Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (2024)

Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (1)?Mathematical formulae have been encoded as MathML and are displayed in this HTML version using MathJax in order to improve their display. Uncheck the box to turn MathJax off. This feature requires Javascript. Click on a formula to zoom.

ABSTRACT

The purpose of this study was to describe and explore an inertial measurement unit-based method to analyse drag forces and external power loss in wheelchair tennis, using standardised coast-down and 10 m sprint tests. Drag forces and power output were explored among different wheelchair-athlete combinations and playing conditions (tyre pressure, court-surface). Eight highly trained wheelchair tennis players participated in this study. Three inertial measurement units (IMUs) were placed on the frame and axes of the wheels of their wheelchair. All players completed a set of three standardised coast-down trials and two 10 m sprints with different tyre pressures on hardcourt surface. One athlete completed additional tests on a clay/grass tennis-court. Coast-down based drag forces of 4.8–7.2N and an external power loss of 9.6–14.4W at a theoretical speed of 2 m/s were measured on hardcourt surface. A higher tyre pressure led to lower drag forces during coast-down tests on hardcourt surface (Fr (4)=10.7, p =0.03). For the single athlete, there was an external power loss of 10.4, 15.6 and 49.4W, respectively, for the hardcourt, clay and grass. The current prediction of power output was implemented during coast-down testing; unfortunately, the power prediction during 10 m sprints was difficult to accomplish.

KEYWORDS:

  • Sprinting
  • rolling friction
  • IMUs
  • wheelchair mobility performance
  • tennis performance

Introduction

Today, wheelchair tennis is part of all grand slam tennis tournaments, like Wimbledon and Roland Garros, alongside the able-bodied tournament (ITF Tennis, Citation2019). The main differences between wheelchair tennis and its able-bodied variant concern the obvious use of a wheelchair and a two-bounce rule. Wheelchair tennis has an open class for men and women, as well as a quad class for players with additional restrictions to the arms. Wheelchair propulsion requires substantial work of the upper body musculature (Veeger et al., Citation2002), potentially impacting racket handling, ball play and subsequently player performance (Goosey-Tolfrey & Moss, Citation2005; De Groot et al., Citation2017). The configuration of the wheelchair should therefore be critically optimised to meet the demands of the individual player and the game (Mason et al., Citation2010, Citation2013; Rietveld et al., Citation2021). One of the key areas identified by wheelchair tennis players is the interaction between tyre pressure and the surface competed on, impacting rolling resistance and thus propulsion and turning effort (Mason et al., Citation2010).

Wheelchair mobility performance in wheelchair court sports was previously defined by De Witte et al. (Citation2018) as all playing actions of a wheelchair athlete in the field, like sprinting, braking and turning. This conceptual framework can, for instance, be used to evaluate an athlete’s on-field wheeling performance in dependence on different aspects of wheelchair configuration. In wheelchair basketball, it was shown that wheelchair mobility performance can be affected by seat height, as well as mass (Van der Slikke et al., Citation2018; De Witte et al., Citation2020), while in wheelchair tennis, only the negative effects of the racket have been established (Goosey-Tolfrey & Moss, Citation2005; De Groot et al., Citation2017). An innovative way to determine elements of wheelchair mobility performance is the use of inertial measurement units (IMUs) during a match, training or testing situation (Van der Slikke, Berger, Bregman, Lagerberg et al., Citation2015; De Witte et al., Citation2018). In wheelchair tennis, this led to the development of inertial measurement unit-based field tests (Rietveld et al., Citation2019). Velocity, acceleration, rotational velocity and rotational acceleration data can be obtained from the gyroscope/accelerometer of IMUs and accurately describe characteristics of wheelchair mobility behaviour and performance (Shepherd et al., Citation2018; Van der Slikke et al., Citation2016a). More advanced algorithms have also been developed, such as a push detection algorithms during straight-line sprinting (Van der Slikke et al., Citation2016b). During wheelchair racing, IMUs were even able to predict the applied forces during the initial start-up, compared to the values of a force plate (<1 s) (Lewis et al., Citation2019). All the above-mentioned studies show the added value of IMUs in wheelchair sports research and its potential to improve performance. One potential role for IMUs is to determine rolling drag and power losses during standardised wheeling conditions.

