Here There be Dragons

As my previous teaser post suggested, I am going to spend some time on dragons over the next week.  This is mostly because dragons are fun, but also because the shapes of things humans have imagined to fly highlight some myths about animal motion and anatomy. To start off with, though, I would like to look at some real dragons.

Draco volans: Flying Dragon
There are actually 20-30 species in the genus Draco (depending on your preferred taxonomy).  Most members of the group have elongate ribs that they can extend, forming airfoils that allow gliding to varying degrees.  The most famous of the group is Draco volans.  This small lizard can extend gliding surfaces on both the trunk and the neck, and while the aspect ratio of the wings is pretty low (so the glide angle isn't great), these animals can manage glides of tens of meters or more.

The wings, when extended, have an elliptical shape, and while this is not the only way to get an elliptical lift distribution (which is typically desirable) it is one way this can happen.  The relatively short span also keeps the inertia low during turns; anecdotal accounts indicate that Draco are actually quite maneuverable. 

The photograph at left  (taken from here) gives an idea of the scale of the lizards and the structure of the wing. Note that the ribs seem to be relatively compliant; part of each spar is actually cartilage. We might suppose the the planform in Draco is just the result of constraint - in other words, we might suspect that there just aren't many shapes that are viable for a lizard (or other lepidosaur) using ribs to make wings. 

However, the fossil record shows that other wing shapes are viable.  Icarosaurus is pictured at left (image by Julius Csotonyi; note the obvious copyright notice and watermark - respect the copyright, please.  You can find it on his website here).  Icarosaurus hails from the Triassic.  Note that the wings have a high aspect ratio shape and that the overall span is relatively much greater than in Draco.  Interestingly, Icarosaurus was also a substantially larger animal than the largest Draco.  As a result, even with a greater relative span, Icarosaurus sported a higher wing loading.  With the greater AR, it would have had a smaller glide angle (gone further for a given amount of lost height), and with the greater wing loading, Icarosaurus would have glided faster than Draco.  Both of these likely came at the expense of lower maneuverability.  The shape of the spars (i.e. the ribs) supporting the wings in Icarosaurus curved posteriorly near the tips, particularly the ribs the near the mid-section of the wing.  This gave a broad, backswept tip shape to the wing of Icarosaurus.  To the best of my knowledge, the specific aerodynamics of this tip shape have not be investigated in the literature for Icarosaurus.

If you are interested in reading more about Draco gliding, and the evolution of gliding in other, similar, fossil forms, then I recommend reading this paper by McGuire and Dudley.  Sadly, a subscription is required.


Chrysopelea: Gliding Tree Snakes
Yup, that's right, gliding snakes.  They may not have the dragon namesake, but many of the historical reconstructions of dragons show flying, serpentine animals (see text from my most recent blog post before this one).  The closest thing to such an animal among real species are the snakes of the genus Chrysopelea.  Jake Socha and his group have done most of the leg work on understanding gliding in these animals.  You can check out his lab page here.  I have already blogged about these critters here, so I won't go into it at length, but there image below (by Tim Laman, from here - again, respect the copyright please) gives a great shot of how these snakes flatten their bodies during gliding. 

 Vortices are spun off either side of the body in these snakes during glides, and this produces a decent lift profile that allows glides averaging 10 meters of horizontal distance (Socha et al., 2005: available here).  This is particularly impressive because the snakes must use a rather unusual launch method (hanging and dropping from the tail) to take off; all other gliders are able to leap to begin flight, and that helps a great deal.


Next time: a look at some pterosaurs, then we begin building a fantasy dragon and consider the limits of size in vertebrate flyers.

Dragons

I have a soft spot for old texts, and Google Books, BHL, and others are a real boon in that they make some older texts available for web browsing. I particularly enjoy old bestiaries and natural history books, and I was pointed to this little gem earlier today: http://biodiversitylibrary.org/page/38946323#page/105/mode/1up

I am not sure how the aerodynamics would work out on those creatures, but I might have to give it a whirl just for fun.

Stay tuned for a post on real aerial dragons.

Why Turkeys are Like Rockets

The photograph at left was taken by David Hone at the Pittsburgh Zoo.  They are actually quite common as wild individuals in that surrounding area, so it's a bit amusing that the shot ended up coming from the zoo. In any case, I give you this turkey to highlight two brief myths.  

Myth 1: Galliform birds (chickens and relatives) are "poor" flyers.  

This shows up in the literature consistently, especially in paleontological studies seeking to create nice categories among living flyers to compare their plots of fossil attributes to.  Now, I agree that domestic chickens are pretty poor at flying by most estimates, but their derived from a group that is, on the whole, not so much "bad" at flying as quite specialized.  Galliform birds are, on the whole, adapted for burst launching - that is, they spend most of their time on the ground, and when startled, can take off with very high accelerations at a steep angle.  This requires large muscles (including a large pectoralis minor; Galliformes includes species with some of the largest relative pec. minor fractions among birds) and stiff forelimb elements.  In short, because takeoff is energetically and mechanically rigorous, being particularly good at takeoff means being "overbuilt" compared to more typical flyers.  So even though galliform birds, such as turkeys, cannot stay in the air very long (their fast twitch flight muscles get tired quickly) they have more extreme flight adaptations than many other birds.  Note that these avian fast twitch muscles generate huge amounts of power: about 390 W/kg (compared with roughly 175 W/kg or less for aerobic muscle in birds).

