Dyke, G.J.

Nudds, R.L.

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Flight of Sharovipteryx mirabilis: the world’s first delta-wingedgliderG. J. DYKE,* R. L. NUDDS & J. M. V. RAYNER*School of Biology and Environmental Science, University College Dublin, Belfield Dublin, IrelandInstitute of Integrative and Comparative Biology, University of Leeds, Leeds, UKIntroductionThe small reptile Sharovipteryx mirabilis (Sharov, 1970,1971; Cowen, 1981; Fig. 1) from the late Triassic ofKyrgyzstan (former Soviet Union) is remarkable in that itis the only known flying vertebrate to have a flightsystem dominated by its hindlimbs. The single knownfossil specimen has a triangular (delta) wing membranedefined by the edges of its hindlimbs (Fig. 1). This delta-wing contains embedded fibres, similar to those seen inthe wings of some pterosaurs (Sharov, 1971; Padian &Rayner, 1993; Unwin & Bakhurina, 1994; Frey & Martill,1998; Bennett, 2000).Because S. mirabilis was so bizarre, several hypotheseshave been put forward to explain its mode of flight andthe extent of its wing membrane; no previous recon-structions, however, have been based on examination ofthe fossil or grounded in aerodynamics. In particular,some of the previous reconstructions of S. mirabilis flightstyle invoke a much larger and wider flight surface thanis actually preserved. Direct evidence from the S. mirabilisfossil, combined with calculations based upon standarddelta-wing aerodynamics (Polhamus, 1971), has allowedus to test competing hypotheses regarding wing mem-brane shape in this unique reptile. Simple aerodynamicmodelling allows us to ask not how S. mirabilis was ableto glide, but how identifying realistic glide performancecan be used to set limits on its aerodynamic design. Themost parsimonious reconstruction of S. mirabilis gliding-mode is one where wing shape is controlled by simpleprotraction of the femora at the knees, and by variationin incidence of a small forelimb canard. This mechanismis unique among vertebrates.Materials and methodsOur reconstruction of S. mirabilis hindlimb membrane isbased on measurements and evaluation of the extent ofsoft tissues preserved on the holotype (Fig. 1). We use abody mass estimation (M) of 4.5 g, derived from the body(snout-vent) length of the single specimen (65 mm),consistent with other similarly sized living gliding lizards(Draco, Ptychozoon; see Shine et al., 1998; McGuire &Dudley, 2005 for Draco data). The total body length of theS. mirabilis specimen is some 200 mm (Fig. 1). This massestimate, however, is not critical to our conclusions –different values of M (with scaled wing sizes) produce thesame solution – flight speed of a wing varies in propor-tion to M1/2 (Pennycuick, 1975). To calculate S. mirabilisflight performance we use standard leading-edge vortextheory of a delta wing (Polhamus, 1971), estimating azero-lift-drag coefficient (CDO) of 0.08 from measure-ments of isolated starling tails fixed in a wing tunnel atspeeds 5–10 m s)1 (Maybury et al., 2001).Correspondence: Gareth Dyke, School of Biology and EnvironmentalScience, University College Dublin, Belfield Dublin 4, IrelandTel.: +353-171-62195; fax: +353-171-61152;e-mail: gareth.dyke@ucd.ieª 2 0 0 6 T H E A U T H O R S 1 9 ( 2 0 0 6 ) 1 0 4 0 – 1 0 4 31040 J O U R N A L C O M P I L A T I O N ª 2 0 0 6 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G YKeywords:delta-winged;flight;gliding;hindlimb;reptile;Sharovipteryx mirabilis;wing-morphology.AbstractThe 225 million-year-old reptile Sharovipteryx mirabilis was the world’s firstdelta-winged glider; this remarkable animal had a flight surface composedentirely of a hind-limb membrane. We use standard delta-wing aerodynamicsto reconstruct the flight of S. mirabilis demonstrating that wing shape couldhave been controlled simply by protraction of the femora at the knees, and byvariation in incidence of a small forelimb canard. Our method has allowed usto address the question of how identifying realistic glide performance can beused to set limits on aerodynamic design in this small animal. Our