Drag forces and power output have however never been assessed using IMU technology for wheelchair athletes. Drag forces during wheeled mobility consist of the rolling resistance (Froll), air resistance (Fair), internal friction (Fint) and gravitational effects (Fg) (Van der Woude et al., Citation2001). Froll is determined by the use of standardised coast-down tests, in other words, a deceleration test (De Klerk, Vegter, Leving et al., Citation2020; Lin et al., Citation2015; Sauret et al., Citation2012, Citation2010; Theisen et al., Citation1996). During a coast-down test, the linear deceleration of an immobile user sitting in a wheelchair is indicative of the momentary frictional losses due to the combination of all drag forces. Information about drag forces is used to estimate the power output at a given speed or steady-state propulsion conditions, which is in any form highly critical to performance (Coutts, Citation1994; Van der Woude et al., Citation1986). The power output of an athlete gives a valid indication of the athletes’ experienced external load, that needs to be produced to maintain a given velocity and which consequently could be compared to the internal load (mechanical efficiency, heart rate, rating of perceived exertion) (Van der Woude et al., Citation2001).

Even though the power output is an important feature of training/game preparation, it often remains an unknown measured condition-dependent aspect of wheeling performance for many coaches and athletes, since it is difficult to determine. An accessible method would help to understand the impact of the individual rolling resistance and subsequently the necessary external power output which would lead to less effort for the athlete to propel the wheelchair at a given velocity. Rolling resistance is influenced by different wheelchair characteristics (e.g., wheel size, seating orientation, camber, tyre type and pressure) (De Groot et al., Citation2013; Mason et al., Citation2015), athlete characteristics (e.g., mass and mass distribution) (Fuss, Citation2009), as well as the playing environment (e.g., court surface) (Cowan et al., Citation2009; Koontz et al., Citation2005). Wheelchair tennis is the only wheelchair court sport played on a variety of surfaces (hardcourt, clay and grass). Knowledge on rolling resistance is necessary to make a better informed choice on wheelchair characteristics and understanding its consequences on testing, training and gameplay in wheelchair tennis (Mason et al., Citation2013).

The aim of the current study is therefore to describe drag force and power loss effects with inertial measurement units in standardised wheelchair tennis coast-down and 10 m sprint tests. The potential role of IMUs in the analysis of tyre pressure and different playing surfaces on drag forces and external power loss was studied. It was hypothesised that this novel IMU-based measurement strategy will prove the principle of determining drag forces and power loss and is a feasible and fruitful addition in wheelchair field testing. A higher tyre pressure would lead to lower drag forces and subsequently reduced external power loss.

Methods

Measurement device

Three inertial measurement units (next-generation IMU, Bristol, UK) were placed on the individual wheelchair, one on each of the axes of the rear wheels and one on the frame of the wheelchair (Rietveld et al., Citation2019; Van der Slikke, Berger, Bregman, Lagerberg et al., Citation2015) (). This IMU consists of a gyroscope, accelerometer and magnetometer and allows measurement of the linear and rotational positions, velocities and accelerations over time. All data were collected at 400Hz via Wi-Fi, which enabled all three IMUs collecting data synchronously.

Figure 1. Placement of IMUs on the wheelchair axes and frame

Participants

Eight highly trained wheelchair tennis players participated in this study using their own competition tennis wheelchair and racket, characteristics are summarised in . Body mass was determined using a digital weighing scale. All athletes played at a national or international competition level. All tests and protocols were approved by the Ethical Committee of Loughborough University (R18-P232). Athletes signed written informed consent prior to participation.

