Guest Post: The Jack Sprat Effect

Today it’s the turn of Colin Palmer, an aero engineer turned pterosaur researcher in Bristol who takes us through his new paper on their flight mechanics. And inevitably has some issues with how his work was portrayed in the media. Colin of course comes into this problem from the opposite end as do most pterosaur workers, but as he explains, that’s no bad thing…

As you may have seen in the media coverage of my recent Proceedings B paper, I am an engineer of a certain age who has come late to the study of pterosaur flight. The media like stories, stories with a human angle, something unusual about someone who does not conform to their ideas of the normal patterns of life, which may be why this story was picked up to widely. Yes I am an engineer and many years ago, in a different life, I ran experiments in wind tunnels and water tanks to investigate the performance of sailing vessels. Through this I came to understand about the dynamics of flexible wings and how to go about testing them, knowledge that is helping me in my pterosaur flight research.

If the media are to be believed, I came up with a simple idea in my paper that had eluded more eminent palaeontologists. Well not really. What I did was to do what I know best, which is to take a practical experimental approach to analysing a problem. I was simply doing what is more or less second nature to an engineer though maybe challenging for a palaeontologist. In the same way, systematics is second nature to palaeontologists but a struggle for me. In engineering terms, there was nothing unusual about what I did – it was the standard approach that has been used in aerodynamics since the days of the Wright brothers. But this the great strength of cross disciplinary work, the Jack Spratt effect. What is easy for me may be difficult for others and vice versa, but if we work together we can bring our combined strengths to solving problems. That’s why I was rather saddened by the media’s idea that somehow I’ve got one over on palaeontologists. Wrong. All I’d done was to take the approach that I know best, relying on information produced by palaeontologists who have a far far deeper understanding of the morphology of these animals than I ever will.

So what was it that seemed to be so simple and logical to do? I was trying to understand the aerodynamic performance of the pterosaur wing using aerodynamic analysis and one way to do this is to start with wind tunnel tests of 2-dimensional wing sections. These are constant section ‘extruded’ models that extend right across the wind tunnel from wall-to-wall so as to avoid the end effects and the effects of different planform shapes. Armed with the data from these tests there are a well-established methods for using it to produce the estimated performance of complete three-dimensional wings. None of this is unconventional or revolutionary and has formed the basis of aircraft design for many years. People also test models of complete aircraft in wind tunnels and make use of sophisticated computer modelling techniques such as computational fluid dynamics, but these methods are very expensive and only really worthwhile once you have a very deep and detailed understanding of a specific geometry. We don’t have that for pterosaurs. What we do know in considerable detail is the bone morphology, particularly for the larger specimens that I’m interested in, because there is very good 3-D preservation from locations such as Brazil and the Cambridge Greensand. This means that we can reliably reconstruct the wing bones of a 5 to 6 m wingspan pterosaur, but sadly we know much less about the actual shape and extent of the wing membrane. Recent work suggests that it was attached proximally at the ankle and presumably also extended to the extreme distal tip of the wing finger, but we can only make a range of bounded assumptions about the shape between these points.

What I did was to take four locations along the wing and to produce a range of possible cross sections at those locations. I was not trying to reproduce one particular specimen or even species in detail, but wanted to get information of a more generic nature that could be applied to a range of possible reconstructions and remain useful in the future as our knowledge of the wing bones and wing morphology develops. This again is a classic engineering approach – to use a parametric methodolgy to provide a range of data that can be interpolated for specific solutions.

The figure shows a selection of the different sections which I tested. One of the advantages of two-dimensional testing, particularly in a small tunnel such as the one I used at UCD in Dublin, is that you can test a lot of different models and configurations very quickly, rapidly building up a wide database of information. It may not be the most accurate data in the world, but at this stage of understanding the accuracy is more than good enough to discern the relative differences between the configurations and comparison with published data for similar shapes such as yacht sails confirmed the absolute magnitude of the results.

I represented the wing membrane in two different ways – with rigid, thin plate sections made from a carbon fibre composite and with flexible, reinforced latex rubber material. You may wonder how a rigid shape can be representative of the flexible wing of a pterosaur. Well, in an overall sense it is not, but it is representative of one particular configuration of that wing, so by fixing the shape it is possible to minimise the number of variables. I made my tests with curved plates having different amounts of curvature (camber in aerodynamic parlance). Then depending on what camber is thought appropriate, the results can be interpolated to get the results for any specific reconstruction geometry.

In order to understand the specific effects of flexibility I also tested some sections made with flexible membrane. They covered the same range of camber as the rigid structures, and so allowed me to understand where the flexibility itself, rather than the simply the geometry had particular effects.

The results showed a number of interesting features. In the proximal region of the wing the propatagium is anterior to the wing bone and so the wing membrane is split into two sections by the wing bones. It had previously been hypothesised that this propatagium had the effect of enhancing the wing’s ability to generate lift. This may well be true to the extent that the camber can be varied, but what I found was that it also reduces drag in a way that had not previously been identified. Because the proximal wing bones are necessarily the largest in diameter in order to take the loads from the wing, they are the ones that will interfere most with the airflow, and a propatagium in this region reduces the otherwise high drag they would create. Thin membrane wings in which the membrane forms a sharp leading edge are very sensitive to the angle of attack – if they’re not correctly orientated to the incident flow, separation can create damaging aerodynamic characteristics. To avoid this is necessary to vary the angle of the wing in the leading edge region and perhaps this is what the pteroid was for – it enabled the animal to manipulate the membrane in that region to optimise the angle to the incident flow.

