The curvilinear motion in a vertical plane is one of the most important features of the supercavitating vehicle. It is of great significance to study the controllability and the maneuverability of the supercavitating vehicle. Models are built for the effects of the angle of attack, the gravity and the inertial force in the curvilinear motion in the vertical plane. Numerical simulations are carried out for the supercavity motion based on these models combined with the Logvinovich model. It is shown that the maximum deviation displacement in the outward normal direction of the trajectory with a constant curvature, which occurs in the tail of the supercavity, increases as the cavitation number or the curvature radius of the supercavity trajectory decreases under the condition that other model and flow parameters are kept constant. For a varied curvature, the supercavity shape changes evidently because of the change of the ambient pressure, but with the same trend as in constant curvature. The deviation displacement increases along the supercavity length gradually.

中文翻译：

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垂直平面上带有惯性力的超腔运动

在垂直平面内的曲线运动是超空化飞行器最重要的特征之一。研究超空化车辆的可控性和机动性具有重要意义。建立了针对攻角，重力和垂直平面中的曲线运动中的惯性力的影响的模型。基于这些模型和Logvinovich模型，对超腔运动进行了数值模拟。结果表明，在其他模型的条件下，超空腔尾部发生的，具有恒定曲率的轨迹在外法线方向上的最大偏差位移随超空腔轨迹的空化数或曲率半径的减小而增大。和流量参数保持恒定。对于变化的曲率，由于环境压力的变化，超腔的形状明显变化，但是具有与恒定曲率相同的趋势。偏差位移沿超腔长度逐渐增加。