Re: starship-design: Pellet track

[kuo@bit.csc.lsu.edu (Isaac Kuo)]

Timothy van der Linden wrote:
>Hello Isaac,
>>>If the pellets are slow moving, then what is the use of pellets?
>>>Catching pellets like this, will not give a significant energy advantage
>>>over taking the pellets with you (=attached to the starship) from the start.

>>The advantages are:

>>1. You only have to accelerate the unfueled ship.

>But you have to do more trouble to add momentum from the pellets.
>The higher their relative velocity, the more energy is needed to add an
>equal amount of momentum. (dE=0.5*dp*v)
>In a self-fueled ship you don't have this problem, the mass that is on board
>has zero relative velocity and thus momentum can be added much easier.

While this is true, the advantage I state is still there.  There is the
disadvantage of the potential extra difficulty in deriving momentum
from the pellets (but due to the way fusion power works, my bet is that
the latter difficulty is not nearly as significant).

>My guess it that both effects cancel out.

Probably not.  The problem of accelerating a fueled ship is a difficulty
which rises in proportion to the propellant/payload ratio--this goes up
exponentially with desired cruise velocity.  The problem of accelerating
pellets is a difficulty which rises _linearly_ in proportion to desired
cruise velocity (or at worst with the square of the desired cruise
velocity).

Thus, if the propellant/payload ratio is rather low, the fueled ship
wins out.  If the propellant/payload ratio is rather high, the unfueled
ship wins out.

>As long as you use the same amount of mass as for a self-fueled ship, a
>pellet track design needs just as much energy!

>However if you use more mass, and thus add less momentum per unit of weight,
>then you can indeed save energy.

I imagine going this route--not to save energy, but to reduce _power_
requirements.  The objective is to make the starship itself as lean
and mean as possible, offloading all the work into whatever is setting
up the acceleration tracks.  However, the starship itself must have
magnetic fields strong enough to contain the fusion reactions, and
can only handle so much at a time (assuming superconductor coils, the
magnetic field strength is limited).  There is a strong desire for
high thrust, and if you're limited in power, the only way to get higher
thrust is to increase reaction mass.

Saving energy is an inherent added bonus, of course.

One thing that a lot of people seem to ignore when discussing traditional
fusion rockets is that any fusion rocket with very high Isp will be
_very_ low thrust, because of power requirements.

>What I didn't think of during all these years of starship discussion, is
>that the pellet track can have quite large amounts of mass. That would mean
>that much less energy is needed.
>On the other hand you'd have quite unlimited amounts of fusion energy too.
>The only disadvantage is that you've to start making the track years in
>advance, depending on the lenght of the acceleration track and the velocity
>of the pellets.

This is the primary reason for wanting high thrust in an acceleration
track design.  In order to limit how much time is needed to set it
up, you _need_ a reasonably short track.

The deceleration track can be set up over a long period of time, so
this is less of a concern.  However, it also can be set up so that
the track can arrive at any "length" desired, so if your starship
is already a high thrust design, there isn't any reason to _not_
make the deceleration run high thrust (and besides, this minimizes
rear shielding requirements).

>>2. You don't have to bend over backwards trying to ignite fusion (since
>>   you're using the pellet's kinetic energy).  It's actually _easier_
>>   to implement a fusion ramjet than it is to implement a onboard
>>   fusion drive.

>Why is it easier?

Because in order to initiate fusion, you need high temperature and
pressure.  In a traditional pulsed fusion rocket design, this is
acheived with either very powerful lasers and/or a fission reaction.

With the lasers, an incredible amount of power is needed (and for
the deceleration run, don't bet on getting power beamed in from
the source system).  That means a powerful on board energy source
and big heavy lasers.

With a pure fission reaction providing confinement (H-bombs), there
is a minimum size to the individual bombs, thus necessitating a big
and heavy "nozzle" to direct the reactants rearward.  A _really_
big and heavy nozzle.  Which is also leaky, because you can't direct
the neutrons rearward.  And you'd better shield the payload and the
fuel stores from the neutrons.

In a traditional continuous fusion rocket design, you need magnetic
confinement, but you can't use superconductors because the field
strengths needed are too high.  Thus, the confinement will be
leaky--but this is sort of okay because you'll use the leaks for
the thrust.  However, those leaks mean a drain on the energy in
the system, and if it's too leaky then you don't have the energy
to sustain fusion.  So far we haven't solved that problem but
let's suppose we have.  That _still_ leaves the problem of the
big heavy non superconducting magnetic coils needed to confine
the fusion reaction.

The ramjet design is essentially a pulsed fusion rocket design.
The big difference is that it uses the kinetic energy of the
incoming pellets to provide the energy to initiate fusion.
Conveniently enough, this power is directly "generated" within
the pellet itself, so no equipment at all is needed to get the
energy where it's needed!  The ship still needs powerful magnetic
coils to provide confinement, but these only need to be powerful
enough to handle pulsed fusion (like the laser confinement pulsed
scheme), and don't need the strength to sustain the pressure
and concentration needed for sustained fusion.

>>3. The fuel requirements for a given cruise velocity go up roughly
>>   linearly, as opposed to exponentially for a fusion drive.

>With "fusion drive" I assume you mean a design that takes all its fuel with it.
>You have to specify what you mean with fuel: mass or energy
>The energy (not mass) requirements for a selffueled design do not increase
>exponentially, but with a 3th power.

Actually, the energy _does_ increase exponentially.  The amount of
propellant required increases exponentially, so the amount of energy
required also does (because the amount of energy used goes up
linearly with the amount of propellant used).  This is well established
in the rocket equation.

You get exponential increases because in order to double your speed,
you need to square the propellant/payload ratio.  Why?  Because you
have to carry the propellant with you.

How in the world do you get a 3rd power?

>I'm not so sure that a pellet track uses linearly more fuel if it increases
>its cruising velocity. My guess is that it will be 3th power too.
>Can you show/explain me why you think it will increase linearly?

Because you do not have to carry the propellant with you.  The
amount of thrust you get is still roughly proportional to the
amount of propellant used, although you are right that it will
get more difficult with speed.  Due to the way the drive works,
this increase shouldn't be much (mostly because it's not very
efficient at low speeds--the amount of momentum added is limited
by the magnetic fields).

However, assuming a perfectly ideal accelerator track scheme,
the increase will be with the square of the velocity.  In the
ideal situation, the same amount of energy is imparted to each
incoming pellet, so the amount of thrust you get from a pellet
is inversely proportional to its relative velocity.  This will
blow up track mass requirements as the square of the desired
cruise velocity.

>>4. The effort involved may be spread over a long period of time.
>>   For the acceleration track, this might not be much of an issue,
>>   because all the time spent setting up the acceleration track
>>   is simply delaying the completion of the mission that much
>>   longer.  For the deceleration track, this is a critical bonus
>>   because you can manufacture and send fuel packet drones over
>>   a period of years while the starship is progressing toward
>>   the target system.

>Ah, this is new as far as I know. The pellets catch up with the starship
>instead of vice versa.
>That indeed decreases the track preparation time.

It's what I've been trying to explain from my first e-mail here.
I'm trying to explain what I had thought was a very obvious idea
for sending a deceleration track to the target system.

However, this idea is only obvious after making what I thought
was a reasonable assumption about the acceleration track.
-- 
    _____     Isaac Kuo kuo@bit.csc.lsu.edu http://www.csc.lsu.edu/~kuo
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