Induced Power Scaling Alone Cannot Explain Griffenfly Gigantism

Paleozoic skies were ruled by extinct odonatopteran insects called "griffenflies," some with wingspans 3 times that of the largest extant dragonflies and 10 times that of common extant dragonflies. Previous studies suggested that flight was possible for larger fliers because of higher atmospheric oxygen levels, which would have increased air density. We use actuator disk theory to evaluate this hypothesis. Actuator disk theory gives similar estimates of induced power as have been estimated for micro-air vehicles based on insect flight. We calculate that for a given mass of griffenfly, and assuming isometry, a higher density atmosphere would only have reduced the induced power required to hover by 11%, which would have supported a flyer 3% larger in linear dimensions. Steady-level forward flight would have further reduced induced power but could only account for a flier 5% larger in linear dimensions. Further accounting for the higher power available due to high-oxygen air and assuming isometry, we calculate that the largest flyer hovering would have been only 1.19 times longer than extant dragonflies. We also consider known allometry in dragonflies and estimated allometry in extinct griffenflies. But such allometry only increases flyer size to 1.22 times longer while hovering. We also consider profile and parasite power, but both would have been higher in denser air and thus would not have enhanced the flyability of larger griffenflies. The largest meganeurid griffenflies might have adjusted flight behaviors to reduce power required. Alternatively, the scaling of flight muscle power may have been sufficient to support the power demands of large griffenflies. In literature estimates, mass-specific power output scales as mass0.24 in extant dragonflies. We need only more conservatively assume that mass-specific muscle power scales with mass0, when combined with higher oxygen concentrations and induced power reductions in higher-density air to explain griffenflies 3.4 times larger than extant odonates. Experimental measurement of flight muscle power scaling in odonates is necessary to test this hypothesis.