# The Prediction of the Performance of a Twisted Rudder
## 2 Experimental Approaches  
Model tests to analyze the hydrodynamic performance of twisted rudders including a reference flat rudder were carried out in the large cavitation tunnel (LCT) at the KRISO. The main dimensions of the LCT in the length (L), width (W), and height (H) directions are 60 m \(\times\) 6.5 m \(\times\) 19.8 m. The test section where the ship model was installed has dimensions of 12.5 m (L) \(\times\) 2.8 m (W) \(\times\) 1.8 m (H). Figure 1a,b show an experimental setup for the current test ship model with full appendages in the LCT test section. The ship hull form is a surface combatant, and its model size has a length of 7.07 m, a breadth of 0.933 m, and a draft of 0.269 m as shown in Table 1. The propeller is a controllable pitch propeller (CPP) with five blades and rotates outboard. The propeller model diameter (\(D_{P}\)) is 0.28 m. As shown in Table 1, the flat rudder has the section profiles of symmetrical NACA sections at the root and the tip. As will be explained in detail later, three twisted rudders were made by rotating each cross-section of the flat rudder around the mid-chord point according to the predicted inflow angle distributions. The chord length (\(c\)) of the rudder model is 0.1967 m at the root and 0.0887 m at the tip. The span length (\(s\)) is 0.2147 m. The sign of the rudder angle, \(\delta_{\text{R}}\), was defined as positive when rotating in the direction of the starboard side. Figure 1c shows the holes on the inboard and outboard surfaces of the flat rudder to measure the pressure distributions along the two-chord lines at the span locations, \(z/s=0.45\) and 0.6. This pressure measurement was carried out at 18-knot ship speed and non-cavitating flow conditions. Fourteen pressure taps were installed along the rudder surface at 60% span of the rudder. The relative pressure was measured with the pressure transducers made by Validyne DP15. The pressure was measured with an uncertainty of 0.18%. The pressure was non-dimensionalized as follows:  
\[C_{p}=\frac{p-p_{o}}{\frac{1}{2}\rho_{w}U_{o}^{2}} \tag{1}\]  
where, \(p\) is the pressure, \(p_{o}\) is the free stream reference pressure, \(\rho_{w}\) is the water density and \(U_{o}\) is the inflow velocity in the LCT test section. The hydrodynamic performances of the flat and twisted rudders were estimated by the surface cavitation, the drag and lift forces, and the moment for each rudder. For this purpose, the model tests were performed for cavitating flows at a relatively high ship speed, \(V_{s}\) = 30 knots. The corresponding test conditions are shown in Table 2. Here, \(K_{T}\) is the thrust coefficient, \(n\) is the propeller rotational speed, \(\sigma_{n,0.5R_{P}}\) is the cavitation number at the radial position of 0.5\(R_{P}\) and \(R_{P}\) is the propeller radius. The thrust coefficient \(K_{T}\) and the cavitation number \(\sigma_{n,0.5R_{P}}\) are given as:  
\[K_{T}=\frac{T}{\rho_{w}n^{2}D_{P}^{4}} \tag{2}\]  
\[\sigma_{n,0.5R}=\frac{p_{T}-p_{v}}{0.5\rho_{w}n^{2}D_{P}^{2}} \tag{3}\]  
where, \(T\) is the thrust of the propeller, \(p_{T}\) is the static pressure in the LCT and \(p_{v}\) is the vapor pressure. The rudder forces and moment were measured by using a dynamometer. A dynamometer was installed in the stern hull over the rudder to measure the drag force (\(\mathcal{D}\)) in the x-direction, the lift force (\(\mathcal{L}\)) in the y-direction, and the moment (\(\mathcal{M}\)) in the z-direction acting on the rudder. The dynamometer was manufactured by Wonbang Forcetech Co. Ltd., Daejeon, Korea, and can measure drag, lift, and moment up to 1000 N, 2000 N, and 45 Nm, respectively with uncertainties of 0.38%, 0.23%, and 1.70%.