7penna ammunition
Stop effect of the 7penna cartridges – estimation and rough comparison with usual types
of pistol cartridges
By:Drahomir Masa, 27^{th} January 2006
email
contact: drahomir.masa@seznam.cz
Independent
brief report
1)
The introduction:
I
came across a problem of an easy and credible assessment of a very unusual
ammunition stop effect for the first time in 1992 year.
I
met very interesting stop effect data samples published in two articles of the
Czech journal “Strelecka revue” (this title means „Shooting
revue” in English) at the time (volume12/1993 and 11/1998). The data contained
“One Shot Stop” probability (i.e. the OSS factor) for the most effective
types of cartridges. The data were based on the
statistics of Evan P. Marshall and Edwin J. Sanow and very clearly expressed
real value of the stop effect of the mentioned pistol cartridges.
Unfortunately,
although the specific statistic data had very high fidelity, it was impossible
to use them directly for assessment of unusual or new ammunition stop effect.
Therefore I tried to find a suitable stop effect criterion in order to easy
generalize the statistic data with high credibility. The statistically obtained
data were used for verification of the stop effect criterion then.
The
classic stop effect criterions based on energy or momentum of the bullet gave
insufficient results (the relations between the criterions values and the real
statistic values were rather indistinct).
That
was why I tried to evolve another easy mathematical model of a firearm bullet
stop effect. A quite sufficient version of the model and correspondent stop
effect criterion were evolved in 1999 year and released for public use in 2000
year (through the Czech journal “Strelecka revue” mentioned above –
volume2/2000).
I
came to know an information regarding parameters of 7penna cartridges recently.
To be honest I was very surprised at an unusual combination of a very high
velocity and low mass of the 7penna bullets. I supposed that the interesting
combination could represent low recoil (still acceptable for small guns) and
very good stop effect. On that ground I applied the mentioned method of the stop
effect estimation both to usual pistol cartridges and to 7penna cartridges and
compared obtained values each other then. The results of the calculation are
mentioned in this report.
2)
The description of the used stop effect criterion:
The
rather new stop effect criterion has two important advantages. Firstly the
criterion gives resultant values which can be directly compared with
statistically obtained OSS values (the criterion credibility can be therefore
clearly verified). Secondly the criterion evidently gives both very transparent
and quite realistic results for huge range of bullets ballistic parameters.
The
criterion can be used in a simplified or full form. The simplified using is
based on the diagram placed at the next page (“Stop Effect estimative diagram”).
The
quantity at the Xaxis is a product of:
i.e.
X = d^{2} ·m
·c^{4}
The
quantity at the Yaxis is a mean probability P
which is consistent with “One Shot Stop” probability i.e. with the OSS factor.
Note:
The
effective diameter is a “mean impact” diameter. If the bullet is rigid (and
stable) enough then the effective diameter approximately equals directly the
bullet calibre. If the bullet is not rigid or is not stable after its impact
upon the target then the effective diameter should be appropriately increased.
The
diagram was calculated exactly with the help of probability theory for different
number of shots. As a basic point for the calculation was used point with
coordinates X=4.4E12 mm^{2}g(m/s)^{4} and Y = P = 50% probability. It means the diagram was
constructed totally independently on the available specific statistical values (represented
as a “testing points” position).
These statistical values were used only for a “basic setting” of the diagram
through the basic point position estimation.
For
the diagram verification are into the diagram put “testing points” which
represent the mentioned statistically obtained OSS values. As you can see for
the criterion d^{2} ·m
·c^{4}
is the correspondence between the diagram and the statistical values really very
good. We have to take into consideration the fact the range of the bullets
ballistic parameters is extremely wide and the “testing points” position has
a significant uncertainty (the multiplying coefficient transforming the bullet
calibre to the bullet effective diameter which is used for expression of the
influence of the bullet plasticity was only very roughly estimated and the
statistical data have its own uncertainty too, for example).
The
diagram gives a possibility of:
the
stop effect rough estimation for new or unusual ammunition (including
shotgun effect at different distances from the muzzle mouth for example)
the estimation of impact of different shots number (“multiply shot”) on the stop effect.
the
estimation of impact of different muzzle length on the stop effect (it is
important especially for small selfdefence guns)
partially
a rough estimation of the stop effect for non lethal ammunition and guns
partially
a rough estimation of the stop effect for shooting at the person protected
with an armour jacket
the
estimation of the stop effect for shooting through another barrier
etc.
The
Stop Effect estimative Diagram:
(the
diagram is turned left for better graphic resolution of its printed version)
3) The tables of the cartridges approximate ballistic parameters, statistically obtained values (OSS), calculated vales and values taken from the
“Stop
Effect estimative diagram” (P):
The
data in the tables were used for the “Stop Effect estimative diagram”
verification and for estimation and comparison of the “7penna” cartridges
stop effect):
tab
no.1
– “rigid” bullets (the bullet form is not
highly changed after the bullet impact to the target)
col.A 
col.B the
bullet estim. eff.
diam. d [mm] 
col.C the
bullet mass m [g] 
col.D the
bullet velocity c [m.s^{1}] 
col.E d^{2}.m.c^{4} [
mm^{2}.g. (m/s)^{4}] 
col.F probability statis. (diag.) value OSS (P) [%] 
col.G m.c momentum h [g.m/s] 
col.H OSS/
h P/
h 10^{3} q [%
/ /(g.m/s)] 
32
AUTO FMJ 
8.1x1 
4.6 
280 
1.855E+12 
50 (36.5) 
1288 
38.82 (28.3) 
380
AUTO FMJ 
9.1x1 
6.1 (6.0
6.2) 
295 (290
300) 
3.8256E+12 
50 (47.5) 
1800 
27.78 (26.39) 
38
Spec. LRN 
9.1x x1.1 
10.2 
260 
4.6704E+12 
50 (51) 
2652 
18.85 (19.23) 
9
mm Luger FMJ 
9x1 
7.5 
350 
9.1162E+12 
60 (62.5) 
2625 
22.86 (23.81) 
45
AUTO FMJ 
11.5x x1 
14.9 
260 
9.0048E+12 
63 (62.5) 
3874 
16.26 (16.13) 
44
Spec. LRN 
11.2x
x1.1 
15.9 
230 
6.7535E+12 
67 (57) 
3657 
18.32 (15.59) 
45
Colt LRN 
11.5x
x1.1 
16.5 
260 
12.065E+12 
69 (68) 
4290 
16.08 (15.85) 
357Magnum LSWC 
9.1x x1.1 
10.2 
380 
21.31E+12 
70 (77) 
3876 
18.06 (19.87) 
added
items: 


