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WWW.STILETTO.UK.COM
INCREASE IN EFFECTIVENESS
OF SMALL-ARMS AMMUNITION
9x19 mm Luger
INCREASE IN EFFECTIVENESS
OF SMALL-ARMS AMMUNITION
Performance improvements to weapons systems are driven by the need for
Increased accuracy and precision, a decrease in the number of errors while
preparing to fire and an increase in projectile penetration capability.
Improvements in ballistic armour (armoured/bullet-proof jackets) have led to
the gradual decrease in the effectiveness of small arms to incapacitate threats.
In general the effectiveness of small arms ammunition depends on the
armour-piercing core of ammunition: the quality of core material, its form
and importantly the kinetic energy being delivered.
This article analyses issues regarding the enhancement of projectile
penetration by means of increasing projectile initial speed.
www.stiletto.uk.com 1
INTRODUCTION
RESEARCH
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Fig. 1. Design of the
Improved Bullet [6].
nozzle
cavity for gun charge
Different techniques available and capable of increasing the initial speed of
projectiles are known. This article analyses one of these techniques, increasing the
boosting pressure without modification of propellant or ammunition structure.
In the course of research it has been revealed that due to ammunition structures,
projectile initial speed may be increased by the motion of propellant gases coming
from the projectiles charge chamber into an after-projectile channel space at the
moment of firing. This means that a rocket gas-dynamic effect is available.
The operating principle of the improved projectile is identical to existing projectiles
except for the fact that it is does not fragment and in the process of burning the
propellant, impinging gases flow through a hole in the nozzle block and creates
propulsive burn numerically equal to the product of speed of gas discharge by their
weight. Due to this, the projectile receives additional impulse to the initial speed in
comparison to existing projectiles.
To better understand the effect emerging, we are going to analyze the simplified
system of differential equations of internal ballistics, which looks as follows:
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where
- I means impinging gases pressure pulse,
- t means time,
- P means pressure of impinging gases,
- θ means indicators of adiabatic of combustion products,
- f means force of powder,
- ω means weight of powder,
- Ψ means powder burning function,
- φ means fictitiousness coefficient which takes into
consideration all secondary operations except
for the operation on movement of the propellant charge,
- m means bullet weight,
- V means bullet current speed,
- S means bullet cross-section area,
- LΨ means function of the length of the charge chamber,
- L means current path travelled by the bullet,
- P0 means boosting pressure.
пппп
о
пппп
н
м
по
пн
м
-ЧЧ
Ј
==
+Ч
ЧЧ-
ЧЧ
Ч==
т тt t
dtPPdtm
S
PPесли
Vdt
dL
LLS
Vmf
Pdt
dI
0 0
0
0
2
)(
......0
)(2
j
j
q
fw
qf
,
(1)
However, as it is proved in practice, such measures do not lead to the significant
increase in the initial speed of the projectile.
As seen in (1) mathematical equation, which describes the main task of internal
ballistics, the equation does not take into account the motion energy of
propellant (powder) gases inside the bore at the moment of firing. In the
projectile scheme offered (Fig. 1), as was already mentioned, the propellant
charge is located directly in the projectile. In the process of burning propellant
gases the flow to the after-projectile space of the bore through the rear
calibrated orifice takes place. Due to this, jet propulsion emerges. Consequently
it is fair if the relevant adjustment is made to the mathematical model examining
internal ballistics.
For this purpose, we are going to consider the formula of gas-dynamic forces
acting on the projectile according t:
g
GVPSF газ Ч+Ч= .1
(2)
Where
- F means gas-dynamic force acting on a bullet;
- P1 means pressure on a bullet;
- Vgas means speed of flow of gas from the
bullet nozzle;
- G means rate of flow of combustion products
from the nozzle block of the bullet;
- g means gravity acceleration.
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We are multiplying the right and the left parts of the equation (4)
by the time of action of this force t. The result is as follows:
But this is the equation of the quantity of bullet motion under the
action of gas-dynamic force. Then for this case, we are going to
modify some factors (multipliers):
After substitution, the formula (2) looks as follows:
In the result, we have received the equation of the quantity of bullet
motion which is different from the classic formula by the reactive
(jet/rocket) component:
Now, since propellant charge in experimental cartridges is in the
bullet charge chamber, and as it burns, it leaves it, the bullet weight
(weight of the propellant/powder charge is added to the bullet weight)
is a variable depending on the function of powder burning:
g
tGVgastPStF
ЧЧ+ЧЧ=Ч .1
(3)
jЧЧ=Ч mVtF , and т т-=Чt t
dtPPdttP0 0
01 and fw Ч=Ч
g
tG ,
(4)fwj ЧЧ+-Ч=ЧЧ т т газ
t t
VdtPPdtSmV0 0
0 )( ,
fw ЧЧgasV .
)1(__ fwfww -Ч+=Ч-+= mmweightbulletfull . (5)
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Consequently taking into consideration above mentioned, after simple
conversions, the formula (4) looks finally as follows:
And identically
Finally, equation of the main task of internal ballistics will look as follows:
Now, we are going to make final calculations based on the new mathematical f
ormula and compare calculations with the experimental data. Before this, we
are going to set parameters for boosting pressure and the coefficient of
fictitiousness for the projectile. The speed of gas flow from the projectile
charge chamber into the after-projectile space bore will be taken as equal
to the speed of projectile.
(6)
(7)
(8)
[ ])1(
)(0 0
0
fwj
fw
-Ч+Ч
ЧЧ+-Ч
=т т
m
VdtPPdtS
Vгаз
t t
[ ]
)(2
)1( 2
LLS
Vmf
P+Ч
Ч-Ч+Ч-
ЧЧ
Ч=f
fwj
q
fw
q
[ ]
[ ]пппп
о
пппп
н
м
пп
о
пп
н
м
-Ч+Ч
ЧЧ+-Ч
Ј
==
+Ч
Ч-Ч+Ч-
ЧЧ
Ч==
т т
)1(
)(
......0
)(2
)1(
0 0
0
0
2
fwj
fw
fwj
q
fw
qf
m
VdtPPdtS
PPесли
Vdt
dL
LLS
Vmf
Pdt
dI
газ
t t
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Boosting pressure.
Since the sub-calibre projectile does not run into the main bore in our case, the
gripping force is unavailable. Therefore, boosting pressure will work on ejection
of the projectile from the cartridge case (jacket). Mean statistical gripping force
of the projectiles from cartridge casing is equal to 220 kgs. If we consider the
projectile under the action of propellant gases is squeezed in the case by its ring,
and the width of the ring squeezing is known and knowing the coefficient of
friction of the ring against the case (according to the coefficient of friction of
cadmium-plated projectile against the steel case f = 0,096 ~ 0,1), it is possible
to calculate the value of the force required to get the projectile moving.
Knowing these values we can produce the following equation:
After putting the values into the formula (9), we receive P0 = 901,64 kgs/cm2.
)( 21
0fSS
FP
Ч-= (9)
where
- F means force of ejection of the bullet
from the case (220 kgs);
- S1 means working cross-section area of
the bullet (with the internal diameter of the c
harge chamber of 8,4 mm - S1 ~ 0,554 cm2);
- S2 means external are of the bullet ring,
by which it is squeezed to the case (with
the bullet diameter of 9 mm and width of the
squeezing component of 11 mm - S2 ~ 3,1 cm2);
- F means friction coefficient ~ 0,1.
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Mark on the projectile from the main bore
Fig. 2. Comparative picture of the projectiles (normal projectile is on the left,
Stiletto projectile is on the right) with the marks from the main bore.
Coefficient of fictitiousness.
Since it is not fully known how to calculate the fictitiousness coefficient for
the new projectile design, in our calculations we will take it as equal to
the operating projectile.
After calculations, we have the following outcome:
(6)
(7)
Mark on the Bullet from the Main Bore
L = 11 mm
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Fig. 3. Chart showing dependence of the pressure in the bottom of the case
upon the burst time with the experimental cartridge according to the modified
mathematical model.
