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.
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.
here). More photos of leaping mobula rays by Barcroft here.
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