## 2 Materials and Methods
### Data Acquisition and Analysis  
The non-motorised HRD used to overload the participants in this study is a state-of-the-art device that generates manually adjustable hydraulic resistance. The device is designed for training purposes and monitor sprint performance. A detailed description of its resistance-generating properties can be found elsewhere (see [22] for details). The device measures position and hydraulic pressure, and previous studies have confirmed that the timing of sprints with various overloads is reliable [30]. The device has an integrated magnetic encoder (model AEAT-601B, Broadcom Inc., San Jose, CA, USA), which was used to capture changes in position over time. In addition, an integrated pressure sensor (model NP400, 5 mA, 5 V, NOVUS Inc., Canoas, Brazil) was used to record changes in system pressure over time. The hydraulic pressure and position signals were acquired synchronously with a sampling rate of 1000 Hz using specially developed software (ARS Dynamometry, S2P, Ljubljana, Slovenia; created with LabVIEW 8.1, National Instruments, Austin, TX, USA). The signals were processed in Python using custom-developed code. The start of the sprint was determined when the position signal increased by 0.1 m from standstill. The signals obtained up to 20.1 m were analysed in this way [29]. The instantaneous velocity during the 20 m sprint was calculated as a derivative of the position. A fourth-order Butterworth low-pass filter with a cut-off frequency of 2 Hz was then used to smooth the velocity data [16]. Finally, the velocity-time relationship was calculated, and the \(\
u_{\mathrm{max}}\) was determined for each overload condition. The trials with the highest \(\
u_{\mathrm{max}}\) were used for further analyses. The F\({}_{\mathrm{r}}\) during the sprints was determined using the HRD and the FP. The pressure signal obtained from the HRD was calibrated in a laboratory experiment to determine the F\({}_{\mathrm{r}}\) directly. In addition, a 3D force plate (type 9229A, Kistler Instruments, Winterthur, Switzerland) was firmly mounted under the HRD. The FP reaction forces generated by pulling the HRD were recorded synchronously with pressure and position signals at a frequency of 1000 Hz using MARS software (version 4.9; Kistler Instruments, Winterthur, Switzerland). Since only the antero-posterior force is usually considered in the evaluation of the force output, the power output, and the calculation of the FvP profile of the sprint [17], the horizontal component of the reaction force was considered as Fr calculated via the FP. The F\({}_{\mathrm{r}}\) obtained from the HRD and FP was filtered using a fourth-order Butterworth low-pass filter with a cut-off frequency of 2 Hz [16]. Finally, an average F\({}_{\mathrm{r}}\) from both  
Figure 1: Participant in start position connected to a hydraulic resistance device positioned on a force plate. methods was calculated from the F\({}_{\rm{r}}\) generated via a 20 m sprint. To better illustrate the data acquisition process, readers can see step 1 in Supplementary File. For each overload condition, the force and power outputs were first calculated. Due to the 0.1 m delay between initiation and actual start [31], a monoexponential function was fitted to the \(\
u_{\rm{max}}\) and the relative acceleration constant from the original velocity-distance plots to obtain distance-corrected velocity data [18]. Next, F\({}_{\rm{h}}\) was calculated using the methodology from previous studies evaluating the FvP profile of sled sprints (see Step 2 in Supplementary File) (see step 2 in Supplementary File) [13,14,17]. The aerodynamic drag force calculated from the running velocity, anthropometric data, and environmental variables [23], the net horizontal antero-posterior force derived from the velocity [23], and the Fr measured using either the HRD or FP were combined to obtain F\({}_{\rm{h}}\). An average F\({}_{\rm{h}}\) (F\({}_{\rm{avg}}\)) over the 20 m sprint was calculated and normalised to body mass (N/kg) as a representative parameter for the force output.