Aerodynamic and trajectory characteristics of a typical mortar projectile with a deflectable nose

Yu-ming Ren , Shu-shn Wng ,*, Jing-wei Li , Xun-cheng Guo , Yue-song Mei b Stte Key Lbortory of Explosion Science nd Technology, Beijing Institute of Technology, Beijing 100081, Chin

b Beijing Zhongheng Tianwei Force Defence Science and Technology Limited Company, Beijing 100081, China

Keywords:Nose deflection Aerodynamic characteristics Wind tunnel test Trajectory simulation

ABSTRACT Deflectable nose control is a new trajectory correction method. In this paper, the aerodynamic and trajectory characteristics of a typical mortar projectile with a deflectable nose are investigated with respect to its flight conditions.Using the method of wind tunnel testing,the aerodynamic coefficients of four kinds of mortar models were measured under the conditions of different angles of attack from -10° to 10° and Mach numbers from 0.3 to 0.9.Based on the aerodynamic coefficients,the trajectory ranges at different nose deflection angles and times were calculated. Furthermore, a trajectory optimization was performed by reducing the static margin. The results and discussions show that the nose deflection provided limited lift, while the pitching moment varied significantly. The mortar obtained the extended flight range and trajectory correction ability with nose deflection.

1. Introduction

Conventional guided munitions have many kinds of methods for flight control. For example, canards change the aerodynamic characteristics of projectiles to generate control forces and moments. Impulse engines located around the center of gravity generate direct forces and moments to control flight. In addition,methods such as plasma control,spoilers,pins,and fluid actuators(not used for the center of gravity of the projectile)are also applied for some specific munitions [1e3]. Recently, deflectable nose control has been widely studied. Through the changing of angles between the nose and the body axis,the munitions can generate the required control force with air.This method has some advantages of good aerodynamic shape, compact structure, and quick response.

The concept of deflectable nose control first appeared in the 1950s. Goddard proposed a deflectable nose to control aircraft flight[4].Due to the lack of mature technology, the apparatus had poor anti-overload capability and low reliability. Thompson used nose deflection control for tubular launch weapons for the first time [5]. Landers et al. performed wind tunnel tests on a missile model at supersonic conditions and investigated the aerodynamic characteristics of deflectable nose and canards control [6,7].Through comparison,it was found that the deflectable nose control had the advantages of better control efficiency and smaller drag than canards control for the same conditions. Current studies on the deflectable nose control are mainly concentrated on aerodynamic characteristics, dynamic models, and apparatus design.William B. Blake and Ben Shoesmith used different numerical simulation methods to study the aerodynamic characteristic of Lander's model[8,9].The results were in good agreement with the experimental data. Zhang et al. designed the low-speed wind tunnel test of a deflectable nose projectile [10,11]. A rubber tube was used to connect the surface of the projectile to the U-type manometer, which measured the static pressure at a certain position of the projectile. The influence of the deflectable nose on the ballistic control was also analyzed. Gagan Sharma et al. conducted an experiment and a numerical simulation for the missile models with nose deflection angles of 0°,10°,and 20°.They found that the deflectable nose changed the flow field structure on the leeward side, and the tip vortex became more visible [12]. Scholars from Northwestern Polytechnical University in Xi'an, China used multibody system dynamics to establish the dynamic control models of the deflectable nose missiles [13e15]. Gu et al. proposed different nose deflection apparatuses and analyzed their applicability [16].

In this study,we first examined the aerodynamic characteristics of a typical mortar with four different deflection angles with a wind tunnel test. Then the trajectory characteristics were obtained by solving the six-DOF(degrees of freedom)rigid body ballistic model.Finally, in order to improve the load factor of the projectile flight,trajectory optimization was performed by reducing the static margin.The aerodynamic and trajectory terminology in this paper refer to Ref. [17], and it is not explained in detail.

2. Experimental methods

2.1. Experimental model

A mortar projectile is a typical type of subsonic munition. In recent years, more and more new types of guided mortar projectiles have been developed,such as the XM 395 Precision Guided Mortar Munition [18] and the Strix Guided Anti-Armor Mortar Projectile [19]. Currently, the research work on guided mortar projectile is increasing [20,21]. Guided mortar projectiles play an important role in modern warfare. Therefore, we chose a typical 120 mm mortar projectile as the research object for this study.This projectile has strong scientific research significance and military application value. A diagram of the mortar projectile is shown in Fig.1.

