P95Carry

December 19, 2005, 10:20 PM

Confession - in process of tidying up a post not needed - lost whole thread.! It happens!

Let me try and re construct - from cached page pre delete problem.

First post from Michael Courtenay -

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Defining Stopping Power

Many discussions of handgun stopping power are unproductive because they lack a quantitative definition of the stopping power concept. The issue is clouded by potentially complicating factors such as shot placement, intermediate barriers, and the mindset and individual physiology of the target. This post provides a quantitative definition of stopping power that allows one handgun load to be compared with others for a specified shot placement. The ideas presented here are a quantitative definition of stopping power of a given load for any specific unobstructed shot placement and target species, but we have in mind the specific case of involuntary (see footnote 1) incapacitation of human targets shot near the center of the chest.

It is well known that in the absence of hits to the central nervous system (CNS), handgun bullets do not reliably provide immediate incapacitation, or even reliable incapacitation in the short time span of most gun fights (under 5 seconds). Therefore, any comparative measure of stopping power must be concerned with the probability of a given load to produce incapacitation in a specified time frame for a specific shot placement.

For instance, we could describe the stopping power of a load as the time interval required to achieve involuntary incapacitation in 90% of the cases where the target is hit with that load at the specified placement. For example, a load that produces incapacitation in 90% of targets in fewer than 8.6 seconds would be considered to be better than a load that requires 12.2 seconds to produce incapacitation in 90% of targets.

However, the time to achieve a 90% probability of incapacitation is not a complete definition of stopping power. The 90% probability time is somewhat of a worst-case scenario. (See footnote 2.) We might also consider the average time to incapacitate targets with a specified shot placement. A load which produces a 4.7 s average incapacitation time would be considered better than a load which produces a 7.8 s average incapacitation time.

In addition to 90% incapacitation times and average incapacitation times, we might also consider the 20% incapacitation time, which is something of a measure of how well a load is working in a sort of ?best case scenario.? A load that produces a 20% chance of incapacitation in 2.0 s would be better than a load that produces a 20% chance of incapacitation in 3.8 s.

Footnote 1:

For human attackers, there is an important voluntary aspect to how hits with handgun bullets contribute to the probability of an attack being stopped. This voluntary aspect is real and important, but difficult to quantify, so we focus on the involuntary aspects for now. Our definition of stopping power is constructed with sufficient generality to allow for later inclusion of voluntary effects.

Footnote 2:

The idea of an absolutely worst case scenario cannot be defined with any degree of statistical rigor. As the sample size grows very large, there is always the possibility of a case that is worse than encountered previously. However, we can rigorously define the idea of worst case if we fix the percentage of cases that is better than the worst case. Here, we choose that 90% of the cases should be better than what we consider the ?worst case.?

The totality of these ideas can be represented in a mathematical probability curve that describes the likelihood of a given load with a specific shot placement producing incapacitation within a certain number of seconds. Hypothetical probability curves are shown for three different loads in Figure 1. Keep in mind, that it is not our intent to assert that any given handgun load would produce any one of these three curves, only that curves like these would represent substantial quantitative information about the stopping power of a given load for a specific shot placement. Completely describing the incapacitation potential for a handgun load for a given shot placement requires describing the probability curve for all times that are reasonably encountered in the time span of a lethal force encounter.

http://img492.imageshack.us/img492/9559/figure18os.gif

The three curves shown in Figure 1 all represent the basic idea that a good bullet in a full-sized service caliber handgun delivered with an unobstructed shot near the center of the chest will almost always cause eventual incapacitation of the target. The different curves suggest that some handgun loads might cause incapacitation more rapidly than others, and a means of quantifying and perhaps predicting this is desirable for selecting and designing more effective ammunition. (See footnote 3.)

All the curves have the same basic features: the probability of producing instant incapacitation is very small, and the probability of eventual incapacitation is nearly 100%. The three loads are distinguished by their differing abilities to cause rapid incapacitation. Load A takes only 2.0 seconds to incapacitate 20% of the targets. Written as an equation, t20% = 2.0s. Load A also has an average incapacitation time close to 4.7 s, and takes 8.6 seconds to incapacitate 90% of the targets. One might also consider the probability of Load A causing involuntary incapacitation in under 5 seconds, because what happens after 5 seconds is irrelevant given the time span of most gun fights. Load A achieves roughly a 60% likelihood of involuntary incapacitation in under 5 seconds.

