Abstract
Rolling resistance is a drag force that increases the required propulsion force of manual wheelchair users (MWU) and increases the risk of upper extremity pain and injury. To understand the influence of different design, environmental, and setup factors on rolling resistance (RR), a series of tests were performed on a range of wheels and casters using a drum-based equipment with the capability to measure RR forces. Independent factors were varied including load, camber, toe, speed, tire pressure, and surface, using ranges anticipated in the community. Combined factor testing of these factors was also completed to evaluate of RR changes due interactions of multiple factors. A default reference trial was used to verify repeatability throughout the 924 rear wheel trials and 255 caster trials. Toe angle and tire pressure were found to have large and exponential relationships to RR. Tire/caster type and surfaces are significant influencers but have no specific relationship to RR. Load had a direct linear relationship to RR whereas camber and speed had a relatively small impact on RR. Pneumatic tires had lower rolling resistance compared to airless inserts, solid mag wheels and knobby tires. Combined factor testing revealed a linear additive effect of individual factors. Statistical analysis revealed that tire/caster type is a covariate to all of the results and statistical differences (p < 0.01) were found for toe, tire/caster type, tire pressure, surfaces and load. Factors act in a cumulative manner to impact RR and need to be monitored in device design, development, issuance, and maintenance.
Keywords: wheelchair, friction, propulsion
Introduction
In manual wheelchair propulsion, rolling resistance (RR) is the drag force resisting propulsion. Increased RR increases the required propulsion forces for manual wheelchair users (MWUs), which are linked to increased possibility of upper extremity injuries and pain [1]. It was reported that 55% of individuals with quadriplegia and 64% of individuals with paraplegia experienced UE pain [2]. For individuals with SCI, over two thirds reported having shoulder pain since being in a wheelchair, and over 40% currently had shoulder pain [3]. This study found that the activities associated with the highest shoulder pain intensity were propelling up a ramp, propelling for longer than ten minutes and sleeping [3]. For manual wheelchair users, UE injuries reduce activity and participation, make activities of daily living more difficult and can take away their primary means of mobility [4]. To combat the influence of RR, a clinical practice guide was developed which recommends low chair weight, optimized seating position (farther back), larger diameter wheels, high quality bearings, and a forward axle position. [1]. These steps are important and do provide reduction in RR, but they only provide part of the information needed for stakeholders. To provide better information to impact clinical practice, a closer examination of RR is needed.
RR is caused by hysteresis and energy losses from the tire [5]. Air resistance and bearing resistance are considered to be negligible [6,7]. The rolling resistance free body diagram in Figure 1 illustrates Ft (the tangential force) V, (angular velocity), W (axle loading) and Frr (Force from rolling resistance). During the forward motion of the wheel, energy is transferred into angular velocity. The opposing force is from rolling resistance, and this force is directly related to inelastic deformation and energy loss from the wheel. The coefficient of rolling resistance, µRR (mu) is the drag force (FRR) divided by the weight (W) on the wheel: µRR=FRR/W.
Figure 1.
RR Free Body Diagram, Ft is the tangential force, V is the angular velocity, W is the load on the axle, FRR is the RR force.
Although rolling resistance is easily defined, measuring and minimizing rolling resistance forces are challenging. Previous research identified toe, camber, load, tire pressure, surface and speed as having significant impact on RR (Cowen et al, VanderWiel et al, Sawatsky et al). Toe angle is illustrated in Figure 2 and camber angle is illustrated in Figure 3. A scoping literature review was performed evaluating existing current rolling resistance test equipment and methods which included 41 published articles. These existing methods have a variety of limitations including the inability to measure component level factors, repeatability of testing results, testing only a single factor at a time, large space requirements, requiring human participants and/or testing indirect measures of RR highlighting a lack of standardization to the testing approach and reporting of results.
Figure 2.
Toe Free Body Diagram, V is velocity, Ft is the tangential force, Ftx is the tangential component in the x direction, Fty is the tangential component in the y direction
Figure 3.
Camber Free Body Diagram, W is load, Wx is the x component of the load, Wy is the y component of the load.
To address the limitations identified by previous test methods, a new drum-based machine was developed through an iterative design process and employed to measure RR (Figure 4). Through pilot and sensitivity testing, it was determined that the equipment measured all factors with high repeatability (variance less than 5%) and was sensitive to 0.25 degrees of toe, 10 psi of tire pressure and 7 pounds load changes. The full capabilities of the machine can be seen in Table 1. Furthermore, a calibration was developed to relate drum-based results to simulated overground measurements.
Figure 4.
Drum-based Testing Machine
Table 1.
Rear-wheel and Caster Testing Capabilities
| Rear-wheels | ||||
|---|---|---|---|---|
| Factor | Range | Increment | Sensitivity | Justification |
| Camber | 0 to 5 degrees | 1 degree | 1 degree | User preference where most devices do not allow more than 5 degrees. |
| Load | Up to 150 lbs. | 20 lbs. | 7 lbs. | 75 lbs. equal to the load on one wheel with a 60/40 distribution of 250 lbs. |
| Toe-in/Out | −2.5 to +2.5 degrees | 0.5 degree | 0.25 degree | Community data suggest that less than 2 degrees are commonly found. |
| Speed | Up to 1 m/s | 0.5 m/s | 0.25 m/s | Common propulsion speed is 1 m/s |
| Tire Pressure | Up to 100% of max | 20% of max | 10 psi | Smaller interval than previous tire pressure studies |
| Surfaces | Carpet to start | Level of pile | Per carpet level | Common heights of commercial-grade carpet. |
| Tire Type | 24” rear-wheels varied by type | 1 wheel | Per tire type | Recommended by industry experts |
| Casters | ||||
| Factor | Range | Increment | Sensitivity | Justification |
| Load | Up to 100 lbs. | 10 lbs. | 7 lbs. | 50 lbs. equal to the load on one caster with a 60/40 distribution of 250 lbs. |
| Speed | Up to 1 m/s | 0.5 m/s | 0.25 m/s | Common propulsion speed is 1 m/s |
| Tire Pressure | Up to 100% of max | 20% of max | 10 psi | If applicable, some pneumatic casters on the market |
| Surfaces | Carpet to start | Level of pile | Per carpet level | Common heights of commercial-grade carpet. |
| Caster Type | Casters varied by type | 1 caster | Per caster type | Recommended by industry experts |
The primary aim of this research was to determine the influence of factors on wheelchair wheel and caster RR. To accomplish this, testing of a clinically relevant range of wheelchair wheels and casters was conducted under a series of conditions independently and in combination. With the testing of combined factors and individuals factors separately, it is theorized that RR acts in a cumulative nature. The results from the combined data analysis can be compared to the addition of those two conditions individually. If they are in fact cumulative, the individual factors addition should be a decent representation of the result of the combined factors.
A secondary aim and design goal for the development of this machine was to have a repeatability under 10 percent after changes in testing conditions. Therefore, the reference trials can be averaged with a standard deviation. The percent of the standard deviation relative to the mean will determine the variance across a repeated test condition and must be under 10 percent to meet the design goal.
The first hypothesis is that there is an interaction effect between combined factors with the inclusion of tire/caster type that causes a statistically significant change in RR Force. The second hypothesis is that there is an interaction effect between combined factors without the inclusion of tire/caster type that causes a statistically significant change in RR Force. The third hypothesis is that there is an interaction effect between individual factors with the inclusion of tire/caster type that causes a statistically significant change RR Force. The fourth hypothesis is that there are significant differences in RR Force across the testing increments of individual levels of each factor. The fifth hypothesis is that RR acts in a cumulative manner when multiple factors are involved. The final goal of this research is to inform clinical decision making by providing clinical recommendations based on the results in an effort to preserve the UEs for MWUs.
Methods
To ensure that clinically relevant products, as well as a variety of styles, were being tested, six colleagues working as clinical seating therapists or service providers were consulted at the Center of Assistive Technology, Pittsburgh, PA. Following guidance on the selection of products to be tested, the test factors were established based on the capabilities of the machine as well as what is clinically relevant. For rear-wheels and tires, it was determined that testing would include a range of camber, toe, tire pressure, load, speed, and multiple surfaces, with the details being outlined in Table 2. Casters were tested through a range of load, surfaces, and speed with the single pneumatic caster being tested for inflation pressures. The single-factor testing gives a comprehensive understanding of the influence of each factor on RR.
Table 2.
Single-factor Testing Scope
| Rear-wheels | ||||
|---|---|---|---|---|
| Factor | Range | Increment | Trials | Justification |
| Camber | 0 to 5 degrees | 1 degree | 18 | User preference where most devices do not allow more than 5 degrees. |
| Load | 35 to 115 lbs. | 20 lbs. | 12 | 75 lbs. equal to the load on one wheel with a 60/40 distribution of 250 lbs. |
| Toe-in/Out | −2 to +2 degrees | 0.5 degree | 24 | Community data suggest that less than 2 degrees are commonly found. |
| Speed | 0.5 to 1 m/s | 0.5 m/s | 3 | Common propulsion speed is 1 m/s |
| Tire Pressure | 40 to 100% of max | 20% of max | 9 | Smaller interval than previous tire pressure studies |
| Surfaces | Drum, low-pile, medium-pile, high-pile | N/A | 9 | Common heights of commercial-grade carpet. |
| Tire Type | 6 rear-wheels | 1 wheel | N/A | Recommended by industry experts |
| Total Trials per wheel= 75 for pneumatic, 66 nonpneumatic | ||||
| Casters | ||||
| Factor | Range | Increment | Trials | Justification |
| Load | 30 to 70 lbs. | 10 lbs. | 15 | 50 lbs. equal to the load on one caster with a 60/40 distribution of 250 lbs. |
| Speed | 0.5 to 1 m/s | 0.5 m/s | 3 | Common propulsion speed is 1 m/s |
| Surfaces | Drum, low-pile, medium-pile, high-pile | 1 type | 9 | Common heights of commercial-grade carpet. |
| Caster Type | 6 casters | 1 caster | N/A | Recommended by industry experts |
| Total Trials per caster = 27 for nonpneumatic, 36 pneumatic | ||||
Rear-wheels can easily be changed out for testing and an additional bracket was made to mount casters. Adjustments for all factors are easily controlled to preset values or levels to ensure consistency. Tire pressure is the exception but is standardized by using the percent of max inflation. To ensure a comprehensive data set, each factor is tested with every possible permutation of the other factors, however, testing all possible combinations of factors was too large a study to complete. To accomplish this, a limited range of conditions were selected based on average community observations and previous research. For example, in a sample of 200 MWCs, the average amount of toe was 0.90 degrees, the average camber was 3 degrees, and the average tire pressure was 40% of max inflation. Therefore, these levels of factors were selected for the combined factors testing as shown in Table 3. Camber was tested with toe-out, tire pressure, load, surfaces, and each rear tire respectively. Between the individual factor and the combined factor testing, pneumatic rear-wheels went through 171 tests and the non-pneumatic tires went through 120 tests each not including the extra reference trials mixed into the testing order.
Table 3.
Combined Factors Testing Scope
| Combined Factors Tests | ||||
|---|---|---|---|---|
| Rear-wheels | ||||
| Factor 1 | Factor 2 | Increment (F1/F2) | Trials | Justification |
| Camber | Load | 3/55, 3/95 | 6 | Average value from community data |
| Camber | Toe | 3/−1, 3/−0.5 | 6 | |
| Camber | Tire Pressure | 3/40%, 3/60% | 6 | |
| Camber | Surfaces | 3/LP, 3/HP | 6 | |
| Toe | Load | −1/55, −1/95, −0.5/55, −0.5/95 |
12 | Average from community data of 0.9 degrees; Toe-out is more prevalent |
| Toe | Tire Pressure | −1/40%, −1/60%, −0.5/40% −0.5/60% |
12 | |
| Toe | Surfaces | −1/LP, −1/HP, −0.5/LP, −0.5/HP |
12 | |
| Load | Tire Pressure | 55/40%, 55/60%, 95/40%, 95/60% | 12 | Understand the load relationship with other factors |
| Load | Surfaces | 55/LP, 55/HP, 95/LP, 95/HP | 12 | |
| Surfaces | Tire Pressure | LP/40%, HP/60%, LP/40%, HP/60% | 12 | Community data show an average of 40% of maximum pressure. Low-pile is common while high-pile is an extreme case |
| Total Trials per wheel = 96 for pneumatic, 54 nonpneumatic | ||||
| Casters | ||||
| Factor 1 | Factor 2 | Increment (F1/F2) | Trials | Justification |
| Load | Surfaces | 40/LP, 40/HP, 60/LP, 60/HP | 12 | Understand the load relationship with other factors |
| Load | Tire Pressure | 40/40%, 60/60%, 40/40%, 60/60% | 12 | Only one pneumatic caster but it was important to see the effects. |
| Surfaces | Tire Pressure | LP/40%, HP/60%, LP/40%, HP/60% | 12 | Low-pile is common while the high-pile is an extreme case |
| Total Trials per caster = 12 for nonpneumatic, 24 pneumatic | ||||
To ensure a consistent approach to the testing, a set of reference conditions were established which include 0 degrees of camber and toe, 100% of max tire pressure, 1 m/s surface speed, the steel drum surfaces, 75 lbs. downward force for rear-wheels, and 50 lbs. downward force for casters. For this research, a ‘reference trial’ is defined as a test comprised of all the standard run conditions and was utilized throughout testing to verify the repeatability of test results. A computer-generated randomized testing order was used to ensure each setup was independent, which included each test condition appearing exactly three times to confirm within-conditions repeatability of the results. Randomization was used for all conditions except carpet surfaces and tire pressure because installing carpet on the drum is time-consuming and tire pressure was difficult to change quickly. With the randomized testing order, a ‘reference trial’ was run at the beginning of testing as well as approximately every ten conditions to confirm results were repeatable after conditions where changed on the system. With this being the first large scale study with a new machine, it was important to assess repeatability through its operation. The operating protocol was standardized, so the same steps occur in the same order for every test and all casters followed the same randomized testing order as the rear-wheels with the factors adjusted to caster testing increments.
First, the results of each individual factor is viewed graphically to look at the relationship to RR. Next, the evaluation of the combined factors is examined to see if the factors act in a cumulative manner. Then, reference trials are evaluated for repeatability. Finally, a statistical approach is implemented to determine the relationship between factors.
Data Analysis
The analysis had to be completed in a series of stages to perform a comprehensive analysis of all of the trials. All repeated trials of the same condition were included in the analysis in order to maintain more statistical power. Stages 1 is to determine if there is an interaction effect between combined factors with the inclusion of tire/caster type that causes a statistically significant change in RR Force. In stage 1, we performed ten three-way independent ANOVAs using the combined factors along with tire type as independent variables (IV) and RR Force as the dependent variable (DV) since every tire was tested for all of the combined factors. One three-way ANOVA was completed for casters across load and surfaces. Table 4 shows the conducted tests to determine if there are statistical differences in RR Force of combined factor levels with tire/caster type included in the model.
Table 4.
Stage 1 Analysis Plan
| Stage 1 Combined Factors with Tire Type | |||
|---|---|---|---|
| Rear-wheels | |||
| IV 1 | IV 2 | IV 3 | DV |
| Camber (3 deg) | Load ( 55, 95 lbs.) | Tire Type (6 rear-wheels) |
RR Force |
| Toe (−1, −0.5 deg) | |||
| Tire Pressure (40, 60 %) | |||
| Surfaces (LP, HP) | |||
| Toe (−1, −0.5 deg) | Load ( 55, 95 lbs.) | ||
| Tire Pressure (40, 60 %) | |||
| Surfaces (LP, HP) | |||
| Load ( 55, 95 lbs.) | Tire Pressure (40, 60 %) | ||
| Surfaces (LP, HP) | |||
| Surfaces (LP, HP) | Tire Pressure (40, 60 %) | ||
| Casters | |||
| IV 1 | IV 2 | IV 3 | DV |
| Load ( 40, 60 lbs.) | Surfaces (LP, HP) | Caster Type (6 casters) |
RR Force |
Stage 2 was to determine if there is an interaction effect between combined factors without the inclusion of tire/caster type that causes a statistically significant change in RR Force and if there is an interaction effect between individual factors with the inclusion of tire/caster type that causes a statistically significant change RR Force. This comprised of was ten two-way independent ANOVAs for combined factors of rear-wheels, three for caster combined factors, six for each factor across rear-wheels, and three for factors across the casters. Table 5 shows the combined factors independent ANOVAs to determine if there are statistical differences across RR Force of combined factor levels without the inclusion of tire/caster type. Table 6 displays the independent ANOVAs performed to see if there is a statistical difference between levels of individual factors when tire type is included.
Table 5.
Stage 2 Analysis Plan of Combined Factors
| Stage 2 Combined Factors without Tire Type | ||
|---|---|---|
| Rear-wheels | ||
| IV 1 | IV 2 | DV |
| Camber (3 deg) | Load ( 55, 95 lbs.) | RR Force |
| Toe (−1, −0.5 deg) | ||
| Tire Pressure (40, 60 %) | ||
| Surfaces (LP, HP) | ||
| Toe (−1, −0.5 deg) | Load ( 55, 95 lbs.) | |
| Tire Pressure (40, 60 %) | ||
| Surfaces (LP, HP) | ||
| Load ( 55, 95 lbs.) | Tire Pressure (40, 60 %) | |
| Surfaces (LP, HP) | ||
| Surfaces (LP, HP) | Tire Pressure (40, 60 %) | |
| Casters | ||
| IV 1 | IV 2 | DV |
| Load ( 40, 60 lbs.) | Surfaces (LP, HP) | RR Force |
| Tire Pressure (40, 60 %) | ||
| Surfaces (LP, HP) | Tire Pressure (40, 60 %) | |
Table 6.
Stage 2 Analysis Plan of Single-factors
| Stage 2 Single-factors with Tire Type | ||
|---|---|---|
| Rear-wheels | ||
| IV 1 | IV 2 | DV |
| Camber (0–5 deg) | Tire Type (6 rear-wheels) |
RR Force |
| Load (35–115 lbs.) | ||
| Toe-in/Out (−2–2 deg) | ||
| Speed (0.5, 1 m/s) | ||
| Tire Pressure (40–100%) | ||
| Surfaces (D, LP, MP, HP) | ||
| Casters | ||
| IV 1 | IV 2 | DV |
| Load (30–70 lbs.) | Caster Type (6 casters) |
RR Force |
| Speed (0.5, 1 m/s) | ||
| Surfaces (D, LP, MP, HP) | ||
Stage 3 is to determine if there are significant differences across the testing increments of individual levels of each factor and it was comprised of seven one-way independent ANOVAs for rear-wheels by each factor and five for casters by each factor (Table 7). With multiple ANOVAs being compared, the p-value was set to 0.01 to address the risk of type I error in the results.
Table 7.
Stage 3 Analysis Plan
| Stage 3 Single-factors | |
|---|---|
| Rear-wheels | |
| Factor | DV |
| Camber (0–5 deg) | RR Force |
| Load (35–115 lbs.) | |
| Toe-in/Out (−2–2 deg) | |
| Speed (0.5, 1 m/s) | |
| Tire Pressure (40–100%) | |
| Surfaces (D, LP, MP, HP) | |
| Tire Type (6 rear-wheels) | |
| Casters | |
| Factor | DV |
| Load (30–70 lbs.) | RR Force |
| Speed (0.5, 1 m/s) | |
| Surfaces (D, LP, MP, HP) | |
| Tire Pressure (40–100%) | |
| Caster Type (6 casters) | |
We converted RR forces to a perceived weight gain, by using the linear relationship to loading weight, to help convey the influence of changes in all of the independent factors or the effect of combined factors. This was determined by calculating the increased weight associated with an increase RR based on the relationship between weight and RR measured for each tire. The perceived weight calculation assumes a factor (such as tire pressure) affect both rear-wheels under steady-state propulsion conditions, rather than start-up and a fixed user and device weight of 250 pounds.
Results
Through discussions, a set of six rear-wheels (Table 8) and a set of six casters (Table 9) were identified by colleagues to be tested. Specific tire and caster makes, and models were blinded to not recommend the influence of a particular brand but rather identify general differences across styles of tires and casters. Two high-pressure pneumatic tires (100 or more max psi) were chosen with one on a performance wheel. A common low-pressure pneumatic tire (under 100 max psi) was evaluated on a lite-spoke rim without an airless insert and a second one with an airless insert. Lastly, a knobby tire for softer terrains was picked along with a low polyurethane tire that was mounted on a mag style wheel. All wheels tested were nominal 24” diameter. For casters, four and five-inch diameter polyurethane and soft roll casters were chosen. Additionally, three eight-inch casters were picked to include a solid, semi-pneumatic (a light foam with easy compression and air pockets in the material), and a pneumatic tire (similar to a pneumatic rear tire with an inner tube).
Table 8.
Tires Tested
| Tire Types | |
|---|---|
| HPP | High-pressure tire on Performance wheel Dimensions: 24” diameter and 1” width, low tread Maximum air pressure 100 psi |
| HPS | High-Pressure tire on a Standard lite spoke Dimensions: 24” diameter and 1” width, low tread Maximum air pressure 145 psi |
| LPS | Low-Pressure tire on a Standard lite spoke Dimensions: 24” diameter and 1.375” width, medium tread Maximum air pressure 75 psi |
| KLS | Knobby Low-Pressure tire on a Standard lite spoke Dimensions: 24” diameter and 1.375” width, high tread, Maximum air pressure 65 psi |
| AIS | Airless Insert in a low-pressure tire on a Standard lite spoke Dimensions: 24” diameter and 1.375” width, medium tread |
| SPM | Solid Polyurethane tire on a Mag style wheel Dimensions: 24” diameter and 1” width, no tread |
Table 9.
Casters Tested
| Caster Types | |
|---|---|
| 4PO | Four by One Poly Dimensions: 4” diameter with 1” width, polyurethane on an aluminum hub, no tread |
| 5PO | Five by One Poly Dimensions: 5” diameter with 1” width, polyurethane on an aluminum hub, no tread |
| 5SR | Five by One and a half Softroll Dimensions: 5” diameter and 1.5” width, polyurethane on an aluminum hub, no tread |
| 8PO | Eight by One Poly Dimensions: 8” diameter and 1” width, polyurethane, rounded profile, on a plastic hub |
| 8SP | Eight by One and three quarters Semi-Pneumatic Dimensions: 8” diameter and 1.75” width, polyurethane, ribbed tread, on a plastic hub |
| 8PN | Eight by One and a quarter Pneumatic Dimensions: 8” diameter and 1.25 “ width, pneumatic, ribbed tread, on a plastic hub Maximum air pressure 36 psi |
The RR force as a function of force across tire type is shown in Figure 5. Our results indicate that pneumatic tires have a lower RR than airless insert (highest RR) solid polyurethane (second highest), and the knobby tire (third highest), and are linearly related to load. Camber was found to have little influence on RR and Figure 6 displays mostly horizontal lines.
Figure 5.
RR Force versus Load For Rear-wheels with Linear Lines
Figure 6.
RR Force versus Camber for Rear-wheels with Linear Lines
The RR force as a function of toe angle has a non-linear relationship and RR increases in conditions of both positive and negative toe angle (Figure 7). The RR of the airless insert was least influenced by the toe angle (flatter curve) but has, on average, a higher RR across all angles tested.
Figure 7.
RR Force versus Toe for Rear-wheels with Polynomial Lines
Speeds were verified using a tachometer to ±0.05 meter per second (m/s). Speed was tested at two levels, 0.5 and 1m/s. Figure 8 shows little change in the two levels across all six wheels.
Figure 8.
Force versus Speed for Rear-wheels with Linear Lines
Tire pressure has an inverse and non-linear relationship to RR, where a decrease in tire pressure increases RR. Figure 9 shows the relationship between RR for different tires and at different pressures as a percentage of max inflation. Only four pneumatic tires were included in this testing for tire pressure. Table 10 shows the values for the tire pressure test compared to the airless insert tire (AIS). All four pneumatic tires had a lower RR at 40% inflation than the airless insert at the reference trial.
Figure 9.
RR Force versus Tire Pressure for Rear-wheels with Polynomial Lines
Table 10.
RR Force versus Tire Pressure
| Tire Pressure* | HPS - 145 psi** | HPP - 100 psi** | LPS - 75 psi** | KLS - 60 psi** | AIS** |
|---|---|---|---|---|---|
| 40% | 0.561 | 0.652 | 0.673 | 0.800 | N/A |
| 60% | 0.508 | 0.551 | 0.551 | 0.675 | N/A |
| 80% | 0.486 | 0.500 | 0.497 | 0.615 | N/A |
| 100% | 0.474 | 0.465 | 0.472 | 0.564 | 0.978 |
percent of max inflation
RR force in pounds
RR force measurements on the steel drum were the lowest RR, and medium-pile carpet was the highest (Figure 10). Surface type showed variance based on the pile of carpet and tire type. For some tires, low-pile was the carpet with the least RR, while for other tires it was the high-pile.
Figure 10.
Force versus Surfaces for Rear-wheels
The influence of factors on the RR of casters and rear-wheels were similar. A positive linear relationship for load and RR was found for all casters tested. One interesting result is that all the eight-inch casters had higher RR than the four and five-inch casters. Overall, the four and five-inch casters are fairly similar through loading scenarios as seen in Figure 11.
Figure 11.
RR Force versus Load for Casters with Linear Lines
The influence of caster speed on RR was minimal, similar to the rear-wheels. Evaluating tire pressure, the single caster that was pneumatic also showed an inverse non-linear relationship similar to the rear-wheels. On the drum surface (D), it visually appears that smaller diameter casters have a lower RR than the eight-inch casters. With low and medium-pile carpet, these differences between casters were less pronounced. (Figure 12). Medium-pile carpet (MP) surface resulted in the highest RR for all casters, but low-pile carpet (LP) recorded higher RR than the high-pile carpet (HP).
Figure 12.
RR Force versus Surfaces for Casters
System-level understanding of the results is best to convey in Figure 13, which shows some possible tire and wheel combinations. It was made under the assumptions of a 250 pounds user with a device that had a 60/40 rear to front distribution. The first combination is a high-pressure tire (HPS) and a 4-inch caster (4PO), which represents an active user over a hard surface replicated by the drum. The second combination is an airless insert (AIS) with an 8-inch caster (8PO), representing a depot style device. The third combination is the first setup traversing medium-pile carpet.
Figure 13.
System-level Comparison of Tires and Casters
As noted in the methods, each individual factor was tested with every permutation of a secondary factor for all rear tires and casters. As a preliminary step, the testing results from single-factor testing were combined to determine if the linear addition of RR due to the individual factors would predict the combined factor RR testing results. This was evaluated for each testing permutation and these predictions varied less than ten percent from what the actual combined factors tests reported. The RR measured with combined factors where the conditions were most extreme compared to the reference setup (40% tire pressure at 55 lbs.) was 14% lower than would be predicted by summing the RR increases that occur due to the same conditions individually, suggesting a relatively small error (Table 11). Table 11 shows a slight overestimate from the addition of the factors compared to their measured value but overall, there was an equal variance of overestimation and underestimation. Therefore, we argue that RR from combined factors can be estimated accurately by adding the contributions of RR from individual factors.
Table 11.
Comparison of Single-factor Addition versus Combined Factor Testing
| Load (lb.) | HPS @ 58 psi* | HPP @ 40 psi* | LPS @ 30 psi* | KLS @ 26 psi* | Average | |
|---|---|---|---|---|---|---|
| Addition of Load and Tire Pressure 40 % Single-factor RR Results | 55 | 0.434 | 0.521 | 0.531 | 0.637 | N/A |
| 95 | 0.735 | 0.776 | 0.820 | 0.969 | N/A | |
| Combined Factors RR Results at 40% Tire Pressure | 55 | 0.388 | 0.470 | 0.447 | 0.521 | N/A |
| 95 | 0.686 | 0.816 | 0.871 | 0.999 | N/A | |
| Error between combined factors testing vs. summing effects of single-factors testing (% of Single-factor) | 55 | −11% | −10% | −16% | −18% | −14% |
| 95 | −7% | 5% | 6% | 3% | 2% |
RR Force in pounds
Reference trials were evaluated for repeatability with the calculation is based on 12 or more tests for each tire. Table 12 shows the mean, standard deviation and confidence levels and confirms that repeatability is very high during random repeated tests. The standard deviations observed are far less than ten percent of the mean as stated in the design goals. The repeatability was also evaluated for casters and the overground testing and results were similar in amount of variance.
Table 12.
Mean, Standard Deviation, and Confidence Interval for Rear-wheels on Drum
| HPS* | HPP* | LPS* | AIS* | KLS* | SPM* | |
|---|---|---|---|---|---|---|
| Mean | 0.477 | 0.473 | 0.466 | 0.959 | 0.566 | 0.654 |
| Standard deviation | 0.013 | 0.010 | 0.012 | 0.018 | 0.015 | 0.010 |
| Confidence level | 0.008 | 0.005 | 0.006 | 0.012 | 0.008 | 0.005 |
| Conf. interval low | 0.469 | 0.468 | 0.460 | 0.947 | 0.557 | 0.648 |
| Conf. interval high | 0.484 | 0.478 | 0.473 | 0.971 | 0.574 | 0.659 |
| Variance (Std. Dev/Mean) | 2.73% | 2.11% | 2.58% | 1.88% | 2.65% | 1.53% |
RR Force in pounds
Statistical Analysis
To determine if there are statistical interaction effects between combined factors with the inclusion of tire/caster type that causes a statistically significant change in RR Force (Stage 1), nine of the ten three-way independent ANOVAs had significant main effects (p < 0.01) as seen in Table 13. For simplicity, only the three-way interaction effect results has been reported. The camber*surface combination did not produce a significant result. The significant three-way independent ANOVAs indicate significant differences across the averages of the combined factors when accounting for tire type. For the caster three-way ANOVA of load*surface*caster, it also had a significant result indicating an interaction.
Table 13.
Stage 1 ANOVA Results
| Stage 1 ANOVA Combined Factors by Tire Type | |||
|---|---|---|---|
| Rear-wheels | |||
| Factor 1 | Factor 2 | p-value | Interpretation |
| Camber | Load | 0.003 | Significant interaction |
| Toe | 0.004 | Significant interaction | |
| Tire Pressure | 0.007 | Significant interaction | |
| Surfaces | 0.354 | No Significant interaction | |
| Toe | Load | < 0.001 | Significant interaction |
| Tire Pressure | < 0.001 | Significant interaction | |
| Surfaces | < 0.001 | Significant interaction | |
| Load | Tire Pressure | < 0.001 | Significant interaction |
| Surfaces | < 0.001 | Significant interaction | |
| Surfaces | Tire Pressure | < 0.001 | Significant interaction |
| Casters | |||
| Factor 1 | Factor 2 | p-value | Interpretation |
| Load | Surfaces | < 0.001 | Significant interaction |
| Tire Pressure | N/A | Not possible with only one caster | |
| Surfaces | Tire Pressure | N/A | Not possible with only one caster |
Significance when p < 0.01
To test whether interaction effect between combined factors without the inclusion of tire/caster type that causes a statistically significant change in RR Force, Stage 2 testing of combined factors (Table 14) removed the tire type variable from the Stage 1 model and reran the independent ANOVAs. For simplicity, only the two-way interaction effect results has been reported. No collapsing or averaging was done, but the tire type variable was no longer included in the model. It did not yield any significant results for rear-wheels. Thus, tire type is a dominating factor across combined factor testing. For casters, the load*surface main effect was not significant, but surface*tire pressure and load*tire pressure were significant. The caster results for pressure should be interpreted with caution since only one caster was pneumatic.
Table 14.
Stage 2 ANOVA Combined Factors Results
| Stage 2 ANOVA Combined Factors | |||
|---|---|---|---|
| Rear-wheels | |||
| Factor 1 | Factor 2 | p-value | Interpretation |
| Camber | Load | 0.981 | No Significant interaction |
| Toe | 0.727 | No Significant interaction | |
| Tire Pressure | 0.917 | No Significant interaction | |
| Surfaces | 0.562 | No Significant interaction | |
| Toe | Load | 0.856 | No Significant interaction |
| Tire Pressure | 0.745 | No Significant interaction | |
| Surfaces | 0.972 | No Significant interaction | |
| Load | Tire Pressure | 0.174 | No Significant interaction |
| Surfaces | 0.893 | No Significant interaction | |
| Surfaces | Tire Pressure | 0.369 | No Significant interaction |
| Casters | |||
| Factor 1 | Factor 2 | p-value | Interpretation |
| Load | Surfaces | 0.835 | No Significant interaction |
| Tire Pressure | < 0.001 | Significant interaction | |
| Surfaces | Tire Pressure | < 0.001 | Significant interaction |
Significance when p < 0.01
The Stage 2 analysis, to determine if there is an interaction effect between individual factors with the inclusion of tire/caster type that causes a statistically significant change RR Force, found that five of the six factors result in significant two-way independent ANOVAs (Table 15). For simplicity, only the two-way interaction effect results has been reported. Two-way independent ANOVAs for casters revealed a significant relationship between RR and all three of the factors when evaluated by caster type. Consequently, the tire and caster type have a significant main effect on single-factors as well as combined factors with one exception being the speed of rear-wheels. An interesting post-hoc result from Stage 2 is that the LPS and HPP tires are not statistically significantly different in camber results, as well as two and four degrees of camber, respectfully. Additionally, HPP and LPS were not significantly different in tire pressures when the model is controlled for by tire type. Lastly, 5SR and 5PO are not significantly different when analyzing speed or surfaces and controlling for caster type.
Table 15.
Stage 2 Single-factors ANOVA Results
| Stage 2 ANOVA Single-factors by Tire | ||
|---|---|---|
| Rear-wheels | ||
| Factor | p-value | Interpretation |
| Camber | 0.001 | Significant interaction |
| Load | < 0.001 | Significant interaction |
| Toe-in/Out | < 0.001 | Significant interaction |
| Speed | 0.351 | No Significant interaction |
| Tire Pressure | < 0.001 | Significant interaction |
| Surfaces | < 0.001 | Significant interaction |
| Casters | ||
| Factor | p-value | Interpretation |
| Load | < 0.001 | Significant interaction |
| Speed | < 0.001 | Significant interaction |
| Tire Pressure | N/A | Not possible with only one caster |
| Surfaces | < 0.001 | Significant interaction |
Significance when p < 0.01
Stage 3 is the single-factor analysis of rear-wheels (Table 16) to determine if there are significant differences in RR Force across the testing increments of individual levels of each factor, which is the most critical point to this analysis. Camber angle was not significant across all levels when evaluated individually. Toe was more complex to analyze with an overall significant main effect, but post-hoc testing revealed there was no statistical difference from 0 to ± 1-degree. When examining percent tire pressure levels, one hundred percent was statistically significant from eighty and sixty percent inflation as well as eighty from sixty percent independently. This contrasts the Stage 2 results of significant differences at all levels when controlled for by tire type. The analysis of load determined that the increments are not significantly different in a range of ± 20 lbs. when not controlling for tire type. While using the load data, tire type was also analyzed and determined that every tire except SPM is significantly different from AIS, the airless insert. Similar to Stage 2, speed had no significant difference in results between the two levels. Conversely, surfaces exhibited significant differences in RR except for HP and LP when not controlling for tire type, but all carpet was significantly different from the drum.
Table 16.
Stage 3 ANOVA Results
| Stage 3 ANOVA Single-factor | ||
|---|---|---|
| Rear-wheels | ||
| Factor | p-value | Interpretation |
| Camber | 0.903 | No Significant interaction |
| Load | < 0.001 | Significant interaction |
| Toe-in/Out | < 0.001 | Significant interaction |
| Speed | 0.971 | No Significant interaction |
| Tire Pressure | < 0.001 | Significant interaction |
| Surfaces | < 0.001 | Significant interaction |
| Tire Type | < 0.001 | Significant interaction |
| Casters | ||
| Factor | p-value | Interpretation |
| Load | < 0.001 | Significant interaction |
| Speed | 0.915 | No Significant interaction |
| Tire Pressure | < 0.001 | Significant interaction |
| Surfaces | < 0.001 | Significant interaction |
| Caster Type | < 0.001 | Significant interaction |
Significance when p < 0.01
The Stage 3 analysis for casters determined that there are significant differences in RR across levels of tire pressure but only one caster was pneumatic. Analysis of the impact of load on the casters revealed similar results to the rear-wheels where ± 10 lbs. was not significantly different when not controlling for caster type. For rear-wheels and casters, this contrasts Stage 2 results where load was significant across all levels when controlled by tire or caster respectively. Casters were found to be significantly different based on diameter. All eight-inch casters were significantly higher in RR than the four and five-inch casters. Speed had no significant difference between the two levels tested for casters. When surfaces were compared for wheels, LP was found to not be significantly different from MP and HP, but all carpet was significantly different from the drum.
The perceived weight equivalent was calculated to convey the relative impact of each factor by viewing a change in load back calculated off of the relationship between load and RR for every caster or tire. For example, HPS’ RR measurements from drum testing can be used to compare the standard trial conditions of each factor as perceived weight increases as seen in Table 17. Simply switching from a high-pressure tire to an airless insert has a detrimental effect and can add the equivalent of ninety-six pounds to a user and their device based on the assumption of a 250-pound user and device. That is a large portion of the MWU’s weight being added in addition to their own weight plus the device weight. Furthermore, if the MWU propels over carpet with low tire pressure, they are approximately doubling the resistance felt during propulsion on a hard surface, such as smooth concrete, with a fully inflated tire.
Table 17.
Perceived Weight Equivalents for Rear-wheel Factors
| Factor | Level | Perceived Weight Equivalent (lbs.) |
|---|---|---|
| Speed | 0.5 | −5.6 |
| Camber | 3 | 6.3 |
| 5 | 13.9 | |
| Tire Pressure | 40% | 16.5 |
| 80% | 2.3 | |
| Toe | −1.0 | 19.6 |
| −2.0 | 59.6 | |
| Surface | LP | 62.3 |
| MP | 81.7 | |
| Tire Type | SPM | 34.6 |
| AIS | 96.0 |
Discussion
The major takeaway from the statistical analysis is that RR is significantly related to the majority of the individual and combined factors. Not only does this demonstrate the importance of component-level testing, but it also indicates that more research needs to be done to measure and report the RR of additional tires and casters on the market. With combined factors not statistically interacting without tire or caster type, it indicates that single-factor testing is sufficient, and it validates the previous approach of adding the two or more single-factors together to estimate the combined effect. While the approach of cumulative estimation is not exact, it provides a reference for understanding the relationship between the factors. It is possible, due to error, to over or underestimate the effect, but that would be a relatively low amount of false approximation with most calculated differences being less than 10 percent.
Related to load on the wheel, it is important to note that the relationship with RR for all the pneumatic tires had loading equations whose slope was less steep and that the airless insert and mag higher RR overall. Casters also displayed a linear relationship similar to the rear-wheels for load tests. A previous study stated that RR is inversely proportional to wheel diameter [8] and another study states that caster diameter is inversely proportional to RR [9]. With smaller diameter casters, we found contradictory results indicating eight-inch casters had a higher RR than four and five-inch casters. This suggests that other factors, such as tire material, may be the dominant factor influencing RR of casters. With casters having a higher RR overall, it is best practice to have a forward axle position to have more of the MWC and MWU’s weight loading in the rear. The rear axles should be as forward as possible without compromising the safety of the user, which is consistent with Clinical Practice Guidelines [1].
The statistical analysis revealed that load was significant regardless of the caster or rear-wheel type. However, one increment up or down (± 20 lbs., ± 10 lbs.) was not significant without tire or casters type included in the analysis. That can be interpreted as small changes are not influential across all tires and casters but are significant when tire/caster type is included in the model. These recommendations for a forward axle position has been verified but it increases the understanding of what a significant weight change is. From a RR perspective, device weight should not be a heavily considered factor when choosing a MWC, since the weight difference is not enough to significantly impact RR. Accessories should be kept to a minimum as well since overall weight can add up easily. A clinician could prescribe an ultralight or lightweight device without being concerned about the weight difference in terms of RR, but the adjustability of the ultralight may be favorable for rear axle potion and higher quality components. Conversely, if a MWU has a substantial change in weight, it will affect RR and therefore, their long-term health in multiple aspects.
While we found a trend that camber slightly increases RR, it may not be enough to make a long-term difference in the health of the MWU. Statistically, camber showed no difference across the levels without tire type, therefore camber is not a significant influencer of RR. Camber is also largely a user preference while providing increased stability, greater access to the push-rim, and easier passage through doorways.
Toe angle has a significant impact on RR which has not been heavily researched in previous literature. Toe could occur due to tolerances in the axles or wear in the bearings over time, factory misalignment of the frame, or poor set up of the MWC, but its prevalence has not yet been explored. Toe could occur if a MWC setup includes camber and /or the axle tube is rotated out of alignment, caster size or height is changed, or seat dump (seat angle) is changed. From the statistical analyses, toe was found to be significantly different after one-degree in either direction from zero. To properly define this, toe should be tested across tires at 0.25-degree increments to find the exact threshold, but across all tires, toe should be less than one-degree.
With only two levels tested for speed, the exact relationship between RR and speed was not explored, but the slope of the line is very low. Casters showed the same trend as the rear-wheels with very minor influence due to speed changes. Speed was only significant with casters with them involved in the model, which means that deceleration testing of casters may be prone to error. Therefore, caster selection is impacting the MWU when propelling at different speeds, when included in the model but not when considering the data from all casters. The variance between casters is great enough to be detected but may be normalizing when the caster type is removed from the model, and therefore, speed is not a significant influencer of RR. Additionally, speed is selected by the MWU and would be very difficult to control in a real-world setting.
The relationship for tire pressure and RR means that tires should always be properly inflated, which is especially important if they fall below 80% of max pressure. A maintenance program developed specifically for MWCs states that tire pressure should be checked weekly [10]. In addition, tire pressure should be checked when travel includes a substantial change in elevation or air travel. Severely underinflated tires could have significant long-term ramifications to the UE of the MWU and their wheels locks would not be effective. The pneumatic caster also followed a similar curve as the rear-wheels with an inverse non-linear relationship to RR.
Carpet increased RR and should be a consideration, especially for MWU’s choices for their home environment and accessibility considerations for commercial buildings. Once again, the pneumatic tires performed had a lower than the airless insert, which the highest RR across all surfaces. It is impossible to control what surfaces a MWU will encounter in the community, but our results confirmed that harder surfaces are more accessible. Casters showed large variance over surfaces with the 8-inch casters still having a higher RR on carpeted surfaces. Compared to the rear-wheels, some casters performed better on high-pile carpet versus low-pile carpet. The high-pile quickly matted down, which most likely reduced its effect. It would be unrealistic to have a new piece of carpet for every tire to be able to prevent this issue. With casters having an overall higher RR across the loading ranges, their selection is critical as well. However, the weight on the casters should be kept as low as possible. Additionally, the larger diameter caster saw less of an increase on the carpet relative to the drum meaning larger diameter casters are better suited for softer surfaces. Weight should be distributed with the majority to the rear-wheels where tires are less likely to sink into softer surfaces. With statistically significant differences across surfaces for both tires and caster when not included in the model, surfaces are an important point to discuss with MWUs, so they are aware of the impact.
Repeatability of test results was verified for all operating conditions with a variance of less than 5%. Therefore, the machine was designed and built effectively to measure RR through a variety of factors. It was further demonstrated with the arm and air bearing mechanism having performed well on the drum for extended periods of time collecting large amounts of data.
The influence of tire or caster type on RR is demonstrated graphically and statistically, with that the airless insert (AIS) having the highest RR compared to all other tires. This system-level chart (Figure 13 above) demonstrates the cumulative nature of component-level testing, as well as the relative influence of casters being higher than rear-wheels. This study can also confirm that even a significantly underinflated pneumatic tires have less RR than an airless insert, which may negate the benefits of the reduced maintenance when using an airless insert [11]. Therefore, airless inserts should be used on a very limited basis such as MWU’s who are propelled by a caregiver, when a wheelchair is used only temporarily or part-time. AIS was followed by the low polyurethane (SPM) for the highest RR, but that was still a statistically significant difference. The knobby tire (KLS) comes in as the third-highest but was not far behind the performance of the three pneumatic tires. These results confirm previous studies that reported that pneumatic tires have lower RR [12–14]. Therefore, if a MWU prefers a slightly wider tire with lower inflation pressures, it does not come with a significant increase in RR and thus, energy expenditure. Ultimately, the best tire choice should meet the needs and wants of the MWU to include contextual factors such as personal, health, or environmental requirements.
The perceived weight equivalent conversions are helpful to identify the most impactful factors that can affect wheels and the same calculations can be done for casters. It is important to remember that the factors that influence RR can be estimated to act in a cumulative manner, and thus, a device can feel significantly heavier than it is due to RR during steady-state propulsion. This tool can be expanded and published to help the understanding of the impact of factors.
The biomechanical consequences of increased push-rim forces that are related to increases in RR have been reported previously in the literature; the results we present here can further inform that work by describing the relative impact of different factors on RR. For instance, the published guidelines state MWC’s should use high-quality bearings, low chair weight, larger diameter wheels, optimized seating position (farther back), and a forward axle position. [1]. High-quality bearings are critical because low-quality bearings likely lead to slop and misalignment of the rear-wheels causing toe. A low chair weight is not harmful but small changes in device weight will be less impactful than a large change in the MWU’s weight. Larger diameter wheels as a recommendation are slightly misleading since most of the industry used standard rear-wheel sizes for research and device prescription for most cases. An optimal seating position and forward axle position are good recommendations that are confirmed to place more of the weight over the rear-wheels which have lower RR than casters. In addition to the current guidelines, our results suggest that both camber and speed do not significantly impact RR. While surfaces are non-controllable, MWUs should be educated on their long-term health impact. Tire pressure should be monitored closely and maintained at over eighty percent of the max inflation pressure. Toe is a significant influencer and clinical tools need to be developed to measure toe-in MWCs and maintenance options need to be developed to reduce toe to an acceptable level (under one-degree). Additionally, the impact of tire type needs to be communicated so clinicians can make more informed decisions. If it is clinically acceptable to give a MWU an airless insert tire with a perceived weight gain of almost one hundred pounds on the rear axles alone, then implementing standards related to other factors, such as toe should be acceptable. While this information provides insight, it does not outweigh clinical judgment and all MWC issuances should meet the wants and needs of the client but also not put them at unnecessary risk for injury.
Limitations
A limitation of this study is that this is a newly developed machine with no similar test equipment for comparison and validation, however, it was shown to have highly repeatable results. A downside of this study is the small number of wheels and casters included. Due to the amount of data collected, the number of tire and caster samples tested had to be kept small but can always be expanded on in the future. This also applies to the overground and combined factors testing since not every level of every factor was included. Lastly, this steady-state testing did not address any issues that may develop over time such as wear between components leading to toe.
Future Work
The future for this work has many possibilities including continued testing to define a precise threshold for toe, conduct a larger overground comparison, exploring the relationship between speed and casters, exploring the impact of more surfaces, and expand testing of combined factors. A primary goal would be to test more wheels and casters in order to develop an expansive data set that could inform product selection. Studies to investigate whether RR is impacted by wheelchair use, temperature, and the prevalence of influential conditions (e.g. toe, low tire pressure) in the community would inform and guide this work.
Additionally, dissemination of this information is imperative, and a reference tool could be built to showcase a model calculated by the sum of the factors. The goal would be to model a MWC as a system and be able to adjust factors to see the effect on RR. This would be a valuable training and clinical tool if developed with enough rigor, requiring more drum and overground testing to have enough data to build such a tool. The alternative is to follow a mathematical model previously developed [15]. The main take away would be for stakeholders to understand the impact of setup choices for MWCs.
Acknowledgments
Thank you to the many individuals who assisted in the development of the rolling resistance drum-based testing equipment and those involved with conducting testing. First, to the co-ops who assisted with design and development of the equipment. London Lee and Mendel Marcus worked extensively on the design and fabrication of the equipment, Travis Henderson worked on the setup and calibration of this equipment, and Holly Wilson-Jene completed a large amount of product testing. Next, for the administrative assistance with purchasing of components and many other details related to this study and to the clinicians and providers for their input to this research. And a special thank you to the Human Engineering Research Laboratories (HERL) for their significant contributions to this development project including the support of many individuals at HERL and their facilities to fabricate and build equipment utilized in this research.
Thank you also to the ISWP-SWG, who has provided significant support, input, advice and guidance from the inception to completion of this research, all of which are greatly appreciated. There were many grants supporting this research work and paper, including the following: Integrative Graduate Education and Research Traineeship award number IGERT 1144584 from the National Science Foundation, Improving Health and Function Through Use of Performance Standards in Wheelchair Selection Grant # 90REGE0001–02-00, and U.S. Agency for International Development through Agreement Nos. APC-GM-0068, SPANS-037, APC-GM-0107, and FY19-A01–6024. This project was supported in part by the National Institutes of Health through Grant Number UL1-TR-001857.
References
- 1.Medicine CfSC. Preservation of upper limb function following spinal cord injury: a clinical practice guideline for health-care professionals. Consortium for Spinal Cord Medicine; 2005. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Sie IH, Waters RL, Adkins RH, et al. Upper extremity pain in the postrehabilitation spinal cord injured patient. Archives of physical medicine and rehabilitation. 1992;73(1):44–48. [PubMed] [Google Scholar]
- 3.Curtis KA, Drysdale GA, Lanza RD, et al. Shoulder pain in wheelchair users with tetraplegia and paraplegia. Archives of physical medicine and rehabilitation. 1999;80(4):453–457. [DOI] [PubMed] [Google Scholar]
- 4.Whiteneck G, Dijkers MP. Difficult to measure constructs: conceptual and methodological issues concerning participation and environmental factors. Archives of physical medicine and rehabilitation. 2009;90(11):S22–S35. [DOI] [PubMed] [Google Scholar]
- 5.Kauzlarich JJ, Thacker JG. Wheelchair tire rolling resistance and fatigue. J Rehabil Res Dev. 1985. Jul;22(3):25–41. [DOI] [PubMed] [Google Scholar]
- 6.Bascou J, Sauret C, Lavaste F, et al. Is bearing resistance negligible during wheelchair locomotion? Design and validation of a testing device. Acta of bioengineering and biomechanics. 2017;19(3):165–176. [PubMed] [Google Scholar]
- 7.Vinet A, Bernard P-l, Ducomps C, et al. A field deceleration test to assess total wheelchair resistance. International Journal of Rehabilitation Research. 1998;21(4):397–402. [DOI] [PubMed] [Google Scholar]
- 8.Frank TG, Abel EW. Measurement of the turning, rolling and obstacle resistance of wheelchair castor wheels. Journal of biomedical engineering. 1989. Nov;11(6):462–6. [DOI] [PubMed] [Google Scholar]
- 9.Zepeda R, Chan F, Sawatzky B. The effect of caster wheel diameter and mass distribution on drag forces in manual wheelchairs. J Rehabil Res Dev. 2016;53(6):893–900. [DOI] [PubMed] [Google Scholar]
- 10.Hernandez MLT. Development, implementation, and dissemination of a wheelchair maintenance training program: University of Pittsburgh; 2015. [Google Scholar]
- 11.Sawatzky BJ, Kim WO, Denison I. The ergonomics of different tyres and tyre pressure during wheelchair propulsion. Ergonomics. 2004. Nov;47(14):1475–83. [DOI] [PubMed] [Google Scholar]
- 12.Hoffman MD, Millet GY, Hoch AZ, et al. Assessment of wheelchair drag resistance using a coasting deceleration technique. Am J Phys Med Rehabil. 2003. Nov;82(11):880–9; quiz 890–2. [DOI] [PubMed] [Google Scholar]
- 13.Mason BS, Lemstra M, van der Woude LH, et al. Influence of wheel configuration on wheelchair basketball performance: wheel stiffness, tyre type and tyre orientation. Medical engineering & physics. 2015. Apr;37(4):392–9. [DOI] [PubMed] [Google Scholar]
- 14.Gordon J, Kauzlarich JJ, Thacker JG. Tests of two new polyurethane foam wheelchair tires. J Rehabil Res Dev. 1989. Winter;26(1):33–46. [PubMed] [Google Scholar]
- 15.Clark SK. Rolling resistance forces in pneumatic tires. United States. Dept. of Transportation. Office of the Secretary; 1976. [Google Scholar]