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Defense and
Vol. 1, No. 1,
https://doi.org

This work is lic
others to share a
authorship and in
 

Axial fo
 
Ammar Tra
1 Defense Tech
 
 

*ammar.trak
© The Auth
2020. 
Published by
ARDA. 

 

1. Introdu

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Studies 
020, pp.1-15 
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Abstract 
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 DSS Vol. 1, No. 1, December 2020, pp.1-15 

2 

 
Figure 1. Main components of APFSDS ammunition [2] 

During the movement of the APFSDS projectile through the barrel of the weapon, the energy of the propellant 
charge acts on the bottom of the projectile (the penetrator is still connected to the sabot) and drives it. After 
the projectile comes out of the barrel, due to the difference in resistance and mass of the sabot and penetrator, 
the sabot separates and the penetrator continues to fly towards the target (Figure 2). When moving through the 
barrel of the cannon, the projectile with the sabot reaches supersonic velocities (up to 5 Mach). 
APFSDS projectiles are statically stabilized projectiles. Stabilization is provided using aerodynamic surfaces-
wings. When determining the axial force (axial force coefficient), the projectile body and the wings are 
observed separately. The sum of these two components of the axial forces on the APFSDS projectile gives the 
total axial force (axial force coefficient) [4]. 
 

        
Figure 2. Process of discarding sabot from APFSDS projectile [3] 

2. Models for prediction of coefficient of axial force 

There are many methods for predicting the axial force coefficient of APFSDS projectiles, but all of them are 
based on the application of three general methods: 

1. experimental (wind tunnel or polygon), 
2. theoretical, and 
3. numerical (CFD - Computational Fluid Dynamics). 



 DSS Vol. 1, No. 1, December 2020, pp.1-15 

3 

Experimental methods determine aerodynamic coefficients in an air (aero) tunnel or on the basis of measuring 
the movement of a projectile in flight (as a material point or a rigid body). This method gives the most 
realistic values for the axial force coefficient; however, the disadvantages of the tunnel experiment are [5]: 

 high price, 
 scaling problems if the model is not life-size, 
 interference from tunnel walls, 
 measurement difficulties. 

Assumptions and simplifications are necessary in theoretical methods for the solving problems. This includes 
simplifying geometry and simplifying equations. Equations known as Navier-Stokes equations, along with the 
energy equation and the continuity equation, describe the flow of fluid around a body. They are analytically 
unsolvable in closed form, but can be simplified for specific geometry or flight conditions [5]. 
Numerical methods are new; they have been used since the advent of computers during World War II. 
Advanced CFD codes numerically solve Navier-Stokes equations and can show the complete flow field 
around an object for specific flight conditions. With these methods, problems arise in determining the 
boundary conditions, because the initial conditions must be defined with great accuracy [5]. 
In the continuation of this chapter, two models for predicting the axial force coefficient APFSDS projectiles 
will be presented. The first model is presented in the STANAG 4655 Ed.1 standard. The second model for 
predicting the axial force coefficient of an APFSDS projectile is the numerical model (CFD). The program to 
be used for the numerical simulation of projectile flow is ANSYS Fluent. The presentation of the models as 
well as the results of the calculations will be shown below. 

2.1. Model defined in standard STANAG 4655 (Ed.1) 
The standard, STANAG 4655, shows an engineering model for prediction of the aerodynamic coefficients of 
conventional projectiles. The details of the standard are given and are divided into three parts [6]: 

1. Body Aerodynamics 
2. Fin Aerodynamics 
3. Generalized Yaw Aerodynamics 

The axial force of a projectile can be divided into two parts: pressure axial force and viscous (friction) axial 
force. The complete axial force coefficient Cx is finally obtained by summing up the relevant, separately 
calculated pressure axial force components and the viscous axial force obtained for entire wetted area. The 
total axial force coefficient of APFSDS projectile (without sabot) is [6]: 
 𝐶 = 𝐶 + 𝐶  (1) 
where 𝐶  is axial force coefficient of projectile body and 𝐶  is axial force coefficient of fins. 
2.1.1. Axial force computation methods for projectile body 
The axial force of a projectile consists of the pressure axial force of the nose, base (including possible tail 
boom), protruding (driving band, grooves and steps), and of the viscous axial force as a sum of the following 
form [6]: 