Table 1. Athlete and wheelchair characteristics (n =8)

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Design

All athletes completed the standardised coast-down tests and 10 m sprints with five different tyre pressures (−30%, −20%, −10%, recommended pressure, +10%) in counter-balanced order on acrylic hardcourt in their own customised tennis wheelchairs and tyres. There was a 2min rest period between all trials. Three athletes were tested with Clincher tyres, the other five used high-pressure TUFO tyres (TUFO, Otrokovice, Czech Republic). All tyres were in good to new condition and had similar widths (22 mm for TUFO, 25 mm for clincher). The recommended tyre pressure was 120 PSI for the Clincher tyres and 200 PSI for the TUFO tyres. Tyre pressure was measured and controlled using a high duty digital floor pump (Lezyne Shock Digital Drive, San Luis Obispo, USA). One athlete completed additional testing using the same protocol on a grass and clay court on two separate days. The grass and clay courts were typical wheelchair competition courts situated at the National Tennis Centre, London, UK.

Protocol

Coast down test

Three coast-down tests per tyre pressure condition were performed to determine the drag forces (De Klerk, Vegter, Leving et al., Citation2020; Sauret et al., Citation2010). For the grass and clay surface, only two coast-down tests were completed, due to time concerns. Without a racket, athletes were instructed to push the wheelchair with one or two pushes, depending on the severity of their disability, to a velocity of around 2–2.5 m/s. Using this velocity range, the air friction showed to be of minimal influence (Barbosa et al., Citation2016; Higgs, Citation1992). During the coast-down, athletes were instructed to place their hands on their knees, bend slightly forward, so castor wheels would stay on the floor, and sit as still as possible.

10 m sprint test

Two 10 m sprint tests per tyre pressure condition were completed using the tennis racket in the playing hand. Taking the average of the two trials gives the most reliable end times (Rietveld et al., Citation2019). Athletes were instructed to position their castor wheels behind the starting line in the backward direction for optimal rolling, after which a 10 m sprint was performed.

Predicting drag forces and external power loss

As previously mentioned, drag forces (Fdrag) consist of the rolling resistance (Froll), air resistance (Fair), gravitational effects (Fgr) and internal friction (Fint) (EquationEquation 1Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (3)(1) Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (4)Fdrag=Froll+Fair+Fgr+Fint(1) ). The components Fair, Fgr and Fint all have relatively small influence; Fair given the low velocities (<2.5 m/s) (Barbosa et al., Citation2016; Higgs, Citation1992), Fgr given no slopes are involved and Fint given low bearing friction around the wheel axes and proper maintenance (Van der Woude et al., Citation2001). In the current approach, the deceleration values, together with the mass of the wheelchair–athlete combination, were used to calculate an approximation of the drag force using Newton’s second law of motion (EquationEquation 2Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (5)(2) Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (6)Fdrag=Froll=ma(2) ), in which Fdrag equals Froll, m is the total mass of the wheelchair–athlete combination and a is the rate of deceleration. Dividing the rate of deceleration (a) by the gravitational constant (g) gives an approximation of the rolling resistance coefficient (μ) (EquationEquation 3Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (7)(3) Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (8)μ=a/g(3) ).

Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (9)(1) Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (10)Fdrag=Froll+Fair+Fgr+Fint(1)

Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (11)(2) Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (12)Fdrag=Froll=ma(2)

Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (13)(3) Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (14)μ=a/g(3)

The power output was also determined (EquationEquation 4Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (15)(4) Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (16)Po=Fdragv(4) ), in which Po is the power output, Fdrag the drag force and v the velocity.

Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (17)(4) Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (18)Po=Fdragv(4)

As an example, an average athlete of 70 kg (m), with a wheelchair of 10 kg (m) and a rate of deceleration of 0.10 m/s2 (a) will have a drag force (Fdrag) of 8N (e.g., (70+10) · 0.10). At steady-state propulsion of 2 m/s this results in an external power loss of 16W (e.g., 8·2).

