Limits to size

Allometry

Fundamental considerations of isometry (and indeed allometry) indicate that if the construction material (i.e. bone) does not change, then there are structural upper limits to the size of animals. Similar scaling arguments can be applied to the ability to fly, though the limits here tend to relate to power rather than structural strength, though landing can be an issue.

With birds, one long standing approach has been to take data from a wide range of species and plot the chosen variables (typically power available, power required) against body mass. Depending upon the assumptions in the analysis, the trends in the two variables will converge and the cross over is taken to define the upper limit to size. There are numerous problems with this approach, but for me an over riding one is the use of data from “all birds” to create trend lines. Different birds have very different morphologies, so some must be better starting points for scaling to large size than others. It is hard to imagine a 40kg chicken shaped bird, but if Ksepka (2014) is right, the extinct Pelagornis sandersi – a seabird with very high aspect ratio wings could fly at that size. So the starting point matters. If this is factored in to studies such as Pennycuick (1996) the possible limits to size range from 2kg to 100kg, which is not very helpful.

Estimating limits to size in pterosaurs

I have been working with Mike Habib on these ideas for a number of years and we presented work related to the limits to size of pterosaurs at the annual SVP conference in 2014 and SVPCA in 2015. The SVPCA presentation is  here: Palmer & Habib SVPCA 2015

We looked at four possible factors that might limit the size. Well, al of them must create limits at one size or another, so we were looking for which was the most severe and also least sensitive to different input assumptions.

The four factors we investigated were:

1. Structural strength required for flight
2. Power required for flight
3. Landing speed and ability to absorb energy
4. Take off

We took the giant azhdarchid body plan as our model and used data that I had collected during my PhD on wing bone strength and body mass, scaling this to wingspans of 6m, 9m, 12m and 15m. It was quickly apparent that the structural strength of the wing spar was a very weak contracting. For sure the bones do need to become disproportionately large as size increases, with adverse effects on the aerodynamics and body mass. But the constraints did not appear to be onerous even at 15m wingspan.

Similarly with the power required for steady flight. It was necessary to invoke high levels of mass specific power, so probably not levels that could be maintained indefinitely, but for long enough to climb out and find thermal or slope lift (in the same way as condors and frigate birds today).

The analysis of landing was more tricky. We made simple computer models of a landing birds and pterosaurs, assuming that they only use flaring (pitching up) as a means to slow down. While this may not be strictly correct, the analysis gave us estimates of landing speeds for a range of birds, which we plotted against body mass. Now, pterosaurs were likely able to fly much more slowly than birds of comparable mass since the membrane wing could be highly cambered, allowing it to generate high coefficients of lift. What we found was that the landing speeds of even the largest pterosaurs were lower than swans and similar large, heavily loaded birds. This is shown in the figure below.

Landing speed alone is not a sufficient indicator of a possible constraint – after all you can drop a mouse to hit the ground a few metres per second and it will run off unscathed, do that with an elephant (!) and it will suffer injury (as Haldane eloquently described in his 1926 paper). This is because the ability to resist impact (to absorb strain energy) and the kinetic energy of impact do not scale together, so put simply, bigger animals are more likely to suffer impact damage. We were not able to examine this issue in detail and it certainly deserves further study. Nice PhD topic. Our conclusion was that the limit was somewhere between 12m and 15m span.

Lastly we looked at take off. It is becoming increasingly widely known that birds obtain almost all their take off power from their legs, not their wings (see Earls 2000 for example). We supposed that it was similar for pterosaurs and that they used the quadrupedal launch technique that Mike had published earlier (Habib 2008). We had to make a range of assumptions about the power that muscle can produce and the amount of muscle the animal could recruit for take-off, so our results produced a range of values. Overall we concluded that 6m individuals would be very agile in take off, at 9m span it gets very difficult and becomes impractical by 12m span.

The pterosaur advantage

Why is it then that pterosaurs were able to remain volant at much larger sizes than birds? Well, quoting from the final section of chapter 8 in my thesis: