Dynamic analysis of firing mechanism of underwater pistol
Tính toán và phân tích động lực học của cơ cấu phát hỏa là một vấn đề rất quan trọng trong tính toán thiết kế súng ngắn bắn dưới nước. Trên cơ sở phân tích hoạt động của súng ngắn dưới nước, bài báo trình bày một mô hình lý thuyết để phân tích động lực cơ cấu phát hỏa súng ngắn bắn dưới nước có kể đến ảnh hưởng do lực cản của nước tác động lên khóa nòng và kim hỏa. Kết quả nghiên cứu của bài báo có thể ứng dụng trong tính toán thiết kế súng ngắn và súng tiểu liên bắn dưới nước.
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TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 20, SỐ K2-2017
61
Abstract — The important problem of designing
underwater pistol was analysed and calculated the
dynamics of firing mechanism. On the basis of
analyzing the performance of the underwater pistol,
the paper presents a theoretical model for analysing
the dynamics of firing mechanism of underwater
pistol with the with the resistance of water acting on
firing pin and slide. The result of this research can be
applied to design the underwater pistol and
underwater firearm.
Index Terms—Dynamics, Firing mechanism ,
Resistance of water, Underwater pistol.
1 INTRODUCTION
HE underwater pistol is designed to destroy
enemy personnel at ranges of up to 20m under
water (depending on diving depth) [1]. Firing under
water is possible from all swimmer positions as
well as against surface targets from under water.
The pistol is intended for combat swimmers. Two
kinds of typical underwater pistol current are
HKP11 of Germany (Fig.1a) and SPP-1M of
Russian (Fig.1b) [2].
In Vietnam, the research on underwater pistol is
limited and water commando forces have not been
equipped with this weapon. The researches are
mainly focused on projectile's motion under water.
So design underwater pistol has become a hot topic.
Manuscript Received on July 13th, 2016. Manuscript Revised
December 06th, 2016.
This research is funded by the state-level project “Design and
manufacture underwater pistol and projectile to serve the water
commando forces” code: KC.03.TN08/11-15. We are also
grateful to our colleagues from Department of Weapons for
valuable discussions which help to conduct the study.
Dung Nguyen Thai is Dean of the Faculty of Weapons
and Director of the Technical Center for Weapons, Military
Technical Academy (e-mail: thaidung1966@gmail.com).
Hung Nguyen Van is with the Department of Weapons,
Faculty of Weapons, Military Technical Academy (e-mail:
hungnv_mta@mta.edu.vn).
In the design process, the dynamic analysis of firing
mechanism is a fundamental problem and very
important [3]. So the article focuses on solving this
problem with the research object is firing mechanism
of SPP-1M underwater pistol.
a)
b)
Figure 1. Two kinds of typical underwater pistol
a. HKP11 underwater pistol; b. SPP-1M underwater pistol
2 DYNAMIC MODEL OF FIRING MECHANISM OF
UNDERWATER PISTOL
The principle of operation of firing mechanism
of underwater pistol based on the operation of
typical pistol but it is improved to reduce the
resistance of water [4]. The firing mechanism of
underwater pistol consists of: trigger, slide, slide
latch, firing pin, and return spring [5,6,7,8]. Fire
process comprising two stages (fig.2):
Stage I: Slide and firing pin moves backward.
After pulling the trigger, trigger (1) motions and
impacts on B point on the slide (3) to make slide
and firing pin moving backwards. Stage I ended
when the catch (2) is not contact with B point on on
the slide.
Stage II: Slide and firing pin moves forward.
After the catch (2) is not contact with B point, Slide
(3) and firing pin (4) move forward under the
Dynamic analysis of firing mechanism of
underwater pistol
Dung Nguyen Thai, Hung Nguyen Van
T
62 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 20, No.K2- 2017
action of recoil force of the spring. Firing pin
moving forward and strike the primer on bullet to
fire.
Figure 2. Structural diagram of firing mechanism of underwater
pistol
1. Trigger; 2. Slide latch; 3. Slide; 4. firing pin; 5. return spring.
The dynamic model of firing mechanism of
underwater pistol is built on the basis of the
following assumptions:
1. The objects in the firing mechanism are
absolute hard.
2. Ignore the resistance of water acting on the
objects rotation in mechanism (Trigger and Slide
latch).
3. Ignore the resistance of water acting on the
return spring and Slide.
4. Ignore friction force acting on the objects
when moving.
5. In stage II, Silde and firing pin are blocked
into an object with mass is 3,4m and it move
forward. Hence the model of firing mechanism is
simple model as shown in firgure 3.
6. Angular velocity of Trigger around origin
O is constant.
In order to analyse dynamics of firing
mechanism, at first we consider kinematic in stage
I. In Fig.2 it is seen that:
2 1
3 2 1
os os
sin sin
Bx l c l c
e l l
=
=
(1)
Derivative equation system 1 we obtain:
1
3 2 1
os (tan tan )
sin sin
Bx l c
e l l
= -
=
(2)
Derivative equation system 2 we obtain:
1 2
3 2 1
(tan tan )
os
(1 tan tan )
sin sin
Bx l c
e l l
= -
-
=
(3)
In equation systems (1), (2), (3): 2
In stage I, external forces acting on the systerm
as follows (Fig.1):
1. Elastic force of the return spring F .
2. The Moment of trigger pull of the gunner
pM .
3. The resistance moment of trigger spring RSM .
Assumption uM is useful moment acting on
trigger to fire, we have:
1 os (tan -tan )-Mu p RSM M Fl c = -
(4)
The total kinetic energy of the system given by
[9]:
1 2 3
2 2 2 2 2 2
1 2 1 3,4 1
2 2 2 2
1 2 1 3,4 1
1 1 1
J os (tan tan )
2 2 2
1
[J os (tan tan ) ]
2
T T T T
m l m l c
m l m l c
= =
=
=
(5)
where: 1 2 3, ,T T T are the kinetic energy of Trigger,
Slide latch and Slide
1J is the moment of inertial of Trigger.
2m is the mass of Slide latch.
3,4m is the total mass of slide anf firing pin.
The dynamic equations of firing mechanism are
in the Lagrangian form given by [10]:
u
d T T
M
dt
- =
(6)
From Eq. (4), (5), (6) we have:
2 2 2 2
1 2 1 3,4 1
2 2
3,4 1
2
1
os (tan tan )
1
[sin2 (tan tan ) 2sin2
2
2(tan tan )]
os (tan -tan )-Mp RS
J m l m l c
m l
M Fl c
-
= -
(7)
Because the angular velocity of Trigger is
constant (assumption 6), so 0 = . From Eq.7 we
obtain:
1
2 2
3,4 1
2
os (tan -tan )+M
1
[(tan tan ) sin 2 2sin2
2
2(tan tan )]
p RSM Fl c
m l
=
-
(8)
In stage II, the article only studying the dynamic
of firing pin. So from the Fig.3 we have:
3,4 1 2( ) ( )m x H x k R R= - - (9)
where 3,4m is the total mass of slide and firing pin.
H is the original length of the spring.
k is a constant factor characteristic of the spring.
TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 20, SỐ K2-2017
63
1 2,R R are resistance forces of water acting on
firing pin and its are determined by the formula
[11]:
2
1 1 1
2
2 2 2
1
2
1
2
d
d
R A C x
R A C x
=
=
(10)
where 1 2,A A are the area of firing pin at nose and
body; is density of water; x is velocity of firing
pin; 1 2,d dC C are drag coefficient. Because the
shapes of nose and body section of firing pin are
the same, so:
1 2
1.2d d dC C C= = =
Figure 3. Model of firing mechanism of underwater pistol in
stage II
From Eq.9, 10 we have:
2
3,4 1 2
2
1
( ) ( )
2
1
( )
2
d
d
m x H x k C A A x
H x k C Ax
= - -
= - -
(11)
where 1 2A A A= is the section area of firing pin.
Initial conditions to solve equations (11) are:
0(0) 0; (0)x x x= = . So the dynamic equations of
firing pin in stage II are:
TABLE 1
INPUT PARAMETERS
No. Items
Symb
ol
Unit Value
1
Geometric dimensions
(Fig.2)
1l mm 16.9
2l mm 44.4
e3=e1-e2 mm 1.2
1
Mass of slide and firing
pin
3,4m
kg 0.08
2
Resistance moment of
trigger spring
RSM
N/mm
0.14.
10-3
3
Constant factor
characteristic of the spring k N/mm 0.65
4 Mass of cartridge case Mvd kg 0,091
5
Angular velocity of
Trigger rad/s 1
6
Section area of firing
pin A mm
2 254.7
7
Original length of the
spring H mm 220
8 Density of water kg/m3 1030
9 Drag coefficient dC 1.2
2
3,4 3,4 3,42
dC A k Hkx x x
m m m
-
= -
(12)
3 CALCULATION RESULTS AND DISCUSSION
For the purpose of presenting results of solution,
we chose object is the firing mechanism of SPP-1M
underwater pistol. The values of the input
parameters to analyse are listed in table 1.
The results calculated of displacement, velocity
and acceleration of slide with 0 0270 ,320 in
stage I shown in figure 4. The displacement,
velocity, acceleration of slide and firing pin with
0,6t ms in stage II shown in figure 5. We can
see maximum velocity of slide in stage I is 18.29
mm/s at 0289.9 = .
4.712 4.8 4.887 4.974 5.061 5.149 5.236 5.323 5.411 5.498 5.585
40
41.6
43.2
44.8
46.4
48
49.6
51.2
52.8
54.4
56
Displacement ( )
180deg
(a)
4.712 4.8 4.887 4.9745.061 5.149 5.2365.323 5.411 5.498 5.585
14.5
14.9
15.3
15.7
16.1
16.5
16.9
17.3
17.7
18.1
18.5
18.29
Velocity ( )
5.057
180 deg
(b)
4.712 4.8 4.887 4.974 5.061 5.149 5.236 5.323 5.411 5.498 5.585
15-
12.7-
10.4-
8.1-
5.8-
3.5-
1.2-
1.1
3.4
5.7
8
Acceleration ( )
180 deg
(c)
Figure 4. Displacement, velocity and acceleration of slide in
stage I
64 SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 20, No.K2- 2017
a. Displacement; b. Velocity; c. Acceleration
0 1.2 10
3-
2.4 10
3-
3.6 10
3-
4.8 10
3-
6 10
3-
0.078
0.0802
0.0824
0.0846
0.0868
0.089
0.0912
0.0934
0.0956
0.0978
0.1
x t( )
t
a)
0 1.2 10
3-
2.4 10
3-
3.6 10
3-
4.8 10
3-
6 10
3-
0
0.7
1.4
2.1
2.8
3.5
4.2
4.9
5.6
6.3
7
t
x t( )
d
d
t
b)
0 1.2 10
3-
2.4 10
3-
3.6 10
3-
4.8 10
3-
6 10
3-
100
299
498
697
896
1.095 10
3
1.294 10
3
1.493 10
3
1.692 10
3
1.891 10
3
2.09 10
3
2
t
x t( )
d
d
2
t
c)
Figure 5. Displacement, velocity and acceleration of slide and
firing pin in stage II
a. Displacement; b. Velocity; c. Acceleration
4 CONCLUSION
Through analysis of operating characteristics,
building mathematical model for analysing the
dynamic of dynamic of firing mechanism of
underwater pistol and application with the SPP-1M
underwater pistol, we see that the calculation results
was suitable for the fact. Therefore, the theoretical
model of the article has been presented is model
have high accuracy and can be applied to design the
underwater piston and underwater firearm and
amphibious assault rifle. The research results of
this paper have been used in the state-level project
“Design and manufacture underwater pistol and
projectile to serve the water commando forces”
code: KC.03.TN08/11-15.
