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Re: Mega-plesiosaurs revisited (again)




> Mike Taylor wrote:
>
> > Now there are two modes of underwater flight.  In both of them, the
> > thrust is produced by lift on the flippers during the power stroke.
>
> There are actually three modes.  The third involves shedding a vortex
> off
> the leading edge, allowing it to exit the trailing edge with some
> delay so
> it can impinge on the other side of the wing (flipper), then capturing
> it
> and inverting it with very close to full-momentum reversal, repeating
> in the
> opposite direction.  It is very similar to the 'fast-start' mechanism
> that
> some fish use, and the 'fluttering' wingstroke that some birds use
> when
> landing.
>
> > Alexander ................ concludes that
> > in plesiosaurs, the down-stoke produced the power, and the up-stroke
>
> > was purely for recovery.
> >
> > Now here's the bit where I don't follow Alexander's logic:.........
> in
> > other words, the net motion of the flippers during the power stroke
> > must be backwards relative to the water.  (Unfortunately, I don't
> have
> > the book here, so I can't explain why this should be so -- can
> someone
> > else?)
>
> Based on several of the illustrations in the book (Figures 8.3, 9.6, &
> 9.7),
> Alexander appears to be ignoring both the induced angle of attack and
> the
> effect of camber on the angle of zero lift.  For example, my Cherokee
> develops cruise lift at a negative angle of attack (the wing chordline
> is
> nose down during cruise).  He is most astute, so I don't know why he
> has
> chosen to do this.  Has anyone asked him?  During the stroke, the wing
> or
> flipper has to impart an aftward momentum component to the freestream,
> but
> the flipper itself doesn't have to move aftward to accomplish this.
> For
> example, airplane propellors impart an aftward momentum component to
> the air
> they pass through while moving forward with respect to that air, and
> boat
> propellors do the same with respect to the water they pass through.
> The
> effects of camber, AOA, and spanwise twist variations can achieve that
> for
> flippers.
>
> > If the pliosaur
> > can manage a beat frequency of, say three cycles per second (which
> > sounds like _a lot_ to me),
>
> Alexander's statement as well, regarding his use of five
> beats/second.  He
> goes on to say that one beat/second seems more realistic.
>
> > then in each second, it's spending about
> > 0.5 seconds in those three
>
> This assumes the same time period is used in both the power and
> recovery
> strokes.  It isn't always true for other flying animals (the fraction
> varies
> with gait), so probably wasn't true for plesiosaurs either.  However,
> the
> ratio usually doesn't vary from 50-50 by more than about 20%.
>
> > so if it's achieved the "Alexander maximum" where the flippers are
> > exactly stationery relative to the water,
>
> At first glance, this doesn't appear to be necessary.
>
> > then the plesiosaur's body
> > equally moves forwards 1m during each of those three cycles, and
> > perhaps during the recovery stroke too (due to momentum) -- yielding
> a
> > maximum speed of 6m/s.
>
> This doesn't seem to allow for variable advance ratio.  What am I
> missing?
>
> > Secondly, are there flaws in this reasoning?
>
> Why not set up a spanwise strip model in Excel or QuattroPro and run
> the
> calcs for various beat periods and beat fractions, modifying spanwise
> twist
> during the flapping cycle?  Your results might overestimate the speed
> somewhat if you ignore viscous effects, but it should get you fairly
> close.
> Based on Alexander's assumption of 'flight muscle' fraction, I too,
> would
> expect the animal to be rather slow, but I haven't done any
> calculations to
> see what might be reasonable. The apparent ability (based only on
> Figure
> 9.5) to retain substantial mobility in a long neck would also lead one
> to
> predict a relatively slow speed, but I haven't attempted to determine
> what
> that speed might be.
>
> JimC