# Estimation of power output in wheelchair propulsion with a 3D accelerometer

Philippe Vaslin, Nicolas de Saint Rémy, Michel Dabonneville

► To cite this version:

Philippe Vaslin, Nicolas de Saint Rémy, Michel Dabonneville. Estimation of power output in wheelchair propulsion with a 3D accelerometer. 12th Conference of the European Society of Biomechanics, Trinity College, Aug 2000, Dublin, Ireland. pp.78. hal-05000530

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Submitted on 21 Mar 2025

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# Estimation of power output in wheelchair propulsion with a 3D accelerometer

Ph. Vaslin, N. de Saint Rémy and M. Dabonneville

Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes, Université Blaise Pascal, Clermont Ferrand 2, France.

## Introduction

External power output in wheelchair propulsion has been evaluated on different populations, in various situations and with different laboratory devices. Therefore the values of this parameter may highly vary between studies, from 12 to 63 W at steady state velocities on a roller ergometer [1], up to 660 W for the maximal power output calculated over one stroke during a 30-s sprint test on a stationary ergometer [2]. Although accelerometry is particularly suited to kinetic analysis [3], it has not yet been used for estimating power output in wheelchair propulsion. This technique has been used in a preliminary study with some simplifying assumptions.

## Materials and methods

### Theoretical considerations and simplifying assumptions

In the general case of a point G moving in a non Galilean reference frame R*, itself moving in a Galilean reference frame R, the acceleration of G with respect to R is expressed by:

$$a(G/R) = a(R^*/R) + a(G/R^*) + a_c \quad (1)$$

where $a(G/R)$ is the absolute acceleration of G, $a(R^*/R)$ is the driving acceleration of R* with respect to R, $a(G/R^*)$ is the acceleration of G in the moving reference frame R* and $a_c$ is the complementary acceleration of Coriolis.

When the moving reference frame R* does not rotate with respect to R, the absolute acceleration of G becomes:

$$a(G/R) = a(O/R) + a(G/R^*) \quad (2)$$

where $a(O/R)$ is the linear acceleration of the origin O of R* with respect to R.

Identifying G as the centre of mass of the subject-and-wheelchair's system and assuming that the subject's action is symmetrical so that the movement of the wheelchair is only a translation along the fore-and-aft axis of the absolute reference frame R, the term $a(O/R)$ represents the resulting linear acceleration of the wheelchair. Equation (2) clearly states that this acceleration does not exactly correspond to the absolute acceleration of G, because it is influenced by the movements of G with respect to the wheelchair ($R^*$) during the propulsion.

The external mechanical work is generally calculated by summing the variations of kinetic energy and the variations of potential energy of G over each time interval [4]. Although G obviously moves downwards and upwards during the propulsion, it can be assumed that there are no variations of potential energy when the wheelchair is moving on an horizontal plane. The elementary external mechanical work ($dW$) is thus reduced to the variation of kinetic energy ($dEc$), that can easily be calculated from the velocity obtained by the first integration of the wheelchair's horizontal acceleration.

The instantaneous power output ($P$) is then expressed by the variation of kinetic energy over each time interval ($dt$):

$$P = dEc/dt \quad (3)$$

## Experimental procedure

One able-bodied sedentary subject (50 years, 180 cm, 80 kg) accustomed to wheelchair locomotion propelled himself straightforwards over 7 metres according to two modalities: 'normal': the subject propelled the wheelchair at a slow speed corresponding to that used in a household displacement; 'fast': the subject propelled the wheelchair as fast as possible over the measurement distance.

The subject had to stay stock-still before and after each trial and he performed five trials of each modality.

The acceleration $a(O/R)$ has been measured by a triaxial accelerometer (Analog Devices: ADXL05EM-3, range: +/-5 g) fixed under the seat of a standard basket-ball wheelchair, approximately at the level and in the middle of the rear wheels axles. The sensor was connected with a 10 metres cable to an A/D conversion card (National Instrument, AT-MIO-64E-3) slotted in a PC and the three components of the acceleration were recorded at a sampling rate of 1000 Hz ($dt = 0.001$ s).

## Results

Wheelchair propulsion is a cyclic movement composed of a push phase and a free-wheeling phase. In this study, the total propulsive work is the sum of the elementary works performed by the subject during each push phase, and the power output is the mean of the instantaneous powers calculated over each time interval of each push phase.

The subject performed four pushes in the 'normal' modality as against only three in the 'fast' modality (fig.1).

<figure><img src="image_2.png" /><figcaption>Fig. 1: Fore-and-aft acceleration and velocity of a 'fast' trial.</figcaption></figure>

All velocities, propulsive works and power outputs were significantly different between the two modalities (Table 1).

<table><caption>Table 1. Mean velocities, works and powers of both modalities</caption><thead><tr><td>Modality</td><td>Velocity (m.s<sup>-1</sup>)</td><td>Work (Joules)</td><td>Power (Watts)</td></tr></thead><tbody><tr><td>'Normal'</td><td>1,13</td><td>292</td><td>96</td></tr><tr><td>'Fast'</td><td>1,62</td><td>737</td><td>371</td></tr></tbody></table>

## Discussion and conclusions

Mean power outputs computed in this study over the first 3 or 4 pushes in wheelchair propulsion are much higher than those obtained at steady state velocities ranging from 0.56 to 2.50 m/s on a roller ergometer [1]. However these results withstand the comparison with those obtained in a similar situation on a stationary computer-controlled wheelchair ergometer during a 30-s sprint test at a mean velocity of 4 m/s [2].

The results of this preliminary study are thus encouraging for future investigations on power output in wheelchair propulsion with a 3D accelerometer. Furthermore, this sensor is simpler and cheaper than any ergometer, and it may allow to realize measurements outside the laboratory, within the simplifying assumptions presented in this paper.

## References

[1] D. Theisen, M. Francaux, A. Fayt and X. Sturbois (1996) Int. J. Sports Med. 17: 564-571. [2] H.E.J. Veeger, E.M.C. Lute, K. Roeleveld and L.H.V. van der Woude (1992) Eur. J. Appl. Physiol. 64: 158-164. [3] Z. Ladin and G. Wu (1991) J. Biomech. 24: 1173-1187. [4] K. R. Williams and P. R. Cavanagh (1983) J. Biomech. 16: 115-128.