It has long been acknowledged that an optimization of wheelchair geometry to complement the users’ physical characteristics is a necessity for improving the ergonomics of manual wheelchair propulsion and sports performance (17,38 23 23 3,15,31 24
From a theoretical perspective, the mechanical effects of adjusting wheel size are clear, with smaller wheels known to increase rolling resistance (20 Po ) for the user (36 11,14,16,37 Po are likely to be unaffected. Despite this, increases in physiological demand were still established in larger hand-rim diameters (14,37 16,33,37 23
Although an increase in physiological demand is anticipated in smaller wheels, because of the relationship previously alluded to between Po and physiological demand (36 5 4,13,21,22,25
The aim of the current investigation was to determine the effect of different wheel sizes with fixed gear ratios on the physiological and biomechanical responses to submaximal wheelchair propulsion in a group of highly trained athletes. Based on the limited quantitative literature, it was hypothesized that smaller wheels would increase the Po requirements from the user and the physiological demand. Increases in stroke frequency, upper body joint excursions, and hand-rim kinetics were expected to account for any changes in physiological demand resulting from wheel size manipulations. These anticipated changes in propulsion biomechanics were also hypothesized to potentially exacerbate the risk of injury in smaller wheel sizes.
METHODS
Participants
Thirteen highly trained wheelchair basketball players (age = 24 ± 7 yr, body mass = 66.6 ± 15.6 kg) volunteered to participate in the current study. Based on previous research (24 a priori power analysis revealed that a sample size of ≥10 was required to achieve a minimum statistical power of 90% at an α level of P = 0.05. Procedures for the current investigation were approved by Loughborough University’s Ethical Committee, and all participants provided their written informed consent before testing. Details of participants’ physical characteristics and their current wheelchair configurations are documented in Table 1 . These included participants’ self-selected wheel sizes and sitting height (called elbow extension). Sitting height was determined for each participant in their own sports wheelchair, using the degree of elbow extension induced when the hands were positioned on top dead center (TDC) of the hand-rims. Greater degrees of elbow extension reflected a higher sitting position.
TABLE 1: Physical characteristics of the participants and details of their sporting involvement.
Experimental design
All participants were tested in an adjustable sports wheelchair (Top End Transformer; Invacare, Elyria, OH) in three different wheel sizes commonly used in the wheelchair court sports (24 inches = 0.592 m, 25 inches = 0.614 m, and 26 inches = 0.646 m). The hand-rim diameters of these wheel sizes were as follows: 24 inches = 0.533 m, 25 inches = 0.552 m, and 26 inches = 0.585 m. Veeger et al. (33
Each wheel size was configured with a separate and individually calibrated force-sensing hand-rim (SMARTWheel; Three Rivers Holdings, Mesa, AZ) to determine the three-dimensional forces and moments applied during propulsion. Each SMARTWheel weighed approximately 4.7 kg. To counterbalance the superior weight and inertia of the SMARTWheel in relation to a conventional wheel, additional weight was added around the hub of the opposing wheel, resulting in an overall wheelchair mass of 18 kg. Each participant’s self-selected sitting height was replicated in the adjustable wheelchair by making minor adjustments to the seat height to ensure that the aforementioned elbow extension angles and was controlled across wheel size conditions. The only area of configuration that could not be standardized between conditions was the distance between TDC of both wheels owing to the use of a fixed length camber bar in each wheel size. This subsequently led to minor differences between wheel sizes (24 inches = 0.496 m, 25 inches = 0.477 m, and 26 inches = 0.468 m). Rear-wheel camber was kept constant at 18° owing to the favorable performance of wheelchair basketball players in this setting (24 −1 ; 0.7%) on a motor-driven treadmill (H/P/Cosmos Saturn, Nussdorf-Traunstein, Germany). The wheel size conditions were randomized, and the protocol ensured a full recovery between conditions with a 15-min rest period implemented between trials. This was monitored by comparing heart rate (HR) values to the pretest values.
