Let's talk about handgun FMJ effectiveness

[curl]

You are not reading this correctly. Note that you are reading a description of a GSW in the neck (marked #2 on the diagram). The description "11" from the top of the head and 2" left of anterior midline" is giving you the X and Y coordinates of where the coroner is visualizing the bullet to have entered, not how deeply it traveled. i.e. measuring 11" down from the top of the head and going left 2" from anterior midline would place entry wound just above the left clavicle (on me). This is supported by the coroner's illustration on the cover page of her report.

To estimate the depth of penetration, you would need a different set of measures entirely (the Z axis), which are not provided in this report.

To illustrate how to read the coroner's descriptions -



(I know that the exit wound is 12" and not 11" below the top of the head but I am lazy, it is late, and this will have to suffice).

I am reading it correctly, and there is NO exit wound. The bullet entered 11" below top of the head and was recovered 12" below top of the head, after traveling left to right 7.0". Using simple Pythagorean theorem, that distance (in two dimensions) is 7.07". Note: "Direction is left to right (7.0") and SLIGHTLY (12"-11"=1.0") downward," and this planar path (7.07") has now been taken into account. Further, "direction is SLIGHTLY front to back" so if it's 0.5, 1.0, or 1.5" front to back distance it doesn't really matter much because the final distance will be the square root of (7.07" squared + (SLIGHT front to back distance) squared. Obviously, the total distance the bullet traveled in 3-D will be no more than 7.5" with any "SLIGHT" front to back distance.

[Nephrology]

I am reading it correctly, and there is NO exit wound. The bullet entered 11" below top of the head and was recovered 12" below top of the head, after traveling left to right 7.0". Using simple Pythagorean theorem, that distance (in two dimensions) is 7.07". Note: "Direction is left to right (7.0") and SLIGHTLY (12"-11"=1.0") downward," and this planar path (7.07") has now been taken into account. Further, "direction is SLIGHTLY front to back" so if it's 0.5, 1.0, or 1.5" front to back distance it doesn't really matter much because the final distance will be the square root of (7.07" squared + (SLIGHT front to back distance) squared. Obviously, the total distance the bullet traveled in 3-D will be no more than 7.5" with any "SLIGHT" front to back distance.

...the Pythagorean theorem is used to measure the hypotenuse of a two-dimensional triangle - i.e, 3 points connected on the same plane. Last I checked, humans exist in 3 dimensions.

In the case of GSW #2, you can sort of use your assumption because the bullet is traveling primarily along the Y axis, for which we have a distinct measurement. For the majority of the rest of the penetrating trauma (i.e. GSW #15), you cannot use the Pythagorean theorum, because again, we have no measurement for the Z axis.

[BehindBlueI's]

Exercise:

Take a soft tape measure and hold it to the wall over your kitchen counter. Say, 12" so the end of the tape is under your thumb and 12" is at the edge of the counter. Move the 12" toward you roughly 4-5", note that 12" no longer reaches the counter and you'll need to let out more tape to about 14". This is what you've done so far with your math. Now take the 14" and move it roughly 4-5" left. You'll find the tape no longer touches the counter again and you'll have to let it out another 2" or so to touch.

That's what Nephrology is telling you. You have one triangle, you can do the math to get to the first tape movement. You don't know how far to move the tape the second time, so to speak.

At this point, other than for the sake of argument and to show you don't understand things as well as you think you do, what's the point of continuing? You've already stated you carry bonded HP.

[Nephrology]

You can use Pythagoras' Theorem in 3 dimensions, you essentially just have to do it twice (as curl did in his example in post #215). I'd likely be unsuccesful explaining math over the internet in as few words as I'm willing to type, so I'm just use a screenshot of the pertinent portion of this page:

Attachment 5249

It's also important to remember that 2 points will always be co-planar. They may not reside in the XY, YZ, or ZX planes of an arbitrarily defined cartesian coordinate system, but they will always share a plane (actually they'll share an infinite number of planes since you need 3 points to uniquely define a single plane).

This is a fair counterpoint (2AM is not a time of the day I associate with my strongest mathematical reasoning skills). That said, you still need the "b" value in order to find "h", which is the essence of my point - without knowing the distance between the anterior and posterior boundaries of the cadaver (b), we cannot find h.