Myth 2: Big birds have to run to take off.

This one comes up pretty often in general texts (see Vogel, 2003) and paleontological discussions of flight performance in fossil taxa.  The turkeys apparently didn't get the memo, though, as they are among the heaviest living flying birds and (as discussed above) are not only able to launch without a run, but are actually burst launchers, so they are taking off at a steeper angle than many smaller birds.

As it turns out (and I'll write more on this some other time) running launch in birds has very little association with size, assuming you correct for habitat differences.  You see, water birds are, on average, a bit bigger than land birds, and water birds often run to take off - but that's because of the dynamics of water launching, not size.

Aquaflyers Again: Skates and Rays

Previously I wrote a bit about the wonders of aquaflying in penguins.  This time, I thought it would be fun to write briefly on some of the interesting details of aquaflying in skates and rays.

Not all rays are aquaflyers in the sense I am using here.  Many rays propel themselves by moving a series of waves down either pectoral complex like this.  I'd like to talk more about that in the future, but for now, I am talking about those rays that propel themselves by flapping underwater flight - that is, reciprocating the entire pectoral complex on either side of the body as wings, like this.

Aquaflying rays, such as cownose rays, often move in large groups (see photograph above by Chris Hobaugh.  She retains all copyright; do not use without permission).  There are some quite interesting potential dynamics there in terms of motion in neighbor wakes and combined tip vortex effects, but so far as I am aware there are no data on those aspects for rays, so there isn't much that can be said on it for now (though there might be something on it down the road, hint hint).

One thing that is known, however, is that aquaflying rays move with almost absurdly large advance ratios.  Ridiculous, even.  To understand what this means, we need to examine the idea of advance ratios.

For an airplane with a propeller, advance ratio is simple: it is the ratio of the forward speed over the product of the revolution rate of the propeller and the diameter of the circle made by the propeller blades.  So, we have:

Advance Ratio = v/(f * d)

Where v is forward speed, f is the rate of propeller spin, and d is the diameter of the swept disc.

For a flapping animal, we have to take into account the reciprocating wings/fins, and this can be done using amplitude as an added variable (see Ellington, 1984; Vogel, 2003).  So, this gives us:

Advance Ratio = v/(2*r*f*l)

Where v is forward speed, r is the amplitude of the stroke (in radians), f is the flapping frequency, and l is the wing length.  To get a number you can compare to an airplane or other machine using a propeller, multiple by π.

Now, flapping swimmers often do quite well.  Penguins, for example, manage advance ratios around 0.5, which is quite good for motion in water (Hui, 1988).  However, cownose rays exceed an advance ratio of 2 (Heine, 1992).  This is an extraordinary amount of forward motion for each wing cycle.  The trick is that they use their entire bodies as aquafoils, and therefore get lift (mostly as thrust) not just from motion of the "wings", but also from motion of their bodies.

Now, one thing that's interesting about this in rays is that, theoretically, they should be able to get a highly mirrored stroke.  I mentioned the issue of mirrored strokes in the penguin post, and if you want a more technical discussion check out Habib (2010).  The upshot is that if both the upstroke and downstroke produce similar amounts of thrust, then the animal will proceed at a relatively constant speed, rather than lunging forward on each downstroke.  That "lunging" is called a surge acceleration.  The orthogonal motion (up and down for an aquaflyer) is called a heave acceleration.

Aquaflying animals can waste a lot of energy in surge accelerations if they don't have equal phases to their swimming strokes (example: puffins).  Rays probably have very small surge accelerations, because their stroke cycle is close to a true sine wave and their bodies (which are the aquafoil) are relatively symmetrical in the dorsal and ventral aspects. However, to my knowledge this has not been examined in detail despite the fact that accelerometer data do exist for rays.  If this prediction is accurate, however, rays are getting the best of two worlds of aquatic efficiency: high advance ratios from using the entire body for thrust, and low surge accelerations through stroke mirroring.  Presumably this comes at the cost of some additional heave acceleration, but it's still an awfully good bargin, and some of the rays can get a good head of speed going, too.  So much so, that they can do things like leap multiple body lengths out of the water.  See photo at left (taken from here).  More photos of leaping mobula rays by Barcroft here.













References

Ellington CP. 1984. The aerodynamics of hovering insect flight. Philosophical Transacations of the Royal Society of London, Series B. 305: 1-181

Habib M. 2010. The structural mechanics and evolution of aquaflying birds. Biological Journal of the Linnean Society. 99(4): 687-698

Heine C. 1992. Mechanics of flapping fin locomotion in the cownose ray, Rhinoptera bonasus (Elasmobranchii: Myliobatidae). Ph.D. dissertation, Duke University, Durham NC

Hui  CA. 1988. Penguin swimming. I. Hydrodynamics. Physiological and Zoology. 61: 333-343

Vogel S. 2003. Comparative Biomechanics. Princeton University Press. 580 pp

Guest Post: Thin vs Thick Wings

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.

------------------------
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.