# Re: Fw: avian flight

```David Marjanovic wrote:

> > <<Remember the tail of *Archaeopteryx* that prevented it from gliding? >>
> > Mr Cunningham answer to this...
>
> In his answer (thanks for the explanation of glide ratio) HP James R.
> Cunningham writes:
>
> > However, it will arrive at the
> > touchdown point in only 70.7% of the time it took at the lighter weight.

This applies only to the effect of a doubling of weight on airspeed and sink
rate when gliding.  Note that it has no effect whatever on gliding range.

> That's it.

That's it, in what way?  Based on the description of Ebel's work below, my
comment wasn't at all what Ebel addressed mathematically.  He seems to have been
talking mostly about parachuting which is not at all the same thing as gliding.
As sort of an overgeneralization -- for the most part, parachuters don't glide,
and gliders don't parachute.

> Ebel has addressed this mathematically. First he refutes the
> possibility that *Archaeopteryx* could have parachuted:

I tend to agree -- Archaeopteryx doesn't appear likely to have been a
parachuter.

> When assuming
> present air density (small changes there would hardly alter the outcome),

Those changes can alter the outcome.  For a given flight speed, lift is directly
proportional to air density.  If Archie flew in an atmosphere that was 10% more
dense than now (I'm not saying it was), then his flight speed would have been
reduced correspondingly.

> a weight of 250 g and a wing area of 479 cm² (too low),

Yalden's estimate doesn't appear to be any less likely than Rietchel's estimate
of 754 cm^2.  Yalden's estimate leads to a more efficient wing,  but that's not
grounds for a decision in favor of either.

> Archie's speed of descent was 9. m/s,
> "corresponding to a free fall from a height of 4.2 m, would hardly be
> acceptable to a bird with delicate bones";

??? Steady-state, the Yalden wing would probably be most efficient at a lift
coefficient on the loose order of about 0.9.  If the tail were acting as a low
aspect ratio wing lifting about 15% of the gross weight (part of the weight of
the tail and legs, to create a net 'tail' download) then the tail would have
been operating at a CL of about 0.54, and the overall L/D would have been about
3:1.  Sink rate would have been about 2.95 m/s, which is the free fall velocity
from a height of 0.444 meters (1.46 feet). This is a far cry from a fatal sink
rate or a fatal fall distance. I've seen squirrels fall (not leap) kerflop out
of a tree from a height of maybe 10 meters and run off with only a startled

> more recent estimates of wing
> area (754 cm²) still give 7.283570407 m/s. This is still very much.

Rietchel's wing leads to cruise sink rate of about 2.35 m/s, the equivilent of a
freefall drop from a height of 0.28 meters (11 inches).  Again, hardly enough to
be fatal, though I don't agree with this line of reasoning, since it doesn't
appear to address the actual physics of the situation.

> (754 cm² is probably too high, as it assumes a full set of tertials instead of
> a gap
> between the wings and the body,

It may be too high, but aerodynamic convention takes the extended wing area all
the way to the midline of the body anyway.

> but on the other hand it does not take into
> account tail area; these two effects more or less cancel each other out.)

No -- they don't.

> Then he addresses gliding. Unfortunately, he does not give the formula here
> (it can probably be derived from the figure, but I can't do that);

There isn't a single formula for this so it is unlikely that it can be derived
from the figure (which I haven't seen). If you go for a non-cascaded tail, you
have to balance the wings acting at a relatively high aspect ratio with an
assumption of tail load and compute the effect of the tail on both lift and
drag, then compute the effect of both the wings and tail (plus body drag) on L/D
and sink rate.  The procedure is similar for a cascaded tail, but the net L/D
winds up being better by a factor of about two with the cascade, and the sink
rate is much lower.  So far, no one appears to have satisfactorily addressed the
question of whether the tail is cascaded or not.  I'm not saying that it was,
but someone should look at the possibility.  This is something that was touched
on briefly at one of the discussion sessions at the Ostrom Symposium.   Mary
Kirkaldy, you may remember this discussion and response better than I do.  The
details are gone from my mind.

> however, he writes:
> ................................ The speed
> of *Archaeopteryx* during gliding would be approximately v = 12.9 m/s, with
> an estimated lift coefficient of cL [index L] = 0.5, which is surely not
> toosmall [I can't decide this].

Based on the aspect ratio, I'd expect the wing to be more efficient at a CL of
roughly about 0.8-0.9, though this wouldn't lead directly to the optimum point
on the drag polar because of the effect of the low aspect ratio tail.  If the
animal with the Rietchel wing is flying at a CL of 0.9, then the low aspect
version of the tail would be flying at about 0.85 (unlikely), and the airspeed
would be about 7.07 m/s. A CL of 0.5 seems awfully fast.

> This corresponds to a free fall from a height
> of 8.5 m and would probably lead to an injury [rather, death]

Again, this isn't a description of the actual physical situation, but if it
were, the freefall height would be closer to 11 inches (0.28 meters).  My plane
touches down at an airspeed of about 90 feet/second and a sink rate of about 2
feet/second, and I don't recall it being particularly uncomfortable.

> if the speed
> could not be reduced prior to touch-down. However, the available mechanisms
> for speed reduction are restricted, since the maximum lift coefficient
> during landing could hardly be greater [what an understatement] than the
> maximum drag coefficient of cD-max = 1,4 of a cup-shaped parachute.

during landing, they achieve an effective CL of about 3.0.  A frigate bird can
do about 1.63 steady-state.  I don't remember what the frigate bird can manage
when flapping, but wouldn't be much surprised at something around 2 or more.

> To be
> able to achieve a lift coefficient of cL-max = 1,4 an airfoil section must
> be perfectly developed.

Not true.  See above.  By comparison, a Selig s1223 airfoil can do 2.1 or 2.2
steady-state, and a flat plank can manage 0.9.

> This cannot be expected at the beginning of the
> [sic] bird flight evolution.

No one knows how much camber the Archaeopteryx wing had, so determination of the
steady-state CLmax is a bit iffy, but the steady-state CLmax would likely have
been on the loose order of 1.5, similar to that of a pigeon.

> To be able to fly up a landing site in
> a curve so that the speed is completely reduced at arrival, as Recent birds
> can do, requires completely developed flight abilities.

Does this mean that flying squirrels have completely developed flight
abilities?  I must admit though that in the case of birds, I am predjudiced
towards flapping before gliding.  I also suspect Archie is too highly derived to
address the question of flight origins in birds.

> ..............................
> > <<Prey in
> > the mouth would have pulled the center of gravity forward and thus made
> > flight easier. >>
> >
> > has someone tried to quantify this "easier"?
>
> No, not even Ebel. Good idea.

Actually, a number of people have quantified this, though 'easier' may not be
the appropriate term for the effect on flight.  Within limits, moving the cg
forward of the center of lift increases the load that the craft has to carry
(because the  tail must carry a download to combat the nose-down pitching moment
weight) and it tends to increase the pitch stability.  Minimum load occurs when
the cg is slightly aft of the center of lift, but it makes flight rather
squirrelly in pitch. However, the 'prey in mouth' issue isn't really an issue
for birds, bats, and pterosaurs, because for the most part, they simply sweep
their wings fore or aft to put the center of lift where they want it to be with
respect to the cg.

There are several other mechanisms for developing high lift coefficients and
high drag for landing that we haven't addressed here, and they are probably more
important than the ones we have addressed.

All the best, and my apologies for the long response.

Jim

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