I have a special treat this evening. Colin Palmer has been kind enough to write a guest post on the relative performance advantages and dynamics of thin and thick wings, especially in the context of animal flyers. Colin is located at Bristol University. He is an accomplished engineer with an exceptional background in thin-sectioned lifting surfaces (particularly sails). Colin has turned his eye to pterosaurs in recent years, and he has quickly become among the world's best pterosaur flight dynamics workers. You can catch his excellent paper on the aerodynamics of pterosaur wings here. Press release on it can be found here.
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Thin And Thick Wings
Colin Palmer
In the early days of manned flight the designers took their inspiration from birds. One of the consequences was that they used thin, almost curved plate aerofoil sections. This seemed intuitively right and certainly resulted in aeroplanes that flew successfully. However towards the end of the First World War the latest German Fokker fighters suddenly started to outperform the Allied planes. Counterintuitively their wing sections were thicker-surely these sections would not cut the air so well so how could they possibly have enabled aeroplanes to fly faster and climb more quickly. But that was what was happening, the Germans had done their research and discovered that a combination of a cambered aerofoil with the correct thickness distribution gave superior aerodynamic performance. Subsequently all aircraft had similar teardrop shaped wing sections and soon there was a massive body of experimental and theoretical work available that enabled designers to select just the aerofoil they required.
Fast forward to the period after the Second World War and an explosion of interest in applying the latest aerospace science to the traditional arts of sailing. Many people looked to aircraft and logically assumed that sailboats would perform better if only they could be fitted with wing sails, like up-ended aircraft wings. Surely this had to be more efficient than the old-fashioned sails made of fabric and wire, just like the earliest aircraft. But the results were disappointing. Not only on a practical level where the wing sails proved unwieldy and unsuited to operating in a range of wind conditions, but perhaps more worrying they offered no obvious performance advantage and indeed in light winds they were significantly inferior, area for area. What was going on? Why didn't the massive investment in the development of aircraft wing sections have anything to offer to sailboats?
The answer lay in understanding the effect of Reynolds number. From the very earliest days of manned flight aircraft were operating at Reynolds number approaching 1 million and as speeds increased so did the Reynolds numbers, so it became customary for aerofoils to be developed for operation at Reynolds numbers of 2 to 3 million or more. But sailboats are much slower than even the slowest aircraft so the operational Reynolds numbers are lower than for aircraft, typically in the range from 200,000 to 500,000, right in the so-called transition region. It turns out that in this Reynolds number range the experience and intuition gained from studies at significantly higher values can be very misleading indeed. In the transition region a curved plate, (membrane) aerofoil can be more aerodynamically efficient than a conventional thick aerofoil.
This transition Reynolds number range is also where most birds and bats operate, and from what we know of pterosaurs it was also their domain. Consequently natural forms are not necessarily disadvantaged by having the membrane wings of bats or pterosaurs or the thin foils of the primary feathers in the distal regions of bird wings.
But there is a complication. A curved plate or, to an even greater extent, a membrane aerofoil has very little intrinsic strength and requires some form of structure to keep it in place and keep it in shape. On sailing yachts this structure is a thin tension wire that supports the headsail or the tubular mast in front of the mainsail. In order to tension the wire for the headsail, very large forces are required which places the mast in considerable compression, normally requiring a guyed structure that can have no direct analogue in nature. Natural forms are restricted to using a supporting structure which is loaded in bending and restrained by attached muscles and tendons. Generally speaking, the bending resistance of a structure depends upon the depth of the cross-section, so as bending load increases the diameters of the bones must increase otherwise the wing will become too flexible.
This is where the apparent superiority of the membrane wing may be compromised, because the presence of structural member severely degrades the aerodynamic performance. The structural member may be along the leading edge of the aerofoil as in the case of bats and pterosaurs, or close to the aerodynamic centre as in the case of the rachis of the primary feathers of birds. In all cases the loss of performance is less if the supporting structure is on the pressure side (the ventral side) of the aerofoil. It is therefore most likely no coincidence that this is the arrangement of the wing bones and membrane in bats and the rachis and vane in primary feathers. It was therefore also most likely that the wing membranes of pterosaurs were similarly attached to the upper side of the wing finger. Even in this configuration there is a substantial penalty in terms of drag, although it may result in some increase in the maximum lift capability of the section, due presumably to an effective increase in camber. (Palmer 2010).
This aerodynamic penalty arising from the presence of the supporting structure may perhaps be the reason why birds’ wings have thickness in the proximal regions, where the performance of such a thick aerofoil is superior to a thin membrane obstructed by the presence of the wing bones. More distally, where the wing bones become thinner or are not present, the wing section reverts to a thin cambered plate formed by the primary feathers. On the bird’s wing the proximal fairing of the bones into an aerofoil section is achieved by the contour feathers with very little weight penalty. This is not possible in bats (and presumably also in pterosaurs) where any fairing material would, at the very least, need to be pneumatised soft tissue, resulting in a considerable weight penalty as compared to feathers. In the absence of aerodynamic fairing around the supporting structure, aerodynamic efficiency can only be improved by reducing the cross-section depth of the bones - the general shape of the section having very little effect. But reducing the section depth results in a large increase in flexibility since the bending stiffness varies as the 4th power of section depth, so there are very marked limits to the effectiveness of this trade-off.
It may therefore be no coincidence that where the cross section depth has to be greatest, in the proximal regions of the wing, both bats and pterosaurs have a propatagium, which means that the leading-edge of the wing section is more akin to the headsail of a yacht, stretched on a wire, than a membrane with the structural member along the leading-edge. Wind tunnel tests have shown that moving the structural member back from the leading-edge, while keeping it on the underside of the wing section, results in a significant increase in aerodynamic performance.
