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Numerical simulation of the aerodynamics of a ballistic projectile for experimental development of standard samples


This article is aimed at developing a mathematical model and conducting numerical modelling of aerodynamic processes during the flight of a ballistic projectile using the method of computational aerodynamics. The use of a ballistic projectile as a prototype allows various units and systems of any size and mass to be included in the design of a guided artillery projectile. At the same time, the design of the developed ballistic projectile is characterized by simplicity, compact size and reduced weight. Several layouts of the proposed ballistic projectile with different tail sections were developed. The flow calculations were performed under the Mach numbers of M = 0.6, 0.8, 0.9 and the attack angles of α = 2° and a = 5°. Engineering calculations produced three-dimensional models of a ballistic projectile, flow patterns and main aerodynamic characteristics for various design layouts.

For citations:

Kolkotina M.S., Soshnikova N.V. Numerical simulation of the aerodynamics of a ballistic projectile for experimental development of standard samples. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2020;(4):54-61.


At present, JSC V. P. Makeyev State Rocket Centre is working to develop a domestic prototype of a guided artillery projectile (GAP) with improved firing accuracy and extended flight range.

The ballistic projectile under consideration is designed for experimental testing of standard units and systems of GAP in order to reduce costs and shorten the cycle of the GAP prototype development.

This work is intended to develop simulation models of ballistic projectiles, to determine aerodynamic characteristic (AEC) [1] by computations and to refine the aerodynamic shape of a ballistic projectile (BP) including retrievable BP versions.

The following tasks were set:

  • research and development;
  • numerical calculations of BP;
  • BP ADC analysis;
  • analysis of opportunities to reduce costs of BP manufacture and assembly;
  • refinement of BP aerodynamic shape.

Based on R&D efforts, the following version of a ballistic projectile is proposed for development (Figure 1).

Fig. 1
. Ballistic projectile: 1 – open-type tail section – unit under test, 2 – end-piece – standard type, 3 – propulsion module casing – shorter version, 4 – front compartment casing – standard version with modified docking unit, 5 – rear compartment casing – standard type

Previously, experimental testing of units and systems included in a standard GAP sample required procurement of illuminating projectiles for accommodating proprietary assembly units to be tested. Such an approach is expensive and takes a lot of effort.

Besides, the section of an illuminating projectile where the assembly unit under test can be accommodated has small overall dimensions preventing accommodation of standard experimental units.

Nowadays, experimental testing of units and systems included in GAP is carried out using full-scale GAP mock-ups developed by JSC V. P. Makeyev State Rocket Centre.

A proposal was put forward to develop an in-house ballistic projectile capable of accommodating any GAP units and systems irrespective of their overall dimensions and weight and at the same characterised by simple design, compact sizes, and reduced weight. This solution would help reduce its manufacturing costs, and therefore, testing costs as well.

According to the analysis, the casing of the standard propulsion module can be shorter, the front casing needs modification, while the endpiece and rear casing can remain unchanged with their components borrowed from the previous tests. The unit under test is an open-type tail section (without tray) to be manufactured in compliance with the design documentation.

For testing advanced GAP units and systems, such as homing head, on-board control system, and telemetry, it is reasonable to develop a version of GAP with the recovery system.

Design conditions, flow patterns, and configurations’ ADC

To select the best suitable aerodynamic configuration of GAP, including a retrievable version, and to obtain the desired aerodynamic characteristics of GAP, we developed 3D models and conducted flow analysis for three versions of the GAP model configurations shown in Figures 2–4.

Fig. 2
. Ballistic projectile

Fig. 3
. Ballistic projectile (retrievable, version 1)

Fig. 4
. Ballistic projectile (retrievable, version 2)

Fig. 5
. Mach number field M = 0.8 at α = 2º

Fig. 6
. Temperature field at represented as isolines at M = 0.9, α = 5º

Flow analysis was conducted based on the Navier – Stokes equations, using the CFD package. We studied the external air flow at subsonic velocities. The following parameters of ram airflow were set at the computational domain limits: the velocity parameter was set in non-dimensional form by the Mach number M = 0.6; 0.8 and 0.9; angles of attack α = 2º and 5º, pressure P = 101,325 Pa, and temperature T = 293.2 K were considered. The condition of symmetry along the OZ axis was applied, reducing the period of time required for the analysis. Periodic computational grid adaptation was used with the total number of cells within the entire computational domain of about 10,000,000.

