# Research on a Strategy for Prediction Methods of Submarine Self-Propulsion Hydrodynamic Performance
## 4 Analysis of Hydrodynamic Performance under Different Computational Strategies
In computational strategy 3, the unsteady RBM method is used, with propeller rotational speeds set to \(n=9\) r/s, 10 r/s, 11 r/s, 12 r/s, and 10.145 r/s. Numerical simulations of the submarine with propeller self-propulsion hydrodynamic performance were conducted for these rotational speeds. The calculation results are shown in Tables 10 and 11. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Propeller Rotational Speed \(n\)** & **Submarine Hull** & **Propeller Thrust** & **Propeller Torque** & **Total Solver Actual** \\ **(r/s)** & **Resistance \(R\) (N)** & \(T\) (N)** & **Q (N-m)** & **Runtime \(t\) (h)** \\ \hline
0 & 90.247 & & & 20.228 \\
9 & 110.564 & 75.323 & 4.037 & 38.399 \\
10 & 114.950 & 109.519 & 5.517 & 39.217 \\
11 & 119.537 & 148.559 & 7.160 & 38.385 \\
12 & 124.324 & 192.494 & 8.968 & 37.783 \\
10.145, self-propulsion point & 115.605 & 114.900 & 5.746 & 36.920 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Analysis of load characteristics during self-propulsion simulation of submarine first and propeller second (strategy 2). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Propeller** & **Submarine Resistance \(R\) Error** & **Propeller Thrust \(T\) Error** & **Propeller Torque \(Q\) Error** \\ \cline{2-7}
**Rotational** & **Steady-State** & **Unsteady-State** & **Steady-State** & **Unsteady-State** & **Steady-State** & **Unsteady-State** \\ \hline
9 & \(-\)0.016\% & \(-\)0.070\% & \(-\)0.035\% & 0.543\% & \(-\)0.247\% & 0.374\% \\
10 & 0.011\% & \(-\)0.042\% & \(-\)0.223\% & 0.416\% & \(-\)0.441\% & 0.274\% \\
11 & \(-\)0.035\% & \(-\)0.050\% & \(-\)0.369\% & 0.297\% & \(-\)0.579\% & 0.219\% \\
12 & \(-\)0.055\% & \(-\)0.060\% & \(-\)0.391\% & 0.355\% & \(-\)0.505\% & 0.237\% \\
10.145 & 0.016\% & 0.015\% & \(-\)0.223\% & 0.304\% & \(-\)0.447\% & 0.186\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Error analysis between strategy 2 and strategy 1. As shown in Table 10, compared to strategy 1 and strategy 2 computational strategies, using the unsteady RBM method for the numerical simulation of the submarine with propeller self-propulsion hydrodynamic performance results in a longer total solver actual runtime. For simulating a single propeller rotational speed, the time required reaches 100 h, and the total solver actual runtime increases with the propeller rotational speed. If this method were used to conduct numerical simulations of the submarine model's self-propulsion hydrodynamic performance at four different propeller rotational speeds to determine the propeller rotational speed corresponding to the self-propulsion point, the total time required would be 419.989 h. This is 29 times longer than the time required for the steady-state method in strategy 1 (14.576 h), 12 times longer than the time required for the steady-state plus unsteady-state method (35.313 h), and 2.4 times longer than the time required for the unsteady-state method in strategy 2 (174.012 h). Therefore, the total solver actual runtime required by the strategy 3 method to determine the propeller rotational speed corresponding to the self-propulsion point of the submarine model is significantly longer than that of the strategy 1 and strategy 2 methods. Table 11 provides an error analysis of the data obtained using the strategy 3 method, based on the strategy 1 data. As shown in Table 11, the maximum errors using the strategy 3 compared to the steady-state results are \(-0.054\%\), \(-0.715\%\), and \(-0.787\%\) for submarine hull resistance, propeller thrust, and torque, respectively. Compared to the unsteady-state results, the maximum errors are \(-0.060\%\), \(0.341\%\), and \(0.250\%\), respectively. The errors between the two computational strategies are very small. Additionally, in strategy 3, the submarine hull resistance is slightly reduced compared to the unsteady-state method, while the propeller thrust and torque are slightly reduced compared to the steady-state method and slightly increased compared to the unsteady-state method.