KPersimmon
April 7, 2003, 09:23 AM
Sellier's Formula
(Penetration Predictor)
I've decided to share this formula that I found in a European website several years ago. It is an old formula attributed to the German ballistician/physicist Sellier, and has been used to estimate the soft-tissue penetration of bullets of moderate to low velocity. (Probably of about 2000 fps or less, I suppose.) I personally won't swear to its accuracy or its validity, but I think it's interesting nevertheless.
There are a couple of drawbacks to this formula: 1--it uses metric units and 2--it's mathematically sophisticated (i.e. it's geeky.). However, it can probably be employed on any half-decent scientific calculator. (It most certainly can be used with the standard Windows calculator set to the Scientific view mode.)
I'll now give a step-by-step walkthrough of the deal in hopes that some of you might find it interesting, even if it's only useful for entertainment purposes.
#1--Determine the sectional density (in grams per square centimeter). (NOTE: This is the pivotal point of the formula, as you might expect.)
a. To convert to grams, multiply the bullet weight in grains by 0.0648.
b. To convert to cm, multiply the bullet diameter by 2.54. Now square this result.
c. Divide (a) by (b)
d. Label the result SD for reference.
(Example: 115-grain 9mm Para. bullet of. 0.355 inch diameter.)
a. 115 X 0.0648 = 7.452 g
b. (0.355 X 2.54) X (0.355 X 2.54) = 0.813
c&d. So SD = 7.452 / 0.813 = 9.165 g/sq-cm
#2--Determine the estimated velocity loss from impact with "soft tissue" (in meters per second.)
Vloss = 125 / SD + Constant
For the Constant, assume either a value of 22 for impact with clothing or 100 for bare "soft tissue." (I'm going to use the constant 100 in my example.)
(So from my example: Vloss = 125 / 9.165 + 100 = 113 m/s, rounded.)
#3--Determine the velocity after "impact." (Label the result "Vimp" for reference.)
a. Convert feet per second to meters per second by dividing fps by 3.2808
b. Subtract Vloss from (a)
So, Vimp = V (m/s) - Vloss
( In my example, I'll be assuming a velocity before impact of 1100 fps. So: Vimp = 1100 / 3.2808 - 113 = 222 m/s)
#4--Determine the "multiplier" (Call it "Vmult")
a. Divide Vimp by the "velocity constant" of 50
b. Take the Natural Logarithm (ln) of [a].
So, Vmult = ln (Vimp / 50)
(Example: 222 / 50 = 4.44.
So, Vmult = Natural Logarithm (ln) of 4.44 = 1.49)
#5-- Now get the estimated (hypothetical) penetration depth (You can label this "Pen" if you like.)
Pen = 2.3 * SD * Vmult
(Example: 2.3 X 9.165 X 1.49 = 31.4 cm
To convert to English units, divide this result by 2.54 to get: 12.3 inches.)
To all ballistics geeks: Hope you enjoy!
Many thanks to Mr. Edoardo Mori and his excellent Italian-language ballistics page, where this formula was found.
http://www.earmi.it/balistica/baltermi.htm
(Penetration Predictor)
I've decided to share this formula that I found in a European website several years ago. It is an old formula attributed to the German ballistician/physicist Sellier, and has been used to estimate the soft-tissue penetration of bullets of moderate to low velocity. (Probably of about 2000 fps or less, I suppose.) I personally won't swear to its accuracy or its validity, but I think it's interesting nevertheless.
There are a couple of drawbacks to this formula: 1--it uses metric units and 2--it's mathematically sophisticated (i.e. it's geeky.). However, it can probably be employed on any half-decent scientific calculator. (It most certainly can be used with the standard Windows calculator set to the Scientific view mode.)
I'll now give a step-by-step walkthrough of the deal in hopes that some of you might find it interesting, even if it's only useful for entertainment purposes.
#1--Determine the sectional density (in grams per square centimeter). (NOTE: This is the pivotal point of the formula, as you might expect.)
a. To convert to grams, multiply the bullet weight in grains by 0.0648.
b. To convert to cm, multiply the bullet diameter by 2.54. Now square this result.
c. Divide (a) by (b)
d. Label the result SD for reference.
(Example: 115-grain 9mm Para. bullet of. 0.355 inch diameter.)
a. 115 X 0.0648 = 7.452 g
b. (0.355 X 2.54) X (0.355 X 2.54) = 0.813
c&d. So SD = 7.452 / 0.813 = 9.165 g/sq-cm
#2--Determine the estimated velocity loss from impact with "soft tissue" (in meters per second.)
Vloss = 125 / SD + Constant
For the Constant, assume either a value of 22 for impact with clothing or 100 for bare "soft tissue." (I'm going to use the constant 100 in my example.)
(So from my example: Vloss = 125 / 9.165 + 100 = 113 m/s, rounded.)
#3--Determine the velocity after "impact." (Label the result "Vimp" for reference.)
a. Convert feet per second to meters per second by dividing fps by 3.2808
b. Subtract Vloss from (a)
So, Vimp = V (m/s) - Vloss
( In my example, I'll be assuming a velocity before impact of 1100 fps. So: Vimp = 1100 / 3.2808 - 113 = 222 m/s)
#4--Determine the "multiplier" (Call it "Vmult")
a. Divide Vimp by the "velocity constant" of 50
b. Take the Natural Logarithm (ln) of [a].
So, Vmult = ln (Vimp / 50)
(Example: 222 / 50 = 4.44.
So, Vmult = Natural Logarithm (ln) of 4.44 = 1.49)
#5-- Now get the estimated (hypothetical) penetration depth (You can label this "Pen" if you like.)
Pen = 2.3 * SD * Vmult
(Example: 2.3 X 9.165 X 1.49 = 31.4 cm
To convert to English units, divide this result by 2.54 to get: 12.3 inches.)
To all ballistics geeks: Hope you enjoy!
Many thanks to Mr. Edoardo Mori and his excellent Italian-language ballistics page, where this formula was found.
http://www.earmi.it/balistica/baltermi.htm