Re: Pterosaur arm supination (getting long)

[Michael Habib <mhabib5@jhmi.edu>]

> > And actually, the aspect ratios in most vultures are not as low as 
> > many people seem to think.
>
> I agree.  Particularly when the tip slots are open and increasing the 
> effective aspect ratio (multiple high aspect ratio tips mitigating the 
> gross low aspect ratio at the expense of some additional interference 
> drag at the inboard end of the slots).  I don't think anyone has 
> written extensively on that, but it would make a good topic, 
> particularly the aerodynamics near the crossover point.

I'm actually surprised to hear that no one has written much on that 
topic; it would indeed be excellent (adding to list of things to do 
someday...)

>  BTW, there are two crossover points -- one apparently related to the 
> relationship between the bending strenth of avian arm bones and 
> feather shafts (the approximate 12:1 limit), and the other related to 
> the relationship between lift coefficient and induced drag (the speed 
> at which individuals will close the tipslots when traveling faster).

Ironically enough, it is the latter relationship that occurs to me 
first, despite the fact that I actually work largely on bending 
strength in avian arm bones!  I do wonder, though, if the 12:1 limit 
may also incorporate other factors, given the variance in bone strength 
in birds, even within a narrow AR range.  For one thing, any birds with 
an AR over 12 are going to be cruising pretty fast; no inland species 
have an aspect ratio that high except for some small-bodied aerial 
hawkers.  As such, most high AR birds should be in a speed regime that 
is beyond the crossover point related to induced drag.  Do you happen 
to know where the bone/shaft strength crossover was first cited?  In 
any case, inland soaring forms with slotting do have stronger forelimb 
elements, as expected (though, again, I think there are multiple 
reasons for this...)

> Again, me too.  We agree on a totally disgusting amount of stuff.

I know, it's scary.

> I've done some inboard airfoil sections, and the inboard drag appears 
> to me to be fairly well mitigated, with the lower surface inboard eddy 
> being used to enhance inboard lift (potentially a beneficial 
> compromise).

That's quite interesting; I'll have to keep it in mind.  How much in 
the way of air sacs are you included external to the bone spaces?

> BTW, I think you restore Quetz with more wing area than I do, but I 
> restore with more tail area, so that the total lifting surfaces 
> probably aren't all that far apart.  For Qn, if I remember correctly, 
> my wing area is on the loose order of  78 or 80 s.f. or thereabouts 
> with a tail area of about 25 or 26 s.f. for a total lifting surface of 
> about 103 to 106 s.f. (roughly about 9.8 sq.M.).  Roughly what numbers 
> are you seeing?  Off the top of your head is good enough -- I didn't 
> bother to go look up the ones I just spouted.

Off the top of my head, I think I have a figure around 10.2 sq. m.  So, 
as you suspected, a bit higher, but not by much.  I also ran some 
calculations (mostly for launch) using Mark Witton's mass estimate and 
wing area profile (which is somewhat broader than mine).  Of course, 
with the broader planform comes the accommodation of more mass, so the 
wing loading changes are damped a bit.  Overall, your model is 
presumably a better rapid-glider, and mine is a bit more generalized, 
but the differences are slim.

Cheers,

--Mike


Michael Habib, M.S.
PhD. Candidate
Center for Functional Anatomy and Evolution
Johns Hopkins School of Medicine
1830 E. Monument Street
Baltimore, MD 21205
(443) 280 0181
habib@jhmi.edu