Data analysis

All IMU data were imported and processed using Python (De Klerk, Citation2019). Gyroscope data were low-pass filtered with a recursive Butterworth filter, with a cut off frequency of 10Hz (Rietveld et al., Citation2019; Van der Slikke, Berger, Bregman, Lagerberg et al., Citation2015). Velocity of the coast down trials, as well as the 10 m sprints, were calculated using the gyroscope in the wheels, adjusting for skidding (Van der Slikke, Berger, Bregman, Veeger et al., Citation2015). Distance was calculated by integrating the angular velocity, multiplied by the radius of the wheel. Times on the 10 m sprint were based on the IMU data, as described in the study of Rietveld et al. (Citation2019). The start time of the 10 m sprint was defined as an initial velocity of 0.1 m/s and the end time was defined as the distance of 10 m covered by the wheels.

Coast down analysis

Deceleration values were determined as the slope of the velocity curve of the coast-down trials between two selected points. The selected starting point was taken at the beginning of the velocity curve, approximately 2seconds after the highest peak. The end point was set near the end of the velocity curve, approximately 2seconds before a new peak or a drop in the velocity signal occurred, due to possible movements before braking (). The ‘polyfit’ function from the ‘numpy’ package in Python was used to calculate the best fitting linear slope based on all the collected data points between the two selected points (Numpy, Citationn.d.).

Figure 2. Example of a coast down trial with the fitted polynomial curve (orange line) through the velocity curve (blue line). The green area indicates the selected area for the analysis

A typical example of a single coast-down trial is given in . The green area indicates the selected area and the orange line represent the fitted linear regression function through all samples of the velocity data in this time frame.

10 m sprint analysis

In contrast to a coast-down test, a sprint is a fully dynamic test, where the wheelchair and athlete interact. The main forward acceleration during sprinting is achieved by a push of the athlete on the hand rim (Van der Slikke et al., Citation2016b). Based on the IMU information, during every push, the wheelchair–athlete combination accelerates (push), followed by a short/brief deceleration phase (non-push/recovery) (). This moment of deceleration within the propulsion cycle, the part from the peak of the velocity signal to the bottom within that cycle, i.e., the local minimum, of the velocity signal can be seen as small coast-down elements during sprinting. These deceleration areas were selected and used as coast-down areas, . The acceleration signal was filtered as described in the study of Van der Slikke et al. (Citation2016b). For the first five pushes of the 10 m sprint, also the differences in mean and peak drag forces, power loss, as well as push- and recovery time were determined.

Figure 3. Recovery detection using the main forward deceleration (left). The light thin grey line through the blue line is the raw acceleration signal, the blue thicker line the filtered acceleration signal. The red line represents the velocity signal. Every black dot is a detected (non)-push. Selected coast down areas during a 10 m sprint (right). The red line is again the velocity signal, the green area indicates the selected coast-down area, the orange line is the fitted polynomial curve. The black dot represents the position of the main forward deceleration (non-push), determined using the left figure

Quality of the trials

The quality of the coast-down trials was determined using the ‘R2-score’ and ‘mean-squared-error’ of the ‘scikit-learn metric’ package in Python (Scikit-Learn, Citationn.d.). Taking the square root of the mean squared error resulted in the root-mean-squared-error (RMSE). Since the R2 and RMSE scores are both dependent on the kind of data, the quality cut-off for coast-down trials is advised to be >0.9 on R2 and <0.05 on RMSE.

Statistical analysis

The reliability of the coast-down trials was assessed using the absolute and relative reliability. Bland Altmann Plots with 95% limits of agreement were used as an extra control method. Intraclass correlations (ICC) were determined, using a two-way random ANOVA model, with type absolute agreement and single measurement.

