Advances in Military Technology

Vol. 17, No. 1, 2022, pp. 63-77

ISSN 1802-2308, eISSN 2533-4123
DOI 10.3849/aimt.01449

Mathematical Model of a Gas-Operated Machine Gun

V. D. Tien, M. Macko*, S. Procházka and V. V. Bien
University of Defence, Brno, Czech Republic

The manuscript was received on 9 October 2020 and was accepted

after revision for publication as research paper on 9 April 2022.

Abstract:
The article describes a thermodynamic mathematical model of internal ballistics in the
barrel and in the gas cylinder of a gas-operated gun. In addition, this thermodynamic
mathematical model deals with the mass flow of gas through the ring around the piston
into the atmosphere. The thermodynamic mathematical model and the solution algorithm
are validated and verified experimentally on the example of a 7.62 mm UK-59 machine
gun and 7.62 × 54 R ammunition. The conclusions of this paper are applicable to the
calculation and design of the machine gun gas propulsion structure for similar weapons
with dust gas extraction.

Keywords:
automatic weapons, gas-operated gun, internal ballistic

1 Introduction
In gas-operated automatic weapons, part of the powder gas is removed from the barrel
bore by means of a gas port. The principle of the drive is shown in Fig. 1. It consists of
a piston, a gas port and a gas cylinder. After the initiation of the shot, the projectile
starts to move and when the bottom of the projectile is behind the gas port, the gases
enter the cylinder. The piston is controlled by the pressure of the expanding gases in
the cylinder. The pressure is usually transmitted to the breech of the gun, which is set
in motion by this pressure and performs the functional cycle of an automatic weapon.
The advantage of the principle is that the structure is simple and the amount of
gas entering the gas cylinder can be adjusted. The value of the gas pressure in the gas
cylinder influences the correct function of the gun. There are several small caliber
automatic weapons that use gases drawn from ports in the bore of the barrel to power
the automatic system, such as the AK-47, M16A1, AR-15, RPK, RPD, PKMS, UK-59,
SA-58, BREN, etc.

* Corresponding author: University of Defence, Kounicova 156/65, CZ-662 10 Brno, Czech Re-
public. Phone: +420 973 44 31 87, E-mail: martin.macko@unob.cz. ORCID 0000-0002-3896-
0803.
64 DOI 10.3849/aimt.01449

Fig. 1 Scheme of gas-operated machine gun

1 – gas block, 2 – barrel, 3 – bolt, 4 – bolt carrier, 5 – return spring, 6 – piston,
a – gas port, b – gas cylinder
A gas-operated automatic weapon is a firearm in which a portion of the powder
gas is used to control the movement of the breech. The value of the gas pressure must
be sufficient to cause the breech movement. Thanks to its kinetic energy, breech per-
forms all the important operations: ejecting the empty cartridge case, preparing the
trigger mechanism and loading a new cartridge into the barrel. This pressurized gas in
the gas cylinder impinges on the piston forehead to provide motion for breech and
breech carrier, for more details, refer to [1]. There are several analytical methods to
determine the gas pressure in the gas cylinder such as e.g. the methods presented in [1]
and [4]. However, the amount of propellant gas charged into the gas cylinder is small.
These methods consider that propellant gases do not affect the law of pressure, tem-
perature, mass flow, and velocity projectile in the bore, etc. So, when solving the
interior ballistics, it is not needed to consider the propellant gases taken from ports in
the barrel, and the results of the interior ballistics are used to determine pressurized
gas and motion of piston. In [5] the gas flow between the barrel and the gas cylinder is
considered to be a one-dimensional flow. In this case, only the gas flow from the bar-
rel into the gas cylinder is considered.
In addition, the pressure in the gas cylinder can be calculated based on the empir-
ical and semi-empirical methods, which have been presented in [6]. These methods
can be easily used and simply calculated. However, the accuracy of the results of cal-
culations is not high.
In the last years, besides the analytical methods, the thermodynamic properties of
the propellant gases inside the barrel and inside the gas cylinder were also studied by
numerical methods. Jevtic et al. [7] studied the change of the thermodynamic proper-
ties in the gas cylinder and the movement of the piston of a 20 mm gun. Florio [8]
performed the study of flow characteristics in the barrel and in the gas chamber of
a M16A1 rifle.
This paper aims to develop a novel thermodynamic model that correctly and
completely describes the internal ballistic cycle in the barrel and the phenomenon
which occurs in the gas cylinder, starting with ignition, combustion of the propellant
charge, the process of the projectile moving inside the barrel, the process of the pro-
pellant gases entering to the gas cylinder when the projectile has passed the gas port,
the process of piston movement in the gas cylinder, until the gas pressure in the barrel
rapidly drops to atmospheric pressure for all types of gas-operated automatic weapons.
This model is based on laws, including the first law of thermodynamics; the equations
of state; the law of conservation of mass; the burning rate law of propellant; equations
of motion of a projectile; the relative quantity of burnt-out propellant. To measure gas
pressure in the gas barrel and in the cylinder with different diameter of the gas port, an
 Advances in Military Technology, 2022, vol. 17, no. 1, pp. 63-77 65

