Formation flight design via Constructal Law

Abstract

Formation fliers utilize varying designs to save energy by flying in the wake of preceding fliers, reducing induced drag and boosting lift. The Constructal Law is applied to this formation flight problem to analyze how the distribution of drag among fliers in a V-formation design is related to the optimal formation flight configuration. An analytical model that predicts this optimal configuration is developed and expressed in terms of the fundamental formation parameters (velocity, number of fliers, wingspan, weight, and air density). Results show that there is not a fixed optimal V-formation design for all formation systems. Rather, the optimal configuration is evolutionary: it constantly adapts as parameters change to maximize access to energy savings. Trends predicted by the model are substantiated by observations from nature. In line with Constructal Law predictions, induced drag along the optimal V-formation configuration is distributed as uniformly as possible among fliers.