Re: GEV and Grav Vehicles

On Wed, 1 Dec 1999, Roger Books wrote:

> On 30-Nov-99 at 20:59, Allan Goodall (agoodall@interlog.com) wrote:
>  
> > Sorry, yes you get recoil. It just won't be much of a problem.
> > 
> > Remember, energy is mv**2, but momentum is mv. In other words, if
you have
> > a very small projectile and accelerate it relatively slowly, you
will
> > build up a lot of energy without much reverse momentum.
> > The "v" component
> 
> The easiest way to think of this is the kinetic energy (mv**2) of the
> projectile will be the _same_ as the kinetic energy of the firing
> platform. 

that is incorrect.

Newton's third law of motion tells us that when something is fired from
a
gun, the magnitude of the _momentum_ of the projectile will be the same
as
that for the firing platform. it is possible to look at this a little
more
closely.

<maths>

i'll work in scalar units to keep things simple.

quantities:

m	mass
v	speed
p	magnitude of momentum
E	kinetic energy

relationships:

p	=	mv
E	=	mv^2/2

i'll prime things which apply to the projectile, so x is x for the tank
and x' is x for the projectile.

let's say the things we know are m, m' and E', and the thing we want to
know is v; that is, for a given projectile energy, and given masses of
vehicle and projectile, how much recoil is there? what we're really
interested in is the way v varies with m'.

E'	=	m'v'^2/2 // by definition
m'v'^2	=	2E'
v'^2	=	2E'/m'
v'	=	(2E'/m')^1/2 // call this 'A'

p'	=	m'v'	// by definition
p	=	mv	// by definition
p	=	p'	// newton's third law
p	=	m'v'
mv	=	m'v'
v	=	(m'/m)v'
v	=	(m'/m)(2E'/m')^1/2	// using A to substitute for v'
v	=	(2E'm'/m^2)^1/2

so (where | means 'is proportional to')

v	|	E'^1/2
v	|	m'^1/2
v	|	1/m^2

</maths>

so, for a constant projectile energy and vehicle weight, the recoil
produced by a gun is proportional to the square root of its mass. thus,
if
we use a smaller round, we get less recoil *even though we are putting
the
same amount of energy into it*. we are also more power efficient, as
less
energy is going into recoil.

> So yes, it is a problem, no matter how slowly you accelerate
> the projectile.  You could correct for this with a circular
accelerator
> approach I guess, but I can't see this being small enough to fit in
> a combat vehicle.

it wouldn't work anyway - if you shoot out a projectile of a given mass
and speed, you get a particular recoil, irrespective of how you do it.
to
ref another thread, TANSTAAFL.

tom