I have a special treat this evening. Colin Palmer has been kind enough
to write a guest post on the relative performance advantages and
dynamics of thin and thick wings, especially in the context of animal
flyers. Colin is located at Bristol University. He is an accomplished
engineer with an exceptional background in thin-sectioned lifting
surfaces (particularly sails). Colin has turned his eye to pterosaurs
in recent years, and he has quickly become among the world's best
pterosaur flight dynamics workers. You can catch his excellent paper on
the aerodynamics of pterosaur wings
here. Press release on it can be found
here.
This is a cross post from
Aero Evo. If you want to comment on the post, I recommend going there, as that means Colin only has to watch one site at a time (remember, he supplied this at of the goodness of his heart!)
--MH
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Thin And Thick Wings
Colin Palmer
In the early days of manned flight the designers took their inspiration
from birds. One of the consequences was that they used thin, almost
curved plate aerofoil sections. This seemed intuitively right and
certainly resulted in aeroplanes that flew successfully. However towards
the end of the First World War the latest German Fokker fighters
suddenly started to outperform the Allied planes. Counterintuitively
their wing sections were thicker-surely these sections would not cut the
air so well so how could they possibly have enabled aeroplanes to fly
faster and climb more quickly. But that was what was happening, the
Germans had done their research and discovered that a combination of a
cambered aerofoil with the correct thickness distribution gave superior
aerodynamic performance. Subsequently all aircraft had similar teardrop
shaped wing sections and soon there was a massive body of experimental
and theoretical work available that enabled designers to select just the
aerofoil they required.
Fast forward to the period after the
Second World War and an explosion of interest in applying the latest
aerospace science to the traditional arts of sailing. Many people looked
to aircraft and logically assumed that sailboats would perform better
if only they could be fitted with wing sails, like up-ended aircraft
wings. Surely this had to be more efficient than the old-fashioned sails
made of fabric and wire, just like the earliest aircraft. But the
results were disappointing. Not only on a practical level where the wing
sails proved unwieldy and unsuited to operating in a range of wind
conditions, but perhaps more worrying they offered no obvious
performance advantage and indeed in light winds they were significantly
inferior, area for area. What was going on? Why didn't the massive
investment in the development of aircraft wing sections have anything to
offer to sailboats?
The answer lay in understanding the effect
of Reynolds number. From the very earliest days of manned flight
aircraft were operating at Reynolds number approaching 1 million and as
speeds increased so did the Reynolds numbers, so it became customary for
aerofoils to be developed for operation at Reynolds numbers of 2 to 3
million or more. But sailboats are much slower than even the slowest
aircraft so the operational Reynolds numbers are lower than for
aircraft, typically in the range from 200,000 to 500,000, right in the
so-called transition region. It turns out that in this Reynolds number
range the experience and intuition gained from studies at significantly
higher values can be very misleading indeed. In the transition region a
curved plate, (membrane) aerofoil can be more aerodynamically efficient
than a conventional thick aerofoil.
This transition Reynolds
number range is also where most birds and bats operate, and from what we
know of pterosaurs it was also their domain. Consequently natural forms
are not necessarily disadvantaged by having the membrane wings of bats
or pterosaurs or the thin foils of the primary feathers in the distal
regions of bird wings.
But there is a complication. A curved
plate or, to an even greater extent, a membrane aerofoil has very little
intrinsic strength and requires some form of structure to keep it in
place and keep it in shape. On sailing yachts this structure is a thin
tension wire that supports the headsail or the tubular mast in front of
the mainsail. In order to tension the wire for the headsail, very large
forces are required which places the mast in considerable compression,
normally requiring a guyed structure that can have no direct analogue in
nature. Natural forms are restricted to using a supporting structure
which is loaded in bending and restrained by attached muscles and
tendons. Generally speaking, the bending resistance of a structure
depends upon the depth of the cross-section, so as bending load
increases the diameters of the bones must increase otherwise the wing
will become too flexible.
This is where the apparent superiority
of the membrane wing may be compromised, because the presence of
structural member severely degrades the aerodynamic performance. The
structural member may be along the leading edge of the aerofoil as in
the case of bats and pterosaurs, or close to the aerodynamic centre as
in the case of the rachis of the primary feathers of birds. In all cases
the loss of performance is less if the supporting structure is on the
pressure side (the ventral side) of the aerofoil. It is therefore most
likely no coincidence that this is the arrangement of the wing bones and
membrane in bats and the rachis and vane in primary feathers. It was
therefore also most likely that the wing membranes of pterosaurs were
similarly attached to the upper side of the wing finger. Even in this
configuration there is a substantial penalty in terms of drag, although
it may result in some increase in the maximum lift capability of the
section, due presumably to an effective increase in camber. (Palmer
2010).
This aerodynamic penalty arising from the presence of the
supporting structure may perhaps be the reason why birds’ wings have
thickness in the proximal regions, where the performance of such a thick
aerofoil is superior to a thin membrane obstructed by the presence of
the wing bones. More distally, where the wing bones become thinner or
are not present, the wing section reverts to a thin cambered plate
formed by the primary feathers. On the bird’s wing the proximal fairing
of the bones into an aerofoil section is achieved by the contour
feathers with very little weight penalty. This is not possible in bats
(and presumably also in pterosaurs) where any fairing material would, at
the very least, need to be pneumatised soft tissue, resulting in a
considerable weight penalty as compared to feathers. In the absence of
aerodynamic fairing around the supporting structure, aerodynamic
efficiency can only be improved by reducing the cross-section depth of
the bones - the general shape of the section having very little effect.
But reducing the section depth results in a large increase in
flexibility since the bending stiffness varies as the 4th power of
section depth, so there are very marked limits to the effectiveness of
this trade-off.
It may therefore be no coincidence that where the cross section
depth has to be greatest, in the proximal regions of the wing, both bats
and pterosaurs have a propatagium, which means that the leading-edge of
the wing section is more akin to the headsail of a yacht, stretched on a
wire, than a membrane with the structural member along the
leading-edge. Wind tunnel tests have shown that moving the structural
member back from the leading-edge, while keeping it on the underside of
the wing section, results in a significant increase in aerodynamic
performance.