# Environmental and Economic Aspects of a Containership Engine Performance in Off-Design Conditions
## 2 Containership and Propeller Characteristics  
For this case study, a 6750-TEU containership was selected whose hull lines and 3D model are presented in Figures 1 and 2, respectively. The main particulars of the containership at model and full scale are shown in Table 1. The experiments with a ship model in a scale of 35.18 were carried out in the facility of the Brodarski Institute [30] in a 276 m long, 12.5 m wide, and 6 m deep towing tank, which is equipped with a towing carriage of maximum speed equal to 14 m/s.  
The resistance, open water, and self-propulsion tests were conducted for a wide range of speeds. During the resistance tests, the model speed, total resistance, running trim, sinkage, and water temperature were measured.  
During the self-propulsion tests, the ship model was equipped with a controllable pitch propeller (CPP) model, Table 2.  
Figure 1: Hull lines of the 6750-TEU containership.  
The self-propulsion tests were performed based on the British method, meaning that the propeller load was varied at each speed, and propeller thrust, torque, and the propeller rate of revolution were measured along with the quantities measured in the resistance test. Self-propulsion tests were performed in a range of speeds from 16 knots to 22 knots that include conditions for slow steaming, i.e., the delivered power at the lowest tested speed was equal to one third of the delivered power at the highest speed.  
The ship model during the self-propulsion test at the model speed corresponding to 22 knots in full scale is shown in Figure 3. The obtained experimental results were extrapolated based on the ITTC 1957 Performance Prediction Method using the correlation allowance equal to \(-0.35\cdot 10^{-3}\). The required engine power at each speed was calculated based on the extrapolated value of the delivered power and an increase of 15% to account for the sea margin, 2% to account for the mechanical efficiency of transmission between engine and propeller, and 10% for engine margin.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Main Particular** & **Symbol** & **Unit of Measurement** & **Full Scale** & **Model Scale** \\ \hline Length between perpendiculars & \(L_{\text{PP}}\) & m & 286.58 & 8.1460 \\ Length of waterline & \(L_{\text{WL}}\) & m & 292.37 & 8.3107 \\ Breadth & B & m & 40 & 1.1370 \\ Drawth at forward perpendicular & \(T_{\text{F}}\) & m & 11.98 & 0.3405 \\ Drawth at aft perpendicular & \(T_{\text{A}}\) & m & 11.98 & 0.3405 \\ Drawth at midship & \(T_{\text{M}}\) & m & 11.98 & 0.3405 \\ Wetted surface area & S & m\({}^{2}\) & 13,325 & 10.7668 \\ Displacement volume & \(V\) & m\({}^{3}\) & 85,556 & 1.9650 \\ Longitudinal center of buoyancy (with respect to midship) & \(L_{\text{CB}}\) & m & \(-5.07\) & \(-0.1440\) \\ Vertical center of buoyancy & \(Z_{\text{CB}}\) & m & 6.62 & 0.1882 \\ Block coefficient & \(C_{\text{B}}\) & - & 0.6231 \\ Midship section coefficient & \(C_{\text{M}}\) & - & 0.9850 \\ Longitudinal prismatic coefficient & \(C_{\text{P}}\) & - & 0.6317 \\ Waterplane area coefficient & \(C_{\text{WP}}\) & - & 0.7838 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The main particulars of the containership at the model and full scale.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Propeller Particulars** & **Symbol** & **Measurement Unit** & **V-1124 (CPP)** \\ \hline Diameter & \(D\) & m & 0.2073 \\ Pitch ratio at 0.7\(R\) & \(P_{0.78}/D\) & - & 1.3 \\ Expanded blade area ratio & \(A_{\text{E}}/A_{0}\) & - & 0.633 \\ Ratio of the hub diameter to the & \(d/D\) & - & 0.2957 \\ propeller diameter (hub ratio) & \(\,d/D\) & - & 0.2957 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The main particulars of the propeller model.  
Figure 2: Three-dimensional model of the 6750-TEU containership.