## 6 Application in Hot Wire Calibration
### HotWire Calibration
Table 11 exhibits the deviation between the velocity estimated via the fitting curve by the hot-wire output voltage (i.e., drawing a straight line perpendicular to the \(E\) axis and passing through the point of the output voltage value on the \(E\) axis in the \(E\) vs. \(U\) diagram, then the intersection point of the straight line and the \(E\) vs. \(U\) fitting curve gives the velocity to be determined) and the real velocity controlled by the motion control system at the same output voltage value under each parameter combination of set (nominal) velocity, set temperature, and set humidity. Table 12 shows the maximum of the absolute value of the velocity deviations under all the set temperatures and set humidity values at each set velocity (i.e., the maximum absolute value of the deviations in each line in Table 11), which represents the calibration error of the fitting curve at each set velocity and varies from 0.00512 m/s to 0.02236 m/s, giving a maximum value of 0.02236 m/s that satisfies the calibration accuracy target 0.03 m/s. The maximum relative fitting error is 5.214%. At velocities as low as 1 m/s natural convection is significant and must be taken into account in the relationship describing the heat transfer from the wire. A number of researchers have considered the effects of natural and forced convection, while [PERSON] der \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(T_{\text{set}}\) & \multicolumn{3}{c}{30 \({}^{\circ}\)C} & \multicolumn{3}{c}{40 \({}^{\circ}\)C} & \multicolumn{3}{c}{60 \({}^{\circ}\)C} \\ \hline \hline \(H_{\text{set}}\) (\%RH) & **20** & **60** & **80** & **20** & **60** & **80** & **19** \\ \hline a & 1.644 & 1.669 & 1.615 & 1.507 & 1.502 & 1.59 & 1.358 \\ b & 0.6586 & 0.6538 & 0.687 & 0.6467 & 0.6710 & 0.6047 & 0.521 \\ n & 0.6344 & 0.7074 & 0.6136 & 0.5967 & 0.5578 & 0.6963 & 0.6429 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Constants in the fitting curves of the modified King’s law. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(T_{\text{set}}\) & \multicolumn{3}{c}{30 \({}^{\circ}\)C} & \multicolumn{3}{c}{30 \({}^{\circ}\)C} & \multicolumn{3}{c}{40 \({}^{\circ}\)C} & \multicolumn{3}{c}{40 \({}^{\circ}\)C} & \multicolumn{3}{c}{40 \({}^{\circ}\)C} & \multicolumn{3}{c}{60 \({}^{\circ}\)C} \\ \hline \hline \(V_{\text{set}}\)\(\backslash\)\(H_{\text{set}}\) & **20\%RH** & **60\%RH** & **80\%RH** & **20\%RH** & **60\%RH** & **80\%RH** & **19\%RH** \\ \hline \hline \(0.1\) & 0.000936 & 0.005120 & 0.003931 & 0.003843 & 0.00933 & 0.002976 & 0.000955 \\ \(0.2\) & \(-0.001983\) & \(-0.008284\) & \(-0.006744\) & \(-0.003238\) & \(-0.009262\) & \(-0.001466\) & \(-0.000994\) \\ \(0.3\) & 0.007060 & \(-0.004327\) & \(-0.007101\) & \(-0.007840\) & 0.004476 & \(-0.004627\) & 0.002008 \\ \(0.4\) & \(-0.01316\) & \(-0.002082\) & \(-0.001695\) & \(-0.02086\) & \(-0.002688\) & \(-0.003603\) & 0.002485 \\ \(0.5\) & \(-0.001592\) & 0.001401 & 0.007487 & 0.01130 & \(-0.003538\) & 0.006449 & 0.00636 \\ \(0.6\) & \(-0.000700\) & 0.01030 & 0.006810 & 0.01764 & 0.004099 & 0.001741 & -0.000445 \\ \(0.7\) & 0.01490 & 0.001245 & 0.005058 & 0.02236 & 0.01634 & \(-0.002190\) & 0.006011 \\ \(0.8\) & 0.008045 & 0.01088 & 0.004932 & 0.002771 & 0.009140 & 0.01852 & 0.002805 \\ \(0.9\) & \(-0.004668\) & 0.000303 & \(-0.003850\) & \(-0.01763\) & \(-0.002509\) & 0.004364 & 0.000003 \\ \(1.0\) & \(-0.008005\) & \(-0.01396\) & \(-0.01027\) & \(-0.01095\) & \(-0.01369\) & \(-0.01486\) & 0.001691 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Deviation of fitted velocity from real controlled velocity(m/s).