starship-design: further debate

[wharton@physics.ucla.edu (Ken Wharton)]

Steve,

There IS a trade-off here.  You are right that you can always get more 
momentum out of a given amount of mass/energy by converting as much of 
it to energy as possible.  But you're automatically assuming we would 
WANT get the highest momentum/fuel mass ratio.

Here's an example.  We have an engine capable of coverting 100% of the 
fuel mass into pure energy (photons).  But Timothy thinks it's optimal 
to not convert that much and decides to only convert a small percentage 
to pure energy, and use that percentage to kick out the rest of the fuel 
(at 0.1c, I think he derived).  I'm not sure of the exact number, but I 
think this corresponds to converting only 1% of the fuel mass into 
energy, and using the other 99% as reaction mass.  This, he says, is the 
optimum design.

Not so!  You respond.  You can get more momentum per fuel mass if you 
convert it all to photons.  (and you are correct).  So you design a ship 
that beams only photons out the back, and you find it needs to carry 
less mass in fuel.  Because you have a smaller mass ship, it also needs 
less thrust.  Ah HA, you say: this is the true optimal design.

But Timothy's point is that *The amount of fuel you save is less than a 
factor of 100*

Why does that matter?  Because your ship converts 100 times more fuel to 
energy than Timothy's ship; he only had to convert 1%, you convert 100%.  
And let's guess you can do it with twenty times less fuel; you still 
need 5 times as much ENERGY (this is Kinetic energy, that you MAKE 
onship) than Timothy did.  Timothy has optimized his design to minimize 
*Kinetic Energy*, not total fuel mass.

So although you've minimized the mass of the ship, you still need an 
engine that can handle 5 times the energy as Timothy's design.  You need 
to beam five times the energy out the back.  Timothy's point is that if 
you try to minimize the amount of Energy your onboard reactors need to 
produce (from your fuel), you don't want to use photons as reaction 
mass.

Now, maybe one day antimatter will be so cheap that it won't matter, and 
maybe one day we won't care about how much energy we're processing, in 
which case we'll go your route.  But as long as matter is at least five 
times cheaper than antimatter, Timothy's design has the lowest cost.  
And five times lower power-production requirements.  

As I said before, it's all a question of what you're trying to minimize.

Ken