Because of the size limitation of the wind tunnel, the experimental model was scaled based on the original model. The experimental model was divided into the deflectable nose,the body part,and the tail part for processing. This method was good for manufacturing and reducing costs. The nose section and the body section were connected by pins. The body section and the tail section were connected by screw threads. Different components were connected tightly without bumps on the surface. In the experiment, the nose deflected in the pitch plane. The measured aerodynamic data included the drag, lift, pitching moment, and pressure center. The nose deflection angle is represented by d,which is the angle between the axis of the body and the axis of the nose. d was positively defined when the axis of the body rotated clockwise to the axis of the nose.The angle of attack is represented by a,which is the angle between the flow direction and the axis of the body.a was positively defined when the flow direction rotated clockwise to the axis of the body.The wind speed is represented by V.Fig.2(a)shows the defined angles,and Fig.2(b)displays the nose models with different deflection angles.

2.2. Experimental scheme

The experimental conditions are as shown in Table 1.

The design loads and the accuracies of the aerodynamic balance used for the wind tunnel tests are shown in Table 2.

Fig.1. Diagram of 120 mm mortar projectile.

Fig. 2. Models in the wind tunnel test.

Table 1 Experiment conditions.

The aerodynamic data of the model with a 0° deflection nose were measured first. The 0°deflection nose, the body section, and the tail section were assembled in the working part of the wind tunnel.One end of the force balance was connected to the model's tail,and the other end of the model was connected to the angle of the attack mechanism. After all the equipment was checked correctly,the wind tunnel began to blow.When the gas velocity in the wind tunnel was stable,the angle of attack mechanism started to work, and the digital acquisition system began to collect the original aerodynamic data.After one measurement was completed,the wind tunnel stopped working.Other Mach number conditions were needed to reset the wind speed and repeat the above process.

Then the measurement tests of the models with 3°,6°, and 9°deflection noses were performed. The photographs of the wind tunnel test are shown in Fig. 3.

Table 2 The design loads and the comprehensive accuracies of the balance.

Fig. 3. Photographs of the wind tunnel test.

2.3. Calculating formulas

The formulas for calculating the aerodynamic parameters are summarized below.

where CDis the drag coefficient, CLis the lift coefficient, X is the drag, Y is the lift, mzis the pitching moment coefficient, Mzis the pitching moment relative to the center of gravity of the model,Xcp0is the pressure center coefficient, Xpis the distance from the pressure center to the nose vertex,r∞is the density of the inflow at infinity,v∞is the velocity of the inflow at infinity,S is the reference area,which is the maximum cross-sectional area of the model,and L is the reference length, which is the overall length of the model.The distance between the center of gravity and the nose accounts for 44.63% of the length of the model.

3. Results and discussions

3.1. Aerodynamic characteristics of the deflectable nose control

Fig.4 exhibits the relationship between the drag coefficient and angle of attack at different Mach numbers and nose deflection angles.The drag coefficient increased with the increase of the angle of attack.When the Mach number ranged from 0.3 to 0.8,the drag coefficient under the same angle of attack was not significantly affected by the Mach number. However, the drag coefficient increased rapidly with the increase of the Mach number when Ma>0.8. The main reason for this was that the flow field near the model was complicated due to the transonic flow. There were supersonic and subsonic flows near the model. Shock waves were generated at some locations near the model, which resulted in additional drag. When, the drag coefficient curve showed good symmetry,and the minimal drag coefficient was obtained at a zero angle of attack. When the nose deflected, the minimal drag was not obtained for.

The curves of the drag coefficient-nose deflection angles at different angles of attack and Mach numbers are shown in Fig. 5.The larger the nose deflection angle,the larger the windward area of the projectile to the gas flow,and the greater the difference in the pressure acting on the upper and lower surfaces of the projectile.Therefore,the drag coefficient showed a slight linear increase with the increase of the nose deflection angle. The drag coefficient was more obviously affected by the nose deflection angle when the angles of attack and Mach numbers were large.

Fig.6 exhibits the relationship between the lift coefficients and the angles of attack at different Mach numbers and nose deflection angles.The curves in the figure are approximately linear.The Mach number ranged from 0.3 to 0.8, and the lift coefficient under the same angle of attack remained almost unchanged. When Ma>0.8,the lift coefficient increased with the increase of the Mach number.The larger the angles of attack, the greater the increasing trend.

Fig. 4. The curves of the drag coefficient angles of attack at different nose deflection angles and Mach numbers.

Fig. 5. The curves of the drag coefficient-nose deflection angles at different angles of attack and Mach numbers.