Showing posts with label Pterosaurs. Show all posts
Showing posts with label Pterosaurs. Show all posts
Thursday, July 5, 2012
Sunday, June 10, 2012
Feathers vs Membranes
A recent discussion arose on the Dinosaur Mailing List that included some questions regarding the relative merits of membrane wings and feathered wings, mostly in the context of pterosaurs vs birds. In that spirit, I thought I'd give a little rundown of the relative advantages/costs of each type of vertebrate wing.
Avian Wings
Birds are the only flying vertebrates to use keratinized, dermal projections (i.e. feathers) to form their wings. Feathers have the distinct advantage of being potentially separate vortex-generating surfaces, meaning that a bird can split its wing up into separate airfoils, thereby greatly changing its lift and drag profile as required (Videler, 2005). Tip slots are the most obvious example of this mechanism, whereby the tip of the wing is split into several separate wingtips by spreading the primary feathers of the distal wing. The alula, which lies along the leading edge of a bird’s wing, and is controlled by digit I, is another example of a semi-independent foil unit (Pennycuick, 1989; Videler, 2005). The splayed primaries of a slotted avian wingtip passively twist nose-down at high angles of attack (and therefore at high lift coefficients), and this feather twist reduces the local angle of attack at the distal end of slotted avian wings, preventing them from stalling (Pennycuick, 2008). Slotted avian wingtips may therefore be nearly "unstallable", though this does not prevent the overall wing from stalling (Pennycuick, pers comm.). Feathered wings can also be reduced in span without an accompanying problem of slack and flutter – the feathers that form the contour of the wing simply slide over one another to accommodate the change in surface area. Despite these advantages, feathers have some costs as wing components, as compared to membranous wings. Feathered wings are relatively heavy (Prange et al., 1979) and cannot be tensed and stretched like a membrane wing (which has ramifications for cambering). Theoretically, avian wings should not be able to produce maximum lift coefficients as high as an optimized membrane wing (Cunningham, pers comm.), but experimental data to determine if transient, maximum lift coefficients actually differ significantly between bats and birds are not yet available (Hedenstrom et al., 2009).
Chiropteran Wings
Bats have a wing surface formed primarily by a membrane stretched across the hand, antebrachium, brachium, and body down to the ankle. Unlike birds, which have a limited number of muscles that produce the flapping stroke (two, primarily: m. pectoralis minor and m. pectoralis major), bats have as many as 17 muscles involved in the flight stroke (Hermanson and Altenbach, 1983; Neuweiler, 2000; Hedenstrom et al., 2009). The membranous wings of bats are expected to have a steeper lift slope than the stiffer, less compliant wings of birds (Song et al., 2008). This results from the passive cambering under aerodynamic load that occurs in a compliant wing: as lift force increases, the wing passively stretches and bows upwards, producing more camber, and thereby further increasing the lift coefficient and total lift. While there are some advantages for a flying animal in having such a passive system, bats presumably must mediate this effect with the many small muscles (and fingers) in their wings – tensing the wings actively while under fluid load will mediate the amount of camber that develops. This would be important to mediate drag and stall, though no empirical data currently exist to indicate exactly how bats respond to passive cambering. The work by Song et al. (2008) also indicates that compliant, membrane wings achieve greater maximum lift coefficients than rigid wings, but data have yet to be collected demonstrating that this holds in vivo for bats and birds. Compared to birds, the distal wing spar in bats is quite compliant (Swartz and Middleton, 2008).
Pterosaur Wings
The structure and efficiency of pterosaur wings is obviously not known in as much detail as those of birds or bats, for the simple reason that no living representatives of pterosaurs are available for study. However, soft tissue preservation in pterosaurs does give some critical information about their wing morphology, and the overall shape and structure of the wing can be used (along with first principles from aerodynamics) to estimate efficiency and performance.
It is known from specimens preserving soft tissue impressions that pterosaur wings were soft tissue structures, apparently composed of skin, muscle, and stiffening fibers called actinofibrils, though the exact nature and structure of actinofibrils has been the topic of much debate (Wellnhofer 1987; Pennycuick 1988; Padian and Rayner 1993; Bennett 2000; Peters 2002; Tischlinger and Frey 2002). Associated vasculature is also visible in some specimens, especially with UV illumination (Tischlinger and Frey, 2002). Recent work on the holotype of Jeholopterus ningchengensis (IVPPV12705) seems to confirm that the actinofibrils were stiffening fibers, imbedded within the wing, with multiple layers (Kellner et al., 2009). The actinofibrils were longer and more organized in the distal part of pterosaur wings than in the proximal portion of the wing, which may have implications for the compliance of the wing going from distal to more proximal sections. The inboard portion of the wing (proximal to the elbow) is called the mesopatatgium, and was typified by a small number of actinofibrils with lower organization, which would have made this part of the wing more compliant than the outboard wing.
The outer portion of the wing, which was likely less compliant the mesopatagium, is termed the actinopatagium (Kellner et al., 2009). Because pterosaurs had membrane wings, they could presumably generate high lift coefficients, but exactly how high depends on certain assumptions regarding their material properties and morphology (pteroid mobility and membrane shape being two of these factors).
Now, for some punchlines...
Based on the structural information above, we might expect the following regarding pterosaurs and birds:
- Pterosaurs would have a base advantage in terms of maneuverability and slow flight competency.
- Pterosaurs would also have had an advantage in terms of soaring capability and efficiency
- Pterosaurs would have been better suited to the evolution of large sizes (though this was affected more by differences in takeoff - see earlier posts about pterosaur launch).
- Birds will perform a bit better as mid-sized, broad-winged morphs (because they can use slotted wing tips and span reduction).
- Birds would have an advantage in steep climb-out after takeoff at small body sizes (because they can work with shorter wings and engage them earlier). This might pre-dispose them to burst launch morphologies/ecologies.