[curl]

You can use Pythagoras' Theorem in 3 dimensions, you essentially just have to do it twice (as curl did in his example in post #215). I'd likely be unsuccesful explaining math over the internet in as few words as I'm willing to type, so I'm just use a screenshot of the pertinent portion of this page:

Attachment 5249

It's also important to remember that 2 points will always be co-planar. They may not reside in the XY, YZ, or ZX planes of an arbitrarily defined cartesian coordinate system, but they will always share a plane (actually they'll share an infinite number of planes since you need 3 points to uniquely define a single plane).

That's correct; I assumed that participants in this thread are familiar with simple high-school geometry. So the bullet path in this case, #2, is soft tissue only, penetration of 7.1-7.5". Shall I go on?

[curl]

This is a fair counterpoint (2AM is not a time of the day I associate with my strongest mathematical reasoning skills). That said, you still need the "b" value in order to find "h", which is the essence of my point - without knowing the distance between the anterior and posterior boundaries of the cadaver (b), we cannot find h.

As pointed out previously, it doesn't matter because the depth is "SLIGHT" compared to the 7' lateral penetration. Obviously, that's because when you have a 7" distance squared and you add to it whatever "slight" distance squared, the sum will not change much whatever "slight" is. That's simple math, indeed. The difference in height between entry and retrieval point was 12-11=1" and that was deemed "SLIGHT." So even if the "SLIGHT" difference in depth is twice the "SLIGHT" difference in height, namely 2", it doesn't change the length of the bullet path much, as pointed out above.

[Nephrology]

Can you please explain how you are finding the values d, b, and h, when you are only given c and a?

Also note that there will be two different values for a and c (a' and c'), as the vertical/lateral displacement in the anterior and posterior planes will obviously not be the same.

As pointed out previously, it doesn't matter because the depth is "SLIGHT" compared to the 7' lateral penetration. Obviously, that's because when you have a 7" distance squared and you add to it whatever "slight" distance squared, the sum will not change much whatever "slight" is. That's simple math, indeed. The difference in height between entry and retrieval point was 12-11=1" and that was deemed "SLIGHT." So even if the "SLIGHT" difference in depth is twice the "SLIGHT" difference in height, namely 2", it doesn't change the length of the bullet path much, as pointed out above.

Please apply this reasoning to GSW #15.

[curl]

Can you please explain how you are finding the values d, b, and h, when you are only given c and a?

Also note that there will be two different values for a and c (a' and c'), as the vertical/lateral displacement in the anterior and posterior planes will obviously not be the same.



Please apply this reasoning to GSW #15.

Before we tackle #15, let's settle #2. I take it you don't see how the bullet path calculates close to 7.5". If, you don't see it, define/show precisely what you are referring to as "a-h",so the math can be done in terms of those dimensions. As given from the detailed autopsy we have: lateral penetration of 7", downward ("slight") penetration of 1" (tangent of 1/7), and "slight" front to back penetration. In terms of those specified dimensions, what is your "a,b,c,d, b, h"?

[Nephrology]

Before we tackle #15, let's settle #2. I take it you don't see how the bullet path calculates close to 7.5". If, you don't see it, define/show precisely what you are referring to as "a-h",so the math can be done in terms of those dimensions. As given from the detailed autopsy we have: lateral penetration of 7", downward ("slight") penetration of 1" (tangent of 1/7), and "slight" front to back penetration. In terms of those specified dimensions, what is your "a,b,c,d, b, h"?

I see how you are estimating #2 - as I said many posts back, if the majority of the bullet's displacement is along the X axis and/or Y then your equation roughly fits. Where I am having trouble following your logic is when the bullet penetrates along the depth of the body habitus (i.e. GSW #15, inter alia)

Refer to tom Jones' previous post for the diagram from which I am deriving the variables. For #15, a and c (entry wound) = -28" and right 1 7/8", a' and c' (site where the bullet came to rest along the anterior abdominal wall) = -25" and left 2" (all measurements from top of the head and midline, respectively)

[curl]

I see how you are estimating #2 - as I said many posts back, if the majority of the bullet's displacement is along the X axis and/or Y then your equation roughly fits. Where I am having trouble following your logic is when the bullet penetrates along the depth of the body habitus (i.e. GSW #15, inter alia)

Refer to tom Jones' previous post for the diagram from which I am deriving the variables. For #15, a and c (entry wound) = -28" and right 1 7/8", a' and c' (site where the bullet came to rest along the anterior abdominal wall) = -25" and left 2" (all measurements from top of the head and midline, respectively)

So you accept that the bullet penetration path length for #2 is most probably 7.1 - 7.5" long?