Sensitivity Analysis of the Performance of Olympic Rowing Boats

Abstract

A multidisciplinary approach is implemented to model and analyze the performance of Olympic rowing boats. A reduced-order model that couples rowers motions with the hull, oars and hydrodynamic and hydrostatic forces is detailed. This model is complemented with a sensitivity analysis carried out by means of a non intrusive polynomial chaos expansion. Different strategies for the evaluation of the polynomial chaos expansion coefficients are implemented and tested. Sensitivity analysis results for a lightweight single scull are presented and discussed. This analysis contrasts the effects of varying forces exerted by the rowers, weights of rowers and cadence of motions on the boat performance. I. Introduction Rowing is a sport with a long tradition, where best performance is based on athletic gestures and boat shapes and elements configurations. The boats are narrow and long with nearly semicircular cross sections designed to reduce drag to a minimum. The shells are usually made of carbon-fiber reinforced materials to increase the stiffness and reduce the weight. In rowing configurations, the rowers sit in the boat facing backwards (towards the stern). They use oars that are attached to the boat at pinned points (oarlocks) to propel the boat forward (in the direction of the bow). The oarlocks are held from outriggers away from the hull; thereby, reducing its cross sectional area. By sitting on sliding seats, the rowers are able to apply more power to the oars and increase the distance they can pull with each stroke. Furthermore, by using their legs to slide along the seat rails, they add their leg power to the stroke. Clearly, rowing involves coupled complex dynamics that span across many fields including fluid dynamics, rigid body dynamics, and biomechanics. While advancements made in individual fields can contribute to performance enhancement of rowing boats, the multidisciplinary nature of rowing necessitates the development of modeling and analysis tools that couple the different disciplines and would be used to optimize the boat and rowers performance. In this work, we develop a model that determines sensitivities of mean surge and oscillatory motions to variations in magnitude and frequency of applied forces and rowers weights and distributions. Such a model can be used as an assessment tool in the preliminary design stages of rowing boats. Furthermore, since it incorporates the rowers motions with sufficient details, it could be used by trainers to understand the effects of different rowing styles or crew compositions. The dynamic model for the boat motions is based on the earlier work of Formaggia et al. 1,2 and is defined mainly through the boat geometry, the rowers motions, the forces at the oars and the hydrodynamic forces. Although the model can be applied to wide range of boat classes, the case of a single scull is considered here. As for the rower’s motions and the forces at the oars, which constitute the inputs of the system, data taken from experiments are used. The sensitivity analysis is carried out by means of a non intrusive polynomial chaos technique. First, variations are introduced in input parameters such as the rower’s weight, forces, and frequency of motion, and propagated through the reduced-order model dynamical system. Then, the rates of variations of output parameters such as the mean forward velocity or efficiency of the rowing action, in terms of energy ratio of o and mean surge motions, with variations in input parameters are determined.