experiment on the machine gun UK-59 was set up and carried out. The experimental
results were compared with analytical results.

2 Computational Model

2.1 Physical Model

The mathematical thermodynamic model is based on the laws of thermodynamics
according to the gun scheme as shown in Fig. 2.

Fig. 2 Physical model of gas-operated machine gun

1 – projectile, 2 – gas port, 3 – gas cylinder, 4 – piston, 5 – return spring, 6 – barrel,
lm – barrel length, lp – position of gas port, l – trajectory projectile, xpt – breech dis-
placement, vpt – breech velocity, Fsp – return spring force
The whole process of firing and gas flowing into the gas cylinder is explained in
detail in [1] and [6].

2.2 Mathematical Model

In the establishment of the mathematical thermodynamical model, we use the follow-
ing assumptions:
• the propellants are burned according to the geometric rules of combustion and
the combustion rate is as follows: u = u1p,
• the propellants burn at the same pressure, which is equal to the ballistic pres-
sure p,
• the projectile moves due to the average pressure in the barrel,
• the movement of the projectile through the gas port is instantaneous; the gradu-
al uncovering of the gas port is not considered,
• the return spring characteristic is linear,
• except for the return springs, which are elastic, all parts in the physical model
are rigid,
• the model is an open thermodynamic system,
• the heat transfer between the walls surface and inside of the barrel and the cyl-
inder is neglected,
• the specific heat capacity at constant volume cv and the specific heat capacity at
constant pressure cp are average values and do not change over time.
The mathematical model describes the thermodynamic process of the internal
ballistics of gas-operated automatic weapons, i.e., the combustion process, the gas
generation process, the gas removal process from the barrel bore and the gas expan-
66 DOI 10.3849/aimt.01449

sion process in the gas cylinder. The system of differential equations and algebraic
equations is set up as follows:

a. System equations of the burning rate of propellant gases t ∈ (0, tk) [9]
p
dz  when 0 < e < e1
=  Ik (1)
dt 
0 when e = e1

= (
dψ  κ c + 2κ c λ z + 3κ c µ z 2)dz
dt
when 0 < t ≤ tk
(2)
dt 0 when t > tk

where
p – the spatial averaged pressure in the barrel,
Ik – the total impulse of the propellant gases,
e1 – the thickness burned of propellant,
e – the thickness burned of propellant at the time t,
ψ – the relative burnt mass of the propellant,
κc, µ, λ – the shape characteristic quantity of fast burning propellant,
z – the relative burnt thickness of the propellant,
tk – the time when the propellant burned out.

b. System equations of the projectile movement t ∈ (0, tm) [9]

0 when p ≤ p0
dv  Sp
= when p > p0 (3)
dt  ϕ m
 p
dl
=v (4)
dt
where
v – the velocity of projectile,
mp – the mass of projectile,
S – the cross-sectional area of the bore,
p0 – the projectile starting pressure,
φ – the fictitious factor,
l – the travel of projectile in the barrel,
tm – the time when the projectile passes the muzzle.

c. The equation of determining the gas flow through the gas ports from the barrel
into the gas cylinder and vice versa
• Period l ≤ lp:
dmcg
=0 (5)
dt
where
lp – the distance from gas ports to the initial position of projectile,
 Advances in Military Technology, 2022, vol. 17, no. 1, pp. 63-77 67

dmcg/dt – the mass flow rate of gas through gas port.