Footnote 3:

This is not to assert that barrier penetration and the possibility of other shot placements should not be an important part of the ammunition selection and design process. We believe that they should. However, from a scientific point of view, it is often necessary to reduce the number of variables in play in order to understand a simplified view of an issue. More complete perspectives can be more accurately built once the science of various simplified views is better understood.

Contrast this to Load B which takes 3.8 s for an incapacitation probability of 20%, has an average incapacitation time of 7.8 s, and takes 12.0 s for an incapacitation probability of 90%. Load B has roughly a 34% likelihood of achieving involuntary incapacitation in under 5 seconds.

Also consider Load C which takes 9.1 s to incapacitate 20% of the targets, has an average incapacitation time of 11.0s and has not caused incapacitation in 90% of the targets until 13.4 s. Load C has less than a 1% likelihood of causing involuntary incapacitation in under 5 seconds. In other words, the only way that Load C is likely to be effective in the time span of most gun fights is for the target to voluntarily cease the attack as a result of the shots fired.

The ?best case?, average, and ?worst case? incapacitation times are summarized in Table 1. The probability of incapacitation in under 5 seconds is listed as PI(t<5).

t20% tave t90% PI(t < 5)

Load A 2.0s 4.7s 8.6s 60%

Load B 3.8s 7.8s 12.2s 34%

Load C 9.1s 11.0s 13.4s 1%

These probability curves suggest the possibility of an idealized experiment where the incapacitation time is recorded for a large number of shooting events where the target is hit with a specific load and a specific shot placement. The data from such an idealized experiment could be used to generate the curves in Figure 1 that represent the likelihood of incapacitation within a given time. The hypothetical nature of the curves in Figure 1 do not preclude considering incapacitation probability curves as a valid description of stopping power. In the idealized experiment, loads that produce more rapid incapacitation will produce curves which are further to the left in a graph like Figure 1.

In all areas of science, real experiments and observations represent trade-offs between an idealized experiment and the practical realities of data collection. (See footnote 4.) In the scientific pursuit of quantifying stopping power, some experimental designs might consider a variety of shot placements or use a success/failure criteria rather than a continuous variable to measure incapacitation. Other experimental designs use a small number of shooting events or perform the experiment on a species other than humans. In spite of these trade-offs, if an experimental design is clearly described (so that the strengths and limitations are understood), and data collection is faithful to the experimental method, we might be able to use results from these sub-optimal experiments to make predictions on the outcome of a more idealized experiment.

Footnote 4:

A fundamental aspect of this trade-off is that cost and time required for a certain number of data points scales linearly with the number of data points, but the uncertainty of numerical results is only reduced by the square root of the number of data points. In other words, reducing the experimental uncertainty by a factor of two often requires increasing the number of data points by a factor of four, which is likely to increase the cost and time by a factor of four. Various trade-offs are used to increase the number of data points without a linear increase in cost or time. These include broadening the selection criteria, studying the effect in more accessible/less expensive species, and using more available measures of the effect under study.

Some authors split hairs by attempting to distinguish ?reliable? incapacitation mechanisms from ?unreliable? mechanisms that only contribute some fraction of the time. However, since no handgun incapacitation mechanism is 100% reliable within the time span of a typical gun fight (< 5 seconds), this concept of reliable eventual incapacitation is an artificial construct with little relevance to the stopping power discussion.

In any case, if realistic incapacitation probability curves are anything at all like the hypothetical probability curves for Load A, Load B, and Load C, there are some practical implications for surviving gun fights with handgun loads. Even though some handgun loads might perform significantly better than others, there is no magic bullet. Short of a hit to the CNS, even the best-placed handgun bullets require substantial time (compared to the time span of most gun fights) to cause incapacitation in the majority of cases. As we will discuss later, multiple hits might decrease the time to incapacitation, but short of a direct hit to the CNS, multiple hits do not change this basic result.

Consequently, surviving a gun fight requires more than good shot placement with good handgun bullets; surviving a gun fight requires tangible actions to avoid getting shot during the time interval before incapacitation occurs. Evasive action is necessary, and the significant likelihood that incapacitation is still several seconds away should be sufficient motive for the defensive shooter to be moving rapidly toward cover, or in the absence of cover, at least moving to make for a more difficult target.

In summary, we have defined stopping power using incapacitation probability curves that describe the probability of involuntary incapacitation as a function of time. We make reference to the specific case of involuntary incapacitation of human targets shot near the center of the chest to help explain the concept. However, our stopping power definition also applies to alternate shot placements. Generalizing this definition to include voluntary contributions to incapacitation, contributions of new incapacitation mechanisms, and the probability of incapacitation with multiple hits is straightforward.