The curves of the lift coefficient-nose deflection angles at different angles of attack and Mach numbers are shown in Fig.7.At the same angle of attack,the lift coefficient increased slightly with the increase of the nose deflection angle.Therefore,the effect of the angle of attack on the lift coefficient was more significant than the effect of the nose deflection angle at subsonic conditions. The increment of the lift coefficient that was caused by the unit angle of attack was approximately 15e20 times greater than the increment of the lift coefficient caused by the unit nose deflection angle.

Fig. 6. The curves of the lift coefficient angles of attack at different nose deflection angles and Mach numbers.

Fig. 7. The curves of the lift coefficient-nose deflection angles for some conditions.

Fig. 8. Ma?0.8, curves of the pitch moment coefficient angle of attack at different nose deflection angles.

The relationship between the pitching moment coefficient and the nose deflection angle at Ma?0.8 is shown in Fig. 8. The intersection point of the curve and transverse axis is the static equilibrium point of the projectile flight that satisfies mz?0.The moment equilibrium condition is called the trim. The angle of attack corresponding to this point was required when the projectile maintained longitudinal balance for a specific flight condition.The angle of attack for the trim condition is represented by aB. As the nosedeflection angle increased, the intercept of the curve on the horizontal axis gradually increased. This indicates that the larger the nose-up moment generated by the nose deflection, the larger the required angle of attack.

Table 3 Ma?0.8, nose deflection angles, and angles of attack at trim condition.

Fig.9. The curves of the pitch moment coefficient angles of attack for some conditions.

The pitching moment coefficient in the above figure is fitted linearly.The nose deflection angles and the angles of attack at trim condition are shown in Table 3. The ratio of the nose deflection angle d to the corresponding angle of attack aBwas approximately 3:1.

The curves of the pitching moment coefficient-nose deflection angles at different angles of attack and Mach numbers are shown in Fig. 9. The pitching moment coefficient had a significant increase with the increase of the nose deflection angle, which was approximately linear. The slopes of the curves corresponding to different angles of attack and Mach numbers were approximately the same.

The curves of the pressure center coefficient-nose deflectionangles at different angles of attack and Mach numbers are shown in Fig.10.The pressure center coefficient decreased with the increase of the nose deflection angle, which was approximately linear. The smaller the angle of attack, the more obvious the reduction trend.When the Mach number changed, the pressure center coefficient changed almost the same amount as the nose deflection angle.The nose deflection changed the axisymmetric structure of the model,which was the cause of the forward movement of the pressure center and which led to the decrease of flight stability.There were some statically unstable conditions for couples of d and a. For the trajectory simulation and the actual flight, we controlled the projectile so that it did not work at these couples of d and a.

Table 5 Basic parameters and initial simulation conditions of the mortar projectile.

3.2. Trajectory characteristics of the deflectable nose control

Table 4 The static margins of the model with no deflection angle at different angles of attack and Mach numbers.

Table 6 Trajectory simulation elements results.

Table 7 Landing states of the mortar projectile with different deflection angles.

Fig.11. Curves of the uncontrolled trajectories and velocities.

In order to simulate the flight trajectories of the mortar projectile with different deflection angles and to obtain the correction ability of this method, the aerodynamic coefficients in the above section were substituted into the six-DOF ballistic equations to simulate the trajectories based on MATLAB software. The pitch damping coefficients were assumed to be constant. During the actual flight,the roll position of the deflectable nose was controlled to isolate the rotation of the body part from the deflectable nose.So we assumed that the nose part does not spin during the trajectory simulation. Otherwise, the standard atmospheric model was used for the simulation.First,the uncontrolled trajectory simulation was performed. The basic parameters and the initial simulation conditions of the mortar projectile are shown in Table 5. Jzrepresents the moment of inertia around the z-axis, which changed only a small amount due to the nose deflection.Therefore,we assumed it was constant in the simulation.

Fig.12. Curves of the trajectories, velocities, and angles of attack with different nose deflection angles.

Fig.13. Curves of the control times and ranges.

Table 6 displays the trajectory simulation elements for an emission angle of 40°. The simulation results were in good agreement with the flight trajectory data,which illustrates the accuracy of the simulation method and the aerodynamic data based on the wind tunnel test.The trajectory curve was parabolic with a range of about 7 km.The simulation and flight results of the trajectories and the time histories of the velocities are shown in Fig.11.