Cardiorespiratory measures
During the final minutes, expired air was collected using the Douglas bag technique (Cranlea, Birmingham, United Kingdom) and HR was recorded at 5-s intervals using radiotelemetry (PE4000 Polar Sport Tester, Kempele, Finland). On completion of each condition, rating of perceived exertion (RPE) was obtained for localized, centralized, and overall fatigue using the Borg scale (7 2 ) and respiratory exchange ratios (RER) were calculated for each wheel size condition. Gross mechanical efficiency (ME), defined as the ratio of the external work produced to the energy expended (34 Po values derived from the SMARTWheel and energy expenditure from the V˙O2 and the oxygen energetic equivalent of the RER values using a standard conversion table (27
Kinetic measures
Each SMARTWheel was positioned on the left-hand side of the wheelchair and had been individually calibrated with known weights suspended from the hand-rims when wheels were positioned vertically. A calibration constant for each wheel could then be calculated to determine the raw forces and moments (2 F ) and moments (M ) derived from the SMARTWheel were defined as follows: Fx —horizontally forward, Fy —vertically downward, Fz —horizontally inward, and Mz —referred to the moment produced around the hub in the plane of the wheel (2 Po was calculated from the mean Mz and the mean angular velocity (ω ) of the wheel (26
The mean work per cycle was then derived from the mean Po and the mean stroke frequency (f ) according to Woude et al. (35
The vector sum of the SMARTWheel force components (Fx , Fy , and Fz ) enabled the resultant forces (F res ) applied to the hand-rims to be determined (10
The force that directly contributed to the rotation of the wheels, called the tangential force (F tan ) was also calculated whereby Rr −1 refers to the hand-rim radius (28
Using equations 3 and 4, the fraction of effective force (FEF), which describes the ratio of force that contributed toward forward motion (F tan ) in relation to the total force (F res ), was established (10
To establish an indicator of injury risk, the rate of force development was also calculated as the ratio between the change in F res from initial hand contact to the peak F res and the change in time between these two events (5
All forces and moments were expressed as mean values per stroke, which were then averaged over the total number of strokes produced during the 30-s data collection period. The only exception was in the calculation of mean Po , whereby the recovery phase was accounted for with Mz and the angular velocity of the wheel averaged from the onset of the first push to the completion of the final push.
The temporal parameters associated with propulsion were also computed from the kinetic data. Stroke frequency (strokes per second) was calculated by dividing the number of strokes during the 30 s by the change in time from the beginning of the first push to the end of the last push. Push time (PT) and push angle (PA) were defined as the period and the angle over which the hand exerted a positive moment around the hub of the wheel, respectively. All temporal parameters were derived from the SMARTWheel.
Kinematic measures
Video footage of each wheel size condition was captured via two synchronized, high-speed (100 Hz) gigabit ethernet video cameras (Basler piA640-210gc; Basler AG, Ahrensburg Germany). Cameras were positioned to the left of the treadmill, approximately 4 m back from the performance area to give an estimated optical axis of 60°. Both cameras were calibrated using a three-dimensional 20-point calibration frame with known coordinates (1.4 × 1.4 × 1.0 m). Seven reflective joint markers (19 mm in diameter) were placed on five anatomical landmarks on participants’ left-hand side (C7—neck, acromion process—shoulder, lateral epicondyle—elbow, midpoint between radioulna styloid process—wrist, third metacarpophalangeal joint—finger). Two further markers were positioned on the rear-wheel axle and the seat base–backrest intersects of the wheelchair (Fig. 1 ). Ten seconds of video footage was manually collected for each wheel size condition when kinetic data collection commenced.
FIGURE 1: Experimental setup demonstrating the SMARTWheel and the positioning of joint markers and the associated connections used for the biomechanical analysis.
A three-dimensional motion analysis system (SIMI Reality Motion Systems, Unterschleissheim, Germany) was used to digitize the location of each joint marker in both cameras. Five complete push cycles were digitized, and the middle three were used for analysis to avoid inaccuracies with the extreme data points (8 1
The angular displacements of all joints were analyzed at hand contact (HCon) and hand release (HRel). For analysis purposes, the propulsion cycle was divided into two phases: the push phase (HCon to HRel) and the recovery phase (HRel to HCon). The maximum and minimum displacements were obtained during both phases, and the ranges of motion were derived from these values. Angular displacements of the upper body segments were investigated in reference to the anatomical position, whereby the arms were positioned by the side of the body and the palms of the hands facing inward. Shoulder flexion, abduction, elbow and trunk flexion, and wrist extension were expressed as positive displacement values. Trunk motion was determined in the sagittal plane, as the angle created between the C7, seat base–backrest intersect marker, and the vertical. The maximum and minimum linear velocities of the wrist and hand were also measured throughout both phases of the propulsion cycle.
