Title: A stability of free-flight using vortex: a universal mathematical structure 


Iima, Makoto (Research Institute for Electronic Science , Hokkaido University) 
  makoto@nsc.es.hokudai.ac.jp 

 
Abstract:

It is well-known that insects utilize vortices generated by flapping, 
by which they achieve high performance and maneuverability of their flight.
In this the talk, I would like to present the following two topics about 
the flapping-flight problem.  The first topic is the stability problem. 
Even if the force generated by flapping is balanced with insects weight, 
the stability of the steady state can be unstable. Thus the stability 
problem is a first step to tackle with the maneuverability or control system. 
We numerically analyzed two-dimensiontal simple models including vertical CG 
motion[1,2] to obtain the bifurcation diagram of the stable flight. 
Although the flapping motion and generated vortex pattern are qualitatively 
different in these models, their bifurcation structure has a similarity.
 The second one is an analytical evaluation of the force acting on the 
flapping insect, which will be of great use to study the dynamical process 
during transition from one state to another. Isao Imai(1914-2004), 
a Japanese fluid researcher, proposed a generalised Blasius formula 
in two-dimensional space in 1974, by which the unsteady force can be 
calculated in terms of only an integral on the control surface. 
A simple theoretical model for flapping flight will be discussed.

References:

[1] M. Iima, A two-dimensional aerodynamic model of freely flying insects,
J. Theor. Biol.,247(2007),657--671
[2] M. Iima and T. Yanagita, A transition from ascending flight to vertical 
hovering: a study of a symmetric flapping model, Europhys. Lett., 74(2006) 55--61.