Introduction

Elite swimmers are characterised by their ability to reduce the resistive forces from the water, thus achieving fast swimming velocities with sustainable effort (Cappaert et al., 1996). Therefore the analysis of resistive forces during swimming, otherwise known as 'active drag', is fundamental to understanding how swimming performance can be improved. Several means of measuring active drag experimentally have been used by researchers. These include the Velocity Perturbation Method (Kolmogorov et al., 1997), and the Assisted Towing Method (Mason et al., 2011). While these methods provide an indication of active drag over the period of a complete stroke cycle, they cannot provide accurate detail of the temporal pattern of net forces acting during a stroke cycle because the instantaneous force reflects the motion of the attachment point of the force measuring device to the body, rather than reflecting the acceleration of the whole body mass. The 'Measurement of Active Drag' (MAD) system (Hollander et al., 1986) measures forces directly as the swimmer pushes against a series of underwater fixed plates while swimming. A concern with this system is that stroke kinematics and torques acting on the body differ from those in free swimming thereby affecting body alignment and drag. Further, the force generated by the pushing action of the upper limbs is measured without consideration of the leg kick, thus not providing an accurate representation of the swimmer's propulsive output.

Detail regarding the temporal pattern of the net force provides insight into the effectiveness of the swimming technique. For example, large fluctuations in net force indicate that the resistive force is much larger than the propulsive force and vice versa. Thus, when the acceleration of the whole body centre of mass (CM) is measured, phases of the stroke cycle in which forces are not being applied effectively and when the body encounters great resistance can be identified and linked to the technique of the swimmer to improve performance.

Intra-cyclic velocity variability (IVV) has been analysed by researchers with the rationale that there is an inverse relationship between magnitude of the difference of maximum and minimum velocity within a stroke cycle and swimming efficiency or skill (Barbosa et al, 2006; Cappaert et al., 1995; Togashi and Nomura, 1992). The IVV of the hip during the propulsive phases of right and left upper limbs is frequently used to assess asymmetries in bilateral contributions to propulsion (Payton and Wilcox, 2006). However, the velocity and derived accelerations based on the motion of the hips have been shown to differ considerably from the motion of the CM (Figueiredo et al., 2009; Psycharakis and Sanders, 2009). Psycharakis and Sanders (2009) found mean errors in CM velocity of 10% for maximum and minimum velocity and 20% for the range of velocity relative to mean velocity of male front crawl swimmers. Similarly, Figueiredo et al (2009) reported RMS errors in velocity over the stroke cycle of front crawl swimmers ranging from 0.16 to 0.30 m.s-1 and RMS errors in acceleration between 5.38 and 7.86 m-s-2. These findings indicate that acceleration of the hip does not reflect the acceleration of the CM and cannot be used with confidence to assess effectiveness of technique in minimizing active drag.

Three dimensional (3D) analysis of IVVs based on velocity of the CM derived from digitized video data has been conducted recently (Figueiredo et al, 2009; Psycharakis et al., 2010). However, assessment of velocity changes without calculating or considering forces, limits the confidence with regard to interpreting swimming effectiveness. For example, an inefficient swimmer with a high stroke frequency can have smaller IVVs than a swimmer with a low stroke frequency despite having larger fluctuations in net forces. That is the duration and pattern of the forces, and their links to the swimming actions, must be taken into account.

Acceleration of the CM, and therefore net force, can be obtained using the inverse dynamics approach defined by Whittlesey and Robertson (2004) as 'the process by which forces and moments of force are indirectly determined from the kinematics and and inertial properties of moving bodies'. The position of the CM can be obtained by modelling the body as a series of rigid links from which the CM position is obtained for each video frame. Velocity of the CM is the first time derivative of the CM position and acceleration is the second derivative. The segment mass and centre of mass locations relative to digitized landmarks defining the segment are input to a computational routine that calculates CM by taking moments that is multiplying the segment mass by the perpendicular distance (its respective x, y, or z coordinate) of the segment centre of mass about orthogonal reference axes and dividing by whole body mass. The accuracy of the estimate of the CM then depends on the accuracy of the estimates of body segment masses and their centre of mass locations. These can be improved by 'personalising' the data to the characteristics of the participant. Jensen (1978) developed a personalised model of the human body in which each body segment comprised a stack of elliptical zones of 2cm depth. In Jensen's elliptical zone method, the diameters of the ellipses are obtained by tracing, with a mouse-controlled cursor, the outlines of the images of the segments from front and side camera views. By using the inverse dynamics approach in conjunction with digitized video data and body segment data obtained by the elliptical zone method, the low frequency (