Statistical analyses
Means and SDs were calculated for all variables. The Statistical Package for Social Sciences (Version 16.0; SPSS, Inc., Chicago, IL) was used for all statistical analyses. Data were checked for normality using Shapiro–Wilk tests. Normally distributed dependent variables were examined using one-way ANOVA tests with repeated measures. Post hoc Sidak pairwise comparisons established differences between specific wheel sizes. When assumptions of normality were violated, the Friedman test was used with subsequent post hoc Wilcoxon signed-rank tests to identify specific differences between wheel sizes. Effect sizes (r ) for pairwise comparisons are presented to complement standard probability values where P ≤ 0.05 was considered to be statistically significant; the standardized threshold of r > 0.5 was used to define a large effect (9
RESULTS
The results revealed that wheel size significantly (P < 0.0005) affected the Mz and angular velocity during constant velocity wheelchair propulsion. Inverse relationships were established, with increments in wheel size shown to elicit a reduction in each of these dependent variables (P < 0.005, r = 0.81–0.98). External Po was also shown to be affected by wheel size (P < 0.0005). As originally hypothesized, Figure 2 demonstrated that reductions in Po were associated with increasing wheel size (P < 0.0005, r = 0.93–0.95).
FIGURE 2: Power output requirements (Po ) during each wheel size condition. *Significant difference between wheel sizes, P < 0.0005.
Wheel size significantly influenced the physiological demand of wheelchair propulsion, as displayed in Table 2 . An increased V˙O2 (reduced economy) was revealed for the 24-inch condition in relation to both the 25-inch (P = 0.01, r = 0.76) and 26-inch conditions (P = 0.001, r = 0.75). In addition, reductions in HR were noted in 26-inch wheels compared with 24-inch (P = 0.004, r = 0.81) and 25-inch wheels (P = 0.018, r = 0.74). In contrast, ME improved in smaller wheels, with 26-inch wheels demonstrating a significantly lower ME than 24-inch wheels (P = 0.002, r = 0.60) and 25-inch wheels (P = 0.006, r = 0.55). No significant effect of wheel size on the localized, centralized, or overall RPE was observed (Table 2 ).
TABLE 2: Mean ± SD values for the physiological variables assessed during different wheel size settings.
Work per cycle was also significantly affected by wheel size manipulations (P < 0.0005). As demonstrated in Figure 3 , the Wilcoxon signed-rank tests revealed that work per cycle diminished as wheel size increased (P ≤ 0.015, r = 0.58–0.63). Wheel size was found to have no statistically significant effect on the temporal parameters, stroke frequency, and PT. However, PAs were significantly influenced by wheel size (P = 0.011). Pairwise comparisons revealed that significantly greater PAs were associated with 24-inch wheels (106.3° ± 11.0°) compared with 26-inch wheels (99.8° ± 12.9°, P = 0.017, r = 0.74). Wheel size was shown to have no statistically significant bearing on upper body joint kinematics during the push or recovery phase of propulsion.
FIGURE 3: Changes in work per cycle evoked by different wheel sizes. *Significant difference between wheel sizes, P < 0.0005.
Hand-rim kinetic variables, mean F res (P < 0.0005) and mean F tan (P = 0.001) were also significantly influenced by wheel size. As illustrated in Figure 4 A, increments in wheel size resulted in decreased F res , reinforced by the Wilcoxon signed-rank tests (P ≤ 0.013, r = 0.53–0.63). A similar pattern was observed between wheel size and mean F tan (Fig. 4 B). However, the Wilcoxon signed-rank tests only revealed a statistically significant difference between the 24- and 26-inch conditions (P = 0.005, r = 0.57). Although differences in mean F tan between 24- and 25-inch wheels (P = 0.023, r = 0.47) and 25- and 26-inch wheels (P = 0.051, r = 0.42) approached statistical significance at P < 0.017, effect sizes were only moderate. In contrast, no significant effect of wheel size was observed for the mean FEF (P = 0.924), given the similar values reported in Figure 4 C. Although not statistically significant, the reduction in the rate of force development across wheel sizes approached statistical significance (P = 0.067) and is displayed in Figure 4 D. This was exemplified by the large effect size (r = 0.55) between 24- (399.2 ± 175.0 N·s−1 ) and 26-inch wheels (323.2 ± 125.2 N·s−1 ).
FIGURE 4: Adaptations in hand-rim kinetics to different wheel size conditions: (A) mean F res , (B) mean F tan , (C) mean FEF, and (D) rate of force development. *Significant difference between wheel size conditions, P < 0.05.
