Input Values
Proportions
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)
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.