Coast-down tests with the best quality score and highest R2/lowest RMSE were tested. Differences in drag forces, RMSE and R2 scores during coast-down testing were determined using a Friedman test, a non-parametric test, due to the low sample size. Differences between end time, push/recovery time, mean/peak forces and power during the 10 m sprint were also analysed using a Friedman test for the first 5 pushes (1, 2, 3, 4, 5) and different tyre pressures (−30%, −20%, −10%, recommended, 10%). Statistical significance was set at P <0.05, a post-hoc test with Bonferroni correction was used when a main effect was observed. Kendall’s W effect sizes were used to determine the strength of the relationships, small (0.1–0.3), medium (0.3–0.5) and large (>0.5). The Shapiro-wilk tests were used to determine the normal distribution of the data. All data were analysed using R version 4.0.1.

Results

Quality of coast-down trials

There were no systematic differences in quality observed between the three coast-down trials per participant. The mean quality of all hardcourt trials had an RMSE: 0.025 and R2: 0.977, indicating a good quality of the trials, no differences were observed between trials and tyre pressure for RMSE and R2. The mean quality of the trials of the athlete on the three surfaces was 0.044, 0.042 and 0.041 as RMSE scores and 0.934, 0.965 and 0.993 as R2 scores, respectively, for hardcourt, clay and grass.

Bland–Altman plots of all different trials of all participants can be seen in . The mean difference is almost equal to 0, and only a limited number of samples are outside the 95% limits of agreement. The relative reliability assessed using ICC showed a score of 0.866, indicating good reliability.

Figure 4. Bland Altman Plot. The difference between the deceleration values of the trials vs. the mean of the deceleration values of the trials, including 95% limits of agreement

Coast-down drag force and power loss

Mean deceleration values during coast down testing on hardcourt surface for all tyre pressure types and athletes combined ranged from approximately 0.06 to 0.09 m/s2. Taking an average mass of an athlete of 70 kg, with a wheelchair of 10 kg, this resulted in mean rolling resistance forces of 4.8–7.2N (e.g., 0.06 · (70+10)=4.8). If the athlete pushes at a constant velocity of 2 m/s, there is a predicted external power loss of 9.6–14.4W (e.g., 4.8·2=9.6). This means on average, throughout the complete cycle, the athlete needs to deliver 9.6–14.4W to compensate for the loss in power, more or less power will lead to an acceleration/deceleration.

All coast down trials of the different pressures combined with court-surface can be seen in . Comparison of coast down trials on three different surfaces for one athlete resulted in mean deceleration values of 0.081, 0.117 and 0.391 m/s2 and rolling resistance coefficients of 0.008, 0.012, 0.040, respectively, for hardcourt, clay and grass. Given the mass of this specific athlete–wheelchair combination (65+10=75 kg) and a velocity of 2 m/s, this led to drag forces of 6.1, 8.8 and 29.3N and external power loss values of 12.2, 17.6 and 58.7W, respectively, for hardcourt, clay and grass.

Figure 5. Coast-down trials of all five tyre pressure conditions shown for hardcourt (left), clay (middle) and grass (right) (n=1). Of interest is the slope of the regression lines, the height differences are only dependent on the initial velocities

The drag forces for different tyre pressures (−30%, −20%, −10%, recommended, +10%) and surfaces (hardcourt, clay, grass) can be seen in . A main effect was observed for tyre pressures (Fr (4)=10.7, p =0.03) (). The Bonferroni correction revealed no differences between the individual levels. No effect for court surfaces was explored, due to the n =1 design.

Table 2. Differences in coast-down test and 10 m sprint test variables (Mean (±SD)) between tyre pressures (n =8)

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Figure 6. Rolling resistance force (N) between all different tyre pressures (−30%, −20%, −10%, recommended, +10%) on hardcourt surface (left) (n=8) and surfaces (hardcourt, clay, grass) (right) (n=1). The diamonds indicate outliers, which represents one athlete in the tyre pressure figure

Power loss during 10 m sprint

No differences in sprint times, drag forces, power losses and push/recovery times were observed between the different tyre pressures (). Mean deceleration values during the coast down areas of 10 m sprints on hardcourt surface were on average 4.4 m/s2, while the cycle time was on average 0.52s. Taking an average recovery time of 0.18s, this indicates the loss of power is experienced in approximately 35% of the complete pushing cycle (e.g., 0.18/0.52·100=35). During the first five pushes, the push time decreased, while the recovery time, mean and peak power losses per push increased ().

