Re: [Phys-l] Ballistics divertissement

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

On Friday, 10/6/2006, Bernard Cleyet wrote:

> bc, who notes JS's argument suggests rocket engineers prefer denser 
> fuels (w/ the same specific energy)...

I found this to be a thought-provoking statement.  Clearly it is true
when the mass of all the material being sent out the back of the rocket
is negligible compared to the payload--the more mass sent out the more
momentum the payload winds up with.  But as John Denker has already
pointed out, when the mass of the fuel is a significant fraction, of or
some multiple of, the mass of the payload, a significant fraction of the
momentum acquired by the rocket upon ejection of a particle of matter is
momentum of the remaining fuel rather than the momentum of the payload.

I wrote a little SciLab routine--page 3 of the document:
http://www.anselm.edu/internet/physics/phys-l/rockets.pdf 
to calculate (in a simple model) the final speed of a "payload",
initially at rest and part of a rocket with no external forces acting on
it, as a function of the mass of each particle ejected (assumed to be
the same for all ejected particles) with a fixed total amount of energy
such that, for a given total number of particles, each particle gets the
same amount of energy independent of the value of the mass of the
particle.

As the graph on the last page of the document shows, increasing the mass
of each particle (which in turn increases the total mass ejected which
is what I chose to plot on the abscissa) does increase the final payload
speed up to the point where the total mass ejected is about 4 times the
mass of the payload, but, beyond that, the final speed decreases with
increasing particle mass.

It is interesting to note that (in experimenting with the code I found
that) it does not much matter how you chunk up the matter being ejected
(as long as you chunk up the energy the same way); you get essentially
the same results whether you divide the matter being ejected into 10
pieces and expend 1/10 of the total energy ejecting each piece out the
back or you divide it up into 800 pieces and expend 1/800 of the total
energy ejecting each piece out the back of your rocket.