Re: Rail guns (was: US SOCOM desires...)

["Robert J. Hansen" <rjhansen@xxxxxxxx>]

> Its a given that action and reaction happen but i think you have your 
> numbers gummed up somehow.  the soldier weighs 15000 x what the slug 

Brian, look at the numbers.  If you like, grab a physics book while
you're up--we're going to be covering basic Newtonian mechanics.  You'll
also need a calculus book, since we're going to be covering definite
integrals.

=====

Newton's Law: force equals mass times acceleration (F = Ma).

Kinetic energy equals the sum of all the kinetic forces acting upon an
object.

    Q
  /\                       |-Q
  |  Ma dt = 1/2 m(at)**2  |
\/                         |-N
N

(at) = velocity (definition of velocity)

    Q
  /\                   |-Q
  |  Ma dt = 1/2mv**2  |
\/                     |-N
N

Or, Ke = .5m*Q**2 - .5m*N**2

Or, Ke = .5m*v**2, for Q = v and N = 0

Or, sqrt(2 Ke/m) = v

2 Ke = 30,625 joules of energy, times two = 61,250
2 Ke / .005 (mass of flechette) = 12250000
sqrt(12500000) = 3500 m/s (velocity of flechette)

... so the math works just fine for the flechette.

(2 Ke) / 75 (mass of soldier) = approx. 817
sqrt(817) = 28.58 m/s (velocity of soldier)

The soldier may weigh 15,000 times what the flechette weighs, but the
soldier gets *the exact same amount of energy* as the flechette.  

Remember that kinetic energy is proportional directly to the mass, but
to the *square* of the velocity.  You can't just say "the flechette
masses one fifteen thousandth the soldier".  You have to say "it masses
one fifteen thousandth the soldier, but travels 122.5 times as fast."

And 122.5**2, BTW, is... 15,000.