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.
Thin And Thick Wings
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.