 𝐶 = 𝐶 + 𝐶 + 𝐶 + 𝐶  (2) 
where 𝐶  is axial force coefficient of the nose, 𝐶  is axial force coefficient of the base, 𝐶 is axial force 
coefficient of the protruding and 𝐶  is viscous axial force coefficient. 
The axial force coefficient of the nose at supersonic region for a cone is calculated according to the formula 
(3) giving the pressure coefficient on the nose surface [6]. The second term takes into account the nose shape 
on drag force (see Fig. 3). 

 𝐶 = 𝐶 = 𝑘 sin 𝜀 + 𝑘 sin 𝜀 (cos 𝜀) ( , , )𝑀 + 𝑅𝑅(1 − 𝑅𝑅) , cos 𝜀 (𝑀 ≥ 1)   (3) 
The coefficient k1 is an average pressure coefficient on a blunt projectile face behind a normal shock wave and 
the coefficient k2 takes into account the shape of the nose as a function of radius ratio parameter RR [6].  



 DSS Vol. 1, No. 1, December 2020, pp.1-15 

4 

 
Figure 3. Variable RR (Radius Ratio) [6] 

 
The coefficient k1 is computed from (4), and the coefficient k2 is computed according to (5). The radius ratio 
RR in the formulae is an inverse of the ratio of the true radius of curvature and the tangent-ogive radius r’ 
(formula 6). The nose contour line is to be extended to the projectile center line in case of blunted nose (see 
Figure 3). The extended nose length is used in formula (6). The ratio RR is zero for cones [6]. 

 𝑘 = 53 − 23 𝑀√ (𝑀 ≥ 1) (4) 
 𝑘 = 0,9 − 0,9𝑅𝑅 + 𝑅𝑅  (5) 
 𝑟, = 𝑙,𝑑 + 𝑑4  (6) 
The axial force coefficient of the base 𝑪𝒙𝒃  is computed from formula (7) [6]: 
 𝐶 = −𝐶 𝑑𝑑  (7) 
The pressure coefficient 𝐶  is computed as [6]: 
                                            𝐶 = 𝐶 𝑑𝑑 𝑥 = 2 when 𝑀𝑎 < 0.9, otherwise 1  (8) 
The pressure coefficient on the base of a long cylinder 𝐶  is computed at supersonic speeds (1.1 < Ma) [6]: 
 𝐶 = −0,31𝑒 ,  (9) 
Viscous axial force coefficient 𝑪𝒙𝒇  is calculated by formula [6]: 
 𝐶 = 𝐶 𝑆 𝑆  (10) 
where 𝐶  is average friction coefficient (11 or 12) for a smooth flat, 𝑆  is computed wetted surface area 
and S is reference area .   
The turbulent boundary-layer friction coefficient 𝐶  is computed by equation [6]: 
 𝐶 = 0,455(log 𝑅𝑒) , (1 + 0,21𝑀 ) ,  (11) 
where 𝑅𝑒 is Reynolds number , 𝑙 is projectile/nose length and 𝑣 is kinematic viscosity. 
The laminar boundary-layer friction coefficient 𝐶  is computed by equation [6]: 
 𝐶 = 1,328√𝑅𝑒 (1 + 0,21𝑀 ) ,  (12) 



 DSS Vol. 1, No. 1, December 2020, pp.1-15 

5 

The kinematic viscosity 𝑣 is computed from [6]: 
 𝑣 = 𝜇𝜌  (13) 
The air density ρ is computed according to ICAO standard atmosphere. The dynamic viscosity μ is obtained 
from the Sutherland formula [6]: 
 𝜇 = 𝐶 𝑇 ,𝑇 + 𝐶  (14) 
where  𝐶 = 1,458𝑒  / , 𝐶 = 110,4  𝐾  and T is air temperature, obtained from ICAO atmosphere 
model. 

The axial force coefficient of protruding 𝑪𝒙𝒑𝒓  is computed by estimating the forward and backward facing 
surface pressure drag separately [6]: 
 𝐶 = 𝐶 + ∆𝐶  (15) 
The pressure coefficient sum (of the backward and forward facing parts) 𝐶  will change linearly 
between the sum and 0 when the ratio e/h (width/depth of groove) goes from 7 to 0 [6]. 
 𝐶 = 𝑒7ℎ 𝐶 𝑒ℎ < 7  (16) 
The formulae for the pressure coefficients at velocities above speed of sound are [6]: 
 𝐶 = (−0,067(𝑀 − 1) + 0,4) sin 𝜗 (17) 
 𝐶 = −0,65𝑀 ,  (18) 
where 𝜗 is angle of grove profile. 
Certain types of finned projectiles have a relatively large groove pattern on the surface of the cylindrical part 
of body. These grooves are needed at the internal ballistic phase and after launch, the grooves cause an 
unfavorable flow retarding effect.  
The axial force coefficient of excessive amount of grooves (see Figure 4) is computed in from formula [6]: 
 ∆𝐶 = 1,6 𝑙𝑙 𝐶 (𝐶 − 1) (19) 
The coefficient 𝐶  is the viscous drag coefficient (equation 10) of body cylinder part and the coefficient 𝐶  is used to take into account the groove depth on drag. The coefficient is the surface area ratio of 
grooved cylinder length to that of same length cylinder without grooves; the incremental drag will be zero in 
case the surface coefficient 𝐶  is 1 [6]. 

 
Figure 4. Groove pattern area on the surface of the cylindrical part of body [6] 



A

 

2.1.2. Axia
The axial for
Reynolds nu
the projectile
The axial for
(𝐶 ), ax
as a sum of t
 

The wave d
according to
 

where: K is 
area (see Fig

        Figu

The formula
˄LEfin , wher
expression [
 

The drag coe

   Figure 7. E

Axial force 
reference are

al force com
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rce coefficie
xial force co
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a (21) is app
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6]: 

efficient valu

Exposed win

coefficient o
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mputation m
ent of fins (𝐶
roduced via s
l part.  
ent of fins co
efficient of t
g form [6]: = 𝐶
ersonic spee
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ction factor (
number of fi

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weep angle of

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ethods for p
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6 

projectile fin
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. The referen

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e (𝐶  ) a

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K [6]           

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𝑖𝑛 1𝑀  
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dy [6]      Fig

[6] 

ed by multip
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DSS

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Fig. 7). The M

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. 8. Schemat

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]: 

S Vol. 1, No. 

Mach numbe
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axial force co
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Figure 6. Pro

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2020, pp.1-15

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Axial force 
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oefficient on 

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merical comp
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, 𝑐̅ is Mean A
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included in

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of fins (𝑛

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e skin friction
rojectile bod

kinematic v

spect of mod
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eps (Fig. 10):
imulation, w
is (viscosity

2020, pp.1-15

(23) 

(24) 

(25) 

), taking the

(26) 

according to

(27) 

n drag. In fin
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(28) 

(29) 

iscosity. 

dern research
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:  
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 Air 
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momentum, 
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thematical m
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1. Control vo

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olume [7] 

S Vol. 1, No. 

er-defined fu
 
discretization

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(mesh indep

alyzed to und
ake it possib
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on [8] 

mathematic

air is isotropi

the basic law
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1, December 

unctions sho

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derstand the 
ble to gain in
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ws of mass c
d in integral 
- the limit o

ormal  𝑛 [7]. 