We obtained the following flow patterns based on the conducted 3D numerical calculations:

  • for ballistic projectile;
  • for ballistic projectile (retrievable, version 1);
  • for ballistic projectile (retrievable, version 2).

Figures 7, 10 and 12 show how the differences in geometry of the projectile’s tail section affect the velocity vector field. It is evident that a non-steady-state vortex flow is formed downstream of the stabilizers. Based on the flow patterns of temperature fields, we can observe that the maximum temperature is reached in the areas upstream and downstream of the stabilizers.

Fig. 7
. Velocity vector field at M = 0.9, α = 5º (min = 0 m/s, max = 534.024 m/s)

Fig. 8
. Pressure field at M = 0.9, α = 5º

Fig. 9
. Mach number field M = 0.8 at α = 2º

Fig. 10
. Velocity vector field at M = 0.6, α = 5º (min = 0 m/s, max = 283.274 m/s)

Fig. 11
. Temperature field at M = 0.6, α = 5º

Fig. 12
. Velocity vector field at M = 0.6, α = 5º

Fig. 13
. Temperature field at M = 0.8, α = 5º

Aerodynamic characteristics (ADC) for different variants of the projectile geometry are given below in the tabular form, where cx – longitudinal force coefficient, cy – normal force coefficient, x– centre-of-pressure coefficient counted from the nose section. Wind fixed coordinates were used for representing the resultant aerodynamic forces. To calculate aerodynamic coefficients, the force was normalized by the ram air pressure and by the reference area determined by the diameter of the mid-section area of the configuration.

Numerical calculation results show that if the centre of mass of the ballistic projectile is located on its axis at a distance of 600 mm from the nose section, all the projectile configurations under study are statically stable, and the projectile flight velocity (deceleration) can be reduced to the desired level by increasing aerodynamic drag when selecting the relevant tail section.

Table 1

ADC for ballistic projectile

Table 2

ADC for ballistic projectile, retrievable, version 1

Table 3

ADC for ballistic projectile, retrievable, version 2


The following was accomplished.

1. We developed 3D models and a draft general layout of the ballistic projectile intended for experimental testing of components, units, and systems included in the standard GAP sample.

2. Numerical calculations were conducted to select the best suitable aerodynamic shape of the GAP depending on the scope of application.

3. Completed numerical calculations allowed to obtain flow patterns and aerodynamic characteristics required for the selection of basic design parameters of the BP versions, including the tail section.

4. The obtained ADC are sufficient for BP dynamic motion calculations.

5. We analysed the possibilities to manufacture and assemble this projectile with modification of the existing and previously tested components.


1. Краснов Н.Ф. Аэродинамика. Ч. I. Основы теории. Аэродинамика профиля и крыла. Учебник для втузов. Изд. 2-е, перераб. и доп. М.: Высшая школа, 1976. 384 с.; ил.

2. Анурьев В.Т. Справочник конструктора-машиностроителя: В 3 т. Т. 1. 8-е изд., перераб. и доп. М.: Машиностроение, 2001. 920 с.: ил.

About the Authors

M. S. Kolkotina
V.P. Makeev State Rocket Centre JSC
Russian Federation

Kolkotina Maria Sergeevna - Engineer of the 2nd category, Research interests: aircraft aerodynamics.

Miass, Chelyabinsk region

N. V. Soshnikova
V.P. Makeev State Rocket Centre JSC
Russian Federation

Soshnikova Nadezhda Vladimirovna - Design Engineer of the 3rd category, Research interests: aircraft design.

Miass, Chelyabinsk region


For citations:

Kolkotina M.S., Soshnikova N.V. Numerical simulation of the aerodynamics of a ballistic projectile for experimental development of standard samples. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2020;(4):54-61.

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ISSN 2542-0542 (Print)