Interestingly enough, the fossil record as we currently know it seems to back up all of these expectations. For example, the only vertebrates that seem to have been adapted to dedicated sustained aerial hawking in the Mesozoic were the anurognathid pterosaurs. Large soaring morphs in the Mesozoic were dominated by pterosaurs, also. On the other hand, mid-sized arboreal forms in the Cretaceous were largely avian.
Full references for all of the above literature is available upon request. I'll post the full refs here as soon as I have a chance, but just email me in the meantime if need be (currently traveling in Boston).
Avian Wings
Birds are the only flying vertebrates to use keratinized, dermal projections (i.e. feathers) to form their wings. Feathers have the distinct advantage of being potentially separate vortex-generating surfaces, meaning that a bird can split its wing up into separate airfoils, thereby greatly changing its lift and drag profile as required (Videler, 2005). Tip slots are the most obvious example of this mechanism, whereby the tip of the wing is split into several separate wingtips by spreading the primary feathers of the distal wing. The alula, which lies along the leading edge of a bird’s wing, and is controlled by digit I, is another example of a semi-independent foil unit (Pennycuick, 1989; Videler, 2005). The splayed primaries of a slotted avian wingtip passively twist nose-down at high angles of attack (and therefore at high lift coefficients), and this feather twist reduces the local angle of attack at the distal end of slotted avian wings, preventing them from stalling (Pennycuick, 2008). Slotted avian wingtips may therefore be nearly "unstallable", though this does not prevent the overall wing from stalling (Pennycuick, pers comm.). Feathered wings can also be reduced in span without an accompanying problem of slack and flutter – the feathers that form the contour of the wing simply slide over one another to accommodate the change in surface area. Despite these advantages, feathers have some costs as wing components, as compared to membranous wings. Feathered wings are relatively heavy (Prange et al., 1979) and cannot be tensed and stretched like a membrane wing (which has ramifications for cambering). Theoretically, avian wings should not be able to produce maximum lift coefficients as high as an optimized membrane wing (Cunningham, pers comm.), but experimental data to determine if transient, maximum lift coefficients actually differ significantly between bats and birds are not yet available (Hedenstrom et al., 2009).
Chiropteran Wings
Bats have a wing surface formed primarily by a membrane stretched across the hand, antebrachium, brachium, and body down to the ankle. Unlike birds, which have a limited number of muscles that produce the flapping stroke (two, primarily: m. pectoralis minor and m. pectoralis major), bats have as many as 17 muscles involved in the flight stroke (Hermanson and Altenbach, 1983; Neuweiler, 2000; Hedenstrom et al., 2009). The membranous wings of bats are expected to have a steeper lift slope than the stiffer, less compliant wings of birds (Song et al., 2008). This results from the passive cambering under aerodynamic load that occurs in a compliant wing: as lift force increases, the wing passively stretches and bows upwards, producing more camber, and thereby further increasing the lift coefficient and total lift. While there are some advantages for a flying animal in having such a passive system, bats presumably must mediate this effect with the many small muscles (and fingers) in their wings – tensing the wings actively while under fluid load will mediate the amount of camber that develops. This would be important to mediate drag and stall, though no empirical data currently exist to indicate exactly how bats respond to passive cambering. The work by Song et al. (2008) also indicates that compliant, membrane wings achieve greater maximum lift coefficients than rigid wings, but data have yet to be collected demonstrating that this holds in vivo for bats and birds. Compared to birds, the distal wing spar in bats is quite compliant (Swartz and Middleton, 2008).
Pterosaur Wings
The structure and efficiency of pterosaur wings is obviously not known in as much detail as those of birds or bats, for the simple reason that no living representatives of pterosaurs are available for study. However, soft tissue preservation in pterosaurs does give some critical information about their wing morphology, and the overall shape and structure of the wing can be used (along with first principles from aerodynamics) to estimate efficiency and performance.
It is known from specimens preserving soft tissue impressions that pterosaur wings were soft tissue structures, apparently composed of skin, muscle, and stiffening fibers called actinofibrils, though the exact nature and structure of actinofibrils has been the topic of much debate (Wellnhofer 1987; Pennycuick 1988; Padian and Rayner 1993; Bennett 2000; Peters 2002; Tischlinger and Frey 2002). Associated vasculature is also visible in some specimens, especially with UV illumination (Tischlinger and Frey, 2002). Recent work on the holotype of Jeholopterus ningchengensis (IVPPV12705) seems to confirm that the actinofibrils were stiffening fibers, imbedded within the wing, with multiple layers (Kellner et al., 2009). The actinofibrils were longer and more organized in the distal part of pterosaur wings than in the proximal portion of the wing, which may have implications for the compliance of the wing going from distal to more proximal sections. The inboard portion of the wing (proximal to the elbow) is called the mesopatatgium, and was typified by a small number of actinofibrils with lower organization, which would have made this part of the wing more compliant than the outboard wing.
The outer portion of the wing, which was likely less compliant the mesopatagium, is termed the actinopatagium (Kellner et al., 2009). Because pterosaurs had membrane wings, they could presumably generate high lift coefficients, but exactly how high depends on certain assumptions regarding their material properties and morphology (pteroid mobility and membrane shape being two of these factors).
Now, for some punchlines...
Based on the structural information above, we might expect the following regarding pterosaurs and birds:
- Pterosaurs would have a base advantage in terms of maneuverability and slow flight competency.
- Pterosaurs would also have had an advantage in terms of soaring capability and efficiency
- Pterosaurs would have been better suited to the evolution of large sizes (though this was affected more by differences in takeoff - see earlier posts about pterosaur launch).
- Birds will perform a bit better as mid-sized, broad-winged morphs (because they can use slotted wing tips and span reduction).
- Birds would have an advantage in steep climb-out after takeoff at small body sizes (because they can work with shorter wings and engage them earlier). This might pre-dispose them to burst launch morphologies/ecologies.
