## 3 Results
### Inertia Estimation  
#### 3.4.1 Inertia Estimation Based on Correlation Analysis and Conventional Approaches  
The inertia data obtained was used to create approximations for the determination of the moment of inertia. The background to this was that most of the other vehicle parameters required for vehicle dynamics models (e.g., single-track models) can be determined more easily. The determination of the vehicle inertia, however, is associated with greater experimental effort and special test benches. The aim of this approximation formula was to enable an estimation of the moment of inertia on the basis of vehicle parameters that could be measured easily for the purpose of model building, simulation, crash analysis, and controller development. To determine the main factors influencing the inertia, a correlation analysis was carried out first. The correlation analysis was performed for a total of three different input sets. These groups were: only velomobiles (vehicles 1-10), only trikes (vehicles 11-13), and all vehicles. Correlation analysis is only suitable for determining linear dependencies. To prevent a bias towards vehicles for which a larger number of measurements had been taken, a maximum of three measurements were considered for each vehicle. The measurements of the lightest driver, the heaviest driver, and the driver closest to the mean value of the two were used. The results of the correlation analysis are shown in Table 5. Parameters with a high correlation coefficient and a low \(p\)-value (<0.05) showed a significant influence on yaw inertia. Across all vehicle groups, the correlation analysis showed a significance of the following parameters: wheelbase, total length, empty mass, and total mass. For the group of all vehicles, there also appeared to be a negative weaker correlation with respect to track width. This correlation was not causally traceable and could be attributed to superimposition by other effects. It can be seen, that in some of the vehicles, long wheelbases occurred with short track widths. This resulted in a non-causal correlation between short track widths and high inertias. For driver mass, the analysis showed no significant correlation. Looking at the individual values of each vehicle, it can nevertheless be seen that larger driver masses generally led to greater inertias. Therefore, a partial correlation analysis was performed for the group of all vehicles to detect superposition effects and masked correlations for selected variables. In partial correlation analysis, the individual effects of certain variables were determined by removing the expected effects of the control variables. The target variable continued to be yaw inertia. Table 6 shows the results of the partial correlation analysis. With the wheelbase as a control variable, there was no longer a significant correlation for the track width based on the partial correlation analysis. The previously recognized correlation was therefore due to overlaps with effects of the wheelbase. The influence of the distance of COG to rear axle \(l_{r}\) was also an effect of the dependence on wheelbase and no longer showed a significant influence on inertia. For the driver's mass, on the other hand, there was a significant influence on inertia when the empty mass was used as a control variable. For a single vehicle, a higher driver mass therefore indicated an increase in inertia, in accordance with the expectations. In the correlation analysis, this effect was masked by other relationships. Therefore, for the approximation of the moment of inertia,