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Influence of trajectory and pitch angle on the deflection characteristics of projectiles penetrating into thin concrete targets
Explosion and Shock Waves 2026, 46(10)
Published: 05 October 2026
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To investigate the influence of trajectory angle and pitch angle on the deflection characteristics of a projectile penetrating into concrete thin targets, numerical simulation methods were validated by comparing parameters such as projectile velocity, attitude, and trajectory deflection with experimental data from multi-layered concrete thin-target penetration tests. This verification methodology ensured the accuracy and reliability of the numerical model for subsequent parametric studies.Based on this validation, the projectile was divided into six axial segments (the nose section comprising two segments and the body section divided into four segments) to systematically analyze the force distribution characteristics and overall motion behavior under both individual and combined effects of different trajectory angles (ranging from 5° to 30°) and pitch angles (ranging from −6° to 6°). The results show that the direction of the resultant force acting on the projectile body maintains stability across all tested impact conditions, demonstrating consistent patterns regardless of angle variations.While the reversal of the force direction on the projectile nose and the change in the deflection moment caused by the forward motion of the projectile body jointly contribute to the projectile's deflection. Under a positive trajectory angle, the trajectory exhibits an upward deflection. When a pitch angle is introduced, the deflection direction is dominated by the trajectory angle if the negative pitch angle is less than 2° and the trajectory angle exceeds 20°; otherwise, the pitch angle determines the deflection direction. When the trajectory angle and pitch angle are in the same direction, the projectile's attitude angle first decreases after exiting the target and then reverses to increase. When they are in opposite directions, a small pitch angle causes the attitude angle to continuously increase after exiting the target, while a larger trajectory angle induces three deflection reversals during penetration. If the pitch angle exceeds 2°, the attitude angle initially decreases after exiting the target before reversing to increase.

Open Access Issue
A prediction model for projectile ballistic characteristics in multi-layered spaced concrete thin targets based on CNN
Explosion and Shock Waves 2026, 46(5)
Published: 05 May 2026
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To overcome the high computational cost of traditional ballistic prediction methods and their inability to satisfy rapid assessment requirements, this study proposes an efficient predictive model for the penetration ballistics of multi-layer thin concrete targets based on a convolutional neural network (CNN). First, a numerically simulated approach, validated by experiments, was employed to analyze and confirm the significant influence of projectile angular velocity on trajectory deflection, and this parameter was consequently identified as a key projectile–target engagement condition. By systematically varying the initial conditions, a dataset comprising 127 cases of single-layer thin concrete target penetration was constructed. On this basis, a high-accuracy ballistic prediction model for single-layer targets was developed, taking projectile parameters, target parameters, and engagement conditions as inputs, and post-impact projectile motion parameters as outputs. Furthermore, by incorporating rigid-body kinematic equations describing the projectile flight between successive targets, a complete iterative penetration-flight prediction framework was established, enabling rapid prediction of ballistic characteristics for multi-layer spaced thin concrete targets. The results indicate that an increase in counterclockwise angular velocity leads to a positive increase in the radial residual velocity behind the target and an upward deflection of the trajectory, whereas clockwise angular velocity produces the opposite effect. These findings demonstrate that projectile angular velocity is a critical and non-negligible factor in thin-target penetration. For single-layer target cases, the model exhibited strong predictive capability, with the mean MSE values of the training and test sets stabilizing at approximately 0.0012 and 0.0019, respectively. For multi-layer target predictions, while maintaining high accuracy (with a maximum relative error of 10.65% in residual velocity and a maximum absolute error of 3.47° in attitude angle), the computational time of the proposed method was only about 0.05% of that required by conventional numerical simulation. This study not only elucidates the influence of the key factor-projectile angular velocity-on penetration ballistics, but also proposes a novel “data-driven and physics-equation fusion” modeling paradigm, providing an important methodological reference for weapon damage effectiveness assessment and design optimization.

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