Random geometric graphs as a model for bounding the endurance of soaring aircraft

Soaring aircraft and birds utilize the energy of atmospheric convection to remain aloft. As this source of energy gains attention as a method for prolonging the flight times of small UAVs, it is necessary to evaluate the conditions under which it is a viable option. The indefinite endurance problem for soaring aircraft is cast in terms of a random geometric graph. Tools developed for the analysis of random graphs are used to bound the relationship between aircraft efficiency and energy abundance in the atmosphere. A theoretical threshold is arrived at, over which indefinite endurance flights may be possible in an unbounded domain. Simulation results are presented that confirm the existence of a threshold which compares favorably to what is predicted by random graph theory. Extensions are made to missions restricted to finite domains as well.