Table 3. Differences in 10 m sprint test variables (Mean (±SD)) within the first 5 pushes (n =8)

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Corresponding to the drag tests, differences were observed on the 10 m sprint between all different surfaces, end times were 3.25s for hardcourt, 3.49s for clay and 3.71s for grass (). The mean and peak velocities reduced on grass compared to clay and compared to hardcourt. Mean decelerations were 4.79 m/s2 for hardcourt, 4.35 m/s2 for clay and 5.00 m/s2 for grass. This led to mean power losses per push of 1191W for hardcourt, 1039W for clay and 1112W for grass. The external power losses occurred in approximately 37% of the push cycle for hardcourt, 39% for clay and 36% for grass.

Figure 7. 10 m sprint of one athlete on hardcourt (blue), clay (red) and grass (green)

Discussion and implications

Discussion

The current research showed the added benefit of IMU-based coast-down tests in wheelchair tennis and wheelchair sports in general, which is in accordance with the first hypothesis. It was possible to predict power losses in dependence on the wheelchair-athlete configuration and to compare them to wheelchair tennis relevant 10 m sprints. The method during coast-down testing was shown to be sensitive enough to measure small differences in rolling resistance based on tyre pressure. A higher tyre pressure led to a reduction of the drag forces and external power losses, which is in agreement with our second hypothesis. This research showed a first indication of big differences in rolling resistance between typical tennis court surface types.

The small differences in tyre-pressure dependent rolling resistance did not lead to differences in the 10 m sprint end times. From a theoretical perspective, the athlete probably had to produce more power to get to the same overall sprint results. Cumulatively over a match, this could lead to higher external loads for the athlete and impact endurance and fatigue, since male wheelchair-tennis athletes cover 2200 m per set, reaching peak velocities of 4 m/s (Mason et al., Citation2020). For court type, an effect on sprint times is present, but this was only investigated for one athlete. Finally, an attempt was made to use the continuous IMU sprint time series to look at the decelerations within the individual pushes during a sprint. These decelerations were on average 4.4 m/s2 and took approximately 35% of the cycle time. It is assumed the athlete actively contributes to the acceleration/deceleration of the chair, by moving the upper body towards the castor wheels. This makes separate IMU-based coast-down tests a relevant addition to field tests.

It was shown that IMUs are capable of registering drag forces during coast-down testing, also with good quality scores and inter-trial reliability, looking at the RMSE and R2 scores, as well as the Bland Altman plots. It would be advised to use a trial with the best RMSE and R2 scores within each athlete for further use. Drag forces determined using coast-down testing on hardcourt surface (± 6–7N) were difficult to compare to other literature due to the variety of surfaces and the use of sports wheelchairs (De Groot et al., Citation2013; Hoffman et al., Citation2003; De Klerk, Vegter, Leving et al., Citation2020; Van der Woude et al., Citation2001). In the previous research, grass was also determined as the surface with one of the highest negative torques during wheelchair propulsion (Koontz et al., Citation2005). Although only one athlete has been tested on all surfaces, the predicted drag forces still gave indications about the higher loadings while playing on different tennis court surfaces. The predicted power output values during coast-down testing already gave good indications of the influence of tyre pressure and court surface. Power output is nowadays substantially used in the sports and wheelchair research, but not yet applied to wheelchair sports (Groen et al., Citation2010; Passfield et al., Citation2017; Van der Woude et al., Citation2001). For researchers and coaches, power output should become a more standard outcome in wheelchair sports measurements. Measuring power output gives detailed information about the external load of wheeling and performance, while it can be used as an important indicator of physical capacity of an athlete, which is a more valid measure compared to only peak velocities and end times (Van der Woude et al., Citation2001).

