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 Theoretical Aerodynamics. Show all posts
Showing posts with label Theoretical Aerodynamics. Show all posts
Thursday, July 5, 2012
Sunday, April 29, 2012
Microraptor: Odds and Ends
The top image on the left is from Hone et al. (2010) and shows the holotype of Microraptor gui under UV light. The image below, by Mick Ellison, shows a life restoration of Microraptor, and was taken from here (note: the hindlimbs could not actually get into the position shown in the image; that was done to show off all of the airfoils at once for comparative purposes). One of the key questions regarding flight in Microraptor is whether it evolved flight independently of avialans, or if it represents a morphology that was a more direct precursor to flight in birds proper.
One thing I noticed a few years back is that it seems that Microraptor had a different set of "solutions" to the problem of aero control, as compared to living birds. I have since put some math to it, and the calculus bears out the intuition. Myself, Justin Hall, David Hone, and Luis Chiappe are writing this up now (see earlier cryptic blog post), but Justin has given a couple of talks on the hindwing use recently and some of you out there know that that I have been murmuring about the tail being used in aero control. All will be revealed in the full manuscript (WFTP moment) but I do think it is quite interesting that the aero control surfaces in Microraptor took advantage of pre-existing maniraptoran anatomy. In other words, you don't have to do much to your average dromaeosaurid to get it into the air.
This is a potentially critical observation. For one, it suggests that the origin of flight in dinosaurs may have been more simple than previously supposed. It also suggests that flight control may have had more to do with the gains and losses of aerodynamically active morphology we see near the origin of birds than simple weight support. I am sad to say that most paleontologists don't seem to have a particularly good grip on what lift actually is, how it is used, and how it is generated. Many of my colleagues also seem to struggle with how drag fits into the whole scheme. Of course, I have lots of gaps in my knowledge, too, so I can't go pointing fingers. Nonetheless, I suspect that we are going to see a major overhaul of the models for dinosaur flight evolution in the year or two.
The Ellison image is associated with a recent paper by Li et al. (2012) in Science. The authors favor display characteristics for some of the feathered morphology, particularly the tail fan. I don't discount this function at all, but it should be noted that it doesn't take much to provide a decent stabilizer or control surface for a mid-sized flying animal, and display surfaces don't have to be aerodynamically useless or costly. (Just to shore a common myth, that is not the same as saying that tail fans, crests, flaps, etc would act as rudders on flying animals. As a general rule, rudder use does not work well for a non-fixed wing flyer. Even fixed-wing aircraft do not initiate turns by using rudders; the rudder systems are for stabilization).
References
Hone DWE, Tischlinger H, Xu X, Zhang F (2010) The Extent of the Preserved Feathers on the Four-Winged Dinosaur Microraptor gui under Ultraviolet Light. PLoS ONE 5(2): e9223. doi:10.1371/journal.pone.0009223
Li Q, Gao KQ, Meng Q, Clarke JA, Shawkey MD, D'Alba L, Pei R, Ellison M, Norell MA, Vinther J. 2012. Reconstruction of Microraptor and the Evolution of Iridescent Plumage. Science 335 (6073): 1215-1219
Spiders Incoming
Vadas Gintautas and I have done some more data collection on the spider aero-control work at this point, and the results are proving to be pretty darn exciting.
To bring everyone up to speed, here's the gist. We are working on the issue of aerial righting in spiders. The way in which spiders right themselves after a fall from a ledge, branch, etc. has never been reported in the literature. It is an interesting problem, because:
1) Spiders can't twist around in the air like cats and other mammals can.
2) Spiders that pursue prey over uneven terrain, rather than using burrows or webs for capturing food, are bound to fall sometimes.
3) Most spiders are small enough that they are going to fall in an intermediate Reynolds number regime - i.e. the air will be pretty sticky for them, but they won't just be "sinking" like a tiny gnat would.
4) Spider body plans are already of interest in robotics designs for movement over land. Now imagine that the spider-bot can turn itself in the air using wake capture so that it always lands on its feet. Yup, it's awesome.
What's particularly interesting here, though, is that we are not using the spiders we would expect to be particularly good at aero control. We are using Black Hole Spiders, Kukulcania hibernalis, which hunt and move mostly over the ground. They can climb, though, so we figure they might still have some kind of aerial righting response. If they do, then it would suggest that aero control appears in even those species with limited arboreal habits. A photo of K. hibernalis is shown at left. It comes from the site of Ken the Bug Guy here, which is where we purchased our spiders.