Michael Courtney

Let me try and re construct - from cached page pre delete problem.

First post from Michael Courtenay -

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Defining Stopping Power

Many discussions of handgun stopping power are unproductive because they lack a quantitative definition of the stopping power concept. The issue is clouded by potentially complicating factors such as shot placement, intermediate barriers, and the mindset and individual physiology of the target. This post provides a quantitative definition of stopping power that allows one handgun load to be compared with others for a specified shot placement. The ideas presented here are a quantitative definition of stopping power of a given load for any specific unobstructed shot placement and target species, but we have in mind the specific case of involuntary (see footnote 1) incapacitation of human targets shot near the center of the chest.

It is well known that in the absence of hits to the central nervous system (CNS), handgun bullets do not reliably provide immediate incapacitation, or even reliable incapacitation in the short time span of most gun fights (under 5 seconds). Therefore, any comparative measure of stopping power must be concerned with the probability of a given load to produce incapacitation in a specified time frame for a specific shot placement.

For instance, we could describe the stopping power of a load as the time interval required to achieve involuntary incapacitation in 90% of the cases where the target is hit with that load at the specified placement. For example, a load that produces incapacitation in 90% of targets in fewer than 8.6 seconds would be considered to be better than a load that requires 12.2 seconds to produce incapacitation in 90% of targets.

However, the time to achieve a 90% probability of incapacitation is not a complete definition of stopping power. The 90% probability time is somewhat of a worst-case scenario. (See footnote 2.) We might also consider the average time to incapacitate targets with a specified shot placement. A load which produces a 4.7 s average incapacitation time would be considered better than a load which produces a 7.8 s average incapacitation time.

In addition to 90% incapacitation times and average incapacitation times, we might also consider the 20% incapacitation time, which is something of a measure of how well a load is working in a sort of ?best case scenario.? A load that produces a 20% chance of incapacitation in 2.0 s would be better than a load that produces a 20% chance of incapacitation in 3.8 s.

Footnote 1:

For human attackers, there is an important voluntary aspect to how hits with handgun bullets contribute to the probability of an attack being stopped. This voluntary aspect is real and important, but difficult to quantify, so we focus on the involuntary aspects for now. Our definition of stopping power is constructed with sufficient generality to allow for later inclusion of voluntary effects.

Footnote 2:

The idea of an absolutely worst case scenario cannot be defined with any degree of statistical rigor. As the sample size grows very large, there is always the possibility of a case that is worse than encountered previously. However, we can rigorously define the idea of worst case if we fix the percentage of cases that is better than the worst case. Here, we choose that 90% of the cases should be better than what we consider the ?worst case.?

The totality of these ideas can be represented in a mathematical probability curve that describes the likelihood of a given load with a specific shot placement producing incapacitation within a certain number of seconds. Hypothetical probability curves are shown for three different loads in Figure 1. Keep in mind, that it is not our intent to assert that any given handgun load would produce any one of these three curves, only that curves like these would represent substantial quantitative information about the stopping power of a given load for a specific shot placement. Completely describing the incapacitation potential for a handgun load for a given shot placement requires describing the probability curve for all times that are reasonably encountered in the time span of a lethal force encounter.

http://img492.imageshack.us/img492/9559/figure18os.gif

The three curves shown in Figure 1 all represent the basic idea that a good bullet in a full-sized service caliber handgun delivered with an unobstructed shot near the center of the chest will almost always cause eventual incapacitation of the target. The different curves suggest that some handgun loads might cause incapacitation more rapidly than others, and a means of quantifying and perhaps predicting this is desirable for selecting and designing more effective ammunition. (See footnote 3.)

All the curves have the same basic features: the probability of producing instant incapacitation is very small, and the probability of eventual incapacitation is nearly 100%. The three loads are distinguished by their differing abilities to cause rapid incapacitation. Load A takes only 2.0 seconds to incapacitate 20% of the targets. Written as an equation, t20% = 2.0s. Load A also has an average incapacitation time close to 4.7 s, and takes 8.6 seconds to incapacitate 90% of the targets. One might also consider the probability of Load A causing involuntary incapacitation in under 5 seconds, because what happens after 5 seconds is irrelevant given the time span of most gun fights. Load A achieves roughly a 60% likelihood of involuntary incapacitation in under 5 seconds.

Footnote 3:

This is not to assert that barrier penetration and the possibility of other shot placements should not be an important part of the ammunition selection and design process. We believe that they should. However, from a scientific point of view, it is often necessary to reduce the number of variables in play in order to understand a simplified view of an issue. More complete perspectives can be more accurately built once the science of various simplified views is better understood.