7 
4.5 
435 
7.
8952E+12 
(60.5) 
1957.5 
(30.91) 

7 
5 
380 
5.1085E+12 
(52.5) 
1900 
(27.63) 

7 
3.2 
480 
8.3235E+12 
(62) 
1536 
(40.36) 

7 resp. 7x1.6* 
3.0 
530 
11.599E+12 resp. 29.693E+12 
(67) resp. (83) 
1590 
(42.14) resp. (52.20) 
Note: *
 a very roughly
estimated value to take into the calculation effect of a possible losing
of the bullet stability and sidewardmotion after its impact to the target 
The
approximate parameters of 7penna cartridges are in this table in red colour.
tab
no.2 – nonrigid
(expanding) bullets (the bullet form is
substantially changed after the bullet impact to the target)
col.A 
col.B the
bullet estim. eff.
diam. d [mm] 
col.C the
bullet mass m [g] 
col.D the
bullet velocity c [m.s^{1}] 
col.E d^{2}.m.c^{4} [
mm^{2}.g. (m/s)^{4}] 
col.E probability statis. (diag.) value OSS (P) [%] 
col.G m.c momentum h [g.m/s] 
col.H OSS/
h P/
h .10^{3} q [%
/ /(g.m/s)] 
38
Spec. LSWCHP 
9.1x2 
10.2 
260 
15.439E+12 
up
to 75 (73) 
2652 
28.28 (27.52) 
357
Magnum JHP 
9.1x2 
8.1 
440 
100.56E+12 
up
to 97 (96) 
3564 
27.22 (26.94) 
9
mm Luger HP 
9x2 
8 
345 (340
350) 
36.72E+12 
82 (86.5) 
2760 
29.71 (31.34) 
9
mm Luger JHP 
9x2 
7.5 
350 
36.47E+12 
76
– 81 (86.5) 
2625 
28.95
– 
30.86 (32.95) 
9
mm Luger +P JHP 
9x2 
7.5 
400 
62.21E+12 
up
to 90 (92.5) 
3000 
30 (30.83) 
45
AUTO HP
Hydra... 
11.5xx2 
15.6 
255 (250
260) 
34.893E+12 
88 (86) 
3978 
22.12 (21.62) 
45
AUTO JHP 
11.5xx2 
13 
280 
42.269E+12 
85 (87.5) 
3640 
23.35 (24.04) 
45
AUTO JHP 
11.5xx2 
12 
300 
51.418E+12 
up
to 84 (90.5) 
3600 
23.33 (25.14) 
tab
no.3 – nonrigid
(expanding) bullets (the bullet form is
substantially changed after the bullet impact to the target)
col.A 
col.B the
bullet estim. eff.
diam. d [mm] 
col.C the
bullet mass m [g] 
col.D the
bullet velocity c [m.s^{1}] 
col.E d^{2}.m.c^{4} [
mm^{2}.g. (m/s)^{4}] 
col.F probability statis. (diag.) value OSS (P) [%] 
col.G m.c momentum h [g.m/s] 
col.H OSS/
h P/
h .10^{3} q [%
/ /(g.m/s)] 
.357
Magnum JHP 
9.1x2 
8.1 
442 
102.4
E+12 
96 (96.5) 
3580 
26.8 (26.95) 
.40
S&W JHP 
10.2xx2 
8.7 
396 
89.034
E+12 
96 (96) 
3445 
27.86 (27.86) 
.45
ACP Federal
HS 
11.5xx2 
14.9 
260 
36.019
E+12 
94 (86.5) 
3874 
24.26 (22.33) 
9
Luger JHP
+P 
9x2 
7.5 
412 
70.015
E+12 
91 (93) 
3090 
29.45 (30.10) 
10
Auto JHP 
10x2 
9.7 
396 
95.414
E+12 
90 (96) 
3841 
23.43 (27.99) 
.44
Magnum ST 
11.2xx2 
13.6 
380 
142.28
E+12 
90 (98) 
5168 
17.41 (18.96) 
.41
Magnum ST

