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Journal of Physics: Conference Series
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The Influence of Attack Angle on Projectile Trajectory and Fuze in
Oblique Penetration
To cite this article: Huifa Shi et al 2021 J. Phys.: Conf. Ser. 2029 012023
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ICMTIM 2021
Journal of Physics: Conference Series 2029 (2021) 012023
IOP Publishing
doi:10.1088/1742-6596/2029/1/012023
1
The Influence of Attack Angle on Projectile Trajectory and
Fuze in Oblique Penetration
Huifa Shi, Shaojie Ma*, Feiyin Li, Jian Wei and Tong Tang
School of Mechanical Engineering, Nanjing University of Science and Technology,
Nanjing, 210094, China
*Corresponding author’s e-mail: shaojiem@njust.edu.cn
Abstract. Oblique deep penetration is a common form of projectile penetration into the target.
In view of the fact that most of the research work is focused on the trajectory of vertical
penetration, the trajectory and law of oblique penetration are discussed in this paper. This paper
studies the impact of different initial angles of attack on projectile trajectory and fuze impact in
oblique penetration by simulating projectile penetrating target with LS DYNA software. The
results show that with the increase of attack angle, the deflection of trajectory is more obvious,
the penetration depth is smaller, and the impact acceleration amplitude of fuze is larger. The
research content of this paper provides a reference for oblique penetration of concrete target and
impact performance of fuze, and is of great significance for the construction and protection of
underground fortifications.
1. Introduction
Deep penetration ammunition is the use of the kinetic energy of ammunition to penetrate deep
underground fortifications to damage targets. It is an effective weapon that mainly strikes at the enemy's
important underground solid military targets, such as underground bunkers, underground command
posts, ammunition depots, and underground launch bases. As the control device of detonating warhead
charge, fuze needs to meet certain anti impact performance. Therefore, it is important to study the
influence of different factors on penetration trajectory and fuze impact ability in oblique penetration.
Many teams have conducted oblique penetration studies. Xue et al. [1-3] established an engineering
model of oval shaped projectile penetrating concrete with inclination and angle of attack, and obtained
the relationship between the trajectory of projectile head and inclination, angle of attack and velocity.
Then they got the penetration depth, crater size, deflection angle and other parameters at different speeds
through penetration experiments and numerical simulation, and the results were in good agreement. Sun
et al. [4] established the penetration depth model and the depth formula for Projectile Oblique
Penetration into concrete, and verified the correctness of the model and formula by LS-DYNA. Zhang
et al. [5] used LS-DYNA software to simulate the trajectory trend and law of shaped projectiles with
different impact angles and attack angles. It is found that the influence of high attack angle on the attitude
elevation angle of shaped projectiles is much greater than that of penetration angle. Gao et al. [6] studied
the influence of initial angle of attack on the trajectory deflection of oblique penetration of concrete, and
found that the negative angle of attack has a certain inhibition effect on the trajectory deflection of
oblique penetration, while the positive angle of attack has an amplification effect.
There are many factors that affect the process of oblique deep penetration, mainly including the shape
of the head of the projectile, the angle of incidence, the initial angle of attack, and the velocity of the
projectile [7]. This paper mainly studies the influence of different initial angles of attack on projectile
ICMTIM 2021
Journal of Physics: Conference Series 2029 (2021) 012023
IOP Publishing
doi:10.1088/1742-6596/2029/1/012023
2
trajectory and fuze impact in oblique penetration. The deep penetration finite element model is
established in LS-DYNA finite element software. By comparing the oblique penetrator concrete targets
with different angles of attack, it is found that as the angle of attack increases, the deflection of the
ballistic trajectory is more obvious, the penetration depth is smaller, and the acceleration amplitude of
fuze is greater. By comparing the oblique penetration of reinforced concrete at different angles of attack,
it is found that as the angle of attack increases, the ballistic deflection angle and the fuze acceleration
amplitude also increase, and the penetration depth decreases. However, due to the influence of steel bars,
the degree of change is relatively random. Finally, the law of oblique and deep penetration under
different angles of attack is summarized, and the future work is prospected.