Fig. 4. Chart showing dependence of the projectile speed along the length
of the bore at the time of firing according to the modified mathematical model.
0 5 .104
0.001 0.0015 0.002 0.0025 0.003 0.0035 0.0040
500
1000
1500
2000
2500Ãðàôèê äàâëåí èÿ ï î ðî õî âûõ ãàçî â
Âðåì ÿ (ñ)
Äàâë
åíèå
ïî
ðîõîâû
õãàç
îâ
(êãñ/
ñì
^2
)
2.467 103
ґ
59.313
Päóë
4 103-
ґ4.365 104-
ґt1 r
0 0.02 0.04 0.06 0.08 0.1 0.120
100
200
300
400
500
600Ãðàôèê ñêî ðî ñòè ñí àðÿäà ï î äëèí å ñòâî ëà.
Äëèí à ñòâî ëà (ì )
Ñê
îðîñ
òüñí
àðÿä
à(ì
/ñ)
510.678
0
Vvvv
0.1060.013 Lñò
pow
der
gas
pre
ssure
kgf/cm
2
time
pro
ject
ile v
elo
city
(m
/ s
)
Barrel Length (m)
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It is seen from the calculations that due to such a scheme of ammunition
design the projectile must have high initial speed in comparison with the
projectiles of identical cartridges.
Practical firing has demonstrated the following results.
Cartridges with Stiletto projectiles have preliminary undergone comparative
testing in the Laboratory of Criminal Expert Examination at the State Scientific
and Expert Criminal Research Centre of the Ministry of Internal Affairs of the
Ukraine, in the city of Vinnytsia and the Lugansk Cartridge Plant. Based on
the approved methodology of enterprises, the following measurements
were made:
-Projectile initial speed;
-Free blowback energy;
-Maximum pressure in the bore at the time of firing.
At the same time, the following mean values have been received (Table 1):
As it is seen from Table 2, theoretical calculations coincide with the
data of practical firing.
Table 1. Type of cartridge
Type ofweapon
Mean bullet initial speed
(m/sec)
Free blowback energy
(J)
Maximum pressure in the
bore (kgs cm2)
9,0 mm Пст гс Gun “PM” 317 3,67 - 9,0 mm Пст гс Gun“FORT” 316 3,36 - 9,0 x 18 mm experimental
upgarded
Gun “PM” 514 4,8 2439
Table 2.
Type of cartridge
Measured bullet initial speed
(m/sec)
Calculated bullet initial
speed (m/sec)
Measured maximum
pressure in the bore
(kgs cm2)
Calculated maximum
pressure in the bore
(kgs cm2 9,0 x 18 mm experimental
514
510,678
2439
2467
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The result of increased projectile initial speed due to energy flow of propellant
gas from the charge chamber into the after-projectile space of the bore,
has increased projectile penetration of the new projectile in comparison with
existing projectiles [6].
The new design (Fig. 1) ensures penetration at the distance of 25 meters of steel
plate (Ст. 3) 7 mm wide (Fig. 6) which is an analogue of the ballistic protection
of 4nd class protection armoured jacket [16].
1 2 3
4 5 6 Fig. 5. Target steel plate after conducting the experiment.
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1, 4, 6 are imprints received after firing from a «ТТ» gun with the standard
operating cartridge (projectile with the steel core);
2 is the imprint received after firing from a P – 38 «Walter» gun with
the standard operating cartridge (projectile with the steel core);
3 is penetration from a «Makarov» gun with the experimental cartridge;
5 is an imprint received after firing from gun «Makarov» with the
standard operating cartridge (projectile with the steel core).
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Entrance hole.
Exit hole.
Penetration of hardened steel plate 7 mm at distance of 25 мeters
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Penetration of hardened steel plate 7 mm at distance of 25 мeters
Entrance hole.
Exit hole.
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CONCLUSION
As the result of research performed, it is determined that it is possible to
control the flow of propellant gases in the bore. In the process of such flow
reactive (jet) components emerge, which significantly increases the initial
speed of the projectile.
Use of this new design allows making of ammunition with enhanced fighting
power for existing types of small arms.
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