2020, pp.1-15

ould be used

 model, and

initialization
eck and mesh

solution and
sight into the
waves. [8]. 

of a physica

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form for an

of the contro

5 

d, 

d 

n, 
h 

d 
e 

al 

n, 
n 

ol 



 

The characte
each point in

 Law
 

 Law
 

 Law

 𝜕𝜕𝑡 𝜌𝐸
where �⃗� is v
2.2.2. Sim
The followin

 The 
 The 

chan
temp

 The 
 Spat
 The 

cont
spee

 The 
will 

 A un
In order to r
(Figure 12). 
the outer bou
and 6 length
 

eristics of th
n space and a

w of mass con

w of momentu𝜕𝜕𝑡 𝜌 
w of energy c

𝐸𝑑Ω + 𝜌
velocity of air

mulation of a
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flow around

tial domain d
numerical 

tinuity, amou
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equations w
be compute

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reduce the n
The calculat
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hs from the to

Fi

he air flow (p
at any time, b
nservation: 𝜕𝜕𝑡
um conserva

�⃗�𝑑Ω + 𝜌
onservation:

𝜌𝐸(�⃗� ∙ 𝑛)𝑑𝑆
rflow, p is pr

air flow arou
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ll be observe
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will be lineari
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tion domain 

at distances o
op (cylinder-

igure 12. 3D 

pressure, tan
by a system o

𝜌 𝑑Ω +
ation: 

𝜌�⃗�(�⃗� ∙ 𝑛)𝑑𝑆
 

= 𝑘(∇𝑇
ressure, ρ is 

und projectil
l simulations
ed as 3D geom
n ideal gas, 
characterist

hermal condu
ile is compre
n will be with
ed solver wi

mentum and e

ized in impli
tions that inc
ers a projectil

nite elements
is limited by

of 3 projectil
-shaped mesh

model of AP

9 

ngential stres
of differentia

𝜌(�⃗� ∙ 𝑛)𝑑𝑆
= − 𝑝𝑛𝑑
∙ 𝑛)𝑑Ω −
density, T is 

le 
s [9]: 
metry proble
which is m

tics with the
uctivity are c
essible and tu
h a hybrid m
ill be used, 
energy. This

icit form, i.e.
clude both ex
le at a zero y

s, only the p
y the externa
le lengths fro
h) to avoid d

PFSDS proje

DSS

ss, velocity, 
al equations 

𝑆 = 0 
𝑑𝑆 + (𝜏̿

𝑝(�⃗� ∙ 𝑛)𝑑𝑆
temperature

em (because 
modified in a
e temperature
onsidered co

urbulent (k-ε
mesh. 

which simu
s method wa

. for given va
xisting and un
yaw angle. 

projectile seg
l boundary o
om the shell,
disturbances i

ectile 120 mm

S Vol. 1, No. 

temperature
[9]: 

∙ 𝑛)𝑑𝑆 
𝑆 + (𝜏̿ ∙ �⃗�
e, E is total en

of fins). 
accordance w
e. Density a
onstant. 
model of tur

ultaneously 
as developed

ariables; unk
nknown valu

gment was ta
of the project
 7 projectile
in free stream

m M829A2 [

1, December 

e, etc.) are de

�⃗�)𝑛𝑑𝑆 
nergy, 𝜏̿ is st
with compre
and viscosity

rbulence was

solves the 
d for compr

known value
ues from adja

aken - at an 
tile, symmetr
e lengths from
m [9]. 

[9] 

2020, pp.1-15

etermined, a

(30) 

(31) 

(32) 

tress tensor.

essibility and
y depends on

s used). 

equations o
essible high

s in each cel
acent cells. 

angle of 60
ry planes and
m the bottom

 

5 

at 

d 
n 

f 
h-

ll 

0 
d 

m 



 DSS Vol. 1, No. 1, December 2020, pp.1-15 

10 

The following types of boundary conditions were selected (Figure13) [9]: 
 The "wall" boundary condition, which is used to separate the regions of fluid and solid matter, is 

placed on the outer boundary of the projectile. At the "wall" boundary condition, the "stationary wall" 
and "no-slip" options were chosen, because in the case under consideration, viscous effects cannot be 
ignored.  
The mass flux through the "wall" boundary is zero, and the pressure values at this boundary are 
obtained by extrapolation from inside the solution domain. 

