In this paper, I describe the process and results of my study on the flight trajectory optimization of a continuously flying solar aircraft. Continuous flight is achieved by cyclic operation, where the trajectory is repeated indefinitely, typically every 24 hours. The word continuously is used in the theoretical sense, as continuous or perpetual flight is not achievable in practice due to degradation of batteries and aircraft components over time. The importance of flight trajectory optimization has been recognized in both general aviation and space applications.

I am fascinated by problems that require a blend of computational topology, geometry, and number theory. I have also been studying fractals which interesting geometrical objects that have been used in diverse applications such as cryptography, seismology, network optimization, and even weather forecasting. However, despite the wide range of applications and interest in fractals, the general theory of these objects is still in its infancy. My work on this research project has developed some theorems and conjectures in the field of combinatorics and has begun to shed some light on some areas of fractals, one-cell automata and dynamical systems … This need for optimization has become increasingly more important in today’s society from the perspective of both resource management as well as leveraging new opportunities.