Optimum hovering wing planform

- A theoretical solution for the optimum hovering wing planform is identified.
- Aerodynamic performance of untwisted hovering wings is evaluated.
- An untwisted elliptical planform minimises profile power.
- An untwisted hummingbird-like planform minimises induced power.

Theoretical analysis is used to identify the optimum wing planform of a flapping/revolving wing in hover. This solution is of interest as a benchmark to which hovering wing geometries driven by broader multidisciplinary evolutionary or engineering constraints can be compared. Furthermore, useful insights into the aerodynamic performance of untwisted hovering wings are delivered. It is shown that profile power is minimised by using an untwisted elliptical planform whereas induced power is minimised by a more highly tapered planform similar to that of a hummingbird.