starship-design: Re: Beam properties, control, etc.

```Rex wrote a small summary of problems:

>1. Depth of focus
>
>Assume the beam from a 2.31E6-km-diameter microwave antenna is
>focused to a sail (beam-spot) diameter of 100 km at a distance of
>1 lt-yr.  At the distance from the focus that the beam cross-sec-
>tion has grown from the area at the focus by 10 percent (power per
>unit area reduced by about 10 percent), say, the radius of the
>beam has grown by 100 km * [sqrt(1.1) - 1]/2, or about 2.4 km.
>The distance from the focus for that growth is (2.4/2.31E6) *
>1 lt-yr, or approximately 1E-6 lt-yr.
>
>So, the sail/ship has to stay within about 1.E-6 lt-yr of the
>focus to keep the power from dropping off by more than 10 percent.

Hmmm, how smart of me (not so). All the time I was thinking of an almost
parallel beam (as far as interference allows) instead of one that is focused
at a certain point. This means that the starