## 2 Materials and Methods and Results
### Deadweight Calibrations
#### 2.2.3 Phase 2: Effect of Extended Warm-Up Time on Load-Voltage Relationship  
The second phase had two interrelated purposes: to determine how long we needed to warm up the load cells to achieve steady, reliable load-voltage relationships and if the load-voltage relationship would change after extended run time, as may happen in a long day of field data collection with one or more forward packs. Using the power station as the only power source, we calibrated each load cell after 15 min, 30 min, 45 min, 60 min, and 7 h of continuous run time.  
For the statistical analysis of phase 2, linear regression models were used to examine the effects and interactions of time and individual load-cell differences on the load-voltage relationship. We started with the simple linear regression (disregarding the run time and individual load cells), voltage = \(\beta_{0}\) + \(\beta_{1}\) load, and then we considered both time and individual running cells using multiple linear regression to determine if these factors significantly impacted the load-voltage relationship.  
The simple linear regression, voltage = \(\beta_{0}\) + \(\beta_{1}\) load, explains 98.86% of the variance in voltage. When both time and individual running cells were included in multiple linear regression, we could explain nearly all the variance in voltage (\(R^{2}\) = 0.9999867). Our final multiple linear regression model indicated a significant effect of individual load cells on the load-voltage relationship, creating two groupings: six of the load cells had very similar load-voltage relationships, and another pair had very similar load-voltage relationships (Figure 6). Additionally, 4 of the load cells exhibited no significant effect of time on their load-voltage relationship, indicating that after at least 15 min of run time, the load cells produce stable reliable load-voltage relationships, and this relationship does not change even with 7 h of run time. However, 2 load cells exhibited a significant difference in load-voltage relationship between the 15 min calibration and all other calibrations (\(p\) = 0.014 and 0.036, respectively), with no differences between the 30 min calibration and other calibrations; this indicates that after at least 30 min of run time, those 2 load cells produce a stable reliable load-voltage relationship which does not change with 7 h of run time. Similarly, 1 load cell showed significant differences until 60 min, and 1 load cell showed significant differences at all time points. However, the magnitude of difference in mean volts between any time points with any load cell was so small (the largest difference was 2.2 mV) as to be negligible in a practical sense. A difference of 2.2 mV indicates a difference of about 19 N; in the context of scrum packs producing forces ranging from 8000-16,000 N, 19 N is below the detectable variance, even when compounded across all 8 load cells. Even for individual player scrum trials, where the force magnitudes are lower (e.g., group average peak force of individuals in phase 3 was \(\sim\)2096 N) and where this difference between device warm-up times represents a larger proportion of the measured forces, it is not a meaningful amount, particularly between longer warm-up times (e.g., 30 min versus 7 h). Warming up all load cells for at least 30 min should greatly minimize what is already a relatively small drift over time.  
Considering the results of phase 2, we concluded that the load cells demonstrate acceptable reliability for later application of measuring forces generated by scrum packs. We determined that we would use 30 min of warm-up time as our standard operating procedure moving forward and that we could collect data continuously for up to 7 h without threat to the reliability of our results. In the next phase, we shifted from testing intra-session to between-session reliability.