## 3 Results
### Development of Offline (General) Thermal Comfort Model
The prediction trace analysis [28] of the developed model (2) was based on computing the predicted response as one variable was changing while the others were held constant at certain values. The results showed that the effect of \(R_{h}\) was dependent on the level of \(T_{a}\). At a low level (\(-1\)) of ambient air temperature (\(T_{a}=20\ ^{\circ}\)C), for a change in thermal resistance \(R_{h}\) from a low level (\(-1\)) (i.e., no-bicycle helmet) to a high level (\(1\)) (i.e., using the Lazer-Z1 Fast), the predicted thermal comfort scale (Table 2) decreased by \(0.5\) thermal comfort units but was perceived as comfortable. However, at a high level (\(1\)) of ambient air temperature (\(T_{a}=30\ ^{\circ}\)C), the comfort level increased by \(0.5\) thermal comfort units. This information is important for actively controlling under-helmet thermal comfort, which can be done by manipulating the helmet thermal resistance via, for instance, opening/closing some of the helmet's holes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Term** & **Parameter** & **Estimate** & **Std. Error** & **\(t\)-Ratio** & **\(P>|t|\)** \\ \hline intercept & \(\alpha\) & \(1.86\) & \(0.21\) & \(13.61\) & \(<\)0.0001 \({}^{*}\) \\ \(\Delta T\) & \(\beta_{1}\) & \(1.30\) & \(0.19\) & \(5.22\) & \(0.0031\ ^{*}\) \\ \(H_{R}\) & \(\beta_{2}\) & \(-0.62\) & \(0.13\) &As expected, the heart rate (\(H_{R}\)) of the test subjects was found to be highly correlated (Pearson's correlation coefficient, \(r\) = 0.85) with the power (\(P\)). Additionally, the heart rate was significantly correlated (\(r\) = 0.68) with the recorded thermal comfort for all 15 test subjects. As expected, the temperature difference (\(\Delta T\)) between the average air temperature beneath the helmet (\(\overline{T}_{h}\)) and the ambient air temperature (\(T_{a}\)) was correlated with both relative air velocity (\(\
u\)) and helmet thermal resistance (\(R_{h}\)), with \(r\) = 0.82 and 0.78, respectively. By employing both heart rate (\(H_{R}\)) and the temperature difference (\(\Delta T\)) as input variables to the linear regression model, the best model structure that gave the highest average goodness of fit (with average \(R^{2}\) = 0.89 \(\pm\) 0.04) and lowest Akaike information criterion (average AIC = 123 \(\pm\) 7) was as follows:  
\[T_{C}\ =\ \alpha+\beta_{1}\Delta T+\beta_{2}H_{R}+\beta_{3}[T_{a}R_{h}], \tag{3}\]  
where \(\Delta T\ =\ \overline{T}_{h}-T_{a}\) and \(\overline{T}_{h}\) is the average air temperature under the helmet, which is calculated from the four temperature sensors located under the helmet. It can be noticed that the structure of model (3) is more compact, consisting of three input variables, compared with the structure of model (2), which consisted of five input variables. Model (3) showed better prediction performance for the thermal comfort level than model (2), which had maximum mean absolute percentage errors (MAPEs) of 8.4% and 11%, respectively. The MAPE is given by  
\[MAPE=\ \frac{100\%}{N}\sum_{k=1}^{N}\left|\frac{\hat{T}_{C}(k)-T_{C}(k)}{T_{C}( k)}\right|\]  
where \(N\) is the number of data points and \(\hat{T}_{C}\) is the predicted thermal comfort. It can be noticed that both the mechanical work rate (\(P\)) and air velocity (\(\
u\)) disappeared from the compact model (3). The heart rate (\(H_{R}\)) variable included in the compact model (3) directly linked to the applied mechanical work rate (\(P\)), hence the effect of \(P\), included in model (2), translated by  
Figure 8: Visualisation of the model prediction traces showing the interaction effect of the thermal resistance (\(R_{h}\)) and ambient temperature (\(T_{a}\)) on the predicted thermal comfort. (**a**) When the temperature was low (20 \({}^{\circ}\)C), additional thermal resistance was perceived as comfortable. However, (**b**) when the temperature was high (30 \({}^{\circ}\)C), additional thermal resistance was perceived as uncomfortable.