| From: | Adam Getchell <acgetche@****.UCDAVIS.EDU> |
|---|---|
| Subject: | Momentum and the laws of physics |
| Date: | Thu, 20 Apr 1995 14:04:31 -0700 |
> Could be... except I tried it with momentum and the numbers just didn't match
> either my experiences, or those of others in real life. Energy seemed about
> right, but it's hard to measure accurately from uprange, and nobody wants to
> stand next to the target :-)
Anecdotal evidence is a bit suspect.
> Part of the problem of engineering. Try the "right" theory. Doesn't work.
> Try a slightly less right one. Numbers match. Limited time, so use the theory
> that fits reality...
Point is, the "less right" theory doesn't necessarily match
reality, so much as expectations. I've studied both engineering and
physics, and a "correct" theory for engineering is the least complicated
one they can get away with that gives accurate enough results over the
ranges they're interested in ... that's a lot of qualifiers ;-)
> > you'd come up with the same results. Because, while energy is not
> > conserved in the interaction, momentum always is.
>
> Well, there's the theory, and there's the practice :-)
Well, in this universe, the practice is that momentum is always
conserved, period.
> I did - and I checked around and rechecked my sources. Still talking different
> numbers. Although the force acts for a short duration, it has a high level and
> extremely small area of effect.
Here is where you have a gap in understanding. Force doesn't
matter. Pressure doesn't matter. In a two-body (or multi-body
interaction, such as the classic continuum mechanics problem)
center-of-mass momentum transfer is the determinant on final velocity,
and incidentally, kinetic energy. Take a classical dynamics course
series (or two), do some real physics with the Lagrangian or Hamiltonian
operator formulation of the laws of motion (which do not use the concept
of force, by the way) and you will understand what I am saying.
> I rechecked the articles and read more widely. There is some empirical (reports)
> and enormous anecdotal evidence to suggest that the situation when an individual
Anecdotal evidence is nearly an oxymoron. There is anecdotal
evidence that the earth is flat. Is that true? Has there been any sort
of statistical analysis done on this "anecdotal evidence"? Was the
evidence gathered in a scientific fashion, without preconceptions,
accurately? No. It is therefore suspect, and most scientists would throw
it out. It may not be incorrect, but it is certainly unusable.
> analysis. But consider that a good 9mm pistol round (a police-issue +P+)
> will immediately incapacitate with one shot 85-90% of the time (Marshall and
> Sanow) - and incapacitation means "fell down and stopped being
troublesome".
> That to me suggests that these things knock you down. Not necessarily back:
> but definitely down.
Come on now; using a definition to prove conclusive momentum
transfer? I don't care how Marshall and Sanow define incapacitation;
that doesn't mean the bullet transferred enough momentum to pick up their
assailants! At best, it means the wounded individuals fell down in shock.
> Fackler's a momentum enthusiast, but his work indicates rather higher *local*
> results than your "average-across-the-body" numbers. And even to say
"I have a
> net velocity backwards of only 10cm/s so I'm fine" is very vague. How do you
What's a momentum enthusiast? Does he really like Lagrangian dynamics?
At any rate, this argument is invalid. Consider: a local system is
composed of all the objects in the interaction, minus all exogenous
variables (like, ficticious forces such as Coriolis force). A bullet
that strikes your hand, say, is just an interaction between the bullet
and your hand. But, (what do you know!) your hand is connected to the
rest of your body. In the act of giving your hand momentum, some
momentum is imparted to your body. In order to knock you down (solely on
the basis of the bullet's momentum, and not from you throwing yourself
about due to shock) the bullet still has to overcome the inertia of your
whole body, because it is one system. This is just like a classic physics
problem: m1 at velocity v1 strikes and has a perfectly inelastic (ie
sticks together) with stationary mass m2. Together, they then strike
mass m3. What is the final velocity vf of m1+m2+m3?
This problem illustrates the concept of a changing system. As m1
connects to m2, the system changes ... though it is still a local
system. As m1+m2 connect to m3, the local system changes yet again.
This is exactly analogous to a bullet striking your hand to knock you over.
Finally, if physics won't persuade you, there is the following
non-anecdotal evidence.
During the 1984 L.A. Olympics, my father worked with the L.A.
Swat teams and the special military forces tasked to quick response
against potential terrorist activity. While they were conducting
training he viewed the following demonstration.
Swat team member was geared up in his protective ensemble. Swat
team member was blindfolded. Swat team member stood on one leg. Swat
team member was then shot with a variety of rifle and handgun ammunition,
including 7.62 mm NATO, 5.56 mm NATO, 9mm, .357 magnum, and Soviet 7.62
mm. (Those guys are crazy!). Not in one instance did the Swat team
member fall over from the bullet impact, even with hampered balance.
If Ivy Ryan were still on the list, she could tell you similiar
stories from personal experience.
> Rechecking the math, though, you're right: the energy transfer goes into
> mutilated tissue and sideways cavitation, not velocity. On the other hand, if
> you want to model the dynamic response of the human body to a bullet impact,
> go to it: I really doubt averaging it over the entire body weight is the way
> to go.
If I were in the business of modelling dynamic response of the
human body to anything, I would be constructing a five bar linkage model
with the appropriate lengths and masses for each link, and then calculate
the effect of the negligible momentum transfer of a bullet upon each
link, much the same as I did calculating human bicycling efficiency with
four and five bar linkage models in my engineering dynamics lab. We had
access to extensive data collected from the Air Force as far as average
distribution of human weight in limbs/torso (gotten in the typical
military way of dissecting cadavers and directly measuring masses, then
statistically analyzing the results). But looking at my earlier four bar
model, applying the tiny amounts of momentum a typical bullet generates
has little result.
> Paul J. Adam paul@********.demon.co.uk
========================================================================
Adam Getchell "Invincibility is in oneself,
acgetche@****.engr.ucdavis.edu vulnerability in the opponent."
http://instruction.ucdavis.edu/html/getchell.html
