## 2 Materials and Methods and Results
### Deadweight Calibrations
#### 2.2.2 Phase 1: Effect of Power Source on Load-Voltage Relationship  
To make our instrumented scrum machine viable for use in real-world conditions, we needed to find a way to move it out of the laboratory and onto the rugby field, where AC power sources are often not available. Therefore, we purchased a Yet 1500X Portable Power Station, a high-capacity lithium-ion battery and inverter unit (henceforth \"power station\"; Goal Zero, Bluffdale, UT, USA). This power station provides a 120V AC output plug. We were concerned that with the extended run time, as the battery of the power station reduced, the reliability of our load-voltage relationship might be threatened because of factors such as reduction in output voltage with lowered battery charge or increased temperature of the power station and/or other equipment from the extended run time. In addition, each power source may introduce different noise, potentially influencing output voltages. Therefore, in phase 1, we calibrated 2 of our load cells after 15 min, 1 h, and 2 h of warm-up time with all the equipment plugged into the power station, and on a separate day, we repeated the procedure with all the equipment plugged into the wall outlet in our laboratory.  
For the statistical analysis of phase 1, multiple linear regression models were used to estimate the influence of power source (power station vs. wall plug) on the load-voltage relationship:  
\[\text{voltage}=\beta 0+\beta 1\text{-load}+\beta 2\text{-(load cell)}+\beta 3\text{-(power source)}+\beta 4\text{-time}+\beta 5\text{-(load $\times$ power source)}\]  
The regression parameter of interest was \(\beta 5\) for testing whether the load-voltage relationship depends on the power source. The regression analysis indicated that the main effect of power source is statistically significant (\(p=0.003\)) but not the load \(\times\) power source interaction effect (\(p=0.085\); i.e., the null hypothesis \(\beta 5=0\) cannot be rejected at significance level \(\alpha=0.05\)). On average, voltage values from the load cell were about 0.001 volts greater when the power station was used compared to when the wall plug was used. Time did not affect voltage in one tested load cell (i.e., no main effect of time (\(p=0.73\)) or load \(\times\) time interaction effect (\(p=0.75\))). In the second load cell, there was a significant load \(\times\) time interaction effect (\(p=0.0079\)). Despite the statistical significance, at \(\sim\)200 kg (i.e., the maximum tested load), each minute of additional warm-up time after 15 min and up to 2 h changed the measured voltage by about \(-50\)\(\mu\)V on average; this translates to approximately 0.04 N. This magnitude of difference is largely meaningless considering the size of the expected loads during scrum trials and the resolution of our AD converter and load-cell combination (smallest step \(\sim\)1.2 mV or \(\sim\)1.09 N).  
Figure 5: Block diagram of instrumented scrum machine.  
Overall, this first phase indicated that while the power station may produce significantly different voltage outputs than the wall outlet (albeit negligible in practical magnitude), the load-voltage relationship was just as stable when using the power station as when using the wall outlet. Therefore, we concluded that the power station was suitable and reliable for use in future phases of the calibration as well as in human application. Additionally, this first phase indicated potential changes in the load-voltage relationship across warm-up times, though this difference was only seen in one of the two load cells and had a minimal magnitude. Therefore, it informed us that we would need to conduct more extensive testing of reliability across warm-up times in all our load cells, which led to the next phase of our calibration testing.