Comparison of rolling resistance, propulsion technique and physiological demands between a rigid, folding and hybrid manual wheelchair frame

Figures & data

Figure 1. An overview of mechanical power balance based on van der woude et al. [8] and van Inge Schenau and Cavangh [9]. frictional power (P_drag) consists of rolling resistance (P_roll), internal friction (P_int), air resistance (P_air) and losses due to inclination (P_incl). Frictional power can be determined with a coast-down or drag test. The type of frame not only influences frictional power but also has the potential to impact internal power loss (P_loss), particularly through factors such as frame deformation, which occurs exclusively during propulsion. The difference between P_drag and P_out determines displacement, velocity and acceleration.

The mechanical power balance of wheelchair propulsion. The relationship between power output, performed by the wheelchair user, and the power losses, due to rolling resistance, air resistance, internal friction, inclination and frame deformation, affect the position, velocity and acceleration of the wheelchair.

Table 1. Wheelchair frame types.

			Top view (transverse plane)		Frontal-sagittal view
Wheelchair type	Folding plane	Picture	Before folding	After Folding	Before folding	After folding
Permobil Progeo Joker Rigid frame	N.A.			N.A.		N.A.
Permobil Progeo Ego Hybrid frame	Transverse
Permobil Progeo Exelle Folding frame	Frontal

Notes: The red arrows depict the force the user has to exert on the frame to initiate folding. The grey rods represent the axis of rotation, on which the blue arrows show the direction of rotation. For the hybrid frame the blue arrows are only shown in transverse plane, since that is the plane of rotation. For the folding frame the blue arrows are only visible in the frontal-sagittal view. Abbreviations: A: anterior; P: posterior.

Table 2. Wheelchair characteristics after standardization.

Frame	Rigid	Hybrid	Folding
Name	Permobil Progeo Joker	Permobil Progeo Ego	Permobil Progeo Exelle
Mass (incl. wheels and cushion)	10.9 kg	12.4 kg	13.2 kg
Weight distribution^a	78%	77%	72%
Wheelbase (length)^b	470mm	490 mm	470 mm
Wheelbase (width)^c	535 mm	″	″
Frame material	Aluminium	″	″
Rear wheels’ size	24″	″	″
Rim size	21″	″	″
Rear wheel tire type	Pneumatic	″	″
Rear wheels’ tire pressure (100%)	6 Bar	″	″
Caster wheels’ size	4″	″	″
Caster wheels’ type	Solid	″	″
Axle position (relative to backrest)	90 mm	″	″
Seat Height (front)	490 mm	″	″
Seat Height (back)	425 mm	″	″
Camber / Toe angle	2°/0°	″	″

″Identical to rigid wheelchair.

^aPercentage of load on the rear wheels (measured on a force plate), average of empty and dummy tests.

^bDistance between ground-contact points rear wheel and caster in the forward position.

^cDistance between ground-contact points of the rear wheels.

Figure 2. The study protocol at both locations: Amsterdam (A) and Groningen (G). The practice period took approximately 5 min per wheelchair. The submaximal test, conducted on an ergometer or treadmill, consisted of 4-min of continuous propulsion.

A schematic overview of the study protocol. The order for the location in Amsterdam was free practice, three coast down tests and a submaximal ergometer test. The order for the location in Groningen was free practice, three coast down tests, a drag test on a treadmill and a submaximal treadmill test. Each of these test orders was completed three times, once in each wheelchair in counterbalanced order.

Table 3. Propulsion technique variables.

Variable	Unit	Description	Equation
Average power	Watt (W)	The amount of mechanical energy generated per unit time	Meanslm:elm(Mz · ω)
Ftangential mean	Newton (N)	3-Dimensional mean force amplitude within the push phase	Meanstart(i):end(i)(Ftangential)
Ftangential peak	Newton (N)	3-Dimensional peak force amplitude within the push phase	Maxstart(i) :end(i)(Ftangential)
Net work per cycle	Joule (J)	The moment integrated over the wheel rotation angle during a total cycle	Σstart(i):start(i+1) Mz · ΔØ
Negative work per cycle	Joule (J)	The moment integrated over the wheel rotation angle during a recovery phase	Σstart(i):end(i-1) Mz · ΔØ
Push frequency	Pushes per minute	The number of completed pushes per minute	Npushes /Δt
Push time	Time (seconds)	Time from the start of positive torque to the stop of positive torque for an individual push	tend(i) – tstart(i)
Recovery time	Time (seconds)	Time from the stop of positive torque to the start of positive torque for the subsequent push	tstart(i) – tend(i-1)
Contact angle	Degrees (°)	Angle at the end of a push minus the angle at the start	Øend(i) – Østart(i)

Mean values over the last minute of submaximal propulsion were calculated for all variables.

Slm indicates start of last minute; elm: end of last minute; Mz: torque around the wheel axis; ω: angular velocity; start(i): start of current push; end(i): end of the current push; F: force (N); Pout: power output; Ø: angle (degrees); N: number; t: time (seconds).

