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Re: pteros have lift-off
David, comments inserted below.
----- Original Message -----
From: "David Peters" <email@example.com>
If Qsp has a wingspan of 19-20 feet (is that close?)
.............. No, it's more like 14.75 feet (4.5 meters) to 15.4 feet (4.7
meters) in cruise flight position.
your figures indicate an angle of 11º more or less above
....... The span at the time of maximum upward excursion is about 14.95 feet
(4.55 meters), so horizontal distance from glenoid to wingtip is about 7.05
feet and angle from glenoid to wingtip is about 15.28 degrees above the
horizon (keep in mind that the wing itself isn't anything like a straight
line between those two points.
and below the horizon
........ 6.97 feet horizontal from glenoid to tip, and angle of 16.71
degrees below the horizon.
with a total of 22º. (let me know when I'm substantially off).
........ 15.28+16.71=31.99 degrees. You're off by about 45%.
That's not a lot considering that it has much more range to work with.
all, at rest the wings are nearly parasagittal, at 80-90º, so they
can get there if they want to.
.......That's quite true, but the animal isn't working very hard at cruise
speed, particularly with the Biot-Savvart effect so substantial at these low
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 23.157 fps,
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?)
........ No. The ground speed is 40.11 fps (27.34 mph) and the airspeed is
46.31 fps (31.58 mph)
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.
........ I'm not following -- what does albatross launch have to do with
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.
....... It is quite a different deal.
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
........ You're screwing up the math. If launching all the way to cruise
speed (which isn't required), with a forelimb launch stroke length of about
5.75 feet, and a launch duration of about 0.248 seconds, it works out to
about 5.8 g's if the animal takes the glenoid all the way to cruise speed
simultaneously with the manus leaving the ground. Of course, they don't
have to accelerate all the way to that speed to launch. If they don't, it
requires less acceleration and less structural load on the arm. For this
thread, I just picked cruise speed as a convenient speed that would maximise
launch loads while also being one that we could all identify with. Didn't
want to bring maximum lift coefficients and all that into the discussion.
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.
......... Mike's right, and No, with the wing only partially deployed, the
inner wing is still slack and isn't creating really substantial lift. It
isn't like an airplane or bird wing.
So, shouldn't this delay and less than optimal lift be factored in at the
initiation of launch?
.......... It certainly can be, and I sometimes do, but to make this thread
short, simplistic, and easy to follow, I ignored the contribution of wing
lift and just treated it ballistically which makes it more difficult for the
animal. If you factor even reduced winglift in, things get easier for the
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.
........ That doesn't follow. Herein, we have ignored wing lift in order to
make the explanation easier to follow. Without taking advantage of winglift,
the animal has 0.72 seconds to bring the wing to the beginning of the first
downstroke. They usually do an upstroke in 0.3 seconds, so during the
launch they have an extra 0.42 seconds to bring the wing up if they want to
loaf about it or so desire. They don't have to be in a rush about it. As I
said above, at the end of the first downstroke the wingtip will be 6.23 feet
higher than the glenoid was at the time the manus left the ground. The
glenoid height above ground at the time the manus leaves the ground is about
2.75 to 3.0 feet, so the wingtip is about 2.75+6.23 = 8.98 feet above the
ground at the end of the first downstroke. Needless to say, the animal has
a multiplicity of options on average launch angle and speed, and each option
will lead to somewhat different answers -- but, this one is fairly typical
of an extremely fast launch where the animal has a strong desire to be gone
in a hurry (big, toothy predator? ).
The question is... will it?
........ I've answered that queston a number of times already, but to repeat
myself again -- Yes. the margin isn't even close.
The major questions I would have at this point is 1) why such a small
amplitude wingstroke at take-off?
...... Because in this simplistic explanation, we postulated an extreme
launch all the way to cruise speed, which makes the terrestrial part of the
launch tougher, but minimises the input needed from the wings. If the
animal wishes, he can slow the terrestrial part down, thereby reducing
launch loading and pick up the slack with his wings. It's his choice, and
there are a lot of options that are within his capability.
2) is the G-force at launch similar to what you calculated?
..........Your's isn't similar to mine. And when I'm doing a more realistic
calculation and not trying to simplify the explanation, I'll slow the launch
a bit so that it isn't entirely ballistic, which lowers launch accelerations
substantially while still leaving the animal plenty of vertical margin for
increased wingbeat amplitude.
and finally 3) does this work with a
pterosaur with roughly a 3x longer wing.
......... There aren't any known pterosaurs with roughly a 3x longer wing.
It would work, I suppose,
with a 22º wingstroke, but is that close to reality?
....... As I said above, cruise wingstroke for a robust, mid-sized pterosaur
would be closer to 32 degrees when not taking advantage of atmospheric lift
sources. Larger pterosaurs would use a slightly greater amplitude
excursion. Your 22 isn't all that close to reality.
Or just a fudge
factor to make sure the wingtips don't strike?
.......Well, in the example we've been using, the wingtips could be directed
straight down and the animal would still have about 3.4 feet of ground
clearance. The 32 degree excursion was what was required to maintain a 20Kg
Qsp in level flight at cruise speed while applying a 15% aerodynamic tail
upload to support his hindlimbs when atmospheric conditions are such that he
can't soar. It had nothing to do with launch, except that it was used to
place the most severe terrestrial loads on the example.
Thanks 4 the input. We'll nail this down shortly I think.
....... I believe it was nailed down about 10 years ago. At least Paul
MacCready accepted it, as did the rest of the audience. :-)