• Period l > lp:
depending on the value of the gas pressure in the barrel (p) and the pressure of the gas
in the gas cylinder (pcg), the gas product can be flowed from the barrel into the cylin-
der or vice versa.
• Period p > pcg:
in this case, the gas product flows from the barrel into the cylinder. The equation of
determining the gas flowed through the gas ports from the barrel into the gas cylinder
has the form [1]:
 κ
ϕ S K (κ ) p p  κ + 1  κ −1
when ≥ 
 1 0 0 rT pcg  2 
dmcg 
=  2 κ +1  κ (6)
dt  p 2κ  pcg  κ  pcg  κ  p  κ + 1  κ −1
ϕ1S0   −  when 1 < < 
 rT κ − 1  p   p   pcg  2 
 
  
• Period p < pcg:
the gas product flows from the gas cylinder into the barrel. The equation of determin-
ing the gas flowed through the gas ports from the gas cylinder into the barrel has the
form [1]:
 κ
−ϕ S K (κ ) pcg pcg  κ + 1  κ −1
when ≥ 
 2 0 0 rTcg p  2 
dmcg 
=  2 κ +1  κ (7)
dt  pcg 2κ  p  κ  p  κ  pcg  κ + 1  κ −1
−ϕ2 S0   − 
 pcg  
when 1 < < 
 rTcg κ − 1  pcg     p  2 
  
where
φ1 – the discharge coefficient of gases flowing through the gas vent from barrel bore to
the gas cylinder,
φ2 – the discharge coefficient of gases flowing through the gas vent from gas cylinder
to the barrel bore,
1
 2  κ −1 2κ
K 0 (κ ) =   – the equation of exponent of adiabatic expansion,
 κ +1 κ +1
κ – the Poisson constant (the ratio of the specific heats) of propellant gases,
T – the temperature of gas product in the barrel,
Tcg – the temperature of gas product in the gas cylinder,
r – the specific gas constant of propellant gases,
S0 – the cross-sectional area of gas ports connected the barrel bore with gas cylinder.
• Period p = pcg:
dmcg
=0 (8)
dt
68 DOI 10.3849/aimt.01449

d. The equation of determining the gas flow through annulus around the piston to
the atmosphere
Due to the pressure difference in the gas cylinder and in atmosphere, the gas
flows through annulus around the piston to the atmosphere. The flow gas propellant in
this case is considered critical. This mass flow rate of the flow gas propellant is calcu-
lated by Eq. (9) [1]:
dmatm1 pcg
= ϕ3 SΔ K 0 (κ ) (9)
dt rTcg
where:
φ3 – the discharge coefficient of gases flowing through the annulus,
dmatm1/dt – the mass flow rate of the gas flowing through annulus around the piston to
the atmosphere,
SΔ – the area of the annulus between piston and gas cylinder.