Interestingly enough, the fossil record as we currently know it seems to back up all of these expectations. For example, the only vertebrates that seem to have been adapted to dedicated sustained aerial hawking in the Mesozoic were the anurognathid pterosaurs. Large soaring morphs in the Mesozoic were dominated by pterosaurs, also. On the other hand, mid-sized arboreal forms in the Cretaceous were largely avian.
Full references for all of the above literature is available upon request. I'll post the full refs here as soon as I have a chance, but just email me in the meantime if need be (currently traveling in Boston).
Sunday, May 27, 2012
Beijing Pterosaur Meeting
This was one of four abstracts I was on for the Beijing Pterosaur Meeting a couple of years back. The next pterosaur meeting is schedule for Rio - more on that in the not-to-distant future.
Soaring efficiency and long distance travel in giant pterosaurs
Authors: Michael Habib and Mark Witton
Azhdarchid pterosaurs include the largest known flying animals, with the largest species reaching a potential mass of over 250 kg. Prior work suggests that several features of azhdarchid anatomy could be associated with a soaring-dominated lifestyle, including large size, burst-flapping adapted pectoral girdle and proximal forelimb, moderate to high wing aspect ratio, and exceptional pneumaticity. However, long-range flight ability of azhdarchid pterosaurs has not been quantified in the literature. Furthermore, while the flight of giant pterosaurs has been modeled for a range of large species (Hankin and Watson 1914; Bramwell and Whitfield 1974; Brower 1983; Chatterjee and Templin 2004) and researchers have invariably concluded that they were capable of flight, some recent studies have called into the question the flight abilities of pterosaurs at large body masses (Chatterjee and Templin, 2004; Sato et al. 2009), especially the relatively ‘heavy’ masses in the recent literature (Paul 1991, 2002; Witton 2008). Here we present the results from a quantitative analysis of long-distance travel efficiency in azhdarchid pterosaurs, demonstrating that the largest pterosaurs should not only have been effective flyers, but had the potential to be the furthest-traveling animals known to science.
Power analysis indicates that the largest pterosaurs needed to reach external sources of lift, following launch, before they exhausted anaerobic muscle endurance. Following climb out, even large azhdarchids should have been capable of staying aloft by using external sources of lift. A quantitative framework already exists for estimating maximum migration range in soaring birds using thermal lift. We have extended this framework to pterosaurs by altering existing models to accommodate the membrane wings of pterosaurs and uncertainty in potential muscle physiologies. Maximum fuel capacity (stored as fat and additional muscle) was estimated by taking the difference between body masses scaled from skeletal strength (maximum) versus mass for maximum wing efficiency (maximizing lift coefficient according to reconstructed aspect ratio). This new migration model indicates that the largest azhdarchid pterosaurs had the capacity for non-stop flights exceeding 10,000 miles.
The ability of large pterosaurs, especially azhdarchids, to effectively reach external sources of lift was great augmented by 1) adaptations for a powerful launch (Habib, 2008) that would allow them to exceed stall speed without utilizing excessive amounts of valuable anaerobic capacity, and 2) adaptations for rapid generation of full circulation on the wing, which would have substantially reduced the time and energy expenditure of climb out. Approximately 2.5 chord lengths are usually required before a wing develops full steady state circulation, known in the literature as the “Wagner Effect” (Wagner, 1925). Analysis of the tensile support in azdarchid wings suggests a potential for rapid translation and twisting of the outboard wing, which would be promoted by the T-shaped cross section of the wing phalanges. Such rapid translation can develop full circulation up to five times faster than otherwise possible and greatly reduce the flapping cycles needed to reach maximum circulation during climb out, an observation previously made by at least one other pterosaur worker (Cunningham, pers comm.) but previously unmentioned in the formal pterosaur literature. These improvements to the efficiency of the initial climb out from launch would have extended the required proximity to external lift sources, and broadened the potential habitat range of giant pterosaurs.
Literature Cited
Bramwell CD, Whitfield GR (1974). Biomechanics of Pteranodon. Philosophical Transactions of the Royal Society of London 267: 503-581.
Brower, JC (1983). The aerodynamics of Pteranodon and Nyctosaurus, two large Pterosaurs from the Upper Cretaceous of Kansas. Journal of Vertebrate Paleontology. 3: 84-124
Chatterjee S. and Templin RJ (2004). Posture, Locomotion and Palaeoecology of Pterosaurs. Geological Society of America Special Publication, 376, 1-64.
Habib, M.B. 2008. Comparative evidence for quadrupedal launch in pterosaurs. Zitteliana, B28, 161-168.
Hankin, EH and Watson DMS (1914). On the flight of pterodactyls. Aeronautical Journal, 18, 324-335.
Paul. G. S. 1991. The many myths, some old, some new, of dinosaurology. Modern Geology, 16, 69-99.
Paul GS (2002) Dinosaurs of the Air: The Evolution and Loss of Flight in Dinosaurs and Birds. John Hopkins University Press, Baltimore. 472 p.
Soaring efficiency and long distance travel in giant pterosaurs
Authors: Michael Habib and Mark Witton
Azhdarchid pterosaurs include the largest known flying animals, with the largest species reaching a potential mass of over 250 kg. Prior work suggests that several features of azhdarchid anatomy could be associated with a soaring-dominated lifestyle, including large size, burst-flapping adapted pectoral girdle and proximal forelimb, moderate to high wing aspect ratio, and exceptional pneumaticity. However, long-range flight ability of azhdarchid pterosaurs has not been quantified in the literature. Furthermore, while the flight of giant pterosaurs has been modeled for a range of large species (Hankin and Watson 1914; Bramwell and Whitfield 1974; Brower 1983; Chatterjee and Templin 2004) and researchers have invariably concluded that they were capable of flight, some recent studies have called into the question the flight abilities of pterosaurs at large body masses (Chatterjee and Templin, 2004; Sato et al. 2009), especially the relatively ‘heavy’ masses in the recent literature (Paul 1991, 2002; Witton 2008). Here we present the results from a quantitative analysis of long-distance travel efficiency in azhdarchid pterosaurs, demonstrating that the largest pterosaurs should not only have been effective flyers, but had the potential to be the furthest-traveling animals known to science.
