Geometric Programming for Aerodynamically-Actuated Wingsail Design Optimization

In this article, we describe a deterministic optimization framework for the conceptual-stage design of aerodynamically-actuated wingsails. The primary objective of high-performance sailing is well understood: maximize the conversion of unsteady aerodynamic forces into forward thrust, without inducing excessive overturning moments. However, designing a sail to meet this goal is by no means straightforward due to the existence of multiple recursive, nonlinear design relationships. Consequently, most wingsails are designed in an iterative fashion, using some combination of linear heuristics and engineering intuition. This approach can produce viable designs, but it does so at the expense of time and capital, and provides little physical insight into the underlying design space. By formulating the wingsail design problem as a geometric program, it is possible to quickly generate hundreds of optimal candidate designs, assess their sensitivity to specific constraints and parameters, and determine the shape of Pareto frontiers. Unlike general nonlinear optimization methods, geometric programming optimization is computationally efficient, and requires no initial guesses or hyperparameter tuning. Perhaps most importantly, all the decision variables in a geometric program are determined simultaneously, eliminating the need for iterative piecewise optimization of subsystems. These benefits come at a price: all objective and constraint functions must be described as posynomials. Nevertheless, we demonstrate that this restricted set of functional forms can adequately capture the key physical relationships between wingsail parameters, and provide quantifiable physics-based design guidance.