e. The equation of determining the gas flow from the barrel to the atmosphere
when the projectile passes the muzzle
After the projectile comes out of the barrel, because the pressure of the gas prod-
uct inside the barrel is greater than the atmospheric pressure, the phenomenon of
gushing from the bore of the barrel to the environment occurs. This process ends when
the pressure in the barrel is equal to atmospheric pressure.
• Period p > patm:
The mass flow rate of the gas through the muzzle to the atmosphere is calculated
by Eq. (10) [1]:
 p
dmatm2 ϕ 4 SK 0 (κ ) when t > tm
= rT (10)
dt 0 when t ≤ tm
where
dmatm2/dt – the mass flow rate of the gas through the muzzle to the atmosphere,
patm – the atmospheric pressure,
φ4 – the discharge coefficient of flowing gases through the muzzle.
• Period p = patm
dmatm2
=0 (11)
dt

f. The equation of state in the barrel:

pV = mrT (12)
where
V – the instantaneous volume of the gas product in the barrel,
m – the mass of the gas product in the barrel (space in the barrel after the projectile).
 Advances in Military Technology, 2022, vol. 17, no. 1, pp. 63-77 69

 ω
 m = ωψ ; V = V0 + Sl − δ (1 −ψ ) − αωψ when l ≤ lp
 ω
 m = ωψ − mcg ; V = V0 + Sl − (1 −ψ ) − α (ωψ − mcg ) when lp < l ≤ lm (13)
 δ
 m = ωψ − mcg − matm2 ; V = V0 + Slm when l > lm

where
V0 – the initial volume of the barrel,
δ – the power density of propellant,
α – the covolume of powder gases,
ω – the mass of propellant,
lm – the length of the bore.

g. Energy balance equation in the barrel

• Period t ≤ tm
the energy equation in the barrel is based on the first law of thermodynamics [10]:
dQ = dU + ∑ dL = dU + dEpr + dH cg (14)
where
Q – the energy of propellant,
U – the internal energy of gas in the barrel,
Epr – the kinetic energy of the projectile,
Hcg – the enthalpy of the mass of gas product exchanged between the barrel and the
gas cylinder.
dQ = ( mɺ + dt ) cvTv = cvTv mɺ + dt (15)
where
Tv – the propellant ignition temperature,
dm+/dt – the mass gas flow rate of the propellant burning.
dm+ dψ
mɺ + = =ω (16)
dt dt

( ) ( ) (
dU = d  m+ − mcg cvT  = cv  mɺ + − mɺ cg Tdt + m+ − mcg Tɺdt 
    ) (17)

 ϕ mp v 2 
dEp = d   = ϕ mp vvɺdt (18)
 2 
 

0 when p = pcg or l ≤ lp

dH cg = mɺ cg cpTdt when p > pcg and l > lp (19)
mɺ c T dt when pcg > p and l > lp
 cg p cg
Introducing Eqs (15) and (17)-(19) into Eq. (14), it yields:
dT 1  1 
Tɺ = = (
Tv mɺ + − mɺ + − mɺ cg T −
dt m+ − mcg 
)
cv
(
ϕ mp vvɺ + Hɺ cg  ) (20)

70 DOI 10.3849/aimt.01449

• Period t > tm:

the energy equation in the barrel is based on the first law of thermodynamics [10]:
dQ = dU + ∑ dL = dU + dH cg + dH atm2 (21)
where
dHatm2/dt – the enthalpy rate of the mass of gas product flow from the barrel to the
atmosphere when the projectile passes the muzzle.
( ) (
dU = d ( mcvT ) = cv  mɺ + − mɺ cg − mɺ atm2 Tdt + m+ − mcg − matm2 Tɺdt 
  ) (22)

dH atm2 = H atm2 dt = mɺ atm2 cpTdt (23)

Introducing Eqs (15), (19), (22), and (23) into Eq. (21) we obtain:
dT 1  1 ɺ 
= (
Tv mɺ + − mɺ + − mɺ cg − mɺ atm2 T −
dt m+ − mcg − matm2  cv
) (
H cg + Hɺ atm2  ) (24)

At the time the propellant has burned:
m+ = ω and mɺ + = 0 (25)
h. The equation of state in the gas cylinder:
pcgVcg = mc rTcg (26)
where
mc – the mass of the gas product in the gas cylinder
mc = mcg − matm1 + mc0 (27)
mc0 – the initial mass of the gas in the gas cylinder,
Vcg – the instantaneous volume of the gas product in the cylinder in front of drive piston.
Vcg = Vcg0 + Sc xpt − α mcg − matm1( ) (28)
Vcg0 – the initial volume of the cylinder, when the piston is in its front position,
Sc – the effective area of the piston cross section,
xpt – the displacement of the piston in gas cylinder and parts linked with it.

