On the Scaling of Dragonflies

Any correlation in the scaling of micro-air vehicle parameters would merely reflect the design tools employed. In contrast, correlations found in the scaling of flying insect (Pterygota) parameters could offer insight into the principles that govern the evolution of their morphology. Dragonflies (Odonata, Anisoptera) are of interest in this regard since their physiology may have evolved over the past ~180 million years. In the present epoch their adult forms have wing lengths, L, varying between ~15 mm and ~85 mm, but it is not known what ecological and/or physiological factors constrain their size. One possibility is that adult upper size limit is constrained by flight power demands. Suppose that the scaling of any flying creature is exactly isometric. In this idealised case the total wing area, S, scales with L and total body mass, m, with L. In stationary hover (outside ground effect), according to simple Rankine-Froude theory, the time-averaged, ideal, induced power is given by Pind = W /(2  A), where W = mg is the total body weight,  is the atmospheric density and A is the actuator area which varies with L. Consequently, Pind scales with L, or with m. Since the ‘engine’ (flight muscle apparatus) may be expected to be less than some maximum feasible fraction of the total body mass and the mass-specific power output must also be constrained, the maximum feasible power output may reasonably be expected to scale with m. At first sight, this divergence in scaling indicates a possible fundamental limit: at some upper size the power required to hover would exceed the engine power available or, alternatively expressed, some upper feasible body mass would be reached. This Flight Power Size Limit (FPSL) hypothesis was similarly proposed by Pennycuick [1] for birds and by Lindhe Norberg & Norberg [2] for bats. Unfortunately, whilst the FPSL is compelling, it is difficult to confirm or disprove. As introduced above, the FPSL hypothesis is over-simplistic. For dragonflies (and for other flying creatures) a number of complicating factors need to be considered. First, the scaling of parameters is not isometric. Second, the total flight power in hover is also determined by the wing profile and inertial power of the flapping quad-wing configuration. Third, the muscle power output of dragonflies may not be a simple linear function of muscle mass and could be affected by the efficiency of the power production process which is influenced by heat transfer. Fourth, the maximum power output required by any dragonfly species is unlikely to be determined by the need to perform stationary hover. All species must necessarily perform more power demanding flight manoeuvres during conspecific combat/mating as well as during predator-prey interactions. Male dragonflies also carry females during copula and females carry significant egg loads. In other words, the behavioural repertoire (which strongly influences fitness for natural selection) is dependent on the ability of any species to generate excess power and thrust, i.e. each species must be capable of achieving a maximum thrust NW, where N greater than unity. All these complicating factors will be partially addressed in the following presentation. Despite many unresolved issues and concerns, it is confirmed that for anisopteran dragonflies Pind does scale with ~m and the FPSL hypothesis remains plausible and warrants further investigation.