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Tạp chí Nghiên cứu KH&CN quân sự, Số 71, 02  2021 155
THE INTERNAL BALLISTIC PROBLEM FOR THE 23 MM CANNON
USING CASE TELESCOPED AMMUNITION
Nguyen Thai Dung*, Duong Hai Son
Abstract: The paper presented a calculation model and the results of solving the
internal ballistic problem for the 23 mm cannon using case telescoped ammunition. The
results clearly demonstrate the advantages of case telescoped ammunition and are the
scientific basis for the the
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oretical research process to manufacture and use 23 mm case
telescoped ammunition.
Keywords: 23 mm cannon; Internal ballistic; Case telescoped ammunition.
1. INTRODUCTION
A traditional medium calibre weapon system uses rounds of ammunition having the
propulsion system fitted on the rear half of the projectile. The case containing the propellant has
a larger diameter than the projectile, and hence the ammunition looks like a bottle. The Case
Telescoped Ammunition (CTA) has a special structure whereby the projectile is completely
embedded inside the case. Compared with the traditional ammunition with the same caliber,
CTA yields better terminal performances and a 30% reduction in bulk volume. In addition, with
CTA the loading of the round into the gun chamber is done without connectors. Therefore, the
weapon systems using CTA can effectively prevent weapon jamming and thus are more reliable.
Currently, CTA is still a new weapon that has not been studied in Vietnam. When fired, the
CTA has a stage where the projectile moves in the control tube before cutting the band. This is a
very different period from conventional artillery. Researching the CTA's internal ballistic
problem is the basis for understanding the phenomenon of firing and the characteristics and the
advantages/disadvantages of the weapon system using CTA to use them effectively.
Figure 1. Structure of 23 mm Case Telescoped Ammunitions
1. Primer; 2. Case; 3. Propellant Grain; 4. Control Tube; 5. Projectile.
2. THE PHENOMENON OF FIRING AND THE INTERNAL
BALLISTIC PROBLEM OF CTA
2.1. The phenomenon of firing and periods of the firing phenomenon
When fired, the firingpin acts on the bottom of the primer to ignite the booster charge and
then ignite the propellant grain. The control tube and the forward case seal will work to seal the
Cơ kỹ thuật & Cơ khí động lực
156 N. T. Dung, D. H. Son, “The internal ballistic problem using case telescoped ammunition.”
gas. When the gas pressure was high enough to open the forward case seal, the projectile began
moving in the control tube, during which the projectile moved freely. The projectile moving until
the rotating band contacts with the barrel will perform band cutting. After cutting the projectile
guided by the barrel, the gas continued to expand to make the projectile achieve the required
speed at the muzzle.
Preliminary period: The primer ignites the propellant grain and releases the gas. The
projectile moves in the control tube until the rotating band contacts with the barrel, in this period,
the pressure increased continuously until the pressure at the bottom of the projectile was equal to
the linkage force between the rotating band and the control tube.
The period of projectile movement in the control tube: In this period, the pressure
increased continuously until the pressure at the bottom of the projectile was greater than the
linkage force between the rotating band and the control tube. The projectile starts moving in the
control tube until the roating band cutting into the barrel, the speed when the roating band
contacts barrel 20 40 /gv m s .
First period: Starts from the moment the roating band is completely cut into the barrel until
the propellant burns out. The pressure of the gas will increase, pushing the projectile to move in
the barrel, increasing the volume of the gas behind the bottom of the projectlie, this will be the
factor that reduces the pressure. In this period, the pressure reached the maximum value Pmax.
The second period: Start from the moment the propellant burns out until the projectile comes
out of the muzzle. During this period, the gas still had high reserves of energy, so it continued to
expand, increasing the speed of the projectile and the reverse speed of the barrel. Due to the
movement distance of this period was very short, the speed of the projectile was fast, so the time
of this period was very short that allowed us to ignore the heat transfer from the gas to the barrel.
Thus, this period can be considered as the adiabatic expansion period of gas.
The last period of the gas effects: After the projectile comes out of the muzzle, the gas
continues to flow, increasing the speed of the projectile and the reverse speed of the weapon
system. That effect is called the final effect of the gas. At the end of this period, the speed of the
projectile reaches its maximum value vmax.
2.2. The internal ballistic problem of CTA
2.2.1. Assumptions
To make it easy to set up equations describing the firing phenomena and solving the internal
ballistic problem, we accept the following assumptions [2]:
 Burning of the propellant grains follow the law of geometric fire;
 Burning of the propellant grains follow the law of linear fire speed: u = u1p;
 All propellant burn under the same pressure conditions and equal to pressure P;
 The composition of the combustion product is constant, the characteristics of the propellant
grains f and are constants;
 The adiabatic exponent k=1+ is considered as a constant and is equal to its average value
in the temperature range from the combustion temperature of the gas to the temperature of the
gas at the time the projectile flew out of the barrel;
 By the time the gas pressure reaches the pressure P0, the rotating band was cut immediately,
and the projectile started moving;
 The movement of a projectile is considered until the moment the projectile flies out of
the muzzle.
2.2.2. The differential equations system of the internal ballistic problem
 The gasgenerating equation of propellant: 32 ..... zzz
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Tạp chí Nghiên cứu KH&CN quân sự, Số 71, 02  2021 157
 The combustion rate equation of propellant:
K
dz P
dt I
 The motion equation of projectile:
m
PS
dt
dv
.
.
 The basic equation of internal ballistic: 2. ( ) . . . .
2
S P l l f m v
Transform the above equations gives us a differential equations system of the internal ballistic
problem with: Z  Relative thickness of fire; P  Average pressure in the barrel [kG/cm
2
]; S 
Cross section of the barrel [dm
2
]; f  Propellant power [kG.dm/kG]; Ik  Total momentum of the
gas [kG.s/dm
2
]; Φ  Coefficients for calculating secondary work; Ψ  The amount of propellant
was relatively burnt; W  The volume behind the projectile bottom [dm
3
]; l  Distance of
projectile movement over time t [dm]; t  The motion time of projectile [s].
Solving the system (2) we identify the relationships:
(z, Ψ, P, V, l, W) = f(t)
(z, Ψ, P, V, t, W) = f(l)
Initial conditions of the differential equations system:
Propellant power of the primer fmoi=250000 [kG.dm/kG];
Ignition pressure Pmoi=5000 [KG/dm
2
];
Shot start pressure P0=30000 [KG/dm
2
].
when t=0 then v=0; l=0; z=0; P=Pmoi;
1
11
0
moi
moi
P
f
2.2.3. Solving the internal ballistic problem for Case Telescoped Ammunition 23 mm
The input data of the 23 mm CTA is designed and manufactured by the Weapon Faculty 
Military Technical Academy as follows:
 Cross section of barrel S: S = ηs.d
2
ηs is the depth characteristic of the groove, and ηs= 0,80÷0,83.
take ηs= 0,80 and we get: S = 0,80.(0,23)
2
= 0,042 dm
2
.
 Coefficients for calculating secondary work:
q
K
.
3
1
With 23 mm cannon, we get K = 1,05 so: 092,1
157,0
02,0
.
3
1
05,1
We will choose any 5 values to calculate. The values are given in table 1:
Table 1. Values of ω ,φ.
ω 0,02 0,025 0,03 0,037 0,04
φ 1,092 1,103 1,113 1,128 1,134
 The shape characteristics of the propellant [3]:
Calculate the shape characteristics of propellant according to the formulas in the document
[2]. Intermediate parameters:
1
2,2 7.0,2
5,5
.
0,653;
2
D n d
c
Cơ kỹ thuật & Cơ khí động lực
158 N. T. Dung, D. H. Son, “The internal ballistic problem using case telescoped ammunition.”
2 2 2 2
1 2 2
2,2 7.0,2
0,151;
4.2,75
.
4
Q
D n d
c
.073,0
75,2
2,01
c
e
The shape characteristics of the propellant:
1 1
1
2 2.0,655 0,151
.0,073 0,73
0,151
Q
Q
1
1 1
1 2 7 1 2.0,655
0,073 0,233
2 0,151 2.655
n
Q
2 2
1 1
1 1 7
0,127 0,018
2 0,455 2.1,137
n
Q
The input data to calculate the internal ballistic problem for 23 mm CTA is given in table 2.
Table 2. Input data to calculate the internal ballistic problem for 23 mm CTA.
Quantity Sign Sign on computer Unit Value
Gun caliber d d dm 0,23
Crosssectional area S S dm
2
0,042
Combustion chamber volume W0 W0 dm
3
0,0447
Distance traveled of projectile lđ lđ dm 9,2
Projectile weight q q kG 0,157
Propellant weight omega kG 0,020
Propellant power f f kG.dm/kG 988000
Cumulative of gas anfa dm
3
/ kG 1,053
Density of the propellant deta kG/dm
3
1,6
Total momentum Ik Ik kG.s/dm
2
300
The shape characteristics of the
propellant
χ
λ
capa
lamda
muy


0,73
0,233
0,018
Adiabatic exponent θ teta  0,240
Shot start pressure P0 po kG/dm
2
30000
Gravitational acceleration g g dm/s
2
98,1
Figure 2. Algorithm solving the internal ballistic problem of CTA.
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Tạp chí Nghiên cứu KH&CN quân sự, Số 71, 02  2021 159
The results of solving the internal ballistic problem for 23 mm CTA with 0,04 kg propellant
using MatLab software are shown in the following figures:
Figure 3. The result of calculating the internal ballistic with ω=0,04 kG.
From the calculation results and data [3] we can see:
 At the time the pressure reaches its maximum value:
Pm = 2751,68 (kG/cm
2
); Vd = 768,8 (m/s);
Comparing the calculation results of internal ballistic with data [3] we can see:
Maximum pressure: Pmlt= 2800 (kG/cm
2
) difference is 48,3 (kG/cm
2
);
Tolerance is 48,3/2800 = 1,73%;
Muzzle velocity: Vdlt = 720 (m/s) difference is 48,8 (m/s);
Tolerance is 48,8/720 = 6,77%.
Thus, the maximum pressure difference and the muzzle velocity calculated with [3] are
1.73% and 6.77%, respectively, within the allowable limits.
3. CONCLUSION
The article investigated the firing phenomenon of weapons using CTA. The paper also
reviewed the process of firing phenomena, established the internal ballistic model of the CTA,
set up the differential equations system of the internal ballistic problem, and calculated the
internal ballistic problem for 23 mm CTA is designed and manufactured by the Weapon Faculty
 Military Technical Academy. The results show that there is still a mismatch between theoretical
and internal ballistic problem calculations. However, the error about the maximum pressure
difference and the muzzle velocity is within the permissible limits.
REFERENCES
[1]. Nghiêm Xuân Trình, Nguyễn Quang Lượng, Nguyễn Trung Hiếu, Ngô Văn Quảng, “Thuật phóng
trong”, Học viện Kỹ thuật Quân sự, 2015.
[2]. Nguyễn Quang Lượng, Nguyễn Thanh Điền, “Thuật phóng trong thời kì tống đạn”, NXB Quân đội
nhân dân, Hà Nội, 2015.
[3]. Nguyễn Quang Lượng, Trần Quốc Trình, “Số liệu vũ khí  đạn”, Học viện Kỹ thuật Quân sự, Hà Nội 2009.
Cơ kỹ thuật & Cơ khí động lực
160 N. T. Dung, D. H. Son, “The internal ballistic problem using case telescoped ammunition.”
[4]. “A Simplified Model and Numerical Simulation of the Combustion and Propulsion Process for Cased
Telescoped Ammunition”, 2014 International conference on mechanics and materials Engineering
(ICMME 2014).
[5]. “Technical Evaluation of the DoD Cased Telescoped Ammunition and Gun Technology Programe”
(Project No. 5PT8016), 1996.
[6]. “Experimental Study and Numerical Simulation of Propellant Ignition and Combustion for Cased
Telescoped Ammunition in Chamber”, Xin Lu, Yanhuang Zhou, Yonggang Yu, School of Power
Engineering, Nanjing University of Science and Technology, Nanjing 210094, China.
[7]. В.Ф. Захаренков, “Внутренняя баллистика и автоматизация проектирования
артиллерийских орудий: [учебник]”, Балт. гос. техн. унт. –СПб., 2010. –276 с.ISBN 9785
855465808.
TÓM TẮT
BÀI TOÁN THUẬT PHÓNG TRONG CHO PHÁO 23 MM SỬ DỤNG ĐẠN ỐNG LỒNG
Bài báo xây dựng mô hình tính toán và kết quả giải bài toán thuật phóng trong cho đạn
ống lồng 23 mm. Các kết quả thu được cho thấy rõ ưu điểm của đạn ống lồng và là cơ sở
khoa học cho quá trình nghiên cứu lý thuyết để chế tạo và sử dụng đạn ống lồng 23 mm.
Từ khóa: Pháo 23 mm; Thuật phóng trong; Đạn ống lồng.
Received 22
nd
June 2020
Revised 30
th
July 2020
Published 5
th
February 2021
Author affiliations:
Le Quy Don Technical University.
*Corresponding author: thaidung1966@gmail.com.
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