in3
3
3
lb/s
2
t
dF
m
d
m/d
d
d
d
d
d
md/t
F/d2
md3/t
Fm/d
lead
1122
0.0021
112
40
0.223
0.114
0.769
1.0
6.2
7.2
14.37
0.039
6
17
1.30
1
1
9
13
.223 Rem.
Jacketed SP
3150
0.0005
1101
50
0.224
0.142
1.110
18.0
67.0
84.0
9.25
0.039
23
141
1.09
5
12
13
156
.30-30 Win.
Jacketed FP
2017
0.0015
1536
170
0.308
0.256
0.910
8.7
228.6
237.3
17.72
0.075
49
432
0.54
15
36
11
393
12ga.
lead
1513
0.0016
2222
437
0.693
0.130
0.952
2.2
66.8
69.0
14.17
0.377
94
304
2.68
65
25
11
289
.308 Win.
Jacketed SP
2923
0.0009
2846
150
0.308
0.226
1.110
117.0
301.0
418.0
16.54
0.075
63
581
0.57
19
48
13
643
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
UOM
Pi
d/t
.22 LR
Dimensions
IPF
IPF*
in2
TKO
in
Calculation
in3
3
Calculation
in3
2
M
Twc
lb/in2
Bullet Area
twc
in
Penetration
pwc
gr
Design Function
f t-lbf
Sectional Density
Et
s
Caliber
Impact time
f t/s
Bullet Weight
Impact Velocity
Bullet
Cartridge
Input Values
lbf/in2
12ga.
.308 Win.
Correlation Coef f icient
M:pwc
M:twc
M:Twc
IPF:pwc
IPF:twc
IPF:Twc
TKO:pwc
TKO:Twc
IPF*:pwc
IPF*:twc
16
8
126
0.4
1
36
6
1
1
17
3
2
1
4
5
1.38
4.48
5.04
16
13
119
65
2
15
128
1
3
4
8
2
2
4
13
17
0.65
5.71
16.67
15.73
IPF*:Twc
Penetration:TKO
18
61
TKO:twc
Penetration:M
112
Penetration:IPF
Penetration:sd
4
Et:Penetration
.30-30 Win.
3
Et:Twc
.223 Rem.
2
Et:twc
.22 LR
1
Et:pwc
Cartridge
Proportions
177
7
6
87
69
3
24
202
6
5
5
50
2
2
1
15
16
4.14
6.35
1010
33
32
157
109
7
21
173
43
1
1
138
5
4
0.03
1
1
11.49
2.64
1.05
24
9
7
172
73
4
35
259
1
5
7
5
2
1
6
16
22
0.41
6.23
21.67
0.682
0.734
0.756
0.362
0.682
0.347
0.640
0.147
0.147
0.224
0.382
0.355
0.946
-0.615
-0.098
-0.020
-0.044
0.711
0.946
0.925
where as:
Et is translational kinetic energy (mv2/2gc) in foot-pound force
pwc is Permanent Wound Channel Volume in cubic inched
twc is Temporary Wound Channel Volume in cubic inches
Twc is Total Wound Channel Volume in cubic inches
M is Momentum in pound force per second
Pi is The internal peak pressure in pounds per square inch
IPF is Impact Penetration Factor (as a value only)
IPF* is Impact Penetration Factor properly set to all dimensions (not a reconsigned
measurement)
TKO is Taylor knock-out value (not a reconsigned measurement)
sd is Sectional density in pounds per cross section squared
ft/s is feet per second
ft-lbf is foot-pound force
gr is grains
in3 is inches cubed
in is inch
in2 is inches squared
s is second
lb is pound
F is force
m is mass
d is distance
t is time
mv is mass times velocity
m/d2 is sectional density as mass per diameter squared
Fm/d is not a reconsigned dimension
md3/t is not a recognized term
F/d2 is pressure
Design Function (id) is a value assigned to a bullet to represent its construction at a
specific impact velocity (not a reconsigned factor)
mv2/2gc is mass times velocity squared divided by half times the dimensional constant
gc is the Dimensional Constant of 32.163 based on the local acceleration of gravity
All dimensions, terms and Units of Measure (UOM) are in Imperial units or from the English
Engineering System (FMLO)
Correlation Coefficient
High Correlation:
0.50 to 1.00
Medium Correlation:
0.30 to 0.49
Low Correlation:
0.10 to 0.29
No Correlation:
0.00 to 0.09
Analysis
This comparison in mainly concerned with the relationship between a wound channel and
translational kinetic energy measurements (aka kinetic energy values). However, in the interest of other
competing measurements and values, I put them in mix to be tested. As stated, one of those vales is the
Impact Penetration Factor (IPF) I developed myself.
