The moment of inertia of bird wings and the inertial power requirement for flapping flight

Abstract

The agility and manoeuvrability of a flying animal and the inertial power required to flap the wings are related to the moment of inertia of the wings. The moments of inertia of the wings of 29 bird species and three bat species were determined using wing strip analysis. We also measured wing length, wing span, wing area, wing mass and body mass. A strong correlation (r2=0.997) was found between the moment of inertia and the product of wing mass and the square of wing length. Using this relationship, it was found that all birds that use their wings for underwater flight had a higher than average moment of inertia. Assuming sinusoidal wing movement, the inertial power requirement was found to be proportional to (body mass)0.799, an exponent close to literature values for both metabolic power output and minimum power required for flight. Ignoring wing retraction, a fairly approximate estimate showed that the inertial power required is 11­15 % of the minimum flight power. If the kinetic energy of the wings is partly converted into aerodynamic (useful) work at stroke reversal, the power loss due to inertial effects may be smaller.