# starship-design: Deceleration scheme

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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

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