# Cavitator Design for Straight-Running Supercavitating Torpedoes
## 3 Verification of Mathematical Models
### Experimental Verification  
To verify the mathematical models used in the present design method, experiments were performed in a high-speed towing tank of IHM, NASU. The tank dimensions were 140 \(\times\) 4 \(\times\) 1.8 m. The experiments were performed in accordance with a methodology [25] for performing towing tests. A model of the scaled supercavitating vehicle was manufactured, as shown in Figure 7. The model dimensions were determined by considering the capabilities of the towing tank system and the reliability requirements of the obtained results. The hull of the model was designed as a combination of conical and cylindrical surfaces. The cylindrical part was 80 mm in diameter and 200 mm in length. An adapter was mounted on the nose of the model to fix and rotate the angle of the cavitator. Two cavitators were used in the experiments: a disk-type cavitator with a diameter of 25 mm, and a cone-type cavitator with a 50 mm base diameter and 40\({}^{\circ}\) cone angle. To generate a ventilated cavity, air was supplied through a system of ventilation holes located immediately behind the cavitator. Vertical and horizontal fins, which had a wedge-shaped cross-section with a chord of 20 mm and span of 50 mm, were installed in the aft part of the model. This model was connected to the supporting strut by using a specially devised flexible elastic pipe, which allowed the model to rotate freely relative to a pivot point in a longitudinal vertical plane within the maximum permissible trim angle of \(\pm 2^{\circ}\). The pivot point coincided with the center of gravity of the model. The pressure in the cavity was measured using a differential pressure sensor. Air was supplied to the cavity forcibly using a six-stage axial fan, and the air flow rate was measured using an air flow sensor installed at the inlet of the axial fan. To observe the dynamics and cavity characteristics of the model during the course of the experiments, an underwater video camera was used in the coordinate system associated with the towing cart. The fixed zero trim angle case was first conducted to confirm the accuracy of the cavity shape model used in the present design method. For validation, the cone-type cavitator with an angle of inclination of 2.1\({}^{\circ}\) was arbitrarily selected. The cavitation number \(\sigma=0.064\) was set by adjusting the air ventilation rate at a towing speed of 9.12 m/s. The Reynolds number and Froude number based on the diameter of the cavitator were \(\mathrm{Re}=456,000\) and \(\mathrm{Fr}=13.03\), respectively. The steady cavity shape measured in the experiment is shown in Figure 8a. The corresponding c  
Figure 7: Small-scale supercavitating vehicle. shown in Figure 8b. The cavity dimensions obtained from the experiment and calculation are compared in Table 1. The calculated cavity shape, which includes the cavity axis, deformations due to the effect of gravity and the cavitator inclination, agreed very well with the experimental shapes. Next, the mathematical models were validated by comparing the trim condition of the supercavitating vehicle, which is defined here as a moment equilibrium state, obtained from the experiment with the corresponding calculated one. The model was set to rotate freely in a longitudinal vertical plane relative to the center of gravity, and an experiment was performed by varying the inclination angle of the cavitator in a passive manner until the trim condition was determined. During the experiment, the model was locked at a trim angle of zero at the starting point and unlocked immediately after the cavity enveloped the model completely. No control fins were used to investigate the feasibility of the stationary planing motion scheme for supercavitating vehicles. The experimental results for the disk-type cavitator indicate that the model was stabilized in a steady planing mode in the bottom cavity at \(\delta_{c}=-9^{\circ}\) and \(\alpha_{B}=1.82^{\circ}\), as shown in Figure 9a.