Power analysis indicates that the largest pterosaurs needed to reach external sources of lift, following launch, before they exhausted anaerobic muscle endurance. Following climb out, even large azhdarchids should have been capable of staying aloft by using external sources of lift. A quantitative framework already exists for estimating maximum migration range in soaring birds using thermal lift. We have extended this framework to pterosaurs by altering existing models to accommodate the membrane wings of pterosaurs and uncertainty in potential muscle physiologies. Maximum fuel capacity (stored as fat and additional muscle) was estimated by taking the difference between body masses scaled from skeletal strength (maximum) versus mass for maximum wing efficiency (maximizing lift coefficient according to reconstructed aspect ratio). This new migration model indicates that the largest azhdarchid pterosaurs had the capacity for non-stop flights exceeding 10,000 miles.
The ability of large pterosaurs, especially azhdarchids, to effectively reach external sources of lift was great augmented by 1) adaptations for a powerful launch (Habib, 2008) that would allow them to exceed stall speed without utilizing excessive amounts of valuable anaerobic capacity, and 2) adaptations for rapid generation of full circulation on the wing, which would have substantially reduced the time and energy expenditure of climb out. Approximately 2.5 chord lengths are usually required before a wing develops full steady state circulation, known in the literature as the “Wagner Effect” (Wagner, 1925). Analysis of the tensile support in azdarchid wings suggests a potential for rapid translation and twisting of the outboard wing, which would be promoted by the T-shaped cross section of the wing phalanges. Such rapid translation can develop full circulation up to five times faster than otherwise possible and greatly reduce the flapping cycles needed to reach maximum circulation during climb out, an observation previously made by at least one other pterosaur worker (Cunningham, pers comm.) but previously unmentioned in the formal pterosaur literature. These improvements to the efficiency of the initial climb out from launch would have extended the required proximity to external lift sources, and broadened the potential habitat range of giant pterosaurs.
Literature Cited
Bramwell CD, Whitfield GR (1974). Biomechanics of Pteranodon. Philosophical Transactions of the Royal Society of London 267: 503-581.
Brower, JC (1983). The aerodynamics of Pteranodon and Nyctosaurus, two large Pterosaurs from the Upper Cretaceous of Kansas. Journal of Vertebrate Paleontology. 3: 84-124
Chatterjee S. and Templin RJ (2004). Posture, Locomotion and Palaeoecology of Pterosaurs. Geological Society of America Special Publication, 376, 1-64.
Habib, M.B. 2008. Comparative evidence for quadrupedal launch in pterosaurs. Zitteliana, B28, 161-168.
Hankin, EH and Watson DMS (1914). On the flight of pterodactyls. Aeronautical Journal, 18, 324-335.
Paul. G. S. 1991. The many myths, some old, some new, of dinosaurology. Modern Geology, 16, 69-99.
Paul GS (2002) Dinosaurs of the Air: The Evolution and Loss of Flight in Dinosaurs and Birds. John Hopkins University Press, Baltimore. 472 p.
Monday, May 21, 2012
KLI
Another in the series of abstracts. This was my abstract for the think-tank conference at the Konrad Lorenz Institute in Vienna, Austria in September 2010. These are invite-only sessions on various hot topics related to evolutionary biology. Ours was on the "Constraints and Evolution of Form" - basically an Evo Devo related gig. I was the resident biomechanist for this one.
Emergence of convergent forms under fluid load in plants and animals
Very few biomechanists examine both plants and animals in parallel, apparently under a tacit assumption that the rules of shape determination must differ substantially between such distantly related groups. However, convergent structures suggest that the rules of shape governing these groups are largely the same. Such similarities suggest that environmental constraints are important in determining shape, and/or that genomes are more plastic and prone to morphological convergence than often accepted. I suggest that reference to physical first principles should be made whenever shape is examined in multi-cellular organisms, regardless of their phylogenetic position. As a case example, I report on the presence of highly convergent structures related to resistance and passive yield under aerodynamic fluid load in plants and animals. I utilize examples from both living and fossil forms, including broad-leafed trees, neornithine birds, and azhdarchid pterosaurs.
Emergence of convergent forms under fluid load in plants and animals
Very few biomechanists examine both plants and animals in parallel, apparently under a tacit assumption that the rules of shape determination must differ substantially between such distantly related groups. However, convergent structures suggest that the rules of shape governing these groups are largely the same. Such similarities suggest that environmental constraints are important in determining shape, and/or that genomes are more plastic and prone to morphological convergence than often accepted. I suggest that reference to physical first principles should be made whenever shape is examined in multi-cellular organisms, regardless of their phylogenetic position. As a case example, I report on the presence of highly convergent structures related to resistance and passive yield under aerodynamic fluid load in plants and animals. I utilize examples from both living and fossil forms, including broad-leafed trees, neornithine birds, and azhdarchid pterosaurs.
Sunday, May 20, 2012
Walker Symposium
This was my abstract (co-authored with David B. Weishampel) for the Walker Symposium at the SVP 2009 Meeting. It got a bit complicated as my Romer session was concurrent with this one...
