## 3 Results and Discussion
### Validation of Measurement Results  
To verify the results of thrust measurement during speed trials, the relation of thrust and torque is compared with the prediction results from model test results. The relation between propeller thrust and torque is an important index that decides the accuracy of the thrust measurement and is also a good index for checking the status of the propeller. In  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Engine Load**} & \multicolumn{3}{c}{**PORT**} & \multicolumn{3}{c}{**Starboard**} \\  & \multicolumn{3}{c}{**(Speed Trial/Model Test)**} & \multicolumn{3}{c}{**(Speed Trial/Model Test)**} \\ \cline{3-6}  & & **Thrust** & **Torque** & **Thrust** & **Torque** \\ \hline \multirow{3}{*}{65\%} & 1 st & 97.1\% & 96.5\% & 96.1\% & 97.1\% \\  & 2 nd & 101.3\% & 100.9\% & 100.5\% & 101.6\% \\ \cline{2-6}  & Avg. & 99.2\% & 98.7\% & 98.3\% & 99.4\% \\ \hline \multirow{3}{*}{75\%} & 1 st & 94.4\% & 96.0\% & 93.7\% & 96.3\% \\  & 2 nd & 98.3\% & 99.2\% & 97.6\% & 99.9\% \\ \cline{2-6}  & Avg. & 96.4\% & 97.6\% & 95.7\% & 98.1\% \\ \hline \multirow{3}{*}{90\%} & 1 st & 94.2\% & 96.5\% & 92.9\% & 96.8\% \\  & 2 nd & 95.6\% & 97.9\% & 95.6\% & 98.8\% \\ \cline{2-6}  & Avg. & 94.9\% & 97.2\% & 94.3\% & 97.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Difference ratio between speed trial measurement and prediction results based on the model test of the twin skeg LNG carrier.  
Figure 9: Comparison of thrust and torque between speed trials and prediction results based on the model test of the twin skeg LNG carrier.  
general, the relation of the propeller thrust and torque due to draught and trim conditions is rarely changed, which is confirmed by the model test.  
Figure 10 shows the comparison result of crude oil tankers. It was found that the results of thrust measurement by the strain gauge system showed a discrepancy with thrust by the model test of approximately 2% at same torque. The characteristics of thrust-torque by varying engine loading show a good correlation with those of the model test. In cases of the optical sensor, however, the results of thrust measurement show approximately 11% at designed draught and 4% at ballast draught differences from the model test results, mainly due to the stability of the zero value.  
The slopes of torque-thrust are well correlated with each other from the strain gauge system, the optical-type measurement and model tests. As an operational performance index, the characteristics of thrust and torque, such as the slope, are a main parameter. In terms of the performance index, the changes and uncertainties in the zero values might not be the issue. However, a careful posterior process should be required to obtain the proper slopes from the measurement.  
Figure 11 presents the measurement results during speed trial compared with the prediction result from model test. The measurement results from both side showed the same tendency and a discrepancy with the thrust by model test of approximately 1% at same torque.  
Figure 11: Comparison of thrust-torque of the twin ske LNG carrier.  
Figure 10: Comparison of thrust-torque of crude oil tankers.  
The difference between the prediction results from model test and measurement during speed trial increases gradually as the engine load is increasing. The results of thrust measurement at PORT side showed the discrepancy with the model test results of 0.5% at 65% of MCR, 1.3% at 75% of MCR, and 2.3% at 100% of MCR. The discrepancies at starboard side are 1.3% at 65% of MCR, 2.5% at 75% of MCR, and 3.5% at 100% of MCR. The slopes of thrust-torque are 0.903 from model tests and 0.794 from PORT and starboard side. The discrepancy of the slope is caused by the gauge factor. In general, the gauge factor is evaluated based on the shop test. For reliable results, the gauge factor should be adjusted by speed trials. The propeller thrust is a challenging value to measure. Therefore, even careful installation of a thrust measurement system does not guarantee a high accuracy of measurements.