What's cool is that we have found that our little spider stuntmen can, indeed, right themselves in the air, and they do it using a nice, simple trick: when dropped, the spiders immediately assume a leg position that makes them passively unstable in roll while inverted, but stable in roll when upright - this means that the spiders automatically flip right-side-up if they happened to be falling upside down, and then they stay that way for the rest of the trip. All the spiders have to do is hit the critical position and hold it. We are working on the algebraic solutions that demonstrate why the righting position works, but our simulation study already predicts their motion quite well (i.e. it matches our imaging studies of the real spiders).
The aerial righting response we have captured is somewhat similar to that seen in other arthropods, such as ants and stick insects. Since we have found it in a mostly terrestrial animal, it is looking ever more likely that this is a method of aerial righting that is extremely widespread in terrestrial arthropods, and that's very neat stuff for understanding arthropod evolution (which is handy because arthropods represent most of the animal species on Earth).
We are not the only group working on falling spiders. As I mentioned recently in an earlier post, Robert Dudley of Berkeley has a student working on arboreal spiders from the neotropics that, not surprisingly, are even better at aero control (I won't get into details because they have a paper pending, but it's awesome).
Vadas and I are setting up to work on some additional species of spiders, in order to take a more comparative approach. We will include some arboreal spiders that we expect will be able to actually glide. Not kidding; gliding spiders. There are all sorts of other aerial behaviors we can find in spiders, as well, that take into account the use of silk for producing drag lines and parachuting. There is an entire realm of aerial acrobatics in spiders that has been rather understudied (ballooning being the only one of the bunch to get much play in the literature). So stay tuned for spinning, dropping, gliding, righting, leaping, parachuting spiders.
To bring everyone up to speed, here's the gist. We are working on the issue of aerial righting in spiders. The way in which spiders right themselves after a fall from a ledge, branch, etc. has never been reported in the literature. It is an interesting problem, because:
1) Spiders can't twist around in the air like cats and other mammals can.
2) Spiders that pursue prey over uneven terrain, rather than using burrows or webs for capturing food, are bound to fall sometimes.
3) Most spiders are small enough that they are going to fall in an intermediate Reynolds number regime - i.e. the air will be pretty sticky for them, but they won't just be "sinking" like a tiny gnat would.
4) Spider body plans are already of interest in robotics designs for movement over land. Now imagine that the spider-bot can turn itself in the air using wake capture so that it always lands on its feet. Yup, it's awesome.
What's cool is that we have found that our little spider stuntmen can, indeed, right themselves in the air, and they do it using a nice, simple trick: when dropped, the spiders immediately assume a leg position that makes them passively unstable in roll while inverted, but stable in roll when upright - this means that the spiders automatically flip right-side-up if they happened to be falling upside down, and then they stay that way for the rest of the trip. All the spiders have to do is hit the critical position and hold it. We are working on the algebraic solutions that demonstrate why the righting position works, but our simulation study already predicts their motion quite well (i.e. it matches our imaging studies of the real spiders).
The aerial righting response we have captured is somewhat similar to that seen in other arthropods, such as ants and stick insects. Since we have found it in a mostly terrestrial animal, it is looking ever more likely that this is a method of aerial righting that is extremely widespread in terrestrial arthropods, and that's very neat stuff for understanding arthropod evolution (which is handy because arthropods represent most of the animal species on Earth).
We are not the only group working on falling spiders. As I mentioned recently in an earlier post, Robert Dudley of Berkeley has a student working on arboreal spiders from the neotropics that, not surprisingly, are even better at aero control (I won't get into details because they have a paper pending, but it's awesome).
Vadas and I are setting up to work on some additional species of spiders, in order to take a more comparative approach. We will include some arboreal spiders that we expect will be able to actually glide. Not kidding; gliding spiders. There are all sorts of other aerial behaviors we can find in spiders, as well, that take into account the use of silk for producing drag lines and parachuting. There is an entire realm of aerial acrobatics in spiders that has been rather understudied (ballooning being the only one of the bunch to get much play in the literature). So stay tuned for spinning, dropping, gliding, righting, leaping, parachuting spiders.
Wednesday, April 4, 2012
Reconstructing the past
One of the things I hope to do with Aero Evo is to give some insights into how biomechanists like myself manage to make estimates of performance for fossil animals. In particular, of course, I will focus on how we know things about extinct flying animals.
Three of the parameters of typical interest are the speed at which a flying animal flew, the rate at which it flapped its wings, and how much room it needed to flap them: velocity, flapping frequency, and flapping amplitude, respectively.