Flight morphology and launch dynamics of basal birds, and the potential for competition with pterosaurs
Birds inherited a bipedal gait and feathered airfoils from their theropod ancestry. These features produce specific tradeoffs with regards to launch, maximum size, lift coefficient, and limb disparity. There are subtle effects related to the use of feathered wings, such as the ability to utilize separated wingtip slots and extensive span reduction, which have also influenced avian flight evolution. Combining information from structural mechanics, aerodynamics, and phylogeny, we conclude that the basal state for avian takeoff was a leaping launch, not a running launch. We find that several morphological features of early birds, inherited from theropod ancestry, predisposed them to radiation in inland habitats. We find that Archaeopteryx could sustain substantial loads on both its forelimbs and hindlimbs, but structural ratios between the forelimb and hindlimb of Archaeopteryx are indicative of limited volancy. Limb strength in Confuciusornis was modest, suggesting an emphasis on cruising flight and limited launch power. We find little evidence to support extensive competition between birds and pterosaurs in the Mesozoic. Prior literature has suggested that pterosaurs competed with early birds for resources and may have helped shape the early evolution of birds. There is some evidence of partitioning between pterosaurs and birds in ecological space. Evidence from the Jehol fauna suggests that pterosaurs dominated near coastlines during the Early Cretaceous, while birds were more diverse and important inland. However, flight is not a single, compact character. Flight mechanics vary considerably across volant animals. Some flyers experience only limited competition for resources with other flying species, and might compete most intensely with non-flying taxa. As a baseline for understanding the interactions between Cretaceous birds and pterosaurs, the flight dynamics of the two groups need to be compared in a quantifiable framework. Birds and pterosaurs inherited different morphologies, and this impacted their flight regimes. Comparing the two systems provides a basis for hypotheses related to competition in the Cretaceous, and the influences on early avian evolution.
Flight morphology and launch dynamics of basal birds, and the potential for competition with pterosaurs
Birds inherited a bipedal gait and feathered airfoils from their theropod ancestry. These features produce specific tradeoffs with regards to launch, maximum size, lift coefficient, and limb disparity. There are subtle effects related to the use of feathered wings, such as the ability to utilize separated wingtip slots and extensive span reduction, which have also influenced avian flight evolution. Combining information from structural mechanics, aerodynamics, and phylogeny, we conclude that the basal state for avian takeoff was a leaping launch, not a running launch. We find that several morphological features of early birds, inherited from theropod ancestry, predisposed them to radiation in inland habitats. We find that Archaeopteryx could sustain substantial loads on both its forelimbs and hindlimbs, but structural ratios between the forelimb and hindlimb of Archaeopteryx are indicative of limited volancy. Limb strength in Confuciusornis was modest, suggesting an emphasis on cruising flight and limited launch power. We find little evidence to support extensive competition between birds and pterosaurs in the Mesozoic. Prior literature has suggested that pterosaurs competed with early birds for resources and may have helped shape the early evolution of birds. There is some evidence of partitioning between pterosaurs and birds in ecological space. Evidence from the Jehol fauna suggests that pterosaurs dominated near coastlines during the Early Cretaceous, while birds were more diverse and important inland. However, flight is not a single, compact character. Flight mechanics vary considerably across volant animals. Some flyers experience only limited competition for resources with other flying species, and might compete most intensely with non-flying taxa. As a baseline for understanding the interactions between Cretaceous birds and pterosaurs, the flight dynamics of the two groups need to be compared in a quantifiable framework. Birds and pterosaurs inherited different morphologies, and this impacted their flight regimes. Comparing the two systems provides a basis for hypotheses related to competition in the Cretaceous, and the influences on early avian evolution.
To Quad or Not to Quad
I received a really good question about the relative advantages of bipedal and quadrupedal launch at the Royal Tyrrell Museum. Essentially, they asked what the relative performance tradeoffs of each one might be, and why pterosaurs might have ended up locked into a quadrupedal launch style.
As it turns out, there are really two parts to the answer. In terms of which launch mode ends up as the dominant method of takeoff within a clade, it is likely that phylogenetic inertia plays an important role: birds inherited an obligate bipedal stance from their ancestors, and so every bird (so far as we know) has been a biped and launches bipedally, at least from the ground (more on this later, but some birds are quad launchers from the water, which is pretty neat stuff).
Bats seem to have inherited an obligate quadrupedal lifestyle. Pterosaur origins are more fuzzy, but they probably arose from one of a few different groups where bipedal to quadrupedal transitions were more common, and so their early evolution may have been more phylogenetically plastic with regards to stance. They eventually ended up as obligate quadrupeds, with most species placing most of their weight on the forelimbs (this is apparent because manus tracks from pterosaurs are typically deeper than the pes prints).
In terms of the relative performance advantages, it turns out that we can solve the question algebraically:
1) Both forms of launch will start as a leap (or a run ending in a leap). This means that the immediate post-launch cycle is ballistic. That's handy - ballistic math is easy.
2) Quad launch adds an upstroke immediately after push-off. Bipeds can (and do) raise the wings as they toe-off, so they can engage the first downstroke as soon as the wings have clearance.
3) Quad launch adds more power for initial push-off, so this goes into the ballistic equation. This will mean more height and speed, but at the cost of the added upstroke (the extra upstroke is accomplished with folded wings, so it's quite quick).
So, all we have to do is have an idea of max acceleration and unload time for takeoff, which gives launch speed, combined with the launch angle. We can vary these a bit to get a range of plausible values, and these give us the ballistic trajectory. So, for example, the maximum height gain can be calculated from the launch velocity squared x sin(launch angle) squared, divided by 2 x gravitation acceleration.
It turns out that for just about any flying animal, quadrupedal launch does better in nearly every way. They get a lot more power (because the flight muscles are so strong and can add to the launch in a quad takeoff, whereas in a biped takeoff they add very little). This means more clearance, ballistic time, and speed. It also allows for a greater range of starting wing attack angles, and is essentially "safer" because of the much greater clearance for the wings and body (larger margin of error, as it were). The extra time in the air from the greater push more than makes up for the extra upstroke time. For example, even in a giant like Quetzalcoatlus northropi, the initial upstroke would only take about a tenth of a second. It would have almost a third of second to reach the top of the ballistic leap, however, giving plenty of time to spare.
