https://www.sciencedirect.com/science/article/pii/S0029801822010447
Abstract
This article explores the added resistance due to side forces from wingsails, called the sail-induced resistance. A cargo ship is tested with varying speed, appendages, number of sails, and control algorithms for the sails. The appendages consist of bilge keels, a high aspect-ratio fixed keel, and a dynamically controlled keel. The sails were controlled both to maximize the thrust and to iteratively optimize the angle of attack including hydrodynamic
effects. The physical modelling was done with a combination of CFD, maneuvering theory, discrete lifting line, and empirical models. The magnitude of the sail-induced resistance without any keels was found to be comparable to the added resistance in waves. The main source of the resistance was the rudder, which was forced to operate at large angles in steady state conditions. Adding the appendages reduced the sail-induced resistance, but
the fixed appendages also increased the friction. The dynamic keel was therefore the only appendage that significantly improved the fuel savings. The side force from the sails could be significantly reduced with limits in the control algorithm. Although this limit also reduced the thrust from the sails, the fuel savings remained high due to a roughly equal reduction in the sail-induced resistance.