These three factors are all correlated, and can be summarized by the Strouhal Number. The Strouhal Number is equal to fA/U, where f is frequency, A is amplitude, and U is velocity. As it turns out, the range of strouhal numbers at which a flapping wing or undulating fin can operate efficiently is pretty darn narrow. For creatures as seemingly different as dolphins, birds, fish, and dragonflies, Str in cruising locomotion only varies from about 0.2-0.4. This pattern occurs because of the narrow range of motion in which vortex shedding is efficient.
The classic paper on the topic is by Taylor et al., and can be found here. That link will take you to the abstract; those on campuses should be able to get the full paper, though it is behind a paywall. Fortunately, Nudds, Taylor, and Thomas wrote a followup paper with much of the same information (specifically on birds), and it is open access here.
Now, it should be noted that the limits on Str mentioned above only apply to cruising - that is, the animal is moving steadily at its efficient, long-distance gait. Burst performance is different, and on average, the Str will be higher during things like rapid climbs (say, just after takeoff) or bursts after prey. Nonetheless, we can get a good idea of how extinct animals worked by using Str. I'll post more on how to use Str, and how to combine it with other equations to solve for multiple variables, soon.
Three of the parameters of typical interest are the speed at which a flying animal flew, the rate at which it flapped its wings, and how much room it needed to flap them: velocity, flapping frequency, and flapping amplitude, respectively.
These three factors are all correlated, and can be summarized by the Strouhal Number. The Strouhal Number is equal to fA/U, where f is frequency, A is amplitude, and U is velocity. As it turns out, the range of strouhal numbers at which a flapping wing or undulating fin can operate efficiently is pretty darn narrow. For creatures as seemingly different as dolphins, birds, fish, and dragonflies, Str in cruising locomotion only varies from about 0.2-0.4. This pattern occurs because of the narrow range of motion in which vortex shedding is efficient.
The classic paper on the topic is by Taylor et al., and can be found here. That link will take you to the abstract; those on campuses should be able to get the full paper, though it is behind a paywall. Fortunately, Nudds, Taylor, and Thomas wrote a followup paper with much of the same information (specifically on birds), and it is open access here.
Now, it should be noted that the limits on Str mentioned above only apply to cruising - that is, the animal is moving steadily at its efficient, long-distance gait. Burst performance is different, and on average, the Str will be higher during things like rapid climbs (say, just after takeoff) or bursts after prey. Nonetheless, we can get a good idea of how extinct animals worked by using Str. I'll post more on how to use Str, and how to combine it with other equations to solve for multiple variables, soon.
Do the Twist
Arguably the most adept fliers in the world are those animals who carry flight as their namesake: the dipteran insects, i.e. the flies.
Alexander Wild (whose photography you should check out if you are not already familiar) recently posted some new shots of fruit flies approach a fungal feeding patch. I am particularly fond of this shot.
Note how the plane of the wings are almost perpendicular to the direction of travel at the moment the shot was taken. The degree of wing rotation used by insects, particularly during landing and takeoff, can be quite extraordinary. Sadly, the precise effects and roles of wing rotation in animal flight are poorly understood. Some good work has been done with bees and flies, but even there we are still quite naive. According to Sharon Swartz of Brown University, next to nothing is known about the role of wing twisting in bats. The knowledge base situation is only marginally better in birds.
Those looking for a great experimental project on animal flight: think about working on wing twist. Theoreticians [which I suppose includes myself, though my work is about a 50/50 split] have some good ideas of what should happen, but we need experimentalists to play it out and get the real nuts and bolts.
Alexander Wild (whose photography you should check out if you are not already familiar) recently posted some new shots of fruit flies approach a fungal feeding patch. I am particularly fond of this shot.
Note how the plane of the wings are almost perpendicular to the direction of travel at the moment the shot was taken. The degree of wing rotation used by insects, particularly during landing and takeoff, can be quite extraordinary. Sadly, the precise effects and roles of wing rotation in animal flight are poorly understood. Some good work has been done with bees and flies, but even there we are still quite naive. According to Sharon Swartz of Brown University, next to nothing is known about the role of wing twisting in bats. The knowledge base situation is only marginally better in birds.
Those looking for a great experimental project on animal flight: think about working on wing twist. Theoreticians [which I suppose includes myself, though my work is about a 50/50 split] have some good ideas of what should happen, but we need experimentalists to play it out and get the real nuts and bolts.
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