starship-design: Deceleration scheme

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

Yes, things have been quiet.  How about some scary numbers to deaden 
things even more...

I was working out the details of the deceleration scheme I mentioned, 
converting the incident sunlight into accelerated material, using 
reaction mass from the sail, and beaming it forward to slow down.  The 
numbers look great when you have a 100% efficiency from light to 
particles.  Things get rapidly worse as the efficiency goes down.

For any efficiency percentage, n (n<1), there is an optimum ratio 
between the kinetic energy you should impart to the beam and the rest 
energy of the beam.  For n<0.5 the following formula is an excellent 
approximation:

E (rest mass) / E(kinetic energy) = [2/(n^2)] - 1.5

This ratio is 6.5 for a 50% efficiency, and 198.5 for a 10% conversion 
efficiency.  The n^-2 dependance makes things get progressively worse as 
the efficiency continues to decline.

A big number here, by the way, means you are throwing the fuel out 
slower.  While this is a plus from an engineering standpoint, it's a big 
minus when you consider the maximum speed that this method will let you 
decelerate from.  As Steve recently pointed out, for a given amount of 
Energy+Rest Mass you get the most momentum by throwing things out as 
close to light speed as possible.  A slow beam means we're not getting 
as much momentum to slow us down.

So: the equation for the maximum speed that this method will allow you 
to decelerate from is the following:

Max speed = c ln(original Mass/final Mass)
                                x {[(4-2n^2)^0.5]-1}/[(2/n^2)-1.5]

This is a strange enough formula that I'll plug in a few numbers.  For 
50% efficiency, this becomes:

Max Speed = 0.134c ln(Mo/Mf)

So if you want to decelerate from .3c you need the sail to be 1.24 as 
massive as the rest of the ship.  (I didn't do this relativistically, so 
any number higher than .3c is probably suspect)


For a 30% efficiency this drops to:

Max Speed = 0.046c ln(Mo/Mf)

Now you need the sail to be 5.5 ship masses to stop from 0.3c


For 10% efficiency, we're way down to:

Max speed = 0.005c ln(Mo/Mf), and we now need 59 times the ship mass in 
the sail.  Things are getting worse logarithmically.

And keep in mind that the "efficiency" number doesn't even take into 
account any "down time" of the particle accelerator; if the accelerator 
breaks down for a few days the beamed power starts accelerating the ship 
again, and there's nothing one can do about it until the accelerator is 
fixed.

So, given that the conversion efficiency from light to particles will 
probably never be better than 10%, this technique has some serious 
problems.

But, on the other hand, it's the only "simple" way to slow down...

Adding in extra energy from a fuel-sail concept or anti-matter, or 
adding in extra reaction mass from separate rocket capsules will help 
the situation, so we need to keep thinking about them.

Ken