Figure 3. Boxplots present data with median and interquartile range. A & B: Rolling resistance, C: power output, D: Mean force per push, E: Push frequency, F: contact angle, G: Energy expenditure (EE) and H: Net mechanical efficiency (NME). All measures were significantly impacted by the wheelchair frames (p < 0.05). Outliers are denoted as (o). Significant post-hoc test (LSD) results are depicted as ([

) (p < 0.05).

Nine boxplots comparing the results of the three chairs. The folding chair has the highest values for rolling resistance from both the coast-down and drag tests, power output, mean force per push, push frequency and contact angle, where the hybrid frame had the lowest values. The folding frame resulted in the highest energy expenditure and the rigid frame was the most mechanically efficient.

Table 4. Results of the repeated measures ANOVA for the propulsion technique variables of both the treadmill and wheelchair ergometer submaximal test (n = 48).

Repeated measures ANOVA						Post-hoc (LSD)
	Frame	Mean (±SD)	F-value (DoF)	p-Value	Es	Comparison	Mean diff	95% CI^a	p-Value
Mean force Per push (N)	Rigid hybrid Folding	34 (±9) 31 (±10) 36 (±12)	13.410 (2,92)	≤0.001*	0.226	Rigid vs. hybrid Rigid vs. folding Hybrid vs. folding	3.07 −2.63 −5.70	0.95 : 5.19 −4.93 : −0.33 −7.93 : −3.47	0.005* 0.026* ≤0.001*
Peak force Per push (N)	Rigid Hybrid Folding	57 (±17) 52 (±19) 61 (±12)	10.502 (2,92)	≤0.001*	0.186	Rigid vs. hybrid Rigid vs. folding Hybrid vs. folding	4.71 −4.30 −9.01	0.85 : 8.58 −8.39 : −0.21 −12.9 : −5.09	0.018* 0.040* ≤0.001*
Work per cycle (J)	Rigid Hybrid Folding	10.4 (±3.7) 8.8 (±3.5) 10.1 (±4.1)	4.692 (1.691,74.384)^b	0.016*	0.096	Rigid vs. hybrid Rigid vs. folding Hybrid vs. folding	1.57 0.26 −1.30	0.37 : 2.76 −0.58 : 1.10 −2.54 : −0.07	0.011* 0.553 0.039*
Negative Work Per cycle (J)^c	Rigid Hybrid Folding	−0.6 (-0.8 : −0.3) −0.7 (-1.0 : −0.5) −0.9 (-1.3 : −0.7)	25.042 (2)^d	≤0.001*	0.261	Rigid vs. hybrid Rigid vs. folding Hybrid vs. folding			0.036* ≤0.001* 0.007*
Push frequency (push/min)	Rigid Hybrid Folding	52 (±14) 51 (±15) 55 (±14)	4.204 (2.92)	0.018*	0.084	Rigid vs. hybrid Rigid vs. folding Hybrid vs. folding	0.71 −2.92 −3.63	−2.04 : −0.38 −5.45 : −0.38 −6.34 : −0.91	0.607 0.025* 0.010*
Push time (s)	Rigid Hybrid Folding	0.31 (±0.06) 0.30 (±0.05) 0.31 (±0.05)	4.380 (2.92)	0.015*	0.087	Rigid vs. hybrid Rigid vs. folding Hybrid vs. folding	0.02 0.01 −0.01	0.01 : 0.03 −0.01 : 0.02 −0.02 : 0.01	0.005* 0.072 0.219
Recovery time (s)	Rigid Hybrid Folding	0.91 (±0.28) 0.98 (±0.37) 0.86 (±0.30)	4.347 (1.694,77.915)^b	0.021*	0.086	Rigid vs. hybrid Rigid vs. folding Hybrid vs. folding	−0.07 0.05 0.12	−0.15 : 0.02 −0.01 : 0.11 0.03 : 0.20	0.138 0.099 ≤0.010*
Contact angle (°) (n = 31)	Rigid Hybrid Folding	65 (±13) 61 (±12) 63 (±11)	14.393 (2.58)	≤0.001*	0.332	Rigid vs. hybrid Rigid vs. folding Hybrid vs. folding	6.11 3.95 −2.16	3.90 : 8.32 1.77 : 6.14 −4.81 : 0.50	≤0.001* ≤0.001* 0.108

Notes: Effect size is presented as partial eta squared (${\eta }_p^2$). Abbreviations: diff: difference; DoF: degrees of freedom; Es: effect size; SD: standard deviation.

*Displays a significant effect (p ≤ 0.05).

^aThe 95% confidence interval is displayed as lower: upper; ^bGreenhouse-Geisser test results; ^cNegative work per cycle is displayed as median (interquartile range); ^dχ² test score as result of the Friedman test (Shapiro-Wilk test p < 0.05) and effect size as Kendall’s W, post-hoc results are Wilcoxon test results.

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Data availability statement

Data is available on reasonable request.