### Lipanov A.M. Korolev S.A. Rusyak I.G.

## Optimization of aerodynamic form of projectile for solving the problem of shooting range increasing

### Reporter: Korolev S.A.

The problem of increasing the shooting range is solved in different ways. One of the research directions is to optimize the aerodynamic form of the projectile. The solution to this problem is closely intertwined with the with the accuracy of simulation of the motion of missile body on the flight path, which depends in particular on account of the rotation and vibrations about its center of mass, the accuracy of determining the aerodynamic coefficients of missile bodies, setting accuracy of the weather conditions, the accuracy of the used numerical methods and others. The paper presents a mathematical model for the external ballistics of the projectile based on the solution of a more complete system of motion equations, taking into account the rotation and oscillations about the center of mass, and using aerodynamic coefficients of forces and moments which are calculated on the basis of modeling of hydrodynamics of flow around the projectile [1, 2].

The basic parameters of the projectile for studying the dependences of aerodynamic resistance on the projectile form are: caliber (*d*), length (*l*), length of the head part (*l _{h}*), length of cylindric part (

*l*), length of the bottom part (

_{c}*l*), radius of the curvature of the head part (

_{b}*R*), the taper angle of the bottom part (α

_{h}_{b}).

To calculate the aerodynamic resistance coefficients of the projectile, the problem of modeling the flow around the body by a compressible supersonic flow of air was solved [3-5]. An approach based on the numerical solution of Favre averaged Navier-Stokes equations of continuous medium motion is applied, using the semiempirical *k*–ε turbulence model. Such an approach does not require significant computational resources, which makes it possible to calculate the aerodynamic characteristics of the investigated bodies in a wide range of parameters. Numerical modeling of the flow around the projectile is realized using the ANSYS Fluent fluid dynamics calculation module.

The choice of the optimal aerodynamic form of the projectile was carried out on the basis of the solution of the problem of optimizing the head drag coefficient *C _{x}*:

*C _{x}* =

*F*(

*d*,

*l*,

_{h}*l*,

_{c}*l*,

_{b}*R*, α

_{h}_{b}) → min

with given constraints determined by the stability conditions of the projectile in the barrel channel and geometric relationships. As methods of multidimensional optimization, gradient methods and a genetic algorithm were considered. To analyze and optimize the aerodynamic form, a 152 mm high-explosive projectile was selected.

At the second stage, ballistic parameters were optimized: the angle of shoot and the initial velocity of the projectile. The paper compares two approaches to solving the problem of external ballistics. In the first case, the system of motion equations of the projectile mass center was solved using the aerodynamic drag coefficient according to the laws of 1943 or 1958 and the derivation function for calculating lateral deviation in the case of a rotating projectile [6]. In the second case, the technique proposed in the paper was used, based on the solution of the complete system of motion equations of the projectile, taking into account the oscillations about the mass center and the complete set of aerodynamic coefficients, obtained on the basis of modeling of the flow around the projectile.

The developed method for solving the trajectory problem is more complete, it allows calculating new parameters, and in principle, gives more accurate results for a wide range of shooting parameters. The choice of the optimal aerodynamic form of the projectile can significantly increase the range of shooting. This technique can be used to refine trajectory calculations of the projectiles used in artillery, and the design of new ammunition.

1. **Rusyak I.G., Karpov A.I., Korolev S.A., Karskanov S.A.** Calculation Trajectory of Projectile in the Atmosphere taking into account Hydrodynamics of the External Flow [in Russian]// Voprosy Oboronnoy Tekhniki. Series 14. 2015. Issue 2. P. 130-141.

2. **Ivan Rusyak, Vadim Sufiyanov, Stanislav Korolev, Mikhail Ermolaev** Software Complex for Simulation of Internal and External Ballistics of Artillery Shot // International Conference on Military Technologies 2015 (ICMT 2015), Brno, May 19 – 21, 2015: University of Defence, Brno, 2015. P. 9–17. DOI: 10.1109/MILTECHS.2015.7153682.

3. **Korolev S.A., Karskanov S.A.** Mathematical simulation of supersonic airflow around the rotary body [in Russian] // Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki, 2014. No 3. P. 123-133.

4. **Lipanov A.M.** Theoretical hydromechanics of Newtonian media [in Russian]. Moscow: Nauka, 2011. 551 p.

5. **Lipanov A.M., Lipatov I.I., Karskanov S.A.** Mathematical Modeling of the Flow around a Wing by a High-Velocity Viscous Gas Flow [in Russian] // Trudy Instituta Mekhaniki UrO RAN “Problemy mekhaniki i materialovedeniya”. Izhevsk, 2015. P. 164-179.

6. GOST B 24288-80. Unguided artillery, reactive, active-reactive projectiles. Method for calculating the flight trajectory [in Russian]. Moscow: Publishing house of standards, 1980. 55 p.

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