# Cavitator Design for Straight-Running Supercavitating Torpedoes
## 4 Preliminary Design for a Realistic Supercavitating Vehicle  
A preliminary design was performed for a realistic supercavitating vehicle using the developed design method. Detailed information on the vehicle used in the design is presented in Table 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Value** \\ \hline Vehicle speed/depth & 140 knots/1.5 m \\ Vehicle overall length & 2.4 m \\ Vehicle diameter & 0.165 m \\ Vehicle conical part length & 0.69 m \\ Vehicle mass center from the cavitator & 1.532 m \\ Vehicle mass & 65.8 kg \\ Vertical fin span length & 0.1175 m \\ Vertical fin chord length & 0.02 m \\ Vertical fin wedge angle & \(6^{\circ}\) \\ Vertical fin root location from the cavitator & 2.274 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information for the cavitator design. Figure 10: Experimental and calculated trim conditions in a steady planing mode (cone-type cavitator. V = 9.58 m/s, \(\sigma=0.061\)): (**a**) experiment; (**b**) calculation. Figure 9: Experimental and calculated trim conditions in a steady planing mode (disk-type cavitator. V = 9.12 m/s, \(\sigma=0.064\)): (**a**) experiment; (**b**) calculation. According to the design procedure, the design cavitation number was first determined to satisfy the stability condition of the ventilated supercavity \(1\leq\beta<\beta_{cr}\) described in Section 2. As mentioned before, the critical value of the stability parameter \(\beta_{cr}\) becomes lower in the presence of the vehicle inside the supercavity, and the simulation performed by [PERSON] and [PERSON] [14] indicated that \(\beta_{cr}\approx 1.95\) in such a case. However, this body effect has not been sufficiently addressed, and further studies with various body shapes and operating conditions that may affect the critical value of the stability parameter are required. Therefore, it is reasonable to determine the design cavitation number with a sufficient margin, and a moderate value of \(\beta=1.6\) was selected to determine the design cavitation number for this particular design trial. Accordingly, the corresponding design cavitation number is \(\sigma_{design}=0.028\). This design cavitation number has to be changed if it is not available from the ventilation system of the vehicle. In that case, the design procedure has to be re-performed with a new design cavitation number. Regarding the cavitator type, the disk-type cavitator was chosen because it is more suitable for a straight-running-type supercavitating vehicle. For the iteration to determine the optimal cavitator that minimizes the overall drag of the vehicle in straight level flight, the upper and lower bounds and increments of varying parameters were set as listed in Table 3. The upper bound of the cavitator inclination angle is the maximum allowable inclination of the cavitator. The lower bound of the cavitator diameter and the upper bound of the vehicle trim angle were determined by pre-examining the conditions for the planing motion scheme. Below the lower bound of the cavitator diameter, only partial cavities are generated on the vehicle; over the upper bound of the vehicle trim angle, the lower surface of the cavity collides with the conical part of the vehicle such that the cavity can no longer grow into the supercavity. From the iteration, a disk-type cavitator with a diameter of \(d_{c}=0.04\) m was determined to be the optimal one, producing the lowest overall drag of the vehicle in straight level flight. It was confirmed that the cavitator inclination angle and vehicle trim angle for straight level flight were \(\delta_{c}=-5.0^{\circ}\) and \(\alpha_{B}=0.222^{\circ}\), respectively. Figure 11 shows the straight level flight conditions with the predicted supercavity shape. The figure indicates that, except for a very small planing area of the vehicle transom, the supercavity created by the optimal cavitator tightly envelops the vehicle, resulting in minimum overall drag.