 The "symmetry" boundary condition was used as a plane of axisymmetric geometry. 
 The "pressure far field" boundary condition, which is used to model the parameters of the 

compressible free stream at infinity, is set at the outer boundary of the calculation domain for given 
problem. 

 
Figure 13. Generated mesh around projectile 120 mm, M829A2, and boundary conditions applied [9] 



 DSS Vol. 1, No. 1, December 2020, pp.1-15 

11 

3. Results and discussion 

For prediction of the accuracy of the engineering model (from the NATO related STANAG 4655 standard) 
and CFD numerical model, a comparison was made in the research with the PRODAS model. For calculation 
of axial force coefficients, APFSDS projectile, 120 mm, M829A2, was chosen. The reason for choosing this 
projectile model is because the aerodynamic coefficients are available from PRODAS program for this 
projectile model. 
The PRODAS software was developed to satisfy a need for rapid performance evaluation of ammunition 
characteristics. The development of an effective design/analysis tool for use by the design engineer in the 
development and evaluation of projectiles has been a multi-year project which began at General Electric in 
1972 and has continued at Arrow Tech Associates, Inc. since 1991. The developed tool is now called 
PRODAS which is an acronym for the Projectile Design/Analysis System [10]. 
From the smallest match bullets, to GPS guided artillery shells, PRODAS brings together: 
 Modeling - Building a model from a drawing or even a picture. 
 Aerodynamics - Comparing aerodynamic coefficients from multiple aero estimators. 
 Launch Dynamics - Interior ballistics, balloting and jump. 
 Trajectories - Fly 4DOF, 6DOF and Body Fixed and Guided Trajectories. 
 Terminal Effects - Estimate penetration of KE projectiles and lethality of fragmenting or shaped 

charge warheads. 
 System Effectiveness - Using focused analysis or general purpose macros, compare projectiles or even 

GN&C algorithms [10]. 

3.1. STANAG 4655 vs. PRODAS 
The axial force coefficients of the projectile body, predicted using the model from STANAG 4655 and 
PRODAS models are shown in Figure 14. The axial force coefficients of the projectile body predicted by the 
model from STANAG (Figure 14) shows a significant difference in the range of Mach 3 to 5. It can be seen 
that this difference decreases with increasing Mach number [9].  
The axial force coefficients of the projectile fins, predicted using the model from STANAG 4655 and 
PRODAS models are shown in Figure 15. The downward trend in the value of the axial force coefficient of 
the fins in the STANAG model is higher than in the PRODAS model. The differences between the values 
decrease slightly with increasing Mach number (Figure 15) [9]. 

Figure 14. Coefficients of axial force of the 
projectile body (120 mm, M829A2) [9] 

Figure 15. Coefficients of axial force of the projectile 
fins (120 mm, M829A2)  

The axial force coefficients of the projectile obtained by the model from the STANAG 4655 standard, are 
smaller than the coefficients obtained by the PRODAS model (for projectile 120 mm, M829A2). The 
difference between the values of the coefficients obtained with model from STANAG and PRODAS, 
decreases with increasing Mach number (Figure 16).  
The percentage difference of the coefficients obtained by the model from the STANAG in relation to the 
coefficients obtained by applying the PRODAS model is given in figure 17.   
From figure 17 it can be noticed that the largest percentage difference between the predicted values of the 
model from the STANAG and PRODAS is 16.3 % in the range of 3 to 5 Mach [9]. 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

3 3.5 4 4.5 5

C X
_b

od
y

MACH

PRODAS
STANAG 4655

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

3 3.5 4 4.5 5

CX
_f
in

MACH

PRODAS
STANAG 4655



 