REFERENCES
[1] “Firearms Technical Trivia”, cruffler.com, 2001.
[2] “4.5mm SPP-1M Underwater Pistol”, TsNIITochMash,
2010.
[3] Bộ môn súng pháo, “Nguyên lý thiết kế súng tự động”,
Tập 3, Trường Đại học Kỹ thuật quân sự, 1977.
[4] Võ Ngọc Anh, “Động lực học vũ khí tự động”, Học viện
Kỹ thuật quân sự, 1995.
[5] Popenker, Max R, “SPP-1 underwater pistol”,
world.guns.ru, 2010.
[6] T. O. Zavod(TOZ), “Special Submarine Pistol SPP-1M”,
Tula Arms Plant, 2010.
[7] “SPP-1 and SPP-1M underwater pistol 4.5mm”,
www.securityarms.com,2010.
[8] Bộ môn súng pháo, “Nguyên lý thiết kế súng tự động”,
Tập 1, Trường Đại học Kỹ thuật quân sự, 1974
[9] Nguyễn Đông Anh, “Động lực học hệ vật rắn”, Nhà xuất
bản xây dựng, 2000.
[10] P. D.Benzkofer, “Dynamic analysis of shoulder-fired
weapons”, Proceedings of the seventh U.S.Army
symposium on gun dynamics, p205-225, U.S.Army, 1993
[11] A.M. Mackey, “A mathematical model of water entry”,
AUWE Technical Note, No.636179,1979.
Dung Nguyen Thai was born
in Vinh Phuc Province, Viet
Nam in 1966. He received the
B.S. and M.S. degrees in
weapon engineering from the
Military technical Acedemy,
Viet Nam, in 1990 and the
Ph.D. degree in mechanical
engineering, in 2002.
From 2001 to 2004, he was a Lecturer with the
Department of Weapons, Faculty of Weapons,
Military Technical Academy. Since 2010, he has
been an Asscociate Professor. He is the author of
nine books, more than 40 articles. His research
interests include design and improvement of guns
and rocket motor. He is Dean of the Faculty of
Weapons and Director of the Technical Center for
Weapons, Military Technical Academy.
Hung Nguyen Van was born
in Thanh Hoa Province, Viet
Nam in 1985. He received the
B.S. and M.S. degrees in
weapon engineering from the
Military technical Acedemy,
Viet Nam, in 2009. He is
lecturer of the Department of
Weapons, Faculty of Weapons,
Military Technical Academy. He is the author of
three books, more than 10 articles. His research
interests include design of special ammunition and
guns.
TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 20, SỐ K2-2017
65
Tóm tắt - Tính toán và phân tích động lực học
của cơ cấu phát hỏa là một vấn đề rất quan
trọng trong tính toán thiết kế súng ngắn bắn
dưới nước. Trên cơ sở phân tích hoạt động của
súng ngắn dưới nước, bài báo trình bày một mô
hình lý thuyết để phân tích động lực cơ cấu phát
hỏa súng ngắn bắn dưới nước có kể đến ảnh
hưởng do lực cản của nước tác động lên khóa
nòng và kim hỏa. Kết quả nghiên cứu của bài
báo có thể ứng dụng trong tính toán thiết kế
súng ngắn và súng tiểu liên bắn dưới nước.
Từ khóa - Động lực học, Cơ cấu phát hỏa, Lực cản
của nước, Súng ngắn bắn dưới nước.
Phân tích động lực học cơ cấu phát hỏa
của súng ngắn bắn dưới nước
Nguyễn Thái Dũng, Nguyễn Văn Hưng
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