novelinterpretation of the bizarre flight mode of S. mirabilis is the first based directlyon interpretation of the fossil itself and the first grounded in aerodynamics.doi: 10.1111/j.1420-9101.2006.01105.xWe estimated glide polars for S. mirabilis from twomodels; a single rearward delta-wing that extends to thefemur (Fig. 1), and a rearward delta-wing plus a smallforward canard membrane surface attached to the fore-limb (Fig. 1). Loose membrane is associated with thisregion of the fossil (Sharov, 1971) and recent preparationhas confirmed the presence of small forelimbs. For com-parison we also calculated the glide polar of the similarlysized extant glider Draco using the same method.As S. mirabilis flexed its hindlimbs, it would have alteredthe span of its flight surface. Because a triangular wingwith a swept leading edge and a straight trailing edgeoperates as a delta wing, forces can be modelled usingleading-edge vortex theory (Polhamus, 1971), where thewing generates separated vortices above its leading edge.Airflows of this type are well known in aeronautics, andhave been demonstrated for isolated bird tails of similarReynolds number (Re) and shape (Maybury et al., 2001).Lift generated by a planar delta wing is dependentupon angle of attack (a) and aspect ratio (A), expressed asa lift coefficient:CL ¼ Kp sin a cos2 aþ km sin2 a cos a; ð1Þwhere kp and kv are potential and vortex force constants,determined for a thin, flat triangular wing from A:kp ¼ 1:393A 0:141A2; ð2Þandkm ¼ 3:157 0:020Aþ 0:021A2; ð3Þfor 0 £ A < 4 (Polhamus, 1971; Maybury et al., 2001).Predictions from this model correspond to measurementsof lift from model bird tails (Maybury et al., 2001).Drag for low Re delta wings is less straightforward toestimate, but, provided a is not so large that the airflowabove the wing stalls:CD ¼ CD0 þ CL tan a: ð4ÞWith an appropriate value of the zero-lift drag coefficientCD0, it is possible to also produce estimates of dragcomparable to experimental measurements made usingisolated bird tails (Maybury et al., 2001).To calculate the flight performance of S. mirabilis, CD0was estimated as 0.08. This relatively high drag coefficientexceeds the estimatedBlasius friction drag, but it is derivedfrom empirical measurements of isolated starling tails atspeeds in the range 5–10 m s)1 (Maybury et al., 2001), andis consistent with other measurements of parasite drag onlow Re number, low aspect ratio wings. Note that variablevalues of CD0 do not affect our conclusions.–6–5–4–3–2–105 10 15Vsink (m s–1)Vsink (m s–1)Best glideApex 50°Apex 45°Apex 40°Apex 35°Apex 30°Apex 25°Draco–6–5–4–3–2–105 10 15Best glideApex 25°Apex 30°Apex 35°Apex 40°Apex 45°Apex 50°DracoVground (m s–1)Vground (m s–1)(c)(b)(a)Fig. 1 Sharovipteryx mirabilis and calculated glide polars (a), holotype and only known specimen (Paleontological Institute, Russian Academy ofSciences, Moscow (PIN 2584/8); scale bar, 10 mm), Triassic of Kyrgyzstan (b), glide polars (sinking speed against ground speed for given apexangles) for a single delta wing reaching anterior to the femora (c), incorporating a small forelimb membrane balancing the delta.Flight of Sharovipteryx mirabilis: the world’s first delta-winged glider 1041ª 2 0 0 6 T H E A U T H O R S 1 9 ( 2 0 0 6 ) 1 0 4 0 – 1 0 4 3J O U R N A L C O M P I L A T I O N ª 2 0 0 6 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G YResultsSharovipteryx mirabilis mode of flightOur calculations and estimates of alternative glide polarsillustrate that S. mirabilis triangular hindlimb membranewould have allowed for efficient gliding flight across arange of speeds (Fig. 1). Lift and drag may have beenactively modified by adjusting the shape and span of therearward membrane, by femoral protraction at the kneesor by varying body angle (angle-of-attack) while gliding.With just a hindlimb membrane, however, S. mirabiliswould not have had much control over its glide path.Further, glide polars predict that S. mirabilis’s hindlimbdelta would have allowed landing speeds between 11 and14 m s)1 (Fig. 1). Just like pterosaurs, S. mirabilis had atail but was uniquely adapted aerodynamically solely viaits hindlimbs, not requiring active use of its arms. With itsunique hindlimb membrane, the forelimbs of this smallreptile would have remained free during glides (Fig. 2).Although we are able to demonstrate that S. mirabiliscould glide using just its leg supported delta, our modelalso suggests that a small forelimb membrane (<10% areaof the hindwing) would also have been favourable tobalance this large rearward surface. This additionalsmaller moveable delta would have imparted improvedstability for landing and gliding, allowing shallower glideangles. The presence of a forward area of membrane isnot supported by fossil preservation – although portionsof the forelimbs are preserved in PIN 2584/8) thesediment surrounding this region in PIN 2584/8 hasbeen disturbed by preparation. A triangular canard wing,however, is the only realistic mechanism to providecontrol during a glide, obviating the need for S. mirabilisto administer a degree of control during glides bydepressing or rotating the hindwing or legs to adjustwing angle. Instead, the hindlimbs would only beconcerned with controlling flight speed by varyingwing-area, the leg spread angle. Addition of a smallforward canard to our model allows even better flightperformance than the extant gliding lizard Draco (Fig. 1)– S. mirabilis could have achieved a shallower glide angleand slower, less hazardous landing speeds.DiscussionOur study is the first to use aerodynamic theory anddirect analogy with extant gliding reptiles to estimate theactual flight abilities of the enigmatic Triassic vertebrateS. mirabilis. Consistent with the fossil evidence, a trian-gular hindlimb membrane is likely to have been mosteffective for S. mirabilis (Fig. 2) – previous reconstruc-tions of this reptiles’ mode of flight either restrict limbmovement and the ability to change wing shape bycoupling the hindlimbs to the forelimbs via the wingmembrane (Sharov, 1971; Fig. 2), postulate the centre oflift way behind the centre of mass causing a ‘forward-pitching’ effect (Gans et al., 1987; Fig. 2), or require animpossible angle for the femur held relative to the hipsocket when the wing is angled forward (Wellnhofer,1991; Fig. 2). The triangular, delta-wing reconstructionwe propose (Fig. 2) would also be highly stable if itextended from the pectoral girdle to the feet and tail andwas counteracted by an additional small forelimb canard– consistent with the preservation of the fossil (Fig. 1).With this shape of membrane, S. mirabilis could havesimply controlled its flight speed by varying the spread ofits delta wing; it would not have needed to depress thehindwing or rotate the femur in order to adjust wingangle of incidence.Just a single hindwing (as previously proposed) wouldnot have been enough. One rearward wing would havebeen very unstable in pitch; S. mirabilis would have beenunable to control the position of the centre of lift, whichFig. 2 Alternative reconstructions of the flight surface in Sharovipteryx mirabilis (a), Sharov (1971) (b), Gans et al. (1987) (c), Wellnhofer (1991)(d), our reconstruction of S. mirabilis flight surface (PIN 2584/8). Scale bar is 20 mm.1042 G. J. DYKE ET AL.ª 2 0 0 6 T H E A U T H O R S 1 9 ( 2 0 0 6 ) 1 0 4 0 – 1 0 4 3J O U R N A L C O M P I L A T I O N ª 2 0 0 6 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G Ylies posterior to the femoral articulation and hence thecentre of mass. With just a triangular membrane and nocontrol the landing approach of S. mirabilis would havebeen fast and potentially hazardous rendering thisreconstruction unlikely from an ecological point of view.A small anterior canard wing either attached to theforelimbs as a membrane or the neck as a gular pouch isnecessary to balance the pitching moment created by thelift generated from the large posterior delta wing.Sharovipteryx is unique among vertebrates in the posses-sion of a triangular delta wing formed from a hindlimbmembrane. Although some kind of small forelimb canardis also likely from a purely aerodynamic viewpoint, amoveable delta spanning the legs and tail would provideS. mirabilis with reasonable stability both for landing andglides.Intriguingly, because of the incompleteness of the singleknown specimen, the evolutionary relationships ofS. mirabilis remain poorly understood (Tatarinov, 1989;Unwin et al., 2001) – better preserved fossilmaterialwill berequired to resolve this issue. Most intriguingly, somephylogenetic analyses have postulated a close relationshipbetween this enigmatic small glider and the more wellknown, flapping pterosaurs (Peters, 2000). Althoughcontroversial (Tatarinov, 1989; Benton, 1999; Unwinet al., 2001), a relationship with the actively flapping andforelimb dominated pterosaurs has clear evolutionaryimplications for the origin of flight within this clade –S. mirabilis might then provide support for a ‘trees down’model for the evolution of pterosaurflight. In any case, thisanimal testifies to an unique mode of vertebrate flight –such a distinctive tail and hindlimb membrane surfacewould not have necessitated forelimb development. Someof the basal ‘rhamphorhynchoid’ pterosaurs have alsobeen reconstructed with a flight membrane attached toboth their legs and arms (Unwin & Bakhurina, 1994), butdid these forms evolve from hindlimb dominated sister-taxa? Triassic reptiles (like S. mirabilis) with unusual flightadaptations may illustrate a precedent for the evolution ofhindlimb dominated powered flight within other clades.From an aerodynamic standpoint, it is thus unsurprisingthat hindlimb flight surfaces (feathered legs) have alsobeen described in Microraptor (Xu et al., 2003), a smalltheropod dinosaur closely related to birds.AcknowledgmentsWe thank V. Alifanov, L. Couldrick, E. Kurochkin,J. Martin and D. Peters for their help with this project.M. Benton, K. Kurochkin and an anonymous reviewermade very helpful comments on this manuscript; Fig. 1awas supplied by E. Kurochkin. This work was supportedby the Leverhulme Trust and University College Dublin.ReferencesBennett, S.C. 2000. Pterosaur flight: the role of actinofibrils inwing function. Hist. Biol. 14: 255–284.Benton, M.J. 1999. Scleromochlus taylori and the origin ofdinosaurs and pterosaurs. Philos. Trans. R. Soc. Lond. B 354:1–25.Cowen, R. 1981. Homonyms of Podopterix. J. Paleontol. 55: 483.Frey, E. & Martill, D.M. 1998. Soft tissue preservation in aspecimen of Pterodactylus kochi (Wagner) from the UpperJurassic of Germany. N. Jb. Geol. Paläont. Abh. 21: 421–441.Gans, C., Darevski, I. & Tatarinov, L.P. 1987. Sharovipteryx, areptilian glider? Paleobiology. 13: 415–426.Maybury, W.J., Rayner, J.M.V. & Couldrick, L.B. 2001. Liftgeneration by the avian tail. Proc. R. Soc. Lond. B 268: 1443–1448.McGuire, J.A. & Dudley, R. 2005. The cost of living large:comparative gliding performance in flying lizards (Agamidae:Draco). Am. Nat. 166: 93–106.Padian, K. & Rayner, J.M.V. 1993. The wings of pterosaurs. Am.J. Sci. 293A: 91–166.Pennycuick, C.J. 1975. Mechanics of flight. In: Avian BiologyVolume 5 (D. S. Farner & J. R. King, eds), pp. 1–75. AcademicPress, London, UK.Peters, D.S. 2000. A reexamination of four prolacertiforms withimplications for pterosaur phylogenies. Riv. Ital. Pal. Stratig.106: 293–336.Polhamus, E.C. 1971. Predictions of vortex-lift characteristics bya leading-edge suction analogy. J. Aircraft 8: 193–199.Sharov, A.G. 1970. Peculiar reptile from lower Trias of Fergana.Pal. Zh. 42: 127–130 (in Russian).Sharov, A.G. 1971. New flying reptiles from the Mesozoic ofKazakhstan and Kirghizia. Trudy paleont. Inst. Moscow 130:104–113 (in Russian).Shine, R., Keogh, S., Doughty, P. & Giragossyan, H. 1998. 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Nature 421: 335–340.Received 22 November 2005; revised 20 January 2006; accepted 24January 2006Flight of Sharovipteryx mirabilis: the world’s first delta-winged glider 1043ª 2 0 0 6 T H E A U T H O R S 1 9 ( 2 0 0 6 ) 1 0 4 0 – 1 0 4 3J O U R N A L C O M P I L A T I O N ª 2 0 0 6 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G Y

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