IMUs were already capable of push detection during sprinting, as well as first predictions of applied forces while driving over a force plate (Lewis et al., Citation2019; Van der Slikke et al., Citation2016b). In the current research, this was extended with a reverse non-push algorithm during the 10 m sprint, to determine the most prominent decelerations, as well as a distinction between positive and negative decelerations (push/recovery time), drag forces and power losses. It was in general shown that push time decreased, while recovery time increased during the first five pushes. The mean and peak power losses also increased, which was as expected with an increasing velocity. The power losses during sprinting were similar across surfaces and the slightly higher power losses for hardcourt surface might be explained due to the higher peak velocities reached on this surface or the n =1 design. These measured power losses were observed for approximately 35% of the time, indicating an athlete has about 65% of the total push cycle to compensate for these losses and keep accelerating the wheelchair–athlete combination.

Measured external power losses (1230 to 2370W) in the 10 m sprint are difficult to compare with other available literature. This is caused by the current newly taken approach using IMUs to determine power, the lack of power loss measurements in the field and the different definitions of peak/maximal power output to compensate for these losses across the literature. A study by Van der Scheer et al. (Citation2014) is one of the only few who completed power measurements during sprinting in the field using instrumented measurement wheels. This study found a bilateral peak power output of approximately 450W using a group of students during a 15 s sprint. Two examples of studies that completed sprint testing with wheelchair rugby/basketball players on a wheelchair roller ergometer, with a 15s sprint (Goosey-Tolfrey et al., Citation2018) and 30 s Wingate (Hutzler et al., Citation1995) found bilateral peak power values of approximately 650W (Goosey-Tolfrey et al., Citation2018) and 1100W (Hutzler et al., Citation1995). More similar were the studies of De Groot et al. (Citation2017, Citation2018) in which 5s sprints using a rolling start were completed by wheelchair tennis players on a stationary wheelchair ergometer. Peak power output values of approximately 2000W in total bi-manual power production during a 5s sprint were observed. It was necessary to present the current method of power loss prediction, since wheelchair tennis players already experience power losses before the push, due to the difficulty of coupling/decoupling of the racket to the rim, which results in a higher peak power during the push (De Groot et al., Citation2017). Still important information is missing to draw more precise conclusions, body and/or wheelchair mass highly influence the resistance during wheelchair sprinting (Fuss, Citation2009). During sprinting, the chair is moving backwards when the body/arms are moving forward; in other words, a shift of the centre of mass occurs, which was not taken into account and is an essential part of wheelchair sprinting.

Limitations

Although only a small number of athletes participated in the study, which is a common issue in wheelchair sports research, meaningful significant low-error results were presented (Bernardi et al., Citation2010; Croft et al., Citation2010). The athletes were highly experienced diverse players, which makes the research generalisable to a bigger population. Due to the use of highly experienced athletes, time concerns were also an important aspect, which meant not all field tests (Rietveld et al., Citation2019) and court types could be examined in the most extensive manner. With longer coast-down trials and higher velocities, also other drag components could have been determined, but as previously mentioned this is difficult to achieve taken the limited size of tennis courts. Lastly and most importantly, the current method for power measurement in the field only used the power calculated from the base of the wheelchair. With more IMUs available, IMUs can be placed on the torso to also investigate the influence of body movements and changes in the centre of mass.