Figure
project

3.2. CFD vs
The results o
results of PR
3, where the
%. The perc
coefficients 
Based on the
the projectile
it arises as a
through the
phenomena:
 

Figure 18. C
(P

The pressure
the free stre
oblique shoc
behind the p
During supe
causes the s
supersonic f
circular mo
characterized
change disc
large. In fron

0

0.2

0.4

0.6

0.8

1

1.2

3

C x

0

0.2

0.4

0.6

0.8

1

1.2

1.4

3

C X

e 16. Coeffic
tile (Projecti

s. PRODAS
of the numer
RODAS (fun
e difference 
centage diff
obtained by 
e obtained re
e 120 mm, M
a result of th

e atmosphere
 fluid viscos

Coefficients o
Projectile 120

e and velocit
eam pressure
ck waves ap

projectile.  
ersonic flow
streams to b
flow, the ben
vement of 
d by pronou
ontinuously 
nt of the sho

3.5 M

3.5 M

ients of axia
le 120 mm, M

 
rical simulat
nction Cx = f 
is about 8.4 

ference of th
applying the
esults of num

M829A2 was
he action of 
e. The sour
ity, shock w

of axial force
0 mm, M829

ty fields, sho
e is not the s
ppear at the 

, underpress
bend toward
nt extension 
air is creat
unced shock
(extremely)

ock wave, the

4MACH

4MACH

l force of the
M829A2) [9

ion of air flo
f (M)) are sho

%. As the M
he coefficien
e PRODAS m
merical simu
s done. The r
f a normal fo
rce of fluid
aves (at velo

e of the proje
9A2) [9] 

wn in Figure
same for dif
top of the p

ure is create
ds the projec

of the boun
ed. General

k waves, ext
 in a very s
ere is a zone

4.5

PRODAS
STANAG 465

4.5

PROD
CFD

12 

 
e 

9] 

 

ow around pr
own in figur
Mach numbe
nts obtained 
model is give
ulations, the a
resistance for
orce and a ta
d resistance 
ocities M ≥ 1

ectile Figu

es 20 and 21
fferent Mach
projectile, w

ed behind th
ctile axis. N

ndary layer d
lly speaking
tremely narr
short time in
e of undisturb

5

55

5

DAS

Fig
PR

DSS

rojectile (12
re 18. The lar
er increases, 

by the num
en in figure 1
analysis of th
rce of a fluid
angential for

to body m
), and turbul

ure 19. Relat
Projec

, are comple
h numbers. A

while a chara

he rear part 
Near the axi
draws air fro
g, the supers
row areas of
nterval, with
bed flow, wh

gure 17. Rela
RODAS) - Pro

S Vol. 1, No. 

0 mm, M829
rgest deviatio
the differenc

merical simu
19 [9]. 
he pressure a

d that oppose
rce on the su

motion are p
lence flow be

tive differenc
ctile 120 mm

x. From Figu
As expected 
acteristic und

of the projec
s, the stream
m the rear o
sonic flow 
f fluid in wh
h pressure gr
hile behind it

tive differen
ojectile 120 m

1, December 

9A2), in para
ons are reco
ce decreases

ulation in re

and velocity
es the motion
urface of a b
practically t
ehind the bo

ces (CFD vs 
m, M829A2 [

ure 20, it can
for the supe

derpressure z

ctile. This u
ms must be
of the projec
regime of 

which the flo
radients bein
t there is a z

nces (STANA
mm, M829A

2020, pp.1-15

allel with the
rded for M =

s by almost 1
elation to the

y field around
n of a body in
body moving
three natura
dy [9]. 

PRODAS) -
[9] 

n be seen tha
ersonic flow
zone appear

underpressure
nd again. In

ctile so that a
any body i

ow propertie
ng extremely
one in which

AG vs 
A2 [9] 

5 

e 
= 
1 
e 

d 
n 
g 
al 

 
- 

at 
w, 

s 

e 
n 
a 
s 
s 
y 
h 



 DSS Vol. 1, No. 1, December 2020, pp.1-15 

13 

there are differences in the values of pressure, speed, temperature and density. Figure 21 shows the boundary 
layer that forms around the projectile in flight. It can also be seen that the angle of the oblique shock wave 
decreases with increasing velocity at which the flow is simulated [9]. 
 

 
Figure 30. Pressure field around the projectile for different Mach numbers [9] 

 



 DSS Vol. 1, No. 1, December 2020, pp.1-15 

14 

 
Figure 21. Field of velocities around the projectile 120 mm, M829A2 for different Mach numbers [9] 



 DSS Vol. 1, No. 1, December 2020, pp.1-15 

15 

4. Conclusion 

Based on theoretical considerations and analysis of available models (STANAG 4655 and CFD) for predicting 
the aerodynamic coefficient of axial force for wing-stabilized projectiles, the prediction of the axial force 
coefficient for APFSDS projectile 120 mm, M829A2 was performed. The data obtained using the engineering 
model (from the STANAG 4655 standard), and the data obtained by numerical simulation of projectile flow 
with the available data from the PRODAS database were compared. The following was stated: 

 The total axial force coefficients of the APFSDS projectile (provided with the model from the 
STANAG 4655 standard) have a satisfactory agreement with the total coefficient from the PRODAS 
model. The largest difference between the values is about 16.3 %. As the Mach number increases, the 
difference decreases. 

 The advantage of the STANAG 4655 model is that it allows the calculation of coefficients based on 
the geometric characteristics of the projectile without the use of computers. 

 The CFD model gives very good results, the values of the axial force or the axial force coefficient. 
Good agreement between the results of the CFD model and PRODAS indicates that the initial and 
boundary conditions are well set. 

 The accuracy of the CFD model depends on the mesh, initial and boundary conditions. The accuracy 
of the CFD model can be increased by modifying the mesh (i.e. by increasing the number of finite 
elements). 

 
References 
[1] A. Ćatović: Anti-tank projectiles, Manual for students, University of Sarajevo, Mechanical engineering 

faculty, Defense Technologies Department, Sarajevo, 2019. 

[2] W. Odermatt: http://longrods.ch/compo.php, October 2020 
[3] Z. Huang, Z. Chen: Numerical investigation of the tree-dimensional dynamic process of sabot discard, 

Journal of Mechanical Science and Technology, Vol 28, No 7, 2637-2649, 2014. 

[4] B. Zečević: Anti-tank Ammunition, Lectures for students, University of Sarajevo, Mechanical engineering 
faculty, Defense Technologies Department, Sarajevo, 2018. 

[5] S. S. Kadić: Prediction of drag force at zero yaw angle for conventional artillery projectiles, Master 
thesis, University of Sarajevo, Mechanical engineering faculty, Defense Technologies Department, July 
2007. 

[6] STANAG 4655 Ed.1: An engineering model to estimate aerodynamic coefficients, NATO Standardization 
Agency, 18 January, 2010. 

[7] S. S. Kadić: Aaerodynamic, interior and exterior ballistic request, optimization in base bleed projectile 
design, PhD thesis, University of Sarajevo, Mechanical engineering faculty, Defense Technologies 
Department, Jul 2014. 

[8] A. Ćatović.: Prediction of terminal-ballistic parameters for natural fragmenting high-explosive projectiles 
using experimental data and numerical methods, PhD thesis, University of Sarajevo, Mechanical 
engineering faculty, Defense Technologies Department, Sarajevo, 2019. 

[9] Blazek, J.: Computational fluid dynamics: principles and applications, Elsevier Science Ltd, Oxford, 
United Kingdom, 2001. 

[10] A. Trakić: Axial force coefficients of APFSDS projectiles, Master thesis, University of Sarajevo, 
Mechanical engineering faculty, Defense Technologies Department, July 2020. 

[11] PRODAS V3, http://www.prodas.com/XQ/ASP/P.400/QX/webPageXML4.htm, Arrow Tech, 2020. 
 


