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Re: Pterosaur arm supination (getting long)

----- Original Message ----- From: "Michael Habib" <mhabib5@jhmi.edu>
To: <dinosaur@usc.edu>
Sent: Tuesday, January 15, 2008 12:51 AM
Subject: Re: Pterosaur arm supination (getting long)

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...)

It's possible that I've missed it. I've seen a number of mentions in passing in the literature, but nothing in depth.

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,

It may well do.

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;

I know what you are saying, but think this may be a good place to add (not for your benefit -- you already are aware of the relationship), that the increase in speed is due to the increase in wing loading, not the high aspect ratio. The need for speed creates the advantage for high wing loading. The drag associated with high wing loading creates an advantage for high aspect ratio when these high speed wings are traveling near the slow end of their range. Consequently, animals with high aspect ratio are generally going to be traveling fast even though it is possible to configure high aspect ratio wings with sufficient surface area for slow flight. You'll see that latter trend in some aircraft, but compromise tends to limit the trend toward really large high aspect ratio wings in vertebrate flyers. BTW, there are other advantages for high wingloading that are not related to speed, or even flight itself.

no inland species have an aspect ratio that high except for some small-bodied aerial hawkers.

Once you toss in the oswald efficiency factor, I think you'll find that some inland species have effective aspect ratios (when utilizing the slots) that are similar to the effective aspect ratios of the unslotted marine flyers. As you say, gross aspect ratio does remain higher for the marine flyers.

As such, most high AR birds should be in a speed regime that is beyond the crossover point related to induced drag.

Only when they are flying at high speed (high for them). When flying slowly (for them), their lift coefficient will be high enough that induced drag is a factor. For birds, the advantage to high aspect ratio comes when they are extracting energy from the atmosphere. When they are traveling rapidly between lift sources, the advantage to high aspect ratio disappears because of the reduction in induced drag at low lift coefficients and they retract their wings to lower the profile drag component instead. This increases the induced drag due to the lowered aspect ratio, but at the high speed, the induced drag isn't a factor even with the reduced aspect ratio because of the inverse relationship between induced drag and lift coefficient.

Do you happen to know where the bone/shaft strength crossover was first cited?

I don't know that it has ever been written up. It's just something that occured to me one day, and I've not pursued it. I think it is also related to maximum wingspan in birds, but I've not pursued that either.

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...)

Me too.

We agree on a totally disgusting amount of stuff.

I know, it's scary.

More seriously, I fear that folks who don't see our offline discussions will think we are in total agreement, and I don't want that. I think the snippets where we disagree potentially illuminate our topic. In my case, I don't necessarily carry a searchlight, but maybe at least a candle or two.... :-)

, 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?

Quite a bit, but I think it is variable, under control of the animal (whether passive control or active, I don't know). In any event, the relatively abrupt transition in airfoil thickness immediately behind the humerus and proximal r/u creates a high pressure eddy aft of the skeletal spar that can produce substantial lift without a huge drag increment (there is a substantial drag increment, but not exhorbitant). As an aside, Bill Akersten's videos of transient pelican air sac inflation made a real impression on me.

Overall, your model is presumably a better rapid-glider, and mine is a bit more generalized, but the differences are slim.

Yeah, the difference between 9.8 and 10.2 sq.M. is within individual variation for two animals with identical span. The biggest straight flight difference may be that I presumably load the tail structure relatively more lightly than you do. We probably load the outer wing similarly. With the proviso that your loading may be greater because I think you use a heavier weight for Qn than I do. One of us really ought to take time to do a detailed mass estimate for Qn based on an allometric blowup of Qsp (I do realize how speculative that would be, which is why I've not bothered to do it so far).