2. Establishment of finite element model
2.1. Projectile structure and target plate structure
Eight groups of finite element models are established, which are composed of projectile body, fuze,
concrete target slab and steel bar. The first four groups of models are that the projectile penetrates the
concrete target slab obliquely at 2°, 4°, 6°, and 8° angles of attack at 20° incident angle. The last four
groups of models are that the projectile penetrates the reinforced concrete target slab obliquely at 2°, 4°,
6°, and 8° angles of attack at 20° incident angle.
The projectile material is 35CrMnTiA, with a diameter of 17.5cm and an overall length of 150cm.
The oval length accounts for 1/3 of the total length. A groove is opened with the tail of the projectile,
where the fuse is mounted. The fuze material is Al. The concrete target board is made of C30 concrete
with a size of 600×200×700cm. The steel bar is made of Q235 material with a diameter of 1cm. The
spacing between bars to the mesh is 16cm. The distance between each layer of steel mesh is 40cm. The
first layer of steel mesh is 20cm away from the intrusion surface, and there are 17 layers of steel mesh.
Due to the symmetrical characteristics of the projectile, fuze, and target structure in terms of shape and
load, the 1/2 model is used for modeling. The overall structure is shown in Figure 1.
2.2 Finite element model of projectile and target
The meshing of the finite element model adopts the Lagrangian algorithm. The projectile, fuze and target
all uses the SOLID164 element type, and hexahedral element is used to divide mapping mesh.
Figure 1. Overall structure of projectile and target. Figure 2. Mesh model of projectile and target.
Steel bars use beam element type to bear bending stress. The divided mesh model is shown in Figure
2. The projectile, fuze and rebar adopt ideal elastoplastic model with failure strain, and parameters of
the material model are shown in Table 1. The concrete adopts the HJC model and self-defined failure
criterion model. Parameters of the material model are shown in Table 2.
ICMTIM 2021
Journal of Physics: Conference Series 2029 (2021) 012023
IOP Publishing
doi:10.1088/1742-6596/2029/1/012023
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Table 1. Parameters of projectile, fuze and rebar material model.
Material Constitutive model Density Elastic modulus Poisson's ratio
Projectile 35CrMnSiA RIGID 7.85 206 0.33
Fuze Al PLASTIC_KINEMATIC 2.7 70 0.3
Rebar Q235 PLASTIC_KINEMATIC 7.85 210 0.269
Table 2. *MAT_JOHNSON_HOLMQUIST_CONCRETE concrete material model parameters.
RO G A B C N FC
2.44 0.1240 0.79 1.6 0.007 0.61 3.0e-04
T EPS0 EFMIN SFMAX PC UC PL UL
2.9e-05 1e-06 0.01 7 1.0e-04 0.0007 0.008 0.10
D1 D2 K1 K2 K3 FS
0.04 1.00 0.85 -1.71 2.08 -0.01
After the finite element model is established, the concrete and the steel bar share nodes to connect
[8]. The ASTS contact algorithm is used between the projectile and the fuze, and the ESTS contact
algorithm is used between the projectile, concrete and steel bar. Symmetrical boundary constraints are
imposed on the 1/2 model symmetry plane, and fixed constraints are imposed on the concrete boundary
plane. The initial velocity of the projectile is set to 560m/s. The simulation time is 35ms. After the
control set is completed, the solution is solved in ANSYS solver.
3. Simulation results and analysis
3.1 Oblique penetration of concrete targets at different angles of attack
In order to summarize the trajectory and law of the oblique penetration of the plain concrete target for
different angles of attack, the finite element software is used to obliquely penetrate the concrete target
at 2°, 4°, 6°, 8° attack angles. The penetration trajectory is shown in Figure 3, the penetration depth is
shown in Figure 4, and the fuze acceleration amplitude result is shown in Figure 5.
a) b) c) d）
Figure 3. Oblique penetration to plain concrete target at 2°, 4°, 6° and 8° attack angles.