i. The equation of motion for piston and parts linked with it

dxpt
= vpt (29)
dt
dvpt 1
=  Sc ( pcg − patm ) − Fsp − Ff  (30)
dt M
where
vpt – the velocity of piston and other parts linked with it,
Fsp – the force of return spring.
Fsp = Fsp0 + csp xpt (31)
Fsp0 – the initial pre-stress of return spring,
csp – the return spring constant,
M – the mass of piston and other parts linked with it.
 Advances in Military Technology, 2022, vol. 17, no. 1, pp. 63-77 71

msp
M = mpt + mbk + (32)
3
mpt – the mass of moveable drive piston,
mbk – the mass of breech block carrier,
msp – the mass of return spring,
Ff – the friction force effect to the moving parts, see [9].

j. Energy balance equation in the gas cylinder

The energy equation in the gas cylinder is based on the first law of thermody-
namics [10]:
dQc = dU c + ∑ dL = dU c + pcg d Vcg (33)

where
dQc/dt – the enthalpy rates crossing the boundary in the gas cylinder

dQc = Hɺ c dt = ( mɺ c dt ) cpT = mɺ cg cpTin dt − mɺ atm1cpTcg dt (34)

0 p = pcg or l ≤ lp

mɺ cgTin = mɺ cgT p > pcg and l > lp (35)
mɺ T pcg > p and l > lp
 cg cg
dUc/dt – the internal energy time change in the gas cylinder

( ) (
dU c = d(mc cvTcg ) = cv mɺ c dtTcg + mcTɺcg dt = cv mɺ cTcg + mcTɺcg dt ) (36)
By introducing Eqs (34)-(36) into Eq. (33), it yields
dTcg 1  
( )
pcg
=  mɺ cg κ Tin − Tcg − Tcg (κ − 1) mɺ atm1 − Sc vpt  (37)
dt mc  cv 
Finally, we summarize the system of differential equations and algebraic equa-
tions of the internal ballistics and drive of automatic mechanism of gas-operated
machine gun: Eqs (1)-(12), (20), (24), (26), (29), (30), and (37). Initial conditions of
this system of equations discussed above at the time is:
t0 = 0; v = 0; l = 0; T = Tatm; vpt = 0; xpt = 0; ψ = ψ0; z = z0; V = V0; Vcg = Vcg0;
Fsp = Fsp0; Tcg = Tatm; matm1 = 0; matm2 = 0. Tatm is atmospheric temperature.
The system of differential equations of the model can be fully solved by numeri-
cal method with fourth-order Runge-Kutta method.

3 Application of Presented Equations on the 7.62 mm Machine Gun

UK-59 and Ammunition 7.62 × 54 R.
The mathematical model presented above was applied to the UK-59 machine gun,
which is shown in Fig. 3. The experimental results and the calculated results were com-
pared to test the accuracy of the thermodynamic mathematical model.
The input data and initial parameters: The numerical values and the input parame-
ters of the calculations were obtained by measurements and by estimation on the real
7.62 mm machine gun UK-59 and ammunition 7.62 × 54 R. However, the numbers of
72 DOI 10.3849/aimt.01449

inputs are large so only the most important ones are mentioned in Tab. 1 [9]. The typical
results of the thermodynamic mathematical model are presented in Figs 4-6.
Tab. 1 Input data for solving problem of machine gun UK-59

