Warning: Not for the math/physics phobic.
Someone else kicked off a thread in the handgun forum about sectional density, and this prompted me to start this thread, which might be of interest to some. Sectional density is commonly linked to penetration, but so far few have shown us how exactly in simple terms (assuming that simple terms could apply.)
Some time back, I came across a page on the Internet about a concept that I was unfamiliar with: Momentum density. At first glance, I thought it was junk science, just a few numbers multiplied together, so I wrote it off. Then I decided to look at it more closely, and I considered there might be more to it than first meets the eye.
The concept is mentioned on this page:
http://www.grosswildjagd.de/momentum.htm
About momentum density, the author says:
(Of course, there are several other factors of importance that the author mentions on that page.)
The author states that momentum density is a bullet's momentum divided by the cross sectional area. But guess what? This is virtually the same thing as saying that it is the sectional density times the velocity.
Momentum density = bullet weight, lbs x velocity / area (square inches)
Since we already know that sectional density is already nothing more than a bullet's weight divided by the cross sectional area, just multiply the SD by the impact velocity.
As an example, say we have a mild .44 Magnum load with a 240 grain bullet which impacts at 1000 fps. We probably know alread that the .44 Magnum bullet is actually about .429", so the SD is 240 / 7000 / .429 / .429, or 0.186 lbs/sq inch. Multiply this by the impact velocity of 1000 fps and we get a momentum density of 186. This, according to the author of that page, is the bullet's penetration potential.
Most of us who've been studying terminal ballistics for any length of time know that there is a lot wrong with simple formulas like this. After all, what units are we talking about here? We have momentum, which is ft-lbs / sec (English system) and this divided by the area gives us nothing that makes sense. But you have to remember that momentum is also a unit of force times a unit of time. Like this:
Momentum = pounds (force) x sec
divide this by area in square inches, you get
pounds(force) x sec / sq.in.
which can be rewritten as
pounds(force) / sq. in x sec
In other words, momentum density is a unit of pressure (psi, for instance) times a unit of time. So it could be said that this simple formula may have some actual science behind it.
The problem comes when you try to relate it to practical, easy-to-work examples, such as estimating specific penetration depths, but I've found this can be done in some cases and within certain limitations.
Someone else kicked off a thread in the handgun forum about sectional density, and this prompted me to start this thread, which might be of interest to some. Sectional density is commonly linked to penetration, but so far few have shown us how exactly in simple terms (assuming that simple terms could apply.)
Some time back, I came across a page on the Internet about a concept that I was unfamiliar with: Momentum density. At first glance, I thought it was junk science, just a few numbers multiplied together, so I wrote it off. Then I decided to look at it more closely, and I considered there might be more to it than first meets the eye.
The concept is mentioned on this page:
http://www.grosswildjagd.de/momentum.htm
About momentum density, the author says:
The most important feature for penetration is the momentum density. Momentum density defines the penetration potential of a projectile. Momentum density it defined as the momentum of the projectile divided by the projectile's cross sectional area.
(Of course, there are several other factors of importance that the author mentions on that page.)
The author states that momentum density is a bullet's momentum divided by the cross sectional area. But guess what? This is virtually the same thing as saying that it is the sectional density times the velocity.
Momentum density = bullet weight, lbs x velocity / area (square inches)
Since we already know that sectional density is already nothing more than a bullet's weight divided by the cross sectional area, just multiply the SD by the impact velocity.
As an example, say we have a mild .44 Magnum load with a 240 grain bullet which impacts at 1000 fps. We probably know alread that the .44 Magnum bullet is actually about .429", so the SD is 240 / 7000 / .429 / .429, or 0.186 lbs/sq inch. Multiply this by the impact velocity of 1000 fps and we get a momentum density of 186. This, according to the author of that page, is the bullet's penetration potential.
Most of us who've been studying terminal ballistics for any length of time know that there is a lot wrong with simple formulas like this. After all, what units are we talking about here? We have momentum, which is ft-lbs / sec (English system) and this divided by the area gives us nothing that makes sense. But you have to remember that momentum is also a unit of force times a unit of time. Like this:
Momentum = pounds (force) x sec
divide this by area in square inches, you get
pounds(force) x sec / sq.in.
which can be rewritten as
pounds(force) / sq. in x sec
In other words, momentum density is a unit of pressure (psi, for instance) times a unit of time. So it could be said that this simple formula may have some actual science behind it.
The problem comes when you try to relate it to practical, easy-to-work examples, such as estimating specific penetration depths, but I've found this can be done in some cases and within certain limitations.