## 1 Introduction  
When a projectile enters water from the air at a high speed, a series of complicated phenomena occur, such as the appearance and evolution of cavity or super cavitation, jet flow and projectile vibration and instability, etc., all of which depend on the projectile configuration and entry conditions. There have been many investigations performed on the water-entry phenomena concerning the cavity evolution and conditions of water entry.  
[PERSON] et al. [1] presented a method for modeling the cavity formation and collapse induced by high-speed impact and penetration of a rigid projectile entering water, and found that the cavity induced by a high-speed water-entry projectile is characterized by a cavity that experiences a deep closure prior to surface closure. [PERSON] [2] extended the cavity dynamics model, and calculated the cavity pressure from the one-dimensional quasi-steady flow model, and predicted the time of surface closure. [PERSON] et al. [3] recorded the cavity shape and measured the velocity of steel spheres' water entry by using high-speed photography, and developed a theoretical model for velocity attenuation of steel spheres with cavity. [PERSON] et al. [4] investigated the dynamics of the air cavity created by vertical water entry in the rage of relatively low Froude number, and made a complementation to asymptotic theory by using an axisymmetric boundary integral equation. [PERSON] et al. [5] studied the process of vertical water entry of projectiles, developed a theoretical model to describe the evolution of the cavity shape. [PERSON] et al. [6] characterized the dynamics of the cavity from its creation until its collapsed.  
[PERSON] et al. [7] investigated the transient surface cavity which is created by a disk on a surface at Froude numbers below 200, and presented a model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. [PERSON] et al. [8] simulated the vertical water entry problems of long cylinder and cylinder with 135\({}^{\circ}\) cone nose shape with the initial velocity of 60 m/s, discussing the cavity shape, vapor evolution and pressure distribution.  
In addition, [PERSON] et al. [9] reviewed and surveyed experimental, theoretical, and numerical studies over water entry investigations, a wide range of regimes, from low-speed entry phenomena dominated by surface tension to high-speed ballistics have been introduced. [PERSON] et al. [10, 11] experimentally and theoretically investigated the process of the vertical impact of low-density spheres on a water surface, and characterized the sphere dynamics and the influence of its deceleration on the shape of the resulting air cavity. [PERSON] et al. [12, 13] experimentally and theoretically studied the behaviors of high-speed horizontal water entry of different nose shapes projectiles, and proposed a drag coefficients model independent on the cavitation number. [PERSON] et al. [14] experimentally studied projectile penetrated water with the high speed of 342 m/s where a noninvasive optical measurement technology was used to investigate the formation and collapse of the super-cavitation. [PERSON] et al. [15] experimentally investigated the hydrodynamics of water entry by shooting down a spinning sphere at the horizontal free surface under low Froude number, where the effect of the spin rate and impact velocity were studied.  
Until now, most investigations about water entry mainly focused on the vertical cases, and investigation on the effects of entry angle and velocity of projectile on its ballistic characteristics is far from satisfactory. In Sections 2.1-2.3, we introduce governing equations, turbulence model, ballistic equations and the cavitation model. Section 2.4 describes the computational method and the studied problem. In Section 2.5 the model applied is validated. In Section 3, the entry process of projectiles with different lengths, entry angles and velocities is examined, and their effects on the variations of projectile trajectory, velocity and stability are discussed.