Parameter Value
The sectional area of barrel [m ] 2
47.3 × 10−6
The gun caliber [m] 7.62 × 10−3
The barrel length [m] 0.609
The propellant charge mass [kg] 3.10 × 10−3
The projectile mass [kg] 9.6 × 10−3
The propellant force [J kg−1] 0.73 × 106
The propellant covolume [m3 kg−1] 0.906 × 10−3
The propellant density [kg m−3] 1627
The total impulse of the gas pressure [Pa s] 1.7020 × 105
The propellant ignition temperature [K] 3175
The initial volume of the barrel [m ] 3
3.521 × 10−6
The Poisson constant [–] 1.2505
The projectile starting pressure [Pa] 40 × 106
κc = 1.092
The shape characteristic quantity of fast burning propellant [–] κcµ = −0.092
λ=0
The mass of ammunition [kg] 0.0189
The diameter of piston [m] 13.937 × 10−3
The diameter of cylinder [m] 14.015 × 10−3
The initial volume of cylinder [m3] 12.363 × 10−7
The diameter of gas port [m] 1.31 × 10−3
The position of gas port [m] 0.18
The discharge coefficient φ1 [–] 0.5572
The discharge coefficient φ2 [–] 0.65
The discharge coefficient φ3 [–] 0.1605
The discharge coefficient φ5 [–] 0.98
The mass of breech [kg] 0.21952
The mass of breech block carrier [kg] 0.83028
The mass of recoil spring [kg] 0.068259
The initial pre-stress force [N] 61
−1 666
The recoil spring constant [N m ]
 Advances in Military Technology, 2022, vol. 17, no. 1, pp. 63-77 73

Fig. 3 The machine gun UK-59

Fig. 4 Typical trajectory courses of pressure, temperature in the barrel and velocity of
the projectile in the barrel, time courses of trajectory of the projectile in the barrel

Fig. 5 Time courses of pressure Fig. 6 Typical time courses of accelera-

tion, trajectory, velocity of the piston and
driving force
74 DOI 10.3849/aimt.01449

4 Experiment
The experiment was performed at the laboratory shooting range of the Department of
Weapons and Ammunition of the University of Defence (the Czech Republic). Exper-
imental structure model and layout of measuring positions on the machine gun UK-59
is shown in Fig. 7 [9].
The pressure was measured by piezoelectric pressure sensors S1, S2, S3. The first
piezoelectric pressure sensor S1 was mounted at the mouth of cartridge case to meas-
ure the gases pressure in the barrel. The second piezoelectric pressure sensor S2 was
mounted above the gas ports. This sensor measured the gases pressure in the barrel at
the gas ports. The third piezoelectric pressure sensor S3 was located on the front of the
gas cylinder for measuring the gases pressure in the gas cylinder.

(a)

(b)

Fig. 7 (main figure) – 7.62 mm machine gun UK-59 on STZA12, (a) – Piezoelectric
sensor KISTLER, (b) – Measuring system DEWE – 500
Carrying out the measurement and data processing, we have obtained the results
of the experiment in Fig. 8.

Fig. 8 Time histories of gas pressures in the barrel and in the gas cylinder
 Advances in Military Technology, 2022, vol. 17, no. 1, pp. 63-77 75

5 Discussion
The obtained experimental pressures were compared with the calculated pressure of
gases propellant. The comparison results in the different diameters of gas ports are
shown in Figs 9 and 10, and Tab. 2.

Fig. 9 Time course of gas pressure in the barrel

Fig. 10 Time course of gas pressure in the gas cylinder

The results of solving the mathematical thermodynamic model on the UK-59 ma-
chine gun are consistent with the measured results of the machine gun UK-59 in Figs 9
and 10, and Tab. 2
76 DOI 10.3849/aimt.01449

Tab. 2 Comparison of calculated and measured values with diameter of gas ports
d = 1.81 mm (S0 = 2.573 mm2)
Calculated Measured Difference
Parameter
value [MPa] values [MPa] [MPa]
Maximum pressure in the barrel 297.23 299.72 2.49
Maximum pressure in the gas cylinder 38.91 38.26 0.65
Pressure in the barrel at the gas ports 154.40 156.09 1.69
The research results confirm the correctness of the point of view of building
physical and mathematical models, so this model can be applied in investigating the
factors affecting the thermal-dynamic properties, internal ballistics, and gas drive
machine of gas-operated machine guns.

