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Re: pteros have lift-off
Sounds like you've done your homework! Just a question or two buried
in the text:
On Jan 14, 2009, at 11:11 PM, jrc wrote:
Been away from the computer -- just got back. Re concern about
wingtip on downstroke after launch hitting the ground, for talking
purposes let's take a Qsp glenoid as the reference rather than cg
so that we won't have to worry about the vertical shifts in cg
relative to the glenoid during the launch and flapping strokes
(animal's cg lowers relative to glenoid during the ground based
part of the launch). Note that I'm not implying that the
velocities and coordinates calculated below are actually known to 3
decimal places...... :-)
A 20 Kg Qsp carrying a 15% tail upload in level, steady cruise
flight at a height above ground (HAG) of 5 feet will flap with a
beat period of about 0.6 seconds (frequency 1.667 Hz) doing about
31.58 miles/hour (46.3144 fps). The wingtip flapping amplitude will
be about 4.02 feet, with 1.926 feet of that being up above the
glenoid, and 2.095 feet being down below the glenoid.
If Qsp has a wingspan of 19-20 feet (is that close?) your figures
indicate an angle of 11º more or less above and below the horizon
with a total of 22º. (let me know when I'm substantially off). That's
not a lot considering that it has much more range to work with. After
all, at rest the wings are nearly parasagittal, at 80-90º, so they
can get there if they want to.
Now, at a launch to that cruise speed, if the glenoid path at the
time the manus lifts off is inclined 30 degrees above the
horizontal, then the glenoid is rising at a vertical speed of
Rising at a vertical speed of 23 fps, on that 30 degree angle means
rising at a ground speed of 43.3 fps and an airspeed (the hypotenuse)
of 48 fps or 33 mph. (am I close?) That's a pretty fast initial
launch speed, much faster, or so it would appear, than what I'm
seeing in the Albatross launch sequence. And much faster than the
first second of flight in a pelican or swan, or so it seems. I
realize that being shot out of a cannon, so to speak, in the case of
pterosaurs, is a different deal than a running start, as in birds. I
see in Desmodus " the animal accelerates to a mean take-off velocity
of 2.38±0.24ms-1." or translated: 5.32 mph or 7.81 fps. and at that
rate experiences "Peak vertical force can reach 9.5 times body weight
in approximately 30ms." So if Qsp. is accelerating at roughly 3x
Desmodus, does it reach a G factor of nearly 29x? Or am I screwing up
and the time it takes the glenoid to reach its maximum height of
8.33 feet above glenoid liftoff height on a ballistic path is 0.720
seconds -- this gives the animal enough time to perform a complete
upstroke and finish the first downstroke as the shoulder reaches
its ballistic peak.
Mike mentioned that wing unfolding at the metacarpophalalangeal joint
would be delayed somewhat as the manus lifted off the ground to a
height great enough to enable this. Even so, some lift was generated
by the innner wing. So, shouldn't this delay and less than optimal
lift be factored in at the initiation of launch?
As I mentioned above, at that point in time the glenoid has risen
to a point 8.33 feet higher than it was when the manus lifted off,
and the WINGTIP at the BOTTOM of the first downstroke is 8.33-2.10
= 6.23 feet HIGHER than the GLENOID was at the time of manus liftoff.
And therein lies the problem, because the wing at lift-off starts 80º
BELOW the bottom of your downstroke. Maximum lift does not occur
until the wings are fully deployed, so this initial launch has
trajectory that begins to fade (like all ballistics) immediately
after launch and must employ the first downstroke before reaching
that critical wingtip strike height. The question is... will it?
The major questions I would have at this point is 1) why such a small
amplitude wingstroke at take-off? 2) is the G-force at launch similar
to what you calculated? and finally 3) does this work with a
pterosaur with roughly a 3x longer wing. It would work, I suppose,
with a 22º wingstroke, but is that close to reality? Or just a fudge
factor to make sure the wingtips don't strike?
Thanks 4 the input. We'll nail this down shortly I think.
Which makes it obvious that the wingtip is never in danger of
whacking the ground during a normal launch. Most other pterosaurs
will show similar trends..
----- Original Message ----- From: "David Peters" <email@example.com
All I want now is minimum flight speed and apogee as a multiple
of the unit specified by CG height at the beginning of the leap.
Been gone all day. No reply, so far, to those queries.