Stability is essential to #ying and is usually assumed to be especially problematic in #apping #ight. If so, problems of stability may have presented a particular hurdle to the evolution of #apping #ight. In spite of this, the stability of #apping #ight has never been properly analysed.
Here we use quasi-static and blade element approaches to analyse the stability provided by a #apping wing. By using reduced order approximations to the natural modes of motion, we show that wingbeat frequencies are generally high enough compared to the natural frequencies of motion for a quasi-static approach to be valid as a "rst approximation. Contrary to expectations, we "nd that there is noting inherently destabilizing about #apping: beating the wings faster simply ampli"es any existing stability or instability, and #apping can even enhance stability compared to gliding at the same airspeed. This suggests that aerodynamic stability may not have been a particular hurdle in the evolution of #apping #ight. Hovering animals, like hovering helicopters, are predicted to possess neutral static stability. Flapping animals, like "xed wing aircraft, are predicted to be stable in forward #ight if the mean #ight force acts above and/or behind the centre of gravity. In this case, the downstroke will always be stabilizing. The stabilizing contribution may be diminished by an active upstroke with a low advance ratio and more horizontal stroke plane; other forms of the upstroke may make a small positive contribution to stability. An active upstroke could, therefore, be used to lower stability and enhance manoeuvrability. Translatory mechanisms of unsteady lift production are predicted to amplify the stability predicted by a quasi-static analysis. Non-translatory mechanisms will make little or no contribution to stability. This may be one reason why #ies, and other animals which rely upon non-translatory aerodynamic mechanisms, often appear inherently unstable.