Table 7 displays the landing state of the mortar projectile after deflecting the nose at the highest point of the trajectory. The simulation conditions were the same as those of the uncontrolled flight.The trajectories,velocities,and angles of the attack curves for different deflection angles are shown in Fig.12. It was found that the nose deflection had a certain influence on the range of the projectile. When the deflection angle was 9°, the range reached 7494.4 m, and the relative correction distance was 5.76%. As the nose deflection angle increased, the landing velocity and the trajectory inclination angle decreased.

The deflection time also had a significant effect on the range of the projectile. The simulations were performed at the same nose deflection angle to investigate the influence law of the deflection time.The trajectory curves were similar to the previous ones.Fig.13 displays the relationship between the control times and the ranges at different nose deflection angles.The range correction decreased with the increase of the control time at the same nose deflection angle. The larger the nose deflection, the sharper the decreasing trend. Under different nose deflection angles, the range was approximately linear with the deflection time.

The trajectory characteristics of the mortar projectile controlled by the nose deflection were affected by both the deflection angle and the deflection time. Although the nose deflection provided limited lift at subsonic conditions, the projectile mainly depended on the change of the pitching moment to increase the range and control the trajectory.

3.3. Trajectory optimization of the deflectable nose control

Fig.14. Curves of the trimmed angles of attack at different nose deflection angles.

For a controlled aircraft, in order to obtain good maneuverability, the static margin should not be too large. This margin is generally 5e10%. For the mortar projectile in this paper, reducing the static margin was an effective method for trajectory optimization, and it improved the controlling ability of the nose deflection. Using the methods of adjusting the location of the center of gravity of the projectile at the design stage or optimizing the aerodynamic design, the static margin could be reduced, and the load factor during the flight could be improved.Fig.14 displays curves of the trimmed angles of attack after reducing the static margin by 60%.As displayed in Fig.14,the trimmed angles of attack of the optimization were larger than those of the original results.

Fig.15. Simulation curves of the mortar projectile attacking the target.

In order to observe the ability to attack the target after trajectory optimization,we performed a simple trajectory simulation without consideration of the specific engineering conditions.A hypothetical target was located at a position of x?7500 m,y?2 m,and z?0 m.The nose deflected at the highest point of the trajectory. The nose deflection angle ranged from 0°to 9°.The proportional navigation method was adopted as the guidance law for the new trajectory simulation. Finally, the mortar projectile hit the target. The curves of the trajectory, angle of attack, nose deflection angle, gamma angle,and normal overload are shown in Fig.15.The gamma angle,represented by g, is the angle between the nose axis and the straight line from the projectile to the target.It should be noted that the response time of the nose deflection was ignored in the simulation.

At the highest point of the trajectory,the angle of attack and the nose deflection angle both decreased sharply. When t z 22 s, the angle of attack and the nose deflection angle began to increase. At about 35 s,the two parameters reached their maximum values.The gamma angle decreased throughout the entire flight. Before the projectile reached the highest point, gamma angle decreased linearly. With the nose deflecting, the gamma angle decreased sharply. After the angle of attack and the nose deflection angle began to increase, the gamma angle decreased slowly. For the entire trajectory, the available load factor was larger than the required load factor. The projectile attacked the fixed target successfully. However, the curves show that the effect was not very good.This was related to the projectile,the control system design,the guidance method, the target detection subsystem, and so on.However,a suitable target detection subsystem and its application to the mortar projectile are also important.These will be the focus of our further research.

4. Conclusions

Using the methods of wind tunnel testing and trajectory simulation, the aerodynamic and trajectory characteristics of a typical mortar projectile with a deflectable nose were investigated. The following conclusions were obtained.

1) The aerodynamic coefficients were affected by the nose deflection. For the subsonic conditions, the nose deflection provided limited lift with a significant pitching moment. The ratio of the nose deflection angle to the equilibrium angle of attack was 3:1.The mortar projectile could achieve the purpose of ballistic correction with an additional pitching moment.

2) The effects of the nose deflection on the trajectory were further explained by a trajectory simulation, which proved that this method would be good for trajectory correction. The range increased with the increase of the deflection angle and decreased with the deflection time. The maximum range increased 5.76%by deflecting the nose at the highest point of the trajectory.

3) The trajectory optimization is performed by reducing the static margin of the projectile. Through trajectory simulation, the ability of the load factor and maneuverability of the projectile could be improved.

Acknowledgments

We would like to thank LetPub (www.LetPub.com) for its linguistic assistance during the preparation of this manuscript.