## 2 Materials and Methods  
### Experimental Conditions  
In a ship resistance test, it is very important to ensure that the mechanics of the model ship and the real ship are similar so that the real ship performance can be predicted according to the test results. Therefore, the selection of the ship model size, ship model surface state, test environment, test condition design, etc. should be guided by the similarity theory and meet certain hydrodynamic similarity conditions and principles. The principal scales corresponding to the ship model and the real ship should satisfy the same constant of scale, denoted as follows:  
\[\frac{L_{s}}{L_{m}}=\frac{B_{s}}{B_{m}}=\frac{D_{s}}{D_{m}}=\lambda \tag{1}\]  
where \(L\) is the design water line length; \(B\) is the width; \(D\) is the depth design draft; s represents the actual ship; and m represents the ship model.  
In the ship model resistance test, the test process needs to satisfy a certain ship resistance similarity law in order to ensure the accuracy and reliability of the extrapolation of the test data to the actual ship performance (namely, Reynolds law and Froude law). However, it is actually difficult to achieve the full similarity condition such that both the ship model and the actual ship satisfy the equality of Re and \(F_{r}\). If the ship model and the actual ship are required to satisfy Fr equality, then the equation is satisfied as follows:  
\[F_{rs}=F_{rm},\frac{V_{s}}{\sqrt{gL_{s}}}=\frac{V_{m}}{\sqrt{gL_{m}}} \tag{2}\]  
where \(V_{s}\) is the velocity of the actual ship and \(V_{s}\) is the velocity of the model ship.  
If the ship model and the actual ship are required to satisfy Re equality, then the equation is satisfied as follows:  
\[\frac{V_{s}L_{s}}{v_{s}}=\frac{V_{m}L_{m}}{v_{m}} \tag{3}\]  
If Re and \(F_{r}\) are equal, the length and kinematic viscosity coefficient of the real ship and the ship model should satisfy the following formula:  
\[v_{m}=v_{s}(\frac{L_{m}}{L_{s}})^{\frac{3}{2}} \tag{4}\]  
The scale ratio of the main dimensions of the ship model is 12.22 in the ship resistance test experiment conducted this time. It is obviously difficult to ensure that the viscosity of the medium in the experiment is \(1/42\) that of the medium in the actual ship voyage. Therefore, \(F_{r}\) equality is chosen for the ship model experiments.  
The main dimensions and main elements of the actual ship and the ship model are shown in Table 1, which mainly shows the corresponding relationship between the size of the ship model and the actual ship under fully loaded and lightly loaded conditions. The length of the model is 3.52 m and the width is 0.67 m. The propeller diameter of the real ship is 2.5 m and the power of the main engine is 900 kW. The spare propeller diameter is 204.55 mm, the number of blades is 4 blades, the disk ratio is 0.55, the pitch ratio is 1.0, and the propeller mold material is duralumin. The speed range of resistance test is shown in Table 2. The shape and working conditions of the ship model are shown in Figure 1 below. In the experimental tests, the speed range of the ship model is 0.44 to 2.06 m/s, which corresponds to the speed range of the real ship from 3 to 14 kn. The four types of working conditions are fully loaded without appendages, fully loaded with appendages, lightly loaded without appendages, and lightly loaded with appendages.