[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

starship-design: Back from the wed

Gee - can't a guy go get married these days without coming home to 
hundreds of emails??

I have to confess I didn't read them all in depth, but I liked the 
recent idea of the Fuel/Sail, building the sail out of fusion materials.  
It got me thinking about using the sail for reaction mass for slowing 
down, and our months-old discussion about momentum/energy (P/E) ratios 
came to mind.  (For all I know this has been discussed at length, so 
forgive me if I'm going over old ground)  Photons have a very 
inefficient P/E, compared to massive particles, and I started thinking 
about catching beamed photons, and then transferring the energy into a 
massive particle, and shooting it forward.  Assuming no energy is lost, 
the massive particle would have a higher P/E, and therefore you would 
lose more momentum to the particle (for a given energy) than you would 
gain from catching the photon and using it in the first place.

The key equation is: E^2 = (K + mc^2)^2 = P^2 c^2 + M^2 c^4

This holds for both photons (M=0) and massive particles, where E is the 
total energy (including rest mass) and K is the kinetic energy (really 
all we care about)

This simplifies to P^2 = K^2 / c^2 + 2 K M

At this point I'm going to define E as the kinetic energy, and we can 
get replace those K's:

P = [(E^2 / c^2) + 2 E M]^0.5

So if you "catch" some beamed energy (say 'E' joules) you gain a 
momentum of E/c.  But if you can convert that energy to kinetic energy, 
and accelerate part of the sail forward, you can get a net backwards 
momentum out of the whole deal.  If you want to have a net momentum loss 
of 2E/c (the same as your momentum gain for a reflecting sail), it turns 
out that every particle you accelerate forward must have a kinetic 
energy equal to exactly 1/4 of its rest mass, so M = 4E/c^2, and P = -
3E/c (backwards).  Adding this to the E/c you gained from catching the 
beamed energy in the first place gives you a momentum loss of exactly -
2E/c; the same as you momentum gain during the accleration portion of 
the journey.

Of course, things get more complicated once the ship starts losing mass.  
Fortunately, it works somewhat in our favor; less momentum is needed to 
slow the ship down when it's lighter.  Turns out that accelerating a 
"mere" half of the total ship mass with the M/E=4/c^2 mass/energy ratio 
will slow the ship down from a third of lightspeed.  Faster trips will 
require a larger Sail Mass / Ship Mass ratio.  (I didn't do this 
relativistically, but I know some of you have those equations 

The biggest problem with losing mass (besides whittling away the sail 
without destroying it) will be that the sail will get too small too 
fast:  we won't be able to "catch" all the energy once we start using up 
the sail as reaction mass.  The amount of energy we need will drop in 
proportion to the mass of the ship as a whole, but the amount of energy 
we can catch (due to sail area) will drop faster, as the mass of the 
sail alone.  

However, given that we are talking about mass ratios of 400, these two 
masses are pretty much identical; with a sail that big the two values 
drop should drop pretty much at the same rate.  

So now the deceleration problem simply involves converting light energy 
to particle energy.  Clearly the parabola-shaped sail will reflect the 
beamed power to an onboard engine.  But not only do you have to have a 
decent conversion efficiency, but we're talking about huge amounts of 
energy we have to manipulate.  Even if the "energy storage time" between 
receiving the power and shooting it off is very small, the net power the 
engine would have to handle would be terrible.  

Clearly a "passive-engine" scenario like the plasma mirror would be 
simplest, but we have to give a lot of photons to each proton to get the 
energy/mass ratio to come out right.  Each proton will need 230GeV 
imparted to it, and it seems unlikely we can give a proton that much 
energy from a microwave beam without an "active" engine, where the 
energy distribution is manipulated by an accelerating structure.  For 
mm-sized microwaves, this is 10^15 photons per proton!  Perhaps starting 
off with a lower proton energy would be okay; if you transfer all the 
energy, the slower the protons the more you slow down, paradoxically 
enough.  The problem with slow protons, though, is that you need a LOT 
of them to do the job of a few fast ones.  If you shoot off too much 
mass too slow you'll run out of sail material before you can slow down 

Run with this, someone...

Ken Wharton

"No brakes?  Well, no point in steering now"
(Bob MacKenzie, Strange Brew)