So, on the whole, quad launch is just "better" - with one exception. A bipedal launcher with short wings and a very short flapping time can switch from ballistic phase to flapping phase a bit earlier. This is not as efficient as the quad option, but it can mean a steeper and more immediate climb-out. This is only useful for a burst-launching specialist at moderate or small sizes (at giant sizes quad launch is king), but it is perhaps noticeable that this exact set of morphological features and takeoff strategy is extremely common among living birds - it is highly typical of galliform birds (pheasants, grouse, etc), pigeons and doves, and many of the passerines. It is also perhaps telling that there are no particularly short-winged pterosaurs. For a quadrupedal launching animal, very short wings don't do nearly as much good. The closest example might be anurognathids, and as noted in my GSA abstract, they are quite unique among pterosaurs. More on that later...
As it turns out, there are really two parts to the answer. In terms of which launch mode ends up as the dominant method of takeoff within a clade, it is likely that phylogenetic inertia plays an important role: birds inherited an obligate bipedal stance from their ancestors, and so every bird (so far as we know) has been a biped and launches bipedally, at least from the ground (more on this later, but some birds are quad launchers from the water, which is pretty neat stuff).
Bats seem to have inherited an obligate quadrupedal lifestyle. Pterosaur origins are more fuzzy, but they probably arose from one of a few different groups where bipedal to quadrupedal transitions were more common, and so their early evolution may have been more phylogenetically plastic with regards to stance. They eventually ended up as obligate quadrupeds, with most species placing most of their weight on the forelimbs (this is apparent because manus tracks from pterosaurs are typically deeper than the pes prints).
In terms of the relative performance advantages, it turns out that we can solve the question algebraically:
1) Both forms of launch will start as a leap (or a run ending in a leap). This means that the immediate post-launch cycle is ballistic. That's handy - ballistic math is easy.
2) Quad launch adds an upstroke immediately after push-off. Bipeds can (and do) raise the wings as they toe-off, so they can engage the first downstroke as soon as the wings have clearance.
3) Quad launch adds more power for initial push-off, so this goes into the ballistic equation. This will mean more height and speed, but at the cost of the added upstroke (the extra upstroke is accomplished with folded wings, so it's quite quick).
So, all we have to do is have an idea of max acceleration and unload time for takeoff, which gives launch speed, combined with the launch angle. We can vary these a bit to get a range of plausible values, and these give us the ballistic trajectory. So, for example, the maximum height gain can be calculated from the launch velocity squared x sin(launch angle) squared, divided by 2 x gravitation acceleration.
It turns out that for just about any flying animal, quadrupedal launch does better in nearly every way. They get a lot more power (because the flight muscles are so strong and can add to the launch in a quad takeoff, whereas in a biped takeoff they add very little). This means more clearance, ballistic time, and speed. It also allows for a greater range of starting wing attack angles, and is essentially "safer" because of the much greater clearance for the wings and body (larger margin of error, as it were). The extra time in the air from the greater push more than makes up for the extra upstroke time. For example, even in a giant like Quetzalcoatlus northropi, the initial upstroke would only take about a tenth of a second. It would have almost a third of second to reach the top of the ballistic leap, however, giving plenty of time to spare.
So, on the whole, quad launch is just "better" - with one exception. A bipedal launcher with short wings and a very short flapping time can switch from ballistic phase to flapping phase a bit earlier. This is not as efficient as the quad option, but it can mean a steeper and more immediate climb-out. This is only useful for a burst-launching specialist at moderate or small sizes (at giant sizes quad launch is king), but it is perhaps noticeable that this exact set of morphological features and takeoff strategy is extremely common among living birds - it is highly typical of galliform birds (pheasants, grouse, etc), pigeons and doves, and many of the passerines. It is also perhaps telling that there are no particularly short-winged pterosaurs. For a quadrupedal launching animal, very short wings don't do nearly as much good. The closest example might be anurognathids, and as noted in my GSA abstract, they are quite unique among pterosaurs. More on that later...
Friday, April 13, 2012
Bennettazhia humerus
Wednesday, April 11, 2012
Head Over Heels
I know that it is now technically Wednesday, but this was supposed to be the Tuesday post - got a little held up with work at the Carnegie Museum.
In any case, given that I posted a bit about how bats launch, it seems only fair to also point out that great work has been done on how they land, as well. Dan Riskin and colleagues have a great paper in the Journal of Experimental Biology (freely available here) where they examined the tricky business of landing on ceilings. As it turns out, there are a few ways to do it, and one of them basically involves a cartwheel in the air to bring the feet, and then the hands, in contact with the inverted substrate.
This, in turn, brings me to a point that I have been making at conferences lately: landing and launching from ceilings is tricky business. The exact kinematics of ceiling-launches in bats have not been elucidated in great detail, but it is known that they are quite acrobatic. This is important, because one of the bits of rebuttal I hear rather often about large fossil flyers (mostly pterosaurs) is: "why couldn't they just drop off a cliff for speed?"
The answer is that this turns your average giant pterosaur in a rather elaborate lawn dart. Dropping head-downward to takeoff is actually a pretty inefficient way to go unless one happens to live on ceilings (like bats). Consider this: to successfully launch, one of the giant flyers (such as a large pterosaur or teratorn bird) would probably need around two g's of acceleration upwards (closer to three would be ideal). If they start by falling, then they are accelerating in the wrong direction at a g, not to mention that the poor critter is oriented in a very compromising way.
Launching like a falling stone is tough going - bats do it, but it's a very specialized trick. So, please make myself and other flight folks stop wincing: don't drop your pterosaurs.