Future recommendations and practical implications

The current prediction of power output was implemented during coast-down testing; unfortunately, the power prediction during 10 m sprints was difficult to accomplish. These methods of power prediction during coast-down testing and 10 m sprints still need to be extended in the future research and also validated with the use of high-speed cameras, three-dimensional position registration or the use of measurement wheels, such as a SmartWheel (Cooper, Citation2009). Gathering this information could lead to more precise information about propulsion technique variables in the field (Van der Woude et al., Citation2001; Vegter et al., Citation2014). More detailed information can lead to the investigation of different wheelchair aspects using athletes own sports wheelchair, such as the potential use of different hand rims (De Groot et al., Citation2018). Instrumented measurement wheels are able to directly measure the torques applied on the hand rim and combined with the angular velocity power output can be measured when the hands are coupled to the hand rim. A disadvantage of a measurement wheel is the relative additional mass (± 4 kg), which influences performance (De Groot et al., Citation2013). IMUs are small light devices which can be placed on players own sports wheelchair, making the measurements easy to apply during training and matches. Adding an extra IMU to the torso is an essential part of future research. This extra sensor gives valid information about the active body movements, leading to the next step in the measurement of power in the field during wheelchair sports.

The presented method of power prediction during coast-down testing in wheelchair tennis provides information about the influence of tyre pressure and court-surfaces. Ecologically valid testing is important to make a true comparison between test conditions, test occasions and players. Rolling coefficient values of hardcourt, clay and grass could be used as reference materials for testing on wheelchair ergometers (De Klerk, Vegter, Veeger et al., Citation2020). Using these values, the surfaces could be simulated for steady-state wheelchair propulsion, as well as sprint testing in the lab. It would be recommended to increase the resistance based on the other drag forces during sprint testing, as with higher velocities the air resistance will also come into play (Barbosa et al., Citation2016; Fuss, Citation2009; Higgs, Citation1992; Van der Woude et al., Citation2001). Non-linear fitting could have been a solution to also gather the air drag component; unfortunately, longer trials would have been needed (>15 s) because of the high influence of the initial velocity on this equation (Chua et al., Citation2011; Fuss, Citation2009). On a tennis-court, this is unfortunately impossible to achieve, due to the limited size of the court.

Wheelchair tennis matches are played on a variety of surfaces (grass, hardcourt, and clay). Wheelchair propulsion, transfers and playing wheelchair sports already lead to higher loadings on the shoulder complex (Collinger et al., Citation2008; Heyward et al., Citation2017). Although tyre pressure only showed minimal effects on the drag forces and power losses, good maintenance of tyres is an important issue, all small parts eventually add up. The addition of a tennis racket might make wheelchair tennis athletes even more vulnerable to shoulder issues compared to other wheelchair court athletes (De Groot et al., Citation2017). Clay led to approximately 1.5 times higher drag forces compared to hardcourt and grass even led to five times higher drag forces compared to the other two surfaces. In regular manual wheelchair propulsion, it was already shown that grass has a big influence on the distances travelled (Koontz et al., Citation2005). It is recommended for players to find a good trade-off between training on different surfaces since this leads to higher forces, possible fatigue and more chances of injuries. For coaches, it would be advised to include coast-down testing as part of the regular testing sessions. Coast-down tests provide important insights regarding wheelchair maintenance, as well as external power losses of the wheelchair–athlete combination. External circ*mstances as the wheelchair characteristics (e.g., tyre characteristics or wheelchair maintenance) or court-surfaces have an important influence on performance in wheelchair sports.

Conclusion

This research showed the added value of coast-down testing in wheelchair tennis, by the prediction of drag forces and power loss. The usefulness and sensitivity of these measures were illustrated by the negative effect of reduced tyre pressure on the necessary power output for the group of athletes. Albeit measured in only one person, court type is a more important factor to consider, with clay showing almost 1.5 times higher drag forces compared to hardcourt, while grass showed even five times higher drag forces compared to hardcourt.

Acknowledgements

The authors would like to thank the United Kingdom Lawn Tennis Association for the provided courts, players and financial resources. In particular special thanks to Alex co*ckram. Thanks to the players themselves for their participation. Thanks to the Peter Harrison Foundation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Inertial measurement units to estimate drag forces and power output during standardised wheelchair tennis coast-down and sprint tests (2024)
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