The input values supplied by the drawings are: Cartridge, Bullet, Impact Velocity, Caliber,
Bullet weight and Penetration. The input values supplied by Mr. R. Wakeman are: Translational kinetic
energy measurement and Taylor knock-out values. The input values supplied by myself are: Impact
time, Sectional density, Permanent wound channel volume, Temporary wound channel volume, Total
wound channel volume, Bullet area, Momentum measurement, Peak internal pressure, Impact
Penetration Factor value and Impact Penetration Factor measurement when set correctly for feet.
The proportions including their Correlation Coefficient are:
1. Correlation of translational kinetic energy to the permanent wound channel .628 (High)
2. Correlation of translational kinetic energy to the temporary wound channel .734 (High)
3. Correlation of translational kinetic energy to the total wound channel .756 (High)
4. Correlation of translational kinetic energy to the penetration .362 (Medium)
5. Correlation of penetration to the sectional density .682 (High)
6. Correlation of penetration to the momentum .347 (Medium)
7. Correlation of penetration to the IPF .640 (High)
8. Correlation of penetration to the TKO .147 (Low)
9. Correlation of momentum to the permanent wound channel .147 (Low)
10. Correlation of momentum to the temporary wound channel .224 (Low)
11. Correlation of momentum to the total wound channel .382 (Medium)
12. Correlation of IPF to the permanent wound channel .355 (Medium)
13. Correlation of IPF to the temporary wound channel .946 (High)
14. Correlation of IPF to the total wound channel .615 (High)
15. Correlation of TKO to the permanent wound channel .098 (None)
16. Correlation of TKO to the temporary wound channel .020 (None)
17. Correlation of TKO to the total wound channel .044 (None)
18. Correlation of IPF* to the permanent wound channel .711 (High)
19. Correlation of IPF* to the temporary wound channel .946 (High)
20. Correlation of IPF* to the total wound channel .925 (High)
Here is the Design Function values from my book used in this comparison:
Design Type
Impact Velocity
Id.
shotgun slug
1400 to 1800fps
.952
cast lead
1100 to 1400fps
.769
jacketed flat point 1400 to 2100fps
.910
jacketed soft point 2700 to 2900fps
1.11
This is just a hand full of Design Functions values (id); there are 104 and growing.
So the first thing to look at is the sample. Not to beat a dead horse but I want to make this clear.
The five drawings used for comparison were defiantly pick to make any measurement or value look
bad for the ability to calculate a fatal wound AKA a wound channel.
But what is a fatal wound?
A fatal wound is the ability to take a game animal quickly, humanly and with as little meat loss
as possible. These parameters are as old as time. Parameter set by engineers, doctors, veterinarians or
ballisticians for the study of mechanical, structural or postmortem data concerning a fatal wound are
impotent.
This is because the aforementioned disciplinarians are gathering data based on a past event not
germane to the taking of game animals. This paper is concerned with a current event as it pertained to
the hunting or shooting community at large and the taking of game animals. This event is the creation
of a fatal wound (as defined above) as represented by the temporary wound channel at the time of
bullet impact. This event is generally recorded in the ten thousandths of a second range (.0010).
Thanks to Dr. W. Feckler, I was able to use his drawing s for this comparison. His drawings are
a representations of the event, taken as it happened by radar. Therefore, a postmortem of the permanent
wound “cavity” is not an accurate representation of a fatal wound. A postmortem is a postulation.
Hence, impotent as a comparison or study of translational kinetic energy.
Two values are out of range. If you look at the impact velocity for the .223 Remington and
.308 Winchester you will see that they are 3150 and 2923 feet per second respectively. For both these
cartridge's bullets, there is maximum impact velocity is 2900 feet per second. I feel the extra 23 feet per
second for the .308 Winchester is within an acceptable margin of error. As for the . 223 Remington I
felt compelled to keep it in the sample data set as a matter of continuity. This is because the cartridge is
generally considered a small game/varmint cartridge anyway.
Here are the Design Functions values for varmint bullets:
Design Type
Impact Velocity
Id.
hollow point
0 to 4500fps
1.18
(varmint type)
polycarbonate tip
0 to 4500fps
1.18
(varmint type)
But as you can see I neglected a softpoint “varmint type” bullet in my book. Come to think of it
I need to add a fragmenting varmint bullet to the list too. You can see that the Design Function value is
only a matter of .07 difference. This equates to a differential of .640 to .652 and .946 to .945 for
correlations of penetration to IPF and IPF to temporary wound channel respectively.
It may also be of interest to know that a fragmenting varmint bullets is a design. As is noted on
Data Set drawing 2, it was estimated that the 50gr softpoint bullet had “53% fragmentation”. So in
keeping with my 2005 book, I see no appreciable differences in the calculated data or a bias of
calculated data as presented hereon.
The proportions including their Correlation Coefficient
Column 1, 2 and 3
It is found that translational kinetic energy has a high correlation to any wound channel; .628,
.734 and .756 respectively. Intuitively one would think the correlation would have been a high .9 or 1.
based on the proven science that transitional kinetic energy is directly related to bullet impact wound
depth and volume. But here is what is really happening.
The experimental proof of translational kinetic energy is based on a none deforming object of
the same size and weight. The medium used is unchanging too. If a correlation is done of one specific
bullet that does not deform then the correlation coefficient would be on the order of 1. In fact this
comparative analysis is using 4 different small arm projectiles types (5 individuals), at 5 different
impact velocities. That's a 1 in 19 probability of having any one of the data set bullets correlate exactly
to a single non-deforming bullet at the 4 subject impact velocities. This is why a discrepancy between
the perceived correlation of 1 and the actual average correlation of .706 can be found.
Column 4
It is found that translational kinetic energy has a medium correlation to penetration; .362.
Although it would be expected that translational kinetic energy should have the highest correlation to
penetration as dictated by the above experiments and history of energy, this discrepancy can be
explained by differing bullet sectional density in conjunction with bullet behavior.
Each of the 5 small arm projectiles has a different sectional density. The behaviors is as follows:
the .30-30 Winchester and .308 Winchester bullets along with the shot gun slug mushroom as designed.
The .223 Remington bullet fragments and the .22 long rifle bullet flips around backwards and shows no
deformation.
Again this is the same discrepancy as found in Columns 1-3. The probability that the 5 different
small arm projectiles, at 5 different impact velocities, behaving in 3 different ways as compared to one
non-deforming bullet is 1 in 74. Again, This is why a discrepancy between the perceived correlation of
1 and the actual average correlation of .362 can be found.
Column 5
It is found that penetration has a high correlation to sectional density; .682. This would be
expected at sectional density is directly related to a bullets ability to overcome resistance and is not a
disputed fact.
Again if there is a perceived lower than expected correlation it 5 differing sectional densities, at
5 different impact velocities, behaving in 3 different ways as compared to one non-deforming bullet.
The probability again is 1 in 74.
Column 6
It is found that penetration has a medium correlation to momentum; .347. I believe this is why
so many hunters and shooters still rely on momentum as an indicator of a fatal wound. Because it has
been proven that translational kinetic energy is a measurement of translational kinetic energy the use of
momentum is the wrong application for a mathematical coefficient for energy. Momentum is a correct
measurement for velocity. Because momentum is velocity and translational kinetic energy equation
velocity within it, momentum (v) is expected to mimic translational kinetic energy (v2). For this reason
(the mimic) momentum has a slight x, y alignment (correlation) to penetration.
