Re: Quick question about a STL trip - and another...

On Aug 22, 5:50 am, David Mitchell <da...@xxxxxxxxxxxxxxxxxxxxx>
wrote:
On Thu, 21 Aug 2008 10:53:32 -0700, IsaacKuo wrote:

My prefered braking drive is a kinetic impact powered rocket. The main
starship is a large magloop with perhaps a dozen payload modules
strung along it like necklace beads.  This can use magsail braking to
reduce its speed.  Behind the main starship is an auxiliary ship
containing a payload of zillions of tiny little robot chips, as well
as a nuclear powered laser to provide power to the chips.  Before
arriving at the destination system, the auxiliary ship releases the
chips, and they fly themselves into a linear formation along the
laser.

Since the main starship has used magsail braking, the chip formation
catches up.  The starship maneuvers to line itself up with the laser,
so the chips pass through the loop-shaped starship.  It puffs
propellant gas in front of it.  Relativistic kinetic impacts with the
robot chips cause explosions of plasma far more energetic than nuclear
reactions or even antimatter reactions.  The resulting relativistic
charged particles get deflected by the starship's magnetic field,
producing backwards braking thrust.

This is probably a silly question (since I assume that you've thought this
through), but won't the plasma produced by the impact retain most of the
momentum of the chip?

If so, how does this help you brake?

The key essentially boils down to ensuring that the mass of the
sacrificial propellant is much greater than the mass of the incoming
chip impactor. To a rough approximation, the result of a kinetic
impact is a spherical explosion in the reference frame of the
chip+propellant mass averaged velocity. If the velocity of the
starship in this reference frame is greater than the speed of the
explosion front, then the explosion products will never hit the
starship's magnetic field.

It's actually possible to extract useful thrust even in that case,
but it's a highly nonintuitive result and requires the use of a
very efficient magnetic nozzle. I'll ignore this possibility and
just stick with the intuitive and technically easier possibility
of a simple "blocking" magnetic field.

For simplicity, the following analysis will assume use
non-relativistic newtonian mechanics. The same basic
principles apply in the relativistic case, but it's harder to
comprehend the basic principle:

Let's assume the chip's mass is 1kg and its velocity is
"v" in the reference frame of the starship. Let's assume
the propellant puff's mass is 4kg. It starts of with a velocity
of 0m/s in the reference frame of the starship.

The total initial momentum is v*1kg. We'll shift to a
reference frame moving at v*1kg/(1kg+4kg) = v/5.
This is the reference frame of the center of the explosion,
and in this reference frame the starship is moving away
at v/5.

What is the speed of the explosion front? Roughly,
kinetic energy is preserved. In the reference frame of
the explosion, the initial kinetic energies are:

chip k.e. = 1/2 * 1kg * (v*4/5)^2 = 8/25 kg * v^2
puff k.e. = 1/2 * 4kg * (v/5)^2 = 2/25 kg * v^2
k.e. = 8/25 kg * v^2 + 2/25 kg * v^2 = 10/25 kg * v^2
= 2/5 kg * v^2

Roughly, the kinetic energy of the spherical explosion
is 1/2 * (1kg + 4kg) * V^2, where V is the speed of
the explosion front. Thus, we have:

5/2 kg * V^2 = 2/5 kg * v^2

V^2 = 4/25 * v^2

V = 2/5 v

The starship is moving at 1/5 v away from the explosion,
while the explosion is expanding at 2/5 v. Thus, the
part heading toward the starship can catch up.

The efficiency of this mechanism improves if you increase
the mass ratio. In the ideal situation, the incoming
chips are moving at near-C speeds. This gives you the
biggest bang for your buck.

Isaac Kuo
.

Relevant Pages

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