## 3 Numerical Simulation Analysis
### Parameter Analysis
#### 3.3.2 Effect of Impact Angle on Penetration Performance  
The impact velocity of the projectile was 890 m/s when the impact angle of the projectile was \(0^{\circ}\), \(5^{\circ}\), \(10^{\circ}\), \(15^{\circ}\) and \(20^{\circ}\). The crack distribution results, acceleration versus time curves, depth versus time curves and velocity versus time curves of projectiles penetrating red sandstone and limestone are shown in Figures 13 and 14, respectively. Figure 13: Results of projectile oblique penetration into red sandstone target: (**a**) penetration acceleration curve in X direction; (**b**) penetration acceleration curve in Y direction; (**c**) penetration depth-variation curve in X direction; (**d**) penetration depth-variation curve in Y direction; (**e**) penetration velocity-variation curve in X direction; (**f**) penetration velocity-variation curve in Y direction. According to the damage results of the target in Figures 13 and 14, the larger the impact angle of the projectile was, the more serious the path deflection of the projectile in the target. However, red sandstone was more sensitive to the impact angle of the projectile than limestone. When the impact angle of the projectile was 20\({}^{\circ}\), the projectile deviated out of the target from the side. The cracks deviating from the deflection direction were generally long, and the cracks formed by the red sandstone target were fine and dense, whereas the cracks formed by the limestone target were wide and long. The larger the impact angle of the projectile was, the more serious the collapse at the opening of the target. The collapse at the opening of the limestone was more serious than that of the red sandstone. This was because the material of the red sandstone had a granular elastic structure, which has a good energy absorption effect and can be more easily compacted, whereas limestone is brittle. Figures 13a and 14a show the acceleration curves of the projectile in the X direction with time. The acceleration of the projectile penetrating limestone was larger than that of the projectile penetrating red sandstone. When the impact angle of the projectile was 5\({}^{\circ}\), the maximum acceleration of the projectile was the largest, and then the maximum acceleration decreased slightly with the increasing impact angle. According to the time-varying curves  
Figure 14: Results of projectile oblique penetration into limestone target: (**a**) penetration acceleration curve in X direction; (**b**) penetration acceleration curve in Y direction; (**c**) penetration depth-variation curve in X direction; (**d**) penetration depth-variation curve in Y direction; (**e**) penetration velocity-variation curve in X direction; (**f**) penetration velocity-variation curve in Y direction. of acceleration in the Y direction in Figures 13b and 14b, the acceleration of the projectile penetrating red sandstone was less than that of penetrating limestone as a whole because the deflection of the projectile in the limestone target was less than that of red sandstone. With increasing projectile angle of incidence, the maximum acceleration of the projectile gradually increased. Figures 13c and 14c show the time-varying curves of the depth of the projectile in the X direction. The penetration depth of the projectile in the X direction changed as a log function with time. When the projectile penetrated the red sandstone target at an angle of 20\({}^{\circ}\), the penetration depth of the projectile in the X direction first changed as a log function and then changed linearly with time because the projectile deviated from the target to the side. The penetration depth of the projectile in the X direction increased with increasing landing angle. Figures 13d and 14d show the time-varying curves of the depth in the Y direction of the projectile. The penetration depth in the Y direction of the projectile decreased with increasing landing angle. The penetration resistance of limestone was stronger than that of red sandstone.