# 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 4, the unsteady Rigid Body Motion (RBM) method is used, with an iterative approach where the submarine hull resistance is computed first, followed by sequentially adding propeller rotational speeds for the numerical simulation of the submarine model's self-propulsion hydrodynamic performance. The propeller rotational speeds are adjusted from high to low within the same computational file, with the rotational speeds set to \(n\) = 12 r/s, 11 r/s, 10 r/s, and 9 r/s. The calculation results are shown in Tables 12 and 13. \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
9 & 110.620 & 75.172 & 4.032 & 99.979 \\
10 & 114.993 & 109.220 & 5.507 & 100.135 \\
11 & 119.571 & 148.042 & 7.145 & 105.940 \\
12 & 124.324 & 191.871 & 8.950 & 113.935 \\
10.145, self-propulsion point & 115.666 & 114.559 & 5.735 & 100.583 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Analysis of load characteristics during simulation of submarine with propeller self-propulsion (strategy 3). \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 & 0.035\% & \(-0.019\%\) & \(-0.236\%\) & 0.341\% & \(-0.370\%\) & 0.250\% \\
10 & 0.049\% & \(-0.004\%\) & \(-0.496\%\) & 0.142\% & \(-0.609\%\) & 0.105\% \\
11 & \(-0.007\%\) & \(-0.022\%\) & \(-0.715\%\) & \(-0.052\%\) & \(-0.787\%\) & 0.010\% \\
12 & \(-0.054\%\) & \(-0.060\%\) & \(-0.714\%\) & 0.030\% & \(-0.697\%\) & 0.044\% \\
10.145 & 0.069\% & 0.067\% & \(-0.519\%\) & 0.006\% & \(-0.630\%\) & 0.002\% \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Error analysis between strategy 3 and strategy 1. As shown in Table 12, using the iterative method to sequentially simulate 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 takes 133.557 h. This is 9.2 times longer than the time required for the steady-state method in strategy 1 (14.576 h), 3.8 times longer than the time required for the steady-state plus unsteady-state method (35.313 h), 0.77 times the time required for the unsteady-state method in strategy 2 (174.012 h), and 0.318 times the time required for the unsteady-state method in strategy 3 (419.989 h). Therefore, in terms of the total solver actual runtime for determining the self-propulsion point's propeller rotational speed, the order is strategy 3 \(>\) strategy 2 \(>\) strategy 4 \(>\) strategy 1. In Table 13, an error analysis of the data obtained using the strategy 4 method is conducted based on the strategy 1 data. As shown in Table 13, the maximum errors of the strategy 4 method compared to the steady-state results are 0.092% for submarine hull resistance, \(-\)0.566% for propeller thrust, and \(-\)0.696% for torque. Compared to the unsteady-state results, the maximum errors relative to the unsteady-state are \(-\)0.090%, 0.119%, and 0.237%, respectively, indicating that the errors are very small. Thus, the load prediction errors introduced by the two calculation strategies can be considered negligible.