Contrast this to Load B which takes 3.8 s for an incapacitation probability of 20%, has an average incapacitation time of 7.8 s, and takes 12.0 s for an incapacitation probability of 90%. Load B has roughly a 34% likelihood of achieving involuntary incapacitation in under 5 seconds.

Also consider Load C which takes 9.1 s to incapacitate 20% of the targets, has an average incapacitation time of 11.0s and has not caused incapacitation in 90% of the targets until 13.4 s. Load C has less than a 1% likelihood of causing involuntary incapacitation in under 5 seconds. In other words, the only way that Load C is likely to be effective in the time span of most gun fights is for the target to voluntarily cease the attack as a result of the shots fired.

The ?best case?, average, and ?worst case? incapacitation times are summarized in Table 1. The probability of incapacitation in under 5 seconds is listed as PI(t<5).

t20% tave t90% PI(t < 5)

Load A 2.0s 4.7s 8.6s 60%

Load B 3.8s 7.8s 12.2s 34%

Load C 9.1s 11.0s 13.4s 1%

These probability curves suggest the possibility of an idealized experiment where the incapacitation time is recorded for a large number of shooting events where the target is hit with a specific load and a specific shot placement. The data from such an idealized experiment could be used to generate the curves in Figure 1 that represent the likelihood of incapacitation within a given time. The hypothetical nature of the curves in Figure 1 do not preclude considering incapacitation probability curves as a valid description of stopping power. In the idealized experiment, loads that produce more rapid incapacitation will produce curves which are further to the left in a graph like Figure 1.

In all areas of science, real experiments and observations represent trade-offs between an idealized experiment and the practical realities of data collection. (See footnote 4.) In the scientific pursuit of quantifying stopping power, some experimental designs might consider a variety of shot placements or use a success/failure criteria rather than a continuous variable to measure incapacitation. Other experimental designs use a small number of shooting events or perform the experiment on a species other than humans. In spite of these trade-offs, if an experimental design is clearly described (so that the strengths and limitations are understood), and data collection is faithful to the experimental method, we might be able to use results from these sub-optimal experiments to make predictions on the outcome of a more idealized experiment.

Footnote 4:

A fundamental aspect of this trade-off is that cost and time required for a certain number of data points scales linearly with the number of data points, but the uncertainty of numerical results is only reduced by the square root of the number of data points. In other words, reducing the experimental uncertainty by a factor of two often requires increasing the number of data points by a factor of four, which is likely to increase the cost and time by a factor of four. Various trade-offs are used to increase the number of data points without a linear increase in cost or time. These include broadening the selection criteria, studying the effect in more accessible/less expensive species, and using more available measures of the effect under study.

Some authors split hairs by attempting to distinguish ?reliable? incapacitation mechanisms from ?unreliable? mechanisms that only contribute some fraction of the time. However, since no handgun incapacitation mechanism is 100% reliable within the time span of a typical gun fight (< 5 seconds), this concept of reliable eventual incapacitation is an artificial construct with little relevance to the stopping power discussion.

In any case, if realistic incapacitation probability curves are anything at all like the hypothetical probability curves for Load A, Load B, and Load C, there are some practical implications for surviving gun fights with handgun loads. Even though some handgun loads might perform significantly better than others, there is no magic bullet. Short of a hit to the CNS, even the best-placed handgun bullets require substantial time (compared to the time span of most gun fights) to cause incapacitation in the majority of cases. As we will discuss later, multiple hits might decrease the time to incapacitation, but short of a direct hit to the CNS, multiple hits do not change this basic result.

Consequently, surviving a gun fight requires more than good shot placement with good handgun bullets; surviving a gun fight requires tangible actions to avoid getting shot during the time interval before incapacitation occurs. Evasive action is necessary, and the significant likelihood that incapacitation is still several seconds away should be sufficient motive for the defensive shooter to be moving rapidly toward cover, or in the absence of cover, at least moving to make for a more difficult target.

In summary, we have defined stopping power using incapacitation probability curves that describe the probability of involuntary incapacitation as a function of time. We make reference to the specific case of involuntary incapacitation of human targets shot near the center of the chest to help explain the concept. However, our stopping power definition also applies to alternate shot placements. Generalizing this definition to include voluntary contributions to incapacitation, contributions of new incapacitation mechanisms, and the probability of incapacitation with multiple hits is straightforward.

Michael Courtney