Column 7
It is found that penetration has a high correlation to IPF; .640. This would be expected as IPF
has sectional density as a measurement within it. However, the penetration of a bullet is only a part of
the wound channel volume (d vs. d3). Therefore, only a partial correlation would be found.
Column 8
It is found that penetration has a low correlation to TKO; .147. It is also found that TKO has
little to no correlation to other values and measurements. This to be explained when analyzing columns
15-17.
Column 9 &10
It is found that momentum has a low correlation to permanent wound channel and temporary
wound channel; .147 and .224 respectively. Again, this is because momentum is the wrong
measurement to apply to the wound channel volume. It would be expected that a correlation between
momentum and permanent wound channel would be low as explained in Column 6.
Column 11
It is found that momentum has a medium correlation to total wound channel; .382. Because
momentum has a medium correlation it would be expected that hunters and shooters would interpolate
momentum with a fatal wound. Again this is due to the velocity as explained in Column 6.
Column 12
It is found that IPF has a medium correlation to permanent wound channel; .355. This would be
expected as the value of IPF is not set to feet and the factor is created around a temporary wound
channel.
IPF values are purposefully dimensional incorrect. Because IPF (when corrected to feet) yields
such low measurements it would immediately be dismissed as a copy of the numerous “power”
formulea, not to mention Taylor's Knock-out value and Momentum (aka Elmer Kieth's pound feet).
Column 13
It is found that IPF has a high correlation to temporary wound channel; .946. Here is where the
rubber meats the road. A correlation of .946 out of 1.000 is exactly what would be expected and what
was purposefully created.
Even though an IPF value is not correctly set to feet, it is mathematically an exact proportion of
12. 12 is the coefficient to set the term correct to feet from inches.
This correlation in conjunction with the exceedingly small data set sample, mathematical test
my hypothesis to a very high level of confidence. Remember, IPF was created to reflect both impact
and penetration. This is done by using the mechanism for a temporary wound channel, transitional
kinetic energy in conjunction with sectional density and a coefficient to reflect multiple bullet designs
and materials. In other word, IPF corrects the translational kinetic energy measurements for the
creation of a temporary wound channel when using differencing small arm projectiles.
Column 14
It is found that IPF has a high correlation to total wound channel; .615. The disparity between
the total wound channel and temporary wound channel has not been investigated. It is presumed to be
due to the fact IPF values that are not set to feet and dimensional incorrect.
Column 15-17
It is found that TKO has no correlation to permanent wound channel, temporary wound channel
and total wound channel; .098, .020 and .044 respectively. This is to be expected because TKO is based
on momentum. The addition of caliber as another dimension just exacerbates the correlation and puts it
further out of x,y alignment with momentum which is already out of alinement with transitional kinetic
energy.
Column 18
It is found that IPF* has a high correlation to permanent wound channel; .711. It is expected that
the corrected IPF measurement would have a high correlation to permanent wound channel but not near
perfect alignment. This is because a permanent wound channel is part of a temporary wound channel.
Therefore the correlation is only showing a moderately high correlation coefficient.
Column 19
It is found that IPF* has a high correlation to temporary wound channel; .946. It is expected
that the corrected IPF measurement would have the exact same correlation as IPF value because both
are proportionate to 12. Anything that can be said about a corrected IPF measurement can be found in
Column 13.
Column 20
It is found that IPF* has a high correlation to total wound channel; .925. It is expected that the
corrected IPF measurement would have high if not perfectly alinement with a corrected IPF
measurement and IPF value for temporary wound channel. Arguably, this could be because a total
wound channel is really the temporary wound channel in real time. See the Wound Channel page [20]
for information on a temporary wound channel event.
Conclusion
Well, I hope we can all finally agree that translational kinetic energy (aka kinetic energy) is the
measurement we as hunters and shooters use for the energy of an impacting bullet. I'm not asking you
to like it or use it. Just to accept it as scientific fact.
I think it's time we all stop arguing about it translational kinetic energy. I hope this finally puts
to rest the translational kinetic energy is a marketing ploy, its for heavy slow moving bullets to compete
with small fast moving bullet, it's momentum with half more velocity, it has noting to do with “killing
power” and any other phrase you can think up.
There in no need to find other values to supplant, equate or otherwise supersede translational
kinetic energy as a measurement for the energy of a small arms projectile. Translational kinetic energy
is the mechanism and measurement for a wound channel.
Now, for those hunters and shooters that use a bow or punch holes in plate steel, do not apply
your sport to transitional kinetic energy. Bow hunting or punching holes in plate steel are regulated by
two separate mechanisms not related to wound channel volume. Military small arms and SLAP
ammunition are not considered part of this survey.
For those with an engineers back ground and still feel translational kinetic energy only
translates to a change of state, I think that myth is busted. I hope I never, ever read another article
written by and person that professes translation between kinetic energy and thermodynamic energy.
Case in point: an article published some 12 years ago in ShootingTimes magazine, where the engineer
claimed that bullets melt holes, not punch holes..., in automobile, rear leaf springs.
In the matter of my IPF, I hope I have made a strong case by the testing of my hypothesis
against real time, temporary wound channels on simulated animal biomass. I do understand that some if
not all of my Design Function will change if real testing is done. But my hypothesis will remain intact.
Further, I understand I showed no proof as to where these coefficient come from or how they were
derived. Unfortunately, it would not a have been appropriate to cover that work here, as the focus of
this paper was translational kinetic energy not IPF. I am prepared to provide sources and methodology
if the community wishes another paper. I would be honored to do more work for you.
I feel I have met the burdens of proof for scientific authenticity. As it is dictated by good
science; first do the work, make the hypothesis, do the experimentation and record the observations.
Then to see if the work and hypothesis is validated by the experiment. Pseudo science is to the
experimentation and observations first then make the work and hypothesis fit the experiment and
observations.
I understand that drawings of blocks of ordnance gelatin makes not a game animal let alone a
real life event. But you must admit we have to start some where. A controlled experiment must be done
first to rule out any extemporaneous variables.
If you feel I have not met your burden of proof, ponder this?
How could some “dude” come up with an idea 16 years ago, conclude a hypothesis 12 years
ago, write a book (no matter how badly written) 7 years ago, spout off about it 2 weeks ago, then
proceed to mathematically prove translational kinetic energy and IPF right here on the spot.
That would be pretty weird, don't you think?
Just food for thought my friends.
Finally, given the information contained here, specifically that information contained in the
remaining 14 drawings by Dr. M. Fackler, I should be able to calculate a fatal wound for any game
animal weight based on temporary wound channel volume.
Bibliography
Albert Einstein, To the theory of the static gravitational field, Annalen der Phvsik, Volume 38, Seventh
booklet, Fourth consequence, #8, page 454, May 23rd 1912.
David Bodanis, E=mc2, Walker and Company, 2000.
Edward F. Obert, Thermodynamics, McGraw-Hill Book Co., 1948.
Encyclopedia Britannica, 1995.
Encyclopedia of Chemical Technology, volume 10, 4th Edition, John Wiley and Son, 1993.
Mc Graw-Hill encyclopedia of Science and Technology, volume ice-lev, 9th Edition, Mc Graw-Hill,
2002.
Oxford Dictionary, Oxford Dictionary 1998.
Parker O. Ackley, Volume I: Handbook for Shooters & Reloaders, Plaza Publishing,1962, 17th printing
1988.
Sir Isaac Newton, Philosophiae Naturalis Principia Mathematica, Oxford University, July 5th 1686.
World Book Encyclopedia, volumes 1-20, World Book Encyclopedia 1964,1968,1997.
www.alberteinstein.info, 2005
www.digitaldutch.com/unitconverter, 2003-2007
www.encarts.msn.com, 2003.
www.es.rise.ed.org, 2003
www.history.mcs.st andrews.ac.uk/history.org, University of St Andrews Scotland School of
Mathematics and Statistics, 2003-2005
www.hyperphysics.phy-astr.gsu.edu/hbase/hph.html, 2006
www.scientificworld.wolfram.com, 2003.
www.scienceworld.wolfram.com/biography, 2003-2005
www.wikipidia.com, 2005-2007