Thus, the inverse dynamics approach can be very useful in swimming research to provide detailed information about velocity fluctuations throughout the stroke cycle, the forces causing those fluctuations, and their links to swimming technique. To date, automatic digitizing of a whole body rigid system has been problematic due to the difficulty of tracking markers continuously in an aquatic environment. Tracking of markers is adversely affected by water turbulence, presence of bubbles/vortices and the regular disappearance of body segment markers due to the rolling motion of the swimmer, motion of other body segments, and the transition of body parts across air and water mediums. Consequently, manual digitizing is necessary to minimize errors.

A major problem of applying the inverse dynamics approach to manually digitized data is that random errors are amplified with each derivative (Winter, 2009). A fourth order Butterworth digital filter is commonly used to remove random error and thereby reduce the errors in the derived velocity and acceleration data. However, the filter uses data on either side of the point being corrected and so data points near the start and finish of the data set cannot be filtered. Various means of extending the data prior to digital filtering have been tested. For example Vint and Hinricks (1996) found that errors in acceleration in the period of 10 frames from the end of the data set were reduced by extrapolating the data using either linear extrapolation or reflection. Giakis et al (1998) found that a 20 point extrapolation based on a least squares fit of the final 10 data points was superior to other methods of extrapolating including linear extrapolation, linear autoregressive modelling (DAmico and Ferrigno, 1990), and natural spline functions. Nevertheless, an error in the last 10 points was greater than in the other regions of the data set. Therefore, to attain reliable derived data at the endpoints of the data set it is evident that additional points should be digitized rather than extrapolating from the data points in the data corresponding to the period of interest.

The question of how many additional points need to be digitized to obtain accurate and reliable results is critical for two reasons. First, manual digitizing of several camera views is tedious and time consuming. This limits the number of subjects, trials, and stroke cycles that can be digitized in a study. Second, if a large data set is required, the field of view and the calibrated 3D space must be increased so that the whole swimmer is in view for the whole of the period digitized. This means that the image to be digitized is smaller, body landmarks harder to disAnguish and, as a consequence, accuracy reduced. Therefore, it is advantageous to determine how many additional points are sufficient to obtain reliable results near the start and finish of the stroke cycle.

While several researchers have used the inverse dynamics approach with manual digitizing to estimate three-dimensional kinematics of swimmers (Cappaert et al., 1995; Figueiredo et al., 2009; McCabe et al., 2011; Psycharakis et al., 2009; Sanders and Psycharakis, 2009) there is a paucity of information regarding 3D kinetics in swimming and the reliability of calculating them by inverse dynamics. Consequently knowledge of the patterns of net forces and their links to performance remains limited. The purpose of this study was to explore the reliability of estimating 3D linear kinematics and kinetics of a swimmer derived from digitized video and to assess the effect of framing rate and smoothing window size.

Methods

Participants

Two male swimmers volunteered to participate in this study (S1: age: 18yrs; height: 1.81 m; weight: 72.6 kg: S2: 18yrs; height: 1.86 m; weight: 76 kg). S1 was a front crawl sprint specialist (front crawl: 50m front crawl long course PB 25.00s). S2 was a front crawl and backstroke swimmer (back crawl: 50m short course PB 25.26s; 100m 59.32s; 200m 2:08.2; front crawl short course PB 50m 23.32s; 100m 51.80s; 200m 1:51.81). The study was approved by the Research Ethics Committee and the par ticipant provided informed consent.

Collection of anthropometric data

To enable identification of the endpoints of body segments when digitizing the video...