I have received quite a few questions over the last year or two about wing clearance during takeoff in pterosaurs. This seems to be a sticking point for some, as evidenced by the problem rearing it's ugly head again with the recent Chatterjee et al. GSA conference spectacular (see earlier posts below). It would seem prudent to lay out some of the issues surrounding this problem - or, more specifically, to explain why this isn't really such a huge problem after all.
Because of the way that flying animals scale, larger, long-winged species with greater flight speeds flap with lower amplitudes than smaller species (on average, that is). Interestingly enough, this means that the amount of clearance required by large flyers is comparatively small, so long as they can get up a good bit of speed on takeoff. To examine this issue more closely and quantitatively for giant pterosaurs, we can look at something call the Strouhal number.
Strouhal Number is a dimensionless parameter that describes the "gait" of a flapping flyer (or really, anything that is oscillating its propulsion system in a fluid). As it turns out, because of vortex shedding efficiency constraints, animals are remarkably constrained with regards to their Str during cruising flight: it only varies from about 0.2 to 0.4 including everything from insects to large birds. There is a great explanation of this number, and its application to flying animals, here (I've shared that link elsewhere to good effect).
Str for a flapping flyer can be calculated as the ratio of flapping amplitude to the product of frequency and velocity. The largest pterosaurs probably flapped at a rate just over 1 hertz in cruising flight, and likely had minimum steady state speeds near 12 m/s and a cruising speed a good bit greater, say around 20 m/s or more.
Now, during launch, the animal probably only gets up near steady state stall speed (incidentally, it doesn't have to, contrary to what you often read in basic biology textbooks), and the Str can rise above the 0.4 mark that we might expect during cruising. Let's let the Str rise to 0.50 and constrain the launch velocity to the min steady state stall speed above. That still gives us an amplitude for the very tip of the wing in Quetzalcoatlus of 5.6 meters. Of that total arc, about 40% of it is upstroke, so that leaves a required glenoid height at the end of the launch phase of 3.4 meters or so. Given that Quetzalcoatlus had a glenoid height of about 2.5 meters while standing, it turns out that very little leaping is required at all for sufficient clearance (less than 1 meter). The animal still needs to jump, but nothing extraordinary is required.
Showing posts with label Aerodynamics. Show all posts
Showing posts with label Aerodynamics. Show all posts
Saturday, December 1, 2012
Wednesday, June 13, 2012
Cross-Post: 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. This was also posted on Aero Evo.
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.
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.
Monday, March 19, 2012
Does Air Density Make a Difference?
This is essentially a cross-post from H2VP (with some additions)
One thing I have been asked with some regularity is whether or not a somewhat denser Mesozoic atmosphere, particularly in the Cretaceous (compared to the modern one), could explain the giant size of Late Cretaceous pterosaurs or large dinosaurs. In short, the answer is: probably not.
There is a reasonably good body of information regarding atmospheric composition during the Mesozoic. During the Cretaceous, both oxygen and carbon dioxide levels rose slightly, and the total atmospheric density would have been slightly greater as a result - but the difference would have been relatively mild for large vertebrates.
Here is an example of a paper published on the effects of Cretaceous oxygen concentrations on plants: http://jxb.oxfordjournals.org/content/52/357/801.full, and there is a manuscript examining the effect of paleoatmosphere conditions on insects: http://jeb.biologists.org/content/201/8/1043.full.pdf. There is a relatively recent paper on the Late Cretaceous atmosphere and its potential relationship to mass extinction as well: http://jxb.oxfordjournals.org/content/52/357/801.full
As you can see, plants and insects probably felt the effects of slightly higher oxygen and carbon dioxide concentrations, and indeed the insects of the Cretaceous included some relatively large species, as would be expected. A slight increase in atmospheric density would have relatively little impact on the maximum size of dinosaurs or pterosaurs, however, and there is not actually any need for an extreme explanation for their size, anyway - despite being larger than living animals with similar lifestyles, none of the giant dinosaurs exceeded the expected maximum size for a walking animal, and no pterosaurs exceeded the limits for biological flight. Quite a few pterosaurs exceeded the estimated limit for continuous flapping flight in a vertebrate animal (limit is roughly 25-30 kg, give or take), but that only means that they could not flap continuously over long distances and would have switched to soaring flight for long trips; it does not forbid them from flying.
There are three reasons why changes in atmospheric conditions have greater impacts on insects than vertebrate flyers. First, the tracheal system that insects use for respiration is highly sensitive to oxygen partial pressure. Second, since insects are typically small, they are often highly reliant on unsteady aerodynamics, which are much more sensitive to air density than steady dynamics. Finally, insects are almost purely aerobic flyers, while many vertebrates can utilize some degree of anaerobic power (in large flying vertebrates, anaerobic power dominates). Using anaerobic flight muscle provides a very large burst of power, without using oxygen, after which the muscle quickly fatigues. Large vertebrates can therefore flap for short bursts, followed by periods of gliding, even when oxygen levels are low. This option is typically unavailable to insects.
There are three reasons why changes in atmospheric conditions have greater impacts on insects than vertebrate flyers. First, the tracheal system that insects use for respiration is highly sensitive to oxygen partial pressure. Second, since insects are typically small, they are often highly reliant on unsteady aerodynamics, which are much more sensitive to air density than steady dynamics. Finally, insects are almost purely aerobic flyers, while many vertebrates can utilize some degree of anaerobic power (in large flying vertebrates, anaerobic power dominates). Using anaerobic flight muscle provides a very large burst of power, without using oxygen, after which the muscle quickly fatigues. Large vertebrates can therefore flap for short bursts, followed by periods of gliding, even when oxygen levels are low. This option is typically unavailable to insects.
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