DISCUSSION
The results of the current investigation revealed that different wheel sizes with fixed gear ratio hand-rims significantly affected the physiological demand and propulsion kinetics in a standardized sports wheelchair configuration. These adaptations occurred predominantly through the dimensional changes evoked from wheel size adjustments and the consequential effects observed regarding Po requirements. As expected, an inverse relationship was identified between wheel size and Po because of a higher rolling resistance with decreasing wheel size (20 Po requirements of the user increased. Based on this and in association with the relationship between the energetic cost of wheelchair propulsion at constant velocities and increased Po , physiological demand was elevated in smaller wheel sizes (36 Po resulted from a higher angular velocity and Mz in smaller wheels, as to maintain the constant velocity of the treadmill these wheels needed to rotate at a greater rate and required a larger torque to facilitate this. As a result of the increased Mz and reduced hand-rim radius of smaller wheels, a larger F tan was also demanded in smaller wheel sizes.
As previously mentioned, an elevation in physiological demand was observed in smaller wheel sizes. This was demonstrated by the elevated V˙O2 (reduced economy) and HR responses in the 24-inch condition compared with the 26-inch condition. When using fixed wheel sizes, smaller-diameter hand-rims have been shown to reduce these responses (14,37 33 33 2 and HR when Po was increased, yet gear ratios remained constant. This appeared to support the results of the current study whereby fixed gear ratios were maintained with decreases in wheel size, yet the Po increases in observed in these settings were likely to have evoked the increased physiological demand. Although differences in V˙O2 and HR between wheel sizes appeared minimal in absolute terms, these were supported by large effect sizes (r = 0.74–0.81), suggesting that these differences were extremely meaningful. The value of reporting effect sizes is of increased importance when investigating elite athletes (18,30 29 2 and HR responses resulting from different-sized wheels could hold substantial practical relevance because the onset of fatigue could potentially be delayed during a competitive match.
Despite the increased V˙O2 and HR responses demonstrated in 24-inch wheels, ME was also shown to be improved in this setting because of its dependence on Po (36 Po and ME (36 33 Po was increased. Therefore, in the context of the present investigation, it can be deduced that smaller wheel sizes increased the Po requirement from the user more substantially than the energetic cost of propulsion, given that ME was still seen to improve. However, given the emphasis placed on aerobic fitness and endurance during wheelchair court sport competition (3,15,31 24 Po are highly unfavorable, and subsequently, reductions in Po , oxygen cost, and thus an improvement in economy may be of greater relevance to wheelchair court sport athletes, as seen in larger wheel sizes. Despite the improvements in pushing economy associated with larger wheels, 24-inch wheels were the most common self-selected wheel size adopted by the athletes investigated (38%), whereas only 23% of participants self-selected 26-inch wheels. This further demonstrates the practical relevance of this investigation because most athletes may be competing in a wheel size that is not optimizing their mobility performance.
Limited kinematic adaptations to wheelchair propulsion in different wheel sizes with fixed gear ratios existed. In fact, no significant differences in temporal parameters or upper body joint kinematics were observed between wheel size conditions. Only PA was shown to be affected, whereby decreases in wheel size were accompanied by marginal, yet significant increases in PA. Given that no differences were observed between wheel sizes for PT or the displacement of the hand during the push phase, it was likely that participants were pushing over a similar linear trajectory across wheel size conditions. Subsequently, the changes in physiological demand with regard to fixed gear ratio wheel size adjustments were not the result of any concomitant alterations to upper body joint excursions or timing of propulsion.