6 Conclusion
In this paper, a thermodynamic mathematical model was developed to solve the inter-
nal ballistics and gas propulsion mechanism of automatic weapons. The novel model
correctly and completely describes the internal ballistic cycle in the barrel and the
phenomenon that occurs in the gas cylinder. The system of differential equations and
algebraic equations has been built to solve general cases so that it can be applied to
specific cases with similar structure. All results of the calculations in the example of
7.62 mm UK-59 machine gun and 7.62 × 54 R ammunition agree very well with the
experimental results.
The results of the research confirm the correctness of the physical and thermody-
namic mathematical models, so that they can be used to analyze the factors affecting
the thermodynamic properties, internal ballistics and gas propulsion of these types of
gas-operated automatic weapons.
The results of this paper are important for the calculation and design of an auto-
matic weapon with gunpowder gas extraction and allow calculation according to the
specific technical requirements for a particular automatic weapon.

Acknowledgement
This article was supported by research project “DZRO FVT − Varops” in the Weapon
and Ammunition Department of the University of Defence, Brno.

References
[1] ALLSOP, D. Brassey’s Essential Guide to Military Small Arms: Design Princi-
ples and Operating Methods. London: Brassey’s, 1997. ISBN 978-1-85753-107-8.
[2] FIŠER, M., M. MACKO and S. PROCHÁZKA. Small Arms – Construction (in
Czech). Brno: University of Defence, 2020. ISBN 978-80-7582-336-6.
[3] Engineering Design Handbook. Guns Series. Automatic Weapons. Redstone Ar-
senal: Headquarters, U.S. Army Materiel Command, 1970.
[4] BALLA, J., L. POPELÍNSKÝ and Z. KRIST. Theory of High Rate of Fire Au-
tomatic Weapon with together Bound Barrels and Breeches. WSEAS Transactions
on Applied and Theoretical Mechanics, 2010, 5(1), pp. 71-80. ISSN 1991-8747.
 Advances in Military Technology, 2022, vol. 17, no. 1, pp. 63-77 77

[5] MUTAFCHIEV, N.M. Methodology for Determining the Parameters of Gas

Engine of Automatic Small Weapons. In: Defence Technology Forum 2015.
Shumen: “Vasil Levski” National Military University, 2015. ISSN 2518-167X.
[6] POPELÍNSKÝ, L. Gas Drive of Gas-Operated Automatic Weapons. Brno: Uni-
versity of Defence, 1993.
[7] JEVTIC, D.T., D.M. MICKOVIĆ, S.S. JARAMAZ, P.M. ELEK, M.D. MAR-
KOVIC and S.Z. ZIVKOVIC. Modelling of Gas Parameters in the Cylinder of
the Automatic Gun during Firing. Thermal Science. 2020, 24(6), pp. 4135-4215.
DOI 10.2298/TSCI200118152J.
[8] FLORIO, L.A. Finite-Volume Modelling of System with Compressible Flow
Propelled and Actuated Body Motion. Applied Mathematical Modelling, 2009,
33(8), pp. 3360-3381. DOI 10.1016/j.apm.2008.11.005.
[9] TIEN, D.V. The Calculating Model of Impulse Force Diagram of Gas-Operated
Automatic Weapons [Master Thesis]. Brno: University of Defence, 2013.
[10] BEER, S., L. JEDLIČKA and B. PLÍHAL. Barrel Weapons Interior Ballistics (in
Czech). Brno: University of Defence, 2004. ISBN 80-85960-83-4.
[11] DO DUC, L., V. HORÁK, R. VÍTEK and V. KULISH. The Internal Ballistics of
Airguns. In: 2017 International Conference on Military Technologies (ICMT).
Brno: IEEE, 2017, pp. 1-6. DOI 10.1109/MILTECHS.2017.7988720.
[12] HORÁK, V. and V. KULISH. Thermodynamics. Brno: University of Defence,
2011. ISBN 978-80-7231-793-6.