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

Wait, penguins can fly!?

In short, no, penguins cannot fly in the traditional sense.  But they can aquafly, which is today's topic.

There are relatively small numbers of flying animals that can also swim with the wings - most of these are birds, though some insects can perform this trick, as well.  When the wings are used for lift-based motion through the water this is termed "aquaflight".  Most aquaflying birds do also fly in the aerial sense, but penguins have abandoned aerial locomotion and use the wings exclusively for aquatic locomotion.  This evolutionary transition is among the most interesting functional morphology problems in ornithology.  Understanding how penguin morphology has changed over time in response to their aquaflying habits not only sheds light on aquatic locomotion, but it also gives us information regarding the constraints of aerial locomotion (which is primarily why I figured it was worth a discussion on Aero Evo).

The image at left is a reconstruction (by Chris Gaskin) of Kairuku, as described by Daniel Ksepka and colleagues.  The full paper is available here for free.  Kairuku hails from the Oligocene.  Penguins have quite a good fossil record, and we know from the record that early penguins were often quite large (Kairuku stood nearly five feet tall).  All of the known fossil penguins are also from clearly flightless animals - even early penguins like  Kairuku, or the even earlier Waimanu, possessed wings clearly dedicated to swimming at the expense of aerial locomotion.  However, we can deduce from phylogeny that penguin ancestors were flying animals, probably  amphibious flyers (those animals that use the wings to both fly and swim).  As mentioned above, there are some modern examples of amphibious flyers, and we can use them in functional comparisons with penguins (both living and fossil) to gain a better understanding of what mechanical changes have occurred in penguins.

It might be expected that using the wings underwater would dominate the physical forces acting on the wings of amphibious flyers.  If this were true, then the wing geometry and bending resistance of the wing bones in amphibious flyers (like puffins) should be quite similar to that of penguins.  However, this turns out not to be the case.  In 2010 I published a paper showing that the wings of penguins are tremendously "overbuilt", with regards to their bending strength, when compared to other birds - including other living birds that swim with their wings.  One of the figures from that paper is shown at left.  You will note that the residuals in humeral strength are much greater for penguins (Sphenisciformes) than for any other birds in the sample.  Puffins and auks, which all aquafly as well, are in the Alcidae.  The Procellariiformes include a sample of aquaflyers, as well.  As such, penguins are unique, even among aquaflyers.

In fact, this trend is not even limited to comparisons with aquaflying birds that still engage in aerial locomotion (i.e. those that "fly" proper).  Last November I published a paper with Gareth Dyke and Xia Wang (available from PLoS ONE here) that described new material of plotopterids and compared the functional characteristics of plotopterid structure to penguin morphology.  Plotopterids were flightless, aquaflying birds of the middle Cenozoic that were similar to penguins in many anatomical respects and which also reached large sizes (particularly in the Miocene).  Some of the material we described in that manuscript is pictured at left.

As it turns out, the wings of plotopterids appear to be more similar (in terms of geometric variables known to correlate with mechanical properties) to living auks than to living penguins.  This implies that the swimming stroke of plotopterids was more like that of auks than penguins, even though plotopterids were flightless.

There are more groups that need comparing in this way to generate a firm conclusion (Mancalline auks and Great auks, for example), but the emerging pattern is that the mechanics and evolutionary history of penguins is quite unique.  Their morphology, it seems, is not just about having lost flight - it is presumably the specific trajectory by which they left the aerial realm, as well their specific  phylogenetic history, that has placed penguins in a unique morphological space.  In the 2010 Biological Journal paper I suggested that at least one major factor of importance may be the mirrored aquaflying stroke of penguins - unlike other aquaflying birds, living penguins produce nearly the same magnitude of lift with the wings on the upstroke and downstroke (albeit with opposite signs, of course).  This mode of swimming greatly increases efficiency by reducing surge accelerations.  Where this feature entered penguin evolutionary history has not yet been examined, but may be a fruitful topic of future research.

P.S. If you love penguins then you need to check out the definitive fossil penguin blog by Daniel Ksepka: http://fossilpenguins.wordpress.com/


References
Ksepka, DT, Fordyce RE, Ando T, and Jones CM. 2012. New fossil penguins (Aves, Sphenisciformes) from the Oligocene of New Zealand reveal the skeletal plan of stem penguins. Journal of Vertebrate Paleontology 32: 235-254

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

Dyke GJ, Wang X, Habib M. 2011. Fossil plotopterid seabirds from the Eo-Oligocene of the Olympic Peninsula (Washington State: USA): descriptions and functional morphology. PLoS ONE 6(10): e25672. doi:10.1371/journal.pone.0025672

Swimming Eagle

This video has been making the rounds, so many of you have probably seen it: Swimming Eagle of Baton Rouge.

What I find particularly rewarding about this little clip is that the quantitative model I built over the last year to estimate water launch in  pterosaurs also predicts that eagles (and some other birds) should be able to do this, as unusual it is.  Always validating to see expectations met.

I will post more about water launch in pterosaurs later, but the basic gist is this: the folded wing pivot of a bird (wrist) or pterosaur (base of fourth finger) can produce quite a bit of flat plate drag in the water, if the wing is still mostly folded.  Combined with the powerful flight muscles, this provides a mechanism for generating substantial forces in the water without compromising flight anatomy.