Date Published: May 9, 2019
Publisher: Public Library of Science
Author(s): Lotte L. Lintmeijer, John P. T. Onneweer, Mathijs J. Hofmijster, Willem A. Wijgergangs, Hans de Koning, Bert Clairbois, Jerry Westerweel, Ernst J. Grift, Mark J. Tummers, A. J. van Soest, Anna Pandolfi.
To analyze on-water rowing performance, a valid determination of the power loss due to the generation of propulsion is required. This power los can be calculated as the dot product of the net water force vector (F→w,o) and the time derivative of the position vector of the point at the blade where F→w,o is applied (r→PoA/w). In this article we presented a method that allows for accurate determination of both parameters using a closed system of three rotational equations of motion for three different locations at the oar. Additionally, the output of the method has been validated. An oar was instrumented with three pairs of strain gauges measuring local strain. Force was applied at different locations of the blade, while the oar was fixed at the oarlock and the end of the handle. Using a force transducer and kinematic registration, the force vector at the blade and the deflection of the oar were measured. These data were considered to be accurate and used to calibrate the measured strain for bending moments, the deflection of the oar and the angle of the blade relative to its unloaded position. Additionally, those data were used to validate the output values of the presented method plus the associated instantaneous power output. Good correspondence was found between the estimated perpendicular blade force and its reference (ICC = .999), while the parallel blade force could not be obtained (ICC = .000). The position of the PoA relative to the blade could be accurately obtained when the perpendicular force was ≥ 5.3 N (ICC = .927). Instantaneous power output values associated with the perpendicular force could be obtained with reasonable accuracy (ICC = .747). These results suggest that the power loss due to the perpendicular water force component can be accurately obtained, while an additional method is required to obtain the power losses due to the parallel force.
For an accurate determination of the average power lost to the generation of propulsion per stroke cycle (P¯blade; see Table 1 for a list of all abbreviations), valid information about the net water force vector at the blade of the oar (F→w,o) and its associated point of application (PoA) are essential since:
where T is the time duration of a stroke cycle and r→˙PoA/w is the time derivative of the position vector (i.e. the velocity vector) of the point of the blade where F→w,o is applied relative to an earth-bound frame of reference (r→PoA/w). Determination of F→w,o, r→PoA/w and its time derivative is not trivial due to the (1) deflection of the oar and (2) a constantly changing force distribution at the blade resulting in an unknown and time-variant point of application of the water force. In previous studies [1–8], power loss due to the generation of propulsion has been estimated assuming the oar to be rigid and the PoA of the water force vector to be in the middle of the blade. Additionally, the force component parallel to the blade has been typically neglected. These assumptions are not only unrealistic [9, 10], but do also affect calculated values of P¯blade significantly .
In this article we presented a method in which we used the bending oar moments measured with strain gauges to determine the net propulsion force vector and its r→PoA/w in rowing. Additionally, we validated the accuracy of the obtained force vector and its r→PoA/w for a simulated rowing situation. We confirmed that output of the strain gauges attached at a rowing oar shaft can be accurately calibrated for (1) internal bending moments, (2), the deflection of the oar, and (3) the orientation of the blade relative to an earth-bound frame of reference. Most importantly, we found that the perpendicular component of the propulsion force vector (Fw,oy′) could be validly obtained. Moreover, we found that r→PoA/w could be accurately determined when the beginning of the blade was displaced with more than.58 cm in y-direction, which corresponds to a perpendicular force of 6.0 N for this particular oar. Additionally, we found that an increase in the perpendicular force, resulted in a more accurate determination of r→PoA/w. Subsequently, we have shown that the power output associated with the perpendicular force resulting in bending of the oar could be determined with reasonable accuracy. The parallel force component could not be estimated.
The aim of this study was to describe and evaluate a method that allows for an accurate determination of the power loss due to the generation of propulsion in rowing. As mentioned in the introduction, an accurate quantification of the water force vector, the r→PoA/w, and its time-derivative are crucial for obtaining insight in that power loss. Despite the fact that the parallel force component relative to the blade could not be obtained, we are the first who developed a cost-effective practical method that allows for the determination of a perpendicular force component in combination with its time-varying r→PoA/w in on-water rowing practice. The presented method is therefore a promising option to gain more insight in the power losses due to the generation of propulsion during on-water rowing.