Re: Laser Sail

On Nov 29, 2:31 pm, Ilmari Karonen <usen...@xxxxxxxxxxxxxx> wrote:
IsaacKuo <mech...@xxxxxxxxx> kirjoitti 27.11.2007:

The lowest energy is actually equal to what such things as wheels
and legs would require (assuming no friction losses). A 100%
efficient rocket puts all of the energy input into the kinetic energy
of the payload and 0% of the energy into the exhaust. This can be
accomplished in principle by exactly matching the current exhaust
velocity with the rocket's current velocity. Of course, this rocket
will waste some energy getting going at the very start--an exhaust
velocity of zero doesn't provide any thrust. However, this amount of
wasted energy can in principle be reduced below any arbitrarily
small amount.

The end result of the 100% efficient rocket is a payload with 100%
of the spent kinetic energy, and a trail of exhaust perfectly left
behind at zero velocity. The amount of energy used is 1/2 mv^2,
where m is the mass of the payload and v is the final velocity.

Of course, your 100% efficient rocket will also gain no momentum,
except for the initial "wasted" nudge; dropping behind motionless
exhaust will only serve to concentrate whatever momentum the rocket
already has into a smaller remaining mass.

It will also increase the rocket's speed and kinetic energy. The
amount of energy required for a given momentum is inversely
proportional to the initial mass. So the "wasted" nudge can use
a small amount of energy to provide a large amount of momentum.

Thus, the smaller you make the initial nudge, the smaller your final
payload mass has to be for a given target velocity. In fact, you'd
achieve exactly the same efficiency by just firing the final payload
out of a gun mounted on the rest of the starting mass. Or, indeed,
equipping the payload with legs and having it jump off. (Assuming,
for the sake of the exercise, arbitrarily strong legs of negligible
mass -- just a simple matter of engineering, really.)

This is true, but such a gun will impose an incredible amount of
acceleration on the payload. The advantage of a rocket is that
you can gently accelerate the payload and thus not destroy it.

Also, a rocket can be used to slowly push through the Earth's
atmosphere before applying the bulk of the acceleration.
If you accelerate a payload with a gun up to 10km/s at the
Earth's surface, it will promptly burn itself up soon after leaving
the muzzle (that's assuming it survived the shock of firing,
of course). A rocket can gently fly through the atmosphere
before accelerating to many km/s after climbing above it.

Isaac Kuo
.

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