Figure 4. Projectile penetration depth map.
ICMTIM 2021
Journal of Physics: Conference Series 2029 (2021) 012023
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doi:10.1088/1742-6596/2029/1/012023
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Figure 5. Curve of the fuze acceleration amplitude.
It can be seen from Figure 3 and Figure 4 that the angle of attack has a great influence on the
deflection of the projectile. As the angle of attack increases, the deflection of the ballistic trajectory is
more obvious, and the depth of penetration is smaller. After the Projectile Oblique penetrated the target
plate, the concrete unit are pushed away by the projectile. Due to the action of attack angle, the left and
right sides with the projectile are subjected to unbalanced force, which made the projectile deflect. With
the decrease of the velocity of the projectile, the unbalanced force will gradually decrease, and the
projectile will finally move along a straight line. Figure 5 shows that with the increase in the angle of
attack, the contact area between the projectile and the target increases, and the resistance of the projectile
increases, so the impact force transmitted to the fuze increases.
3.2 Oblique penetration of reinforced concrete targets at different angles of attack
In order to find out the motion track and law of oblique penetration of reinforced concrete target plate
with different attack angles, numerical simulation is carried out at 2°, 4°, 6° and 8° attack angles. The
trajectory, the penetration depth and the fuze acceleration amplitude result are shown in Figure 6, Figure
7, Figure 8.
a) b) c) d）
Figure 6. Oblique penetration to reinforced concrete target at 2°, 4°, 6° and 8° attack angles.
Figure 7. Projectile penetration depth map.
ICMTIM 2021
Journal of Physics: Conference Series 2029 (2021) 012023
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doi:10.1088/1742-6596/2029/1/012023
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Figure 8. Curve of the fuze acceleration amplitude.
It can be seen from Figure 6 and Figure 7 that when the target plate is reinforced concrete, the effect
of attack angle on penetration phenomenon is similar to that of plain concrete. As the angle of attack
increases, the deflection of the ballistic trajectory becomes more obvious, and the penetration depth
becomes smaller. The addition of steel bars adds more random resistance to the concrete target and adds
the randomness of deflection. So that the penetration depth and deflection angle are not as uniform as
the penetration concrete target plate. However, the overall deflection angle still increases as the angle of
attack increases. Figure 8 shows that the larger the angle of attack, the higher the acceleration amplitude
of fuze.
4. Conclusion
In this paper, LS-DYNA numerical simulation is used to study the influence of different initial attack
angles on the oblique penetration process of the projectile into target plate (plain concrete and reinforced
concrete), and the following conclusions are obtained:
Under the condition of initial velocity of 560m/s and incident angle of 20°, when the projectile
penetrates the plain concrete target plate obliquely at the angles of attack of 2°, 4°, 6° and 8°, the
deflection and fuze acceleration amplitude increase with the increase of attack angle. While the
penetration depth decreases with the increase of attack angle.
Under the condition of initial velocity of 560m/s and incident angle of 20°, when the projectile
penetrates the reinforced concrete target plate obliquely at the angles of attack of 2°, 4°, 6° and 8°, the
increase of the angle of attack increases the projectile deflection degree and fuze acceleration amplitude
and decreases the penetration depth. But the penetration depth and deflection angle are not as uniform
as that of the plain concrete target plate.
This paper only studies oblique penetration at the same position, which has some limitations. In the
future, we can study the oblique penetration by adjusting the projectile mass, projectile shape, projectile
position, angle of attack, and shape of steel bar of numerical simulation. And then we can observe the
different conditions such as penetration depth, penetration amplitude, penetration pulse width and so on.
By means of simulation, the cost and safety of the test is compensated, and the comparison results are
provided for the test results. At the same time, simulation results can be used as a reference to the
construction and protection for underground fortifications.
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