Investigations into varying hand-rim diameters and gear ratios have attributed increases in cardiorespiratory stress with larger diameters to kinematic adaptations such as increased ranges of motion (37 16 32
One kinematic parameter that was originally expected to be affected by wheel size adjustments was stroke frequency. It was anticipated that a higher stroke frequency would be required in smaller wheels to overcome the increased rolling resistance associated with these wheels and maintain the constant velocity of the treadmill. Support was added to this hypothesis because stroke frequency has been shown to display a curvilinear relationship with Po (36 Po , a higher stroke frequency was anticipated. Veeger et al. (33 Po increased stroke frequency. These results may again arise from the highly standardized protocols implemented and the experienced nature of the participants sampled in the current investigations. The consistent stroke frequencies observed across wheel size conditions necessitated that a greater amount of work per cycle was performed to meet the Po requirements of the smaller wheel sizes. This is in accordance with previous investigations, whereby work per cycle has been shown to elicit a curvilinear relationship with Po (36 Po conditions, Woude et al. (37
It appeared as though athletes used several adaptations in hand-rim kinetics , which may have served as compensatory factors to meet the Po requirements of smaller wheels in the absence of any increases in stroke frequency. It was clear that by maintaining a relatively constant stroke frequency, athletes alternatively applied a greater torque around the hub (Mz ) of the wheel. Based on its relationship with hand-rim diameter, a greater magnitude of mean F tan was subsequently demanded in smaller wheel sizes to generate a greater Mz . In addition to this, an increase in mean F res was also observed in smaller wheel sizes. Veeger et al. (33 F res (Fx , Fy , and Fz ), yet increases in Po at fixed gear ratios significantly increased each of these subcomponents. This again suggested that the increased Po associated with smaller wheels was predominantly responsible for the greater magnitude of F res in this wheel size. These increased force magnitudes in smaller wheel sizes may also explain the greater physiological demand. It was anticipated that, given the absence of any adaptations in the joint excursions of upper body segments resulting from wheel size adjustments, the increased force application and, subsequently, physiological demand may be the result of an increased muscular activity. However, an EMG analysis would be warranted to confirm or refute this hypothesis.
No changes in the effectiveness of force application were revealed between wheel size conditions because although F res increased with decreasing wheel sizes, it was accompanied by seemingly proportionate increases in F tan , resulting in no effects on mean FEF. This was reinforced by the findings of Veeger et al. (33 Po increased, no changes in mean FEF were observed. Alternatively, under constant Po conditions, a reduction in gear ratio was shown to significantly improve the effectiveness of force application (33
The hand-rim kinetic data also offered a meaningful insight into the injury risk associated with different wheel sizes. It has previously been stated that increases in cadence, force magnitude, and rate of rise of force development are all associated with an increased risk of injury in wheelchair users (5,6 5,33
Although the sample size of the current investigation was adequate for achieving a high level of statistical power (≥90%), future investigations may benefit from even larger sample sizes. This would enable participants to be subdivided into smaller groups based on physical characteristics such as disability, classification level, or self-selected seat height. This would improve the specificity of the results and increase the likelihood of optimal wheel sizes being detected because one wheel size is unlikely to be optimal for all athletes (19 Table 1 that the participants sampled in the current investigation differed across these physical characteristics. Sitting height and classification appeared to be correlated with high-point players (≥3.0) seen to elicit larger degrees of elbow extension, thus inferring a higher self-selected seat height. This caused noticeably large SDs in several biomechanical dependent variables with players who had a higher classification (least impaired) and subsequently sitting height, noticeably seen to apply larger magnitudes of force. A larger sample size would be required to group participants without compromising the statistical power of the study. This was not feasible in the context of the current investigation because elite, highly trained wheelchair basketball players form a relatively small population, and it is acknowledged that future investigations may struggle to improve substantially on these numbers. A further recommendation to assist with the identification of optimal wheel sizes would necessitate that a field-based investigation under similar standardized conditions is warranted. Although smaller wheels were found to be unfavorable in terms of physiological and biomechanical responses during submaximal wheelchair propulsion, improvements in initial acceleration and maneuverability have been alleged with smaller wheel sizes (12,23 23 14,33,37 33
To conclude, the present investigation has demonstrated that decreasing wheel size, with a fixed gear ratio, increases the physiological demand and magnitude of force application during submaximal wheelchair propulsion under highly standardized conditions. The changes in physiological and biomechanical responses were largely the result of the increased Po associated with smaller wheels owing to an increased rolling resistance. There were also implications that smaller wheels may increase the risk of injury to the upper extremities owing to the greater magnitudes of F res and the rate at which peak F res developed. This information is of value to wheelchair athletes, coaches, and manufacturers in particular because most athletes investigated competed on 24-inch wheels, which may not only be limiting their performance but may also be placing them at an increased risk of injury. It provides evidence-based information on the consequences of wheel size selections, which has previously been a subjective process (23
The authors thank UK Sport for their financial support of this research through the Graduate Innovation Programme, the support of the Great Britain Wheelchair Basketball Association, and the athletes who volunteered to participate. The authors also thank members of the PAMELA Lab at University College London for the loan of the 24-inch SMARTWheel and Prashant Srinivasan from Three Rivers for his technical assistance.
The authors declare no conflicts of interest.
The results of the present study do not constitute endorsement by the American College of Sports Medicine.
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