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Reprinted from Wound Ballistics Review; 3(1), 1997: 32-35.
Sanow Strikes (Out) Again
By Duncan MacPherson
Sanow, E.: "Predicting Stopping Power." Handguns, November 1996
In November 1996 I got an excited call from an engineer I had once worked with but whom I had not seen for over 30 years. This man thought I must be the Duncan MacPherson referred to in the referenced article, wanted to verify this, and was surprised that I didn't know what he was talking about. He read me the quote, which was:
"Army officers Thompson, LaGarde, Chamberlain, and Hatcher could not do it. The NIJ's Dan Frank could not do it. Carroll Peters, Martin Fackler and Duncan MacPherson could not do it. No one at the FBI's Firearms Training Unit could do it."
I told him that I undoubtedly was the one referred to even though there wasn't any single thing that all of these people tried to do and so I didn't know exactly what the "it" was. The magazine was no longer on sale, but he offered to send me a photocopy of the article.
The "it" turned out to be making a model of stopping power using Marshall's "actual shootings" data base together with a "uniform gelatin data base"; the quote given above doesn't make much sense in this context. Thompson and LaGarde never attempted to make any kind of a model of stopping power (although they did implement the well know tests that Hatcher used in his model), and Dr. Fackler has always maintained that stopping power models were irrelevant (and certainly never tried to generate one). I used the term wound trauma incapacitation (WTI) rather than stopping power in Bullet Penetration1 to emphasize the fact that the desired incapacitation is a result of physiological and psychological effects of wound trauma in the person being shot rather than some mystical property of a bullet configuration, mass, or velocity that is unrelated to the wound trauma (an inference all too common in articles appearing in general audience "gun magazines").
The model of stopping power that Sanow enthusiastically endorses in his article is an empirical curve fit of the "actual shooting data" that is contained in the Marshall - Sanow books. This data fit was done by Steve Fuller, who wrote a chapter in the latest of these books. As such, this is not news, but yet another recycling of the same material that doesn't really deserve much comment. On the other hand, there is a problem with letting this go without response. It seems clear that the negative reaction from professionals has influenced Sanow's approach to writing: he is turning up "professionals" of his own in attempt to give his position an aura of scholarship. This is not hard to do because there are incompetent physicians, there are incompetent law enforcement personnel, and there are incompetent engineers; all of whom are available for either money or a chance to get recognition that they will never get from competent colleagues (just look at some "expert" witnesses in court cases to confirm this). The problem is that it is not always easy for even an intelligent individual to detect errors in a discipline outside his training when he knows something is wrong. Since the smoke being blown here is engineering smoke, I am making the effort to point out a few things that are not always obvious to non-engineers.
1) The most important thing to remember is GINGO; an acronym which has been used by engineers for garbage in, garbage out. It is clear that Fuller assumed that the Marshall data is totally valid even though most technical analysts have found the regularity of his data not credible. This issue has been discussed by a number of different technical reviewers and will not be gone over again here except to note that this data fitting by Fuller does nothing to the basic data quality; if the Marshall data is flawed, the flaws are just passed on in Fuller's data fit. Fuller's work is called a data fit here because that is what it is; despite Sanow's use of some mathematical jargon, Fuller's work is the functional equivalent of drawing a line through a bunch of data points. The formula does not "duplicate reality" as Sanow claims; in fact, the formula doesn't duplicate anything, it just models Marshall's data points.
Sanow states that Fuller "does not feel it necessary to understand medical aspects of wound ballistics to predict stopping power". Some people will find this position astounding, but it is compatible with (or equivalent to) the assumption that the Marshall data is flawless. This position is not logically wrong, but it is a technically unsound approach because no data set is flawless. Creating a model of a physical process without a clear understanding of the underlying technical principles involved is one of the very best ways to create a worthless model. Fuller's model has been constructed to fit Marshall's data, but it gives preposterous results for other conditions (discussed below); it is by no means a general model of stopping power. If Sanow is aware of this he does not choose to share it with his readers.
2) The FBI formulations for bullet effectiveness have serious flaws that are well known, but which the Bureau has been unwilling to change; these are described in Bullet Penetration.1 It initially seemed that this combination of deficiency and stubbornness was not serious because these calculations were neither generally available nor used by anyone. This assessment now appears wrong because Sanow appears to be trying to tie the flaws in the FBI formulations for bullet effectiveness to everyone who disagrees with him. Sanow also shows an astonishing lack of understanding of negative numbers (a topic usually taught in grade school) in his criticisms of some of the FBI ratings. A temperature of -10° F is not meaningless, it is 10° F colder than 0° F. Likewise, a negative number for a load in the FBI ratings doesn't mean that you feel better if shot with that load (as Sanow foolishly asserts); a negative rating is just a lower rating than zero. A lot of scales are set to avoid negative numbers, but ordinary temperature scales and FBI ratings are not among them; this may be inconvenient, but it is not an error, not ridiculous, and not even a factor in loads that are conventionally considered adequate.
3) The conclusions on the importance of bullet kinetic energy show why the approach of taking Marshall's data at face value with no application of wound ballistics knowledge or even common sense is such a bad idea. To quote Sanow:
"Energy is the most important factor in determining actual stopping power for a given bullet type. In general, the more energy, the more stopping power. However, Fuller found an upper limit to the amount of energy that results in more stopping power. A reasonable upper limit turned out to be 675 foot-pounds for hollowpoint handgun bullets. Handgun bullets like the .41 Magnum and .44 Magnum with 700 to 1,000 foot-pounds of energy do not produce much more stopping power than the .357 Magnum and .40 S&W with 550 to 600 foot-pounds of energy."
For clarity, it should be emphasized that Fuller didn't find anything that wasn't in the data to begin with; he just did a curve fit, and this result is in Marshall's data. The emphasis on handgun bullets seems to imply that these results are not claimed to hold for rifle cartridges. However, the .44 Magnum can be used in rifles; Remington even quotes ballistics for a 20 inch barrel in their literature. Does .44 Magnum kinetic energy suddenly become important again when a long barrel is used? If so, how does the person being shot know that he has been shot with a rifle (.44 Magnum or otherwise) and respond to this energy increase? If not, why has everyone been deluded for years into thinking that high velocity rifle bullets can be much more effective than handgun bullets in taking game (the equivalent of stopping power)? Knowledge of wound ballistics provides answers to all of these questions; these answers make sense, but are not compatible with Fuller's formulation.
4) Sanow makes jokes about the negative numbers that can be generated in the FBI formulations and states that Fuller's formula is designed to prevent this. This assertion is another claim that is not true. Consider a 2 inch diameter steel sphere having a velocity of 2000 ft/sec; this unconventional bullet weights 8250 grains and has a kinetic energy of 73,000 foot-pounds. This projectile would penetrate about 144 inches of gelatin, and it would be hard to find anyone who would not agree that it would create far more wound trauma than any available small arms load despite the relatively inefficient spherical shape. One would think that such a projectile would get a high stopping power rating, but Fuller's formula shows that this projectile has a stopping power rating of minus 888%! Fuller and Sanow's scale is stopping power percentage, and for this scale (unlike the FBI rating scale) negative numbers really do mean a "negative wound".
At the other extreme, consider a steel BB (air rifle shot) having a velocity of 250 ft/sec; this is typical for spring actuated "BB guns". This projectile will not penetrate unprotected human torso skin, but Fuller's formula gives it a stopping power rating of 3%. In fact, Fuller's formula gives a paper spitball at 10 ft/sec a stopping power rating of 3%!
The natural response to these examples is that Fuller's formula was generated to model conventional handgun bullets and not to be applicable to these unconventional projectiles. This response is valid, but it emphasizes the fact that Fuller's formula does not represent any basic truth (newly discovered or otherwise); this formula merely curve fits Marshall's data set and gives preposterous answers outside of the regime where compliance has been forced. Note that neither the FBI formulations nor Hatcher's stopping power calculation were designed for these unconventional projectiles, yet both of these scales give very reasonable results for them. This is not to argue that the FBI formulations and Hatcher's stopping power calculations are valid (I have described their deficiencies myself in Bullet Penetration), but rather to emphasize that formulations that have some basis in physical principles are less much likely to "blow up" to ridiculous results than a model base solely on a data fit with no meaningful consideration of physical principles.
5) Sanow states that Fuller's formula shows maximum stopping power at a penetration depth of 8.4 inches and provides a table showing that the formula gives reductions in stopping power of 2% and 4% at penetration depths of 14.6 inches and 17.1 inches, respectively (these calculations can be easily verified by using the formula). What Sanow doesn't state is that a penetration of 2.5 inches also produces a 2% reduction in stopping power and a penetration of 0 inches produces a 4% reduction in stopping power. This is not a typo; Fuller's formula shows that a 2.5 inch penetration is just as good as a 14.6 penetration and no penetration at all is just as good as a 17.1 inch penetration! This wonderful new model shows that .45 ACP hardball would have about 10% more stopping power if only its high penetration could be reduced to zero penetration!
Once again, the response can be made that no one cares about zero penetration bullets, so the model need not apply to them. And once again, the real issue is the applications of elementary wound ballistics principles would lead to a zero (or possibly a very small) stopping power rating at zero penetration. This could easily be accomplished in a curve fit, but this new curve fit would no longer match Marshall's data as well as Fuller's formula does. Could it be that the problem is in Marshall's data?
6) Sanow states: "The minimum penetration depth of 12 inches mandated by the FBI is arbitrary at best and totally bogus at worst." and also explicitly points out that the difference between the "optimum" 8.4 inch penetration and a 12.8 inch penetration is only 1% in Fuller's formula.
The first point to be made is that a 1% variation in this theoretical stopping power should be compared against the probability that the bullet will require an unusually large penetration to reach the vital structures well inside the body. This can occur when the bullet must traverse non-critical tissue; e.g., the extended left arm of a right handed assailant aiming his handgun at you, and/or an unusual bullet path angle in the torso, and/or an unusually fat or beefy individual. The probability of needing this extra penetration is a judgment call, but most sensible people believe it is a significant factor and certainly much more important than a very conjectural 1% in theoretical stopping power under ideal conditions. This is the reason the FBI specified the 12 inch minimum penetration even though they (and everybody else in the professional wound ballistics community) are well aware that an 8 inch penetration is usually adequate. Sanow (and others) may make a different judgment on this, but to describe the FBI position as "totally bogus" is both ridiculous and irresponsible.
The second point to be made is that a 1% variation in this theoretical stopping power is well below any reasonable confidence level (i.e., it is too small to be significant) for this kind of data. As such, this 1% difference is a very weak argument for a strong position on penetration depth, and emphasizes the irrationality of the "totally bogus" claim. Fuller, who has some technical experience, should recognize this even if Sanow doesn't.
7) The reference article states:
"Jan Libourel, editor of HANDGUNS was the first to point out that published muzzle velocity and muzzle energy figures are not accurate enough to use in the formula. The Fuller Index is heavily dependent on velocity and energy figures. These must come from a chronograph."
This admission with the emphasis on not by Sanow is very interesting and illuminating. This means that in compiling his data base Marshall went around and chronographed rounds from the same lot as the rounds used in all the shootings (generously assuming that this will give the accuracy Sanow says is required). What? You don't think he did this? Neither do I. Well then, this means that you can construct this data base and model it using Fuller's formula without chronographing the loads involved, but once this is done the Fuller formula results aren't accurate unless the loads are chronographed. Marshall's data base contains all the loads of practical interest (and many that are not), so this means that even the loads that were used in constructing the data base are not correctly modeled by Fuller's formulation unless they are now chronographed!
I think it is hard to think of anything anyone can say which can top this statement by Sanow in pointing out just how unscientific and downright foolish this whole business is. Don't forget; Fuller's formulations just modeled Marshall's data base, which means that any nonsense in Fuller's formula represents nonsense in the data itself. I venture a prediction: Sanow's articles will no longer mention any need to chronograph in order to get good results with the Fuller formulation after he realizes how he has shot himself in the foot with this cited quote. This prediction will fail only if Sanow knows he is convincing only the gullible and has given up any hope of persuading sophisticated readers.
8) Sanow asserts that the Winchester Ranger (formerly Black Talon) "does not achieve its full recovered diameter until nearly eight inches of penetration by design" and assumes expansion linear with penetration to make an argument for relative ineffectiveness of this load. This claim and assumption are completely incompatible with the dynamics of handgun bullet expansion during penetration; as a result the derived statements in the article are not correct. The physics of bullet expansion and penetration is understood and valid even if someone sees (or think they see) something in conflict with this physics. This is just like someone's claim to have seen a unicorn; they didn't, and it doesn't really matter whether they sincerely think they did or are simply lying about it.
The reader may feel that writing this review was fun, but it wasn't. The good physician is embarrassed when another physician harms a patient through incompetence, the good law enforcement officer embarrassed when another law enforcement officer breaks the law, and the good engineer is embarrassed when another engineer produces unsound analysis by not adequately understanding what he is doing. The examples given illustrate flaws in Fuller's formula, but it is difficult to make a full exposition of just how simplistic and naïve this model is without getting into technical detail not readily comprehensible to non-technical readers (for technicians, flaws include variables and formulations with no physical significance, small differences of large numbers, and unrealistic numbers of significant digits). The bottom line is that this is just another pathetic chapter in a very pathetic story.
- Duncan MacPherson, Bullet Penetration - Modeling the Dynamics and the Incapacitation Resulting from Wound Trauma, Ballistics Publications, Box 772, El Segundo, CA, 1994.
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