Size scaling and stiffness of avian primary feathers: implications for the flight of Mesozoic birds

The primary feathers of birds are subject to cyclical forces in flight causing their shafts (rachises) to bend. The amount the feathers deflect during flight is dependent upon the flexural stiffness of the rachises. By quantifying scaling relationships between body mass and feather linear dimensions in a large data set of living birds, we show that both feather length and feather diameter scale much closer to predictions for geometric similarity than they do to elastic similarity. Scaling allometry also indicates that the primary feathers of larger birds are relatively shorter and their rachises relatively narrower, compared to those of smaller birds. Two-point bending tests indicated that larger birds have more flexible feathers than smaller species. Discriminant functional analyses (DFA) showed that body mass, primary feather length and rachis diameter can be used to differentiate between different magnitudes of feather bending stiffness, with primary feather length explaining 63% of variance in rachis stiffness. Adding fossil measurement data to our DFA showed that Archaeopteryx and Confuciusornis do not overlap with extant birds. This strongly suggests that the bending stiffness of their primary feathers was different to extant birds and provides further evidence for distinctive flight styles and likely limited flight ability in Archaeopteryx and Confuciusornis.