Velocity loss adjustment for penetration through skin and bone
For whoever is interested, here is the corrected version of the formula I had posted earlier, which is an attempt at estimating the velocity losses after a bullet penetrates skin and bone. This corresponds somewhat with the findings of several ballisticians/scientists, such as Sellier. Mention of his formulas can be found on this Italian
webpage:
http://www.earmi.it/balistica/baltermi.htm
Instead of doing that walkthrough for the desktop calculator, I'll just explain how it works. I came up with a shortcut for it, but this doesn't really show how/why this application might be valid.
As always, you'll need these four variables:
Bullet Diameter (in inches)
Bullet Weight (in grains)
Impact Velocity (in feet per second)
Drag Coefficient/"Form Factor" (unitless)
Values:
0.52 - 0.55 for spitzer-type bullets
0.55 - 0.57 for flatpoint/hollowpoint bullets
0.57 for roundnose bullets
0.7 for mushroomed bullets
0.83 for flat cylinder
Deceleration through 0.06 inch layer of skin:
Deceleration = 0.5 x V^2 x
Density x
Tensile strength /
Atmospheric pressure (lbs per cubic ft) x
area x
drag coefficient /
Bullet Mass
Where:
V= Impact Velocity
Density = 62.4 lb per cubic ft (density of skin)
Tensile strength = 62656 lb per sq ft (tensile strength of skin)
Atmospheric pressure = 2116.8 lb per square ft
Bullet mass = Bullet weight / 7000 = mass in lbs
Area = (Bullet diameter/12) x pi / 4
(Acceleration due to gravity figured in the original equation, but is canceled out in the final version of the formula above.)
Remaining velocity after skin penetration (assuming a 0.06 skin layer)
This is easily solved using textbook physics:
Velocity-resulting = (
V^2 - 2 x
Deceleration x
Depth/12)^.5 [in other words, the square root]
Where
Depth = the skin thickness of 0.06 inch
(Note: if the value within the parenthesis is zero or a negative number, then there is no further penetration!)
Deceleration through 0.25 inch bone:
Use the same formulas for
Deceleration and
Velocity-resulting above, substituting the previously obtained
Velocity-resulting as the
V value. Also substitute:
Density = 124.8 lb per cubic ft (density of bone)
Tensile strength = 3550.5 lb per sq ft (tensile strength of bone)
Depth = 0.25 inch (estimate of bone thickness)
So, even if it's wrong, this is it! If you like the results, you can substitute these in the original Version 2 formula above.
I've worked a few examples for purposes of illustration:
.380 ACP (90gr)
Initial: 1000 fps
After skin penetration: 847 fps
After bone penetration: 788 fps
9mm NATO (124 gr FMJ)
Initial: 1189 fps
After skin penetration: 1061 fps
After bone penetration: 1008 fps
.45 ACP (230 gr FMJ)
Initial: 850 fps
After skin penetration: 771 fps
After bone penetration: 738 fps
.30 Carbine (110 gr FMJ)
Initial: 1572 fps (@ 100 yards)
After skin penetration: 1429 fps
After bone penetration: 1370 fps
.45-70 USG (405 gr RN)
Initial: 1168 fps
After skin penetration: 1106 fps
After bone penetration: 1078 fps