10.4xx2 
11.3 
380 
101.93
E+12 
89 (96.5) 
4294 
20.73 (22.47) 
.38
Special JHP 
9.1x2 
7.5 
380 
51.801
E+12 
83 (90.5) 
2850 
29.12 (31.75) 
.45
Colt LHP 
11.5xx2 
14.6 
275 
44.171
E+12 
78 (88) 
4015 
19.43 (21.92) 
.44
Special ST 
11.2xx2 
13 
247 
24.278
E+12 
75 (80) 
3211 
23.36 (24.91) 
0.380ACP/ 9
K JHP +P 
9.1x2 
5.8 
320 
20.145
E+12 
70 (77.5) 
1856 
37.72 (41.76) 
.38
Special LHP 
9.1x2 
10.2 
262 
15.92
E+12 
67 (74) 
2672 
25.07 (27.69) 
7.65 ST 
7.65xx2 
3.9 
296 
7.0083
E+12 
63 (58) 
1154 
54.57 (50.24) 
6.35
Browning JHP 
6.35xx2 
2.9 
250 
1.8271
E+12 
25 (36) 
725 
34.48 (49.66) 
Note:
The “testing points” coordinates in the “Stop Effect estimative diagram” are taken as values from columns col.E and col.F (black values) in the tables no.1, 2, 3.
4)
Bullets Stop Effect comparison:
In
order to compare values really consistent each other the probability “P”
values taken from the “Stop effect estimative diagram” were used for the
final comparison. The values (as well as the correspondent values of the “q”
quotient) were written in blue for “quite rigid” bullets and in green for
nonrigid bullets (meant as bullets with very high deformation after the bullet
impact).
For
using in small guns are extremely important gun recoil and therefore the bullet
momentum. The momentum “h” is mentioned in column col.G
of the tables.
The
“q” quotient is a ratio between
the stop effect expressed as a probability “P”
and the momentum ”h”.
For better comparison were the values put into diagrams h – P and h – q. A rough limit of the momentum “h” maximum acceptable value (regarding acceptable recoil of small and light guns)
is
marked with a yellow arrow. The limit was really very roughly estimated as 1300
– 1900 gm/s. The diagrams are placed at the next page:
Diagram no.1
Diagram no.2
5)
Brief discussion of the obtained values:
I
think the 7penna (especially its brass version) represents a cartridge with
rigid form of bullets. But contrary to the fact the 7penna stop effect exceeds
all compared cartridges with rigid bullet and comes up to stop effect value of
cartridges with nonrigid bullets.
Its
stop effect for maybe possible sideward moving after impact to the target is
even higher than stop effect of all compared nonrigid bullets.
6)
Conclusion:
Regarding
small (and appropriately light) selfdefence handguns 7 penna cartridges have
–in my opinion an absolutely real chance to become the most effective
ammunition in the world. There are cartridges with substantially higher stop
effect but these cartridges cannot be used in small (and usually rather light)
defensive guns such as small semiautomatic “lady’s pistols”, derringers,
special guns as Spanish “Pressin”, speak nothing of “micro guns” as
“shooting pens” etc. Small revolvers are maybe slightly less suitable due to
an additional loss of bullet kinetic energy (caused by axial clearance between
the revolver muzzle and the cylinder).
The
stop effect of 7penna cartridges with rigid bullet is similar as the stop effect
of common cartridges with nonrigid (expanding) bullets. This circumstance seems
me to be extremely important especially in the countries where expanding/expansive
bullets cannot be used for common citizen defence (due to local law reasons).