Moving more distally, I tested sections representative of the first and second wing phalanxes, which in some specimens have quite different cross sections. The first wing phalanx tends to have an oval cross section whereas the second phalanx is more triangular. No one has explained why these differences exist but one possibility is that they are for aerodynamic reasons, which is something I wanted to investigate. The results showed that there was no difference between these two cross-section shapes in terms of the aerodynamic performance, so presumably the differences are for other reasons, perhaps structural.

The reason for this is that the flow separates from the ventral side of the wing bones before it reaches the region where the shape is different, so in a sense the flow doesn’t know anything about the different wing shapes and this is why they don’t have any material effect on the aerodynamic performance.

The other thing that people had hypothesised was that a small fairing wedge posterior to the wing bone, perhaps comprising pneumatised tissue, might also improve the aerodynamic performance. I tested that, but like the different wing bone sections, it made no difference whatsoever and for the same reason – flow separation. In order to understand the degree of faring necessary to change the aerodynamic performance significantly I ran a computer analysis (using a two-dimensional analysis program called XFOIL) of different sections to come up with one that had the minimum amount of faring needed to remove the separation. A model of this shape confirmed that the drag was indeed much reduced. The minimum drag was about half that of the section which simply had a wing bone attached to the membrane. Whether or not this was a practical possibility is open an open question. The potential extent of pneumaticity in the wing is very difficult to determine since it is rarely, and poorly preserved in the fossil record, but now at least we got some idea of how much pneumaticity would be required in order to achieve a significant improvement in aerodynamic performance.

Once I had the results of the two-dimensional tests it was possible to combine them using a aerodynamic theory to calculate the performance of a full three-dimensional wing. There are a number of ways it can be done and I used a vortex lattice model, based on theory that goes back to the 1930s but which has only become practical relatively recently with the availability of computers. This methodology has its limitations but they are not particularly significant for analysing the soaring flight of the ornithocheirid pterosaurs that I’m interested in.

By putting my data into this model and using it to produce a polar flight performance curve, a curve defining the gliding performance in terms of the horizontal flight speed and the vertical sink (descent) speed I was able to see how the characteristics I was predicting compared to those of previous estimates. What I found was that my results indicated a much less efficient flight performance than previous workers such as Bramwell and Whitfield. The reason for this was that they had not done tests on sections but had used the best available extant aerodynamic data, which was derived from tests on a curved plate airfoil used many years ago on aircraft. This was a sensible enough approach in the absence of specific data, but it gave very optimistic results compared to sections where there is a wing bone on the leading edge affecting the airflow over the whole section. I found that the aerodynamic efficiency of the wing (the lift:drag ratio) with the the sections I tested was about 10, half that predicted by Bramwell and Whitfield. In fact this typical of many birds and the predicted sink rate rate of a little less than 1 m/s is again comparable with soaring birds.

The polar curve also allowed me to predict the optimum flight speed of the animals and this came out to be not dissimilar to the estimates of previous workers – around 10 m/s at cruise speed, though my results showed inferior high speed performance. The big difference however was in the low speed flight capability. I found that the flexible sections were able to distort to a very large camber and this enabled the wing to generate high lift, which extended the low-speed flight envelope beyond what had previously been estimated. This is potentially important because it would allow the animals to make controlled, very low speed landing approaches, so minimising the potential for impact damage on wing bones. These bones were stiff and efficient structures for resisting the overall bending loads experienced in flight, but like an eggshell their thin walls (sometimes less than 1 mm) could be easily fractured by local impact.

In summary, my key conclusions were that the anterior wing bone had an adverse effect on the aerodynamics of the wing sections but that the ability of pterosaurs to vary the camber of their wings, something the birds can’t do and bats can only do to a limited extent, was important in enabling them to fly very slowly on landing approach and thus minimise the possibility of damaging they’re necessarily thin-walled wing bones. I also think that the relatively low aerodynamic efficiency, especially as flight speed increases, and the flexibility of the membrane makes it extremely unlikely that pterosaurs were able to exploit the dynamic soaring flight style used by seabirds such as Albatrosses. They were much better suited to slow speed flight in thermal and or slope lift.

So what next? Well now I think I have a pretty good idea about the basic aerodynamics of the wing sections so I’m turning my attention to the structural aspects of the wing. I want to understand more about the the strength and stiffness of the wing bones and how they deflect under the various loads that would be experienced during flight – both the load due to the lift and also that due to the tension in the membrane. With this information it will be possible to go back into the vortex lattice model and create a more refined three-dimensional wing shape and rework the overall flight prediction programme. And maybe one day I can use all this information to create a free flying model.……

Palmer, C. Flight in slow motion: aerodynamics of the pterosaur wing. Proc. R. Soc. B published online before print November 24, 2010, doi:10.1098/rspb.2010.2179