Geometry and mechanics of insect hindwing fans: a modelling approach

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Abstract
The `umbrella effect', a mechanism of camber generation in the hindwing fans of orthopteroid and dictyopteroid insects, is modelled geometrically and mechanically, treating the fan as a framework whose outer margin describes a truncated logarithmic spiral. Tension in the margin compresses the radial veins, causing them to undergo Euler buckling. The model describes the distribution of compression forces in the veins around the spiral, and predicts conditions which must be met, and departures from the model expected in real wings. Actual insects fit the model and predictions quite well. The functional implications, and those of departure from the model, are discussed.

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