## 2 Materials and Methods
### Sprint Test  
For SP with IMUs, since manual wheelchair (MWC) wheels are assumed to roll without slipping. It is possible to calculate the MWC's linear velocity (\(\mathbf{V}\)) by multiplying the rotational velocities of the wheels around their axis of rotation (\(\dot{\mathbf{\omega}}_{\textit{left}_{\textit{ushed}}}\) and \(\dot{\mathbf{\omega}}_{\textit{right}_{\textit{ushed}}}\)) measured with the gyroscope's IMU and the wheels' radius (\(\mathbf{r}\)), as shown in Equation (1). The \(z\)-axis of gyroscope's IMU was placed perpendicular to the plane of the wheel [24]. \[\mathbf{V}=\mathbf{r}\left(\frac{\dot{\mathbf{\omega}}_{\textit{left}_{\textit{shaped}}}+ \dot{\mathbf{\omega}}_{\textit{right}_{\textit{shaped}}}}{2}\right) \tag{1}\]  
However, sports wheelchairs use positive camber (\(\mathbf{\alpha}\)) for stability and maneuverability, causing gyroscopes on the wheels to capture both the wheel rotational velocity (\(\dot{\mathbf{\omega}}\)) and the rotational velocity of the wheelchair around the vertical axis (\(\mathbf{\theta}\)). To address this, [PERSON] et al., in 2011, and adjusted by [PERSON] et al., in 2012, proposed a methodology to identify the true wheel rotational velocity (\(\dot{\mathbf{\omega}}\)) using Equation (2) [26; 27]. \[\dot{\mathbf{T}}\mathbf{\omega}=\dot{\mathbf{\omega}}-\dot{\mathbf{\omega}}_{\textit{xy}}\mathbf{ \tan}(\mathbf{\alpha})\frac{\dot{\mathbf{\omega}}_{\textit{left}_{\textit{wheel}}}- \dot{\mathbf{\omega}}_{\textit{right}_{\textit{shaped}}}}{\dot{\mathbf{\omega}}_{ \textit{left}_{\textit{wheel}}}-\dot{\mathbf{\omega}}_{\textit{right}_{\textit{ wheel}}}} \tag{2}\]  
In Equation (2), \(\dot{\mathbf{\omega}}_{\textit{xy}}\) is the resultant measured of \(x\)-axis rotational velocities (\(\dot{\mathbf{\omega}}_{\textit{x}}\)) and \(y\)-axis rotational velocities (\(\dot{\mathbf{\omega}}_{\textit{y}}\)), located in the plane of the wheel and perpendicular to IMU's \(z\)-axis. Consequently, the true MWC's linear velocity (\(\mathbf{V}_{\textit{T}}\)) was calculated using Equation (3). \[\mathbf{V}_{\textit{T}}=\mathbf{r}\left(\frac{\dot{\mathbf{T}}\mathbf{\omega}_{\textit{left}_ {\textit{subject}}}+\dot{\mathbf{T}}\dot{\mathbf{\omega}}_{\textit{right}_{\textit{ subd}}}}{2}\right) \tag{3}\]  
For the SP test, the force developed by players during the sprint (\(\mathbf{F}_{\textit{IMU}}\)) was computed with the second law of Newton in Equation (4). \[\mathbf{F}_{\textit{IMU}}=\mathbf{m}_{\textit{t}}*\mathbf{acc}+\mathbf{F}_{\textit{rr}}+\mathbf{F }_{\textit{aero}} \tag{4}\]  
Here, \(\mathbf{m}_{\textit{t}}\) is the system's total mass consisting of the participant and their wheelchair, \(\mathbf{acc}\) is the linear acceleration, \(\mathbf{F}_{\textit{rr}}\) is the rolling resistance force, and \(\mathbf{F}_{\textit{aero}}\) is the aerodynamic drag force. To obtain the acceleration (\(\mathbf{acc}\)), we fitted the velocity data with a polynomial (\(pV\)) at each point in \(x\) as Equation (5). The argument \(p\) is a vector of length \(n+1\) whose elements was the coefficients (in descending powers) of a 4 th-degree polynomial (Figure 1a). \[pV(x)=p1x^{4}+p2x^{3}+p3x^{2}+p4x+p5 \tag{5}\]  
The coefficients for the polynomial (\(p1\), \(p2\ldots,p5\)) were returned to be the best fit (in a least-squares sense) for the velocity data (\(V_{T}\)). The coefficients and the polynomial were computed with the MATLAB functions \"polyfit\" and \"polyval\". \(F_{rr}\) was estimated using a deceleration test [28] on the 20 m sprint field and computed with Equation (6). In this equation, \(g\) is the gravitational constant, \(\mu_{r}\) is the rolling resistance coefficient compute as the deceleration value divided by \(g\). \(k_{f}\) is the coefficient of influence of speed on friction [29]. \[F_{rr}=m_{g}g(\mu_{r}+k_{f}pV^{2}) \tag{6}\]  
The aerodynamic drag force was obtained with Equation (7) where \(C_{d}A\) is the drag coefficient in the function of the frontal area of the system [30] and \(\rho\) is the air density (1.22 kg.m\({}^{-3}\)).