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    

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 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 fire-arm 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 X-axis is a product of:

i.e. X = d2 ·m ·c4

The quantity at the Y-axis 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 mm2g(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 d2 ·m ·c4 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 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

d2.m.c4

[ mm2.g.

(m/s)4]

col.F

proba-bility

statis.

(diag.)

value

OSS

(P)

[%]

col.G

m.c

momen-tum

h

[g.m/s]

 

col.H

OSS/ h

P/ h

 103

 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 – non-rigid (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

d2.m.c4

[ mm2.g.

(m/s)4]

 

col.E

proba-bility

statis.

(diag.)

value

OSS

(P)

[%]

col.G

m.c

momen-tum

h

[g.m/s]

col.H

OSS/ h

P/ h

.103

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 – non-rigid (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

d2.m.c4

[ mm2.g.

(m/s)4]

 

col.F

proba-bility

statis.

(diag.)

value

OSS

(P)

[%]

col.G

m.c

momen-tum

h

[g.m/s]

col.H 

OSS/ h

P/ h

.103

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 H-S

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 non-rigid 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 non-rigid bullets.

Its stop effect for maybe possible sideward moving after impact to the target is even higher than stop effect of all compared non-rigid bullets.

6) Conclusion:

Regarding small (and appropriately light) self-defence 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 non-rigid (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).

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