## 1 Introduction  
In rowing races, success is determined by the minimum time to complete a pre-defined course track of commonly 2000 m [1]. Thus, mathematically, the main performance metric for competitive rowers is the average boat speed to finish the course [2]. Attaining a faster boat speed requires not only a physical effort but also an appropriate boat setup and a skillful technique to transfer the propulsion forces into speed [3; 4; 5]. Therefore, fitness and technique trainings are crucial for competitive rowers [5]. Outdoor rowing training may not always be feasible since performance of rowers can be affected by unpleasant weather conditions [6; 7]. Indoor training conducted with rowing machines offers a valuable alternative to outdoor practice [8]. Over the past decades, various rowing machines have been developed to yield a realistic rowing training [9]. Overall, the developed machines can be grouped in four categories depending on the technical aspects: indoor rowing tanks, ergometers, ergometer simulators, and virtual reality simulators [10]. For indoor-tank rowing, two large unit water-tanks are used next to a fixed rowing boat [11]. Since the oars directly interact with the real water, the resistance at the oar blade is naturally present. However, water tanks require specially constructed large spaces, which might be challenging to maintain. Ergometers provide a useful strength training opportunity indoors. On an ergometer, a rower interacts with a handle to simulate the resistance. Rendered resistance is mainly dependent on the pulling speed of the handle. Ergometers generate the desired resistance forces through friction-based interaction of a flywheel with air or water [12]. Since ergometers built with a stationary footrest were found to increase inertial forces and joint injuries compared to the on-water rowing [13], moving footrest systems were also proposed for ergometers such as Rowperfect(r) Indoor Sculler [14] and Concept(r) Dynamic [15]. Thus, the boat's acceleration and deceleration at each stroke can be simulated on such ergometers. Ergometers do not render the essential kinematic and dynamic characteristics of an oar movement. Thus, advanced ergometer simulators that incorporate the actual handling of a rowing oar with three degrees of freedom were developed [16; 17; 18]. In ergometer simulators, rowers manipulate one (sweep) [16] or two shortened oars (sculling) [17] as in the case of actual rowing boats. The rolling motion of an actual boat can also be simulated on ergometer simulators. However, rowing simulators do not incorporate actual water dynamics to render the resistive forces. Resistance is rendered with an air fan and disc brake system, and the resultant force perceived by the rower is mainly dependent on the speed of the oar. Additionally, none of the ergometer simulators provide any visual or auditory displays to bring the realism of the training closer to the on-water rowing experience. Thus, virtual reality simulators were developed to augment the realism of indoor rowing training [19; 20; 21; 22]. The virtual rowing training platform SPRINT was developed at Scuola Superiore S.Anna, Pisa, Italy [19; 20]. The SPRINT platform included two shortened oars with three degrees of freedom (DoF) each, a fixed foot stretcher, and a sliding seat. Visual rendering of the rowing scenario was coupled to the output of a mathematical model that combined the movement of boat, oars, and a rower. Rendering of hydrostatic vertical forces and oar weight was realized by a mass-spring system. The vertical force model only depended on the vertical rotation of the oar, i.e., the effect of longitudinal rotation of the oar was neglected. Rendering of the horizontal forces in the virtual water was based on a modified form of a dissipation mechanism used in Concept(r) ergometers. Due to this mechanism, haptic rendering of the horizontal forces did not capture the fluid-dynamics characteristics of the oar blade-water interaction.