Saturday, April 7, 2012
Thursday, April 5, 2012
Water Launch: Some Nuts and Bolts
I've been asked about the nuts and bolts of my pterosaur launch models at quite a few meetings. I have a few papers that should be out later this year which include more of the computational details than prior publications (which focused on the comparative differences in maximum load potential, rather than specific performance). In the meantime, though, here are a few of the bit and pieces that go into the water launch model (similar for the terrestrial launch model):
Flapping frequency
Flapping frequency
Based on the expectations from Pennycuick (2008) flapping frequency varies roughly as body mass to the 3/8 power, gravitational acceleration to the ½ power, span to the -23/24 power, wing area to the -1/3 power, and fluid density to the -3/8 power:
f = m3/8g1/2b-23/24S-1/3p -3/8
The result is the expected flapping frequency in hertz; taking the inverse gives the expected flapping time in seconds. This provides a framework for estimating wing motion speed. The wings would have begun launch folded, in the water. As a result, the model begins using the density of saltwater and the folded span and area. I then transition the model through a time-step series in which most of the animal is raised above the water (air drag), but the wing finger pivot and feet still experience subaqueous drag.
Minimum Launch Speed
There are a couple of possibilities for the speed at the end of the launch cycle. The first model forces the launch to provide horizontal speed equivalent to the stall speed (Vmin=2*WL*(1/(1.23*CLMax))0.5) thereby propelling the modeled pterosaur to steady state from the launch alone. The second approach allowed a flapping burst once airborne, and allows the pterosaur in question to accelerate to steady state within its anaerobic window. These estimates can be checked against expectations of Strouhal Number limitations (see Reconstructing the Past post from yesterday). Burst flapping after launch should produce a relatively high Strouhal number (for the size regime of the animal in question), but is still constrained. As a rough rule of thumb, a Str up to 200% of the optimal cruising value is pretty realistic (higher freq, higher amplitude, lower speed). Launch acceleration is calculated as the simple average over the course of the launch cycle. The launch time can then be varied from the starting values to obtain a range of possible launch accelerations, and therefore a range of potential power requirements.
Power estimates are used with ballistic motion model to determine the initial acceleration, velocity, and height during launch. My model species for water launch has been Anhanguera santanae. The contact areas were estimated by mapping muscles onto a laser surface scan of AMNH 22555, which is a particularly nice uncrushed specimen.
Anhanguera input parameters
Flight muscle fraction: 20-26%
Hindlimb muscle fraction: 10-12%
Wingspan: 4.01m
Anaerobic Power: 300-400 W/kg
Taking the above input parameters, taking a conservative estimate of muscle power from living archosaurs, using the motion speed from part 1, and then adding in the reconstructed contact value and an estimate of flat plate drag coefficient for propulsive force efficiency (not actually that difficult as flat plate coefficients are measured for a wide variety of shapes) yields an estimate of potential acceleration.
In my next post, I will briefly discuss what sort of results this yields for Anhanguera.
Wednesday, April 4, 2012
Distance Champs
For those that haven't seen it, there is a press release for the description of Guidraco here. This is yet another example of a large pterosaur whose closest known relative was half a world away (other examples include the anhanguerids/ornithocheirids of Brazil and Europe, giant azhdarchids of Europe and North America, etc). This is rather exciting for me, personally, as I have been suggesting for the last couple of years that large pterosaurs might have had cross-continental travel abilities. I even got to babble about it on NPR: you can check it out here.
Pterosaur Acrobatics
I received a fun message from David Hone of Archosaur Musings fame yesterday. Here's the relevant bit:
"A biology teacher in Ireland tweeted me to ask if I thought a pterosaur could pull off a loop-the-loop or victory roll or similar. My guess was 'probably' especially something like and ornithocherid, but I thought you'd love it as a thought problem..." -- David Hone
It's a fun idea to ponder. The precise maneuvers available to fossil animals are can be difficult to work out with much confidence, but there are a few things that can be said with confidence:
- The most maneuverable pterosaurs were probably anurognathids, and they could certainly pull off a loop-the-loop or just about anything else you could want from a flying animal. In fact, anurognathids were probably among the most agile flying animals of all time, right up there with living vesper bats, swifts, and the like. I talked a bit about their abilities at Pterosaur.net here. Mark Witton dealt with them more while debunking the vampire anurognathid concept here.
- For larger pterosaurs, things get a bit trickier, but the inertial problems would still be pretty minor. The real question becomes whether the animals could handle multiple extra body weights of force on the wings. Based on work I've done on pterosaur wing strength, as well as work by Colin Palmer, it seems that at least pterosaurs as large as Anhanguera (4-5 meter wingspan) could have handled major rolls or loops. I have yet to check the numbers for something bigger, like Quetzalcoatlus northropi, but I might have to give it a shot. I may post a more extensive conversation on it the idea at H2VP soon.
"A biology teacher in Ireland tweeted me to ask if I thought a pterosaur could pull off a loop-the-loop or victory roll or similar. My guess was 'probably' especially something like and ornithocherid, but I thought you'd love it as a thought problem..." -- David Hone
It's a fun idea to ponder. The precise maneuvers available to fossil animals are can be difficult to work out with much confidence, but there are a few things that can be said with confidence:
- The most maneuverable pterosaurs were probably anurognathids, and they could certainly pull off a loop-the-loop or just about anything else you could want from a flying animal. In fact, anurognathids were probably among the most agile flying animals of all time, right up there with living vesper bats, swifts, and the like. I talked a bit about their abilities at Pterosaur.net here. Mark Witton dealt with them more while debunking the vampire anurognathid concept here.
- For larger pterosaurs, things get a bit trickier, but the inertial problems would still be pretty minor. The real question becomes whether the animals could handle multiple extra body weights of force on the wings. Based on work I've done on pterosaur wing strength, as well as work by Colin Palmer, it seems that at least pterosaurs as large as Anhanguera (4-5 meter wingspan) could have handled major rolls or loops. I have yet to check the numbers for something bigger, like Quetzalcoatlus northropi, but I might have to give it a shot. I may post a more extensive conversation on it the idea at H2VP soon.
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