Description
Wing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, however useful analytical results are notably lacking. Here, we develop a small-amplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia, and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing’s emergent pitching motions, along with expressions for how thrust and efficiency are modified by compliance. The solutions recover a range of realistic behaviors and shed new light on how flexibility can aid performance, the importance of resonance, and the separate roles played by wing and fluid inertia. Unlike experiments or simulations, these analytical results afford simple, robust estimates for how flexibility affects propulsion and may prove useful even in situations where details of the flapping motion and wing geometry differ.
Recommended Citation
Moore, M. (2014). Analytical results for how flexibility affects flapping propulsion. In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.). Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014 , West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014. https://docs.lib.purdue.edu/ses2014/mfts/fsi/3
Analytical results for how flexibility affects flapping propulsion
Wing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, however useful analytical results are notably lacking. Here, we develop a small-amplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia, and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing’s emergent pitching motions, along with expressions for how thrust and efficiency are modified by compliance. The solutions recover a range of realistic behaviors and shed new light on how flexibility can aid performance, the importance of resonance, and the separate roles played by wing and fluid inertia. Unlike experiments or simulations, these analytical results afford simple, robust estimates for how flexibility affects propulsion and may prove useful even in situations where details of the flapping motion and wing geometry differ.