Extra Wings?

I was looking over the 1994 review article by John Davenport (in Reviews in Fish Biology and Fisheries) on flying fish aerodynamics, and he makes a very interesting and astute observation:

"The expanded, flat pelvic fins of four-wingers have evolved, not to increase wing area, but to function as tailplanes or stabilizers well behind the centre of gravity, with an area some 20–35% of the total lateral fin area, and an angle of incidence less than that of the cambered pectoral fins."

In other words, the big forward pectoral fins, which are the main wings, are cambered and produce the vast majority of the weight support during gliding.  The "hindwings", i.e. the pelvic fins, are control-related.  Readers should note that the pelvic fins in flying fish are also much shorter and broader in overall shape (i.e. low aspect ratio) - this makes sense for airfoils used to control but not as primary gliding support surfaces.

Those that work with me regularly know where I am going with this, as there is another group of critters with "hindwings".  More on that some other time.

Pterosaur Water Launch: Preliminary Results

Back again for more water launching goodness.  These results were presented at SVP 2011; with luck they will be finalized and appear in a formal journal (PLoS ONE) this summer.

Here's what I get for Anhanguera, using the technique from yesterday's post: 

The initial escape phase could be accomplished with a net remaining acceleration of 17.6 m/s², and an acceleration of up to 39.2 m/s² on the subsequent, unhindered propulsive bound. Sufficient contact area to provide a useable propulsion phase would require that the wing finger be opened 15-25 degrees.  This contact area was greatly augmented by the exceptionally broad MCIV-PHIV joint.  The escape phase would require exceptional shoulder adduction musculature, and I note that Anhanguera appears to have had such expanded musculature: the orientation and enlargement of m. subscapularis appears to be of particular importance, along with the reinforcement of the joint between the scapula and notarium (Bennett, 2009). My model predicts that Anhanguera would have used a series of repeated propulsions when launching from water (unlike terrestrial launch), which would have occurred as a series of “hops” across the water surface.   

This repeated propulsion is required because the animal loses energy to the initial escape from surface tension, and because no lock and release is available on the wing finger joint during water launch, which somewhat reduces power output.  The quadrupedal water launch still greatly outperforms any kind of bipedal launch, however.  In fact, bipedal launch from the water was almost certainly impossible for pterosaurs of practically any size (bipedal terrestrial launch was likely impossible, as well for most species - not to mention inferior in performance in just about every way).  This is particularly true given the recent work on floating position done by Dave Hone and Don Henderson.

One important note is that this water launch model makes predictions about morphological features one should expect to find in pterosaurs adapted to water launching.  In this way, it makes testable predictions from the theoretical model.  This is important, as we will presumably never get water launch trackways.  

Based on this water launch model, we can expect that the following features should be better represented in marine taxa than terrestrial taxa:

expanded scapula 

reinforced scapular-notarial joint

expanded deltopectoral crest 

Warped deltopectoral crest or expanded tip of dp crest

extra-broad MCIV-PHIV wing finger joint

limb length disparity 

expanded posterior brachial musculature

So far, this pattern appears to hold.  While azhdarchids do have expanded dp crests, and somewhat expanded triceps they lack most of the other features in the list (at least comparatively speaking).  So far, only marine pterosaurs exemplify all of the above simultaneously.

Water Launch: Some Nuts and Bolts

I've been asked about the nuts and bolts of my pterosaur launch models at quite a few meetings.  I have a few papers that should be out later this year which include more of the computational details than prior publications (which focused on the comparative differences in maximum load potential, rather than specific performance).  In the meantime, though, here are a few of the bit and pieces that go into the water launch model (similar for the terrestrial launch model):

Flapping frequency

Based on the expectations from Pennycuick (2008) flapping frequency varies roughly as body mass to the 3/8 power, gravitational acceleration to the ½ power, span to the -23/24 power, wing area to the -1/3 power, and fluid density to the -3/8 power:

f = m^3/8g^1/2b^-23/24S^-1/3p -3/8

The result is the expected flapping frequency in hertz; taking the inverse gives the expected flapping time in seconds.  This provides a framework for estimating wing motion speed.  The wings would have begun launch folded, in the water.  As a result, the model begins using the density of saltwater and the folded span and area.  I then transition the model through a time-step series in which most of the animal is raised above the water (air drag), but the wing finger pivot and feet still experience subaqueous drag. 

Minimum Launch Speed

There are a couple of possibilities for the speed at the end of the launch cycle.  The first model forces the launch to provide horizontal speed equivalent to the stall speed (V_min=2*WL*(1/(1.23*C_LMax))^0.5) thereby propelling the modeled pterosaur to steady state from the launch alone.  The second approach allowed a flapping burst once airborne, and allows the pterosaur in question to accelerate to steady state within its anaerobic window. These estimates can be checked against expectations of Strouhal Number limitations (see Reconstructing the Past post from yesterday).  Burst flapping after launch should produce a relatively high Strouhal number (for the size regime of the animal in question), but is still constrained.  As a rough rule of thumb, a Str up to 200% of the optimal cruising value is pretty realistic (higher freq, higher amplitude, lower speed). Launch acceleration is calculated as the simple average over the course of the launch cycle.  The launch time can then be varied from the starting values to obtain a range of possible launch accelerations, and therefore a range of potential power requirements. 

Power estimates are used with ballistic motion model to determine the initial acceleration, velocity, and height during launch.  My model species for water launch has been Anhanguera santanae. The contact areas were estimated by mapping muscles onto a laser surface scan of AMNH 22555, which is a particularly nice uncrushed specimen.

Anhanguera input parameters

Flight muscle fraction: 20-26%

Hindlimb muscle fraction: 10-12%

Wingspan: 4.01m

Anaerobic Power: 300-400 W/kg

Taking the above input parameters, taking a conservative estimate of muscle power from living archosaurs, using the motion speed from part 1, and then adding in the reconstructed contact value and an estimate of flat plate drag coefficient for propulsive force efficiency (not actually that difficult as flat plate coefficients are measured for a wide variety of shapes) yields an estimate of potential acceleration.  

In my next post, I will briefly discuss what sort of results this yields for Anhanguera.

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.