), AR, the aspect ratio, a standard non-dimensional measure of the slenderness of wings, and a set of non-dimensional radii that were originally developed by Charles Ellington (1984) to characterize the spanwise distribution of wing area.  The radii are computed by determining the moments of areas of the wings about their bases. The radii can be interpreted in terms of flight-related functional morphology of the wing.  For example, r₁ is the spanwise location of the centroid of area of the wing as a fraction of the wing length; r₂ is the non-dimensional radius of second moment of area about wing base (%of R), which is related to the mean quasi-steady lift of the flapping wing; r₃ is the non-dimensional radius of third moment of area about the wing base (% of R), which is related to the profile power of the flapping wing.  Ellington also showed that r₂ and  r₃ are allometrically related to r₁.  I have plotted r₂ and r₃ vs r₁ in Figure 10 for the hind wings of a variety of extant Odonata and for Megaypus schucherti. 

Table 1.  Comparison of hind wing morphological two-dimensional geometry parameters.

Figure 10.  Allometric relationships for Ellington’s (1984) radii of area for various extant Odonata and for Megatypus schucherti hind wings.  Extant Odonata values are from Wakeling (1997) and from the author’s measurements.  Second and third radii of area plotted versus first radius of area.

Two additional radii are determined by computing moments of the wing’s virtual mass about the wing base.  The virtual mass is the mass of air that is accelerated along with the wing as it flaps.  It can be shown to be equal to the mass of a volume of air comprised of a cylinder of revolution having as its diameter the local chord of the wing.  The associated radii of virtual mass are r_v1, the center of virtual mass of wing (% of R), and r_v2, the non-dimensional radius of the second moment of virtual mass, which is related to the inertial torque of the air moved by the flapping wing.  Again, the second radius is allometrically related to the first.  Figure 11 depicts the relationship between r_v1 and r_v2 for the hind wings of extant Odonata, including Anax junius, and for Megatypus schucherti. 

Figure 11.  Allometric relationship for Ellington’s (1984) radii of virtual mass for various extant Odonata and for Megatypus schucherti hind wings.  Extant Odonata values are from Wakeling (1997) and from the author’s measurements.  Second radius of virtual mass plotted versus first radius of virtual mass.

Data in Figures 10 and 11 for extant insects are based on the my measurements of Nearctic odonates and on Wakeling’s (1997) measurements for Palearctic dragonflies.  Megatypus falls within the range of scatter for radii of extant Odonata, even though the hind wing of Megatypus is quite slender (AR of 12.23 vs 8.22 for Anax) when compared with that of extant dragonflies. 

Wing Relief

Wing relief data for M. schucherti in this section are based on measurements of the relief of the ventral side of the Wenger-Holmes specimen.  Figure 12 shows the vertical relief of M. schucherti at 25% of the wing length.  Vertical distances are given with respect to the costal vein.  In order to compare the cross section information for the fossil and extant wings, the relief figures were non-dimensionalized by the local wing chord, and a second order best fit curve (y = ax + bx²) was used to account for slope and curvature of the wings.  The vein relief data were then referenced to this best fit line.  Each of these lines is shown in Fig. 12.

Figure 12.  Megatypus schucherti hind wing relief data for the wing cross section at 25% of the wing length distal to the wing base.  Data have been non-dimensionalized by the local wing chord.  The original data (diamond symbols, solid line) include the effect of the uneven substrate geometry.  A second order least squares fit (y = ax + bx2, square symbols and dashed line) is passed through these data points.  By subtracting the fit line from the original data,  the resulting cross section (triangle symbols and solid line) can be compared with those at various wing stations, and the cross sections of extant and fossil wings can be compared.

By referencing the wing relief to the best fit line, slope and second order-camber effects are removed from the extant wing data and substrate slope and second order curvature effects are removed from the fossil data.  This places the relief data for the extant and fossil wings on a comparable baseline.

Figure 13.  Comparison of Megatypus schucherti (square symbols) and Anax junius (diamond symbols) hind wing non-dimensional relief data (adjusted for slope and second order curvature) for the wing cross section at 10% of the wing length distal to the wing base.  Data normalized by local wing chord.

Figures 13 through 15 contain comparisons of the non-dimensional relief of the wings of M. schucherti and A. junius at wing cross sections at spanwise locations of 10, 50 and 70 percent.  In every case, M. schucherti appears flattened in comparison with A. junius.  Figure 16 compares maximum relief values for M. schucherti and A. junius at values of spanwise location from 10 to 90%.  Maximum and mean non-dimensional relief for M. schucherti are 3.7% and 3.1% of the local wing chord, and those of A. junius are 6.5% and 5.8%, respectively.  There is currently no data available on the allometry of wing relief in extant dragonflies, so it is not possible to extrapolate on the basis of variation of relief with span to estimate what the relief of the wing of an M. schucherti sized dragonfly would be.  It is likely that the fossil wing was flattened during preservation, so the measured non-dimensional relief is at best a lower bound for the actual relief. 

Figure 14.  Comparison of Megatypus schucherti (square symbols) and Anax junius (diamond symbols) hind wing non-dimensional relief data (adjusted for slope and second order curvature) for the wing cross section at 50% of the wing length distal to the wing base.  Data normalized by local wing chord.

Figure 15.  Comparison of Megatypus schucherti (square symbols) and Anax junius (diamond symbols) hind wing non-dimensional relief data (adjusted for slope and second order curvature) for the wing cross section at 70% of the wing length distal to the wing base.  Data normalized by local wing chord.

Figure 16.  Comparison of Megatypus schucherti (square symbols) and Anax junius (diamond symbols) hind wing maximum non-dimensional relief data (adjusted for slope and second order curvature) for various wing spanwise stations from 10% to 90% span.  Relief data normalized by local wing chord.

Taphonomic Effects

Figure 17 shows the counterpart of the holotype of M. schucherti (YPM1021b).  The substrate is quite uneven, and it is evident that the wing membrane was sufficiently plastic at some phase in its preservation to allow it to conform to the substrate.  It is also evident that the portions of the wing reinforced by the larger longitudinal veins did not deform as readily as the more membranous areas.  There is an area at about 25% of the wing span on this specimen, between the longitudinal veins MP and CuA, where a small lump on the substrate resulted in deformation of the membrane and a portion of vein CuA.  

Figure 17.  Holotype counterpart specimen of M. schucherti (YPM1021b).  The wing conformed closely to the lumpy and uneven substrate, indicating that the wing membrane had become plastic due to taphonomic effects.  A lump located at about 25% of the wing length distal to the wing base and between longitudinal veins MP and CuA deformed the membrane, but the adjacent veins helped to stiffen the wing.  The black lines drawn on the wing indicate where relief measurments of membrane and vein deformation were made.

The stiffening effect of the veins can be seen in Figure 18, on which the measured relief of the veins and the membrane between them in the area of the lump is plotted.  Vein MP is not deformed at all, while the membrane is deformed by a vertical distance of 0.7 mm by the lump, which is 5 mm in diameter.  Vein CuA is deformed, but only by a vertical distance of 0.25 mm.  This indicates that there was enough elasticity remaining in the longitudinal veins to keep the wing from collapsing completely (there may also be some inherent geometric stiffening due to the longitudinal vein intersections).  It might be possible to study flattening effects in extant dragonfly wings by measuring wing relief before and after extended soaking in water.  In any event, it is apparent that the wing relief measured for the fossil reflects taphonomic flattening of the wing.

Figure 18.  Measurements of relief of M. schucherti holotype counterpart specimen (YPM1021b) wing membrane and longitudinal veins in the vicinity of a lump on the substrate.  Relief in mm plotted versus wing spanwise position from wing base in mm.

DISCUSSIONS AND CONCLUSIONS

Measured relief for the hind wing of the fossil meganeurid M. schucherti amounts to about 3% of local wing width.  Corresponding relief values for the hind wing of an extant odonate, a female Aeshnidae: Anax junius were about 6%.  Inspection of the fossil wing reveals that taphonomic effects resulted in flattening of the wing due to plasticity of the membrane.  The longitudinal veins retained some elasticity and resisted flattening to some degree.  The 3% relief value thus represents a lower bound for the wing relief of live M. schucherti.  Future work aimed at better understanding the wing stiffness characteristics of fossil meganeurids should include:

·        Measurements of relief values need to be made for a large range of extant Odonata to determine allometry of relief with wing size so that relief values can be extrapolated to wings the size of those of meganeurids.

·        Taphonomic effects need to be investigated to identify the mechanics and geometry of flattening in wings of extant Odonata to determine how much elasticity is contributed by longitudinal veins once the membrane has become plastic.

·        Relief data for additional fossil meganeurid taxa should be measured, especially for a variety of wing sizes.

·        Other geometric information on meganeurid wings, especially longitudinal vein widths and cross-sectional areas needto be measured.

ACKNOWLEDGEMENTS

Thanks to Ralph Charlton and Sonny Ramaswamy of the Kansas State University Entomology Department, Manhattan, Kansas, for loaning the KSU Wenger-Holmes specimen of Megatypus schucherti, and to Tim White, Senior Collections Manager, Division of Invertebrate Paleontology at the Yale Peabody Museum, for loaning the holotypes of Elmo Odonatoptera, including those of M. schucherti.  Michael Morales, Director of the Johnston Geology Museum at Emporia State University facilitated specimen loans and provided working space. 

REFERENCES

• Béthoux, O., J. McBride, and C. Maul.  2004.  Surface laser scanning of fossil insect wings.  Palaeontology 47(1):13-19.

• Edmunds, G. F., Jr., and J. R. Traver.  1954.  The flight mechanics and evolution of the wings of Ephemeroptera, with notes on the archetype wing.  Journal of the Washington Academy of Sciences  44(12):390-400.

• Ellington, C.P.  1984.  The aerodynamics of hovering insect flight. II. Morphological parameters.  Philosophical Transactions of the Royal Society of London.  Ser. B.  305:17-40.

• Kesel, A. B., U. Phillipi, and W. Nachtigall.  1998.  Bio-mechanical aspects of the insect wing: an analysis using the finite element method.  Computers in Biology and Medicine 28:423-437.

• Newman, D. J. S.  1982.  The functional wing morphology of some Odonata.  Ph.D. Thesis.  University of Exeter.  vi + 281 pp.

• Newman, D. J. S., and R. J. Wootton.  1986.  An approach to the mechanics of pleating in dragonfly wings.  Journal of Experimental Biology  125:361-372.

• Scudder, S. H.  1893.  Insect fauna of the Rhode Island Coal Field.  Bulletin of the United States Geological Survey No. 101:  vi + 27 pp. + pl. I-II.

• Sunada, S., L. Zeng, and K. Kawachi.  1998. The relationship between dragonfly wing structure and torsional deformation.  Journal of Theoretical Biology A193:39-45.

• Tillyard, R. J.  1925.  Kansas Permian Insects.  Part 5. The orders Protodonata and Odonata.  American Journal of Science (series 5) 10:41-73.

• Wakeling, A.  1997.  Odonatan wing and body morphology.  Odonatologica 26(1):35-52.

• Wootton, R. J.  1981.  Support and deformability in insect wings.  Journal of Zoology, London 193:447-468.

• Wootton, R. J., and J. Kukalová-Peck.  2000. Flight adaptations in Palaeozoic Palaeoptera (Insecta).  Biological Review 75:129-167.

• Wootton, R. J., R. C. Herbert, P. G. Young, and K. E. Evans.  2003.  Approaches to the structural modeling of insect wings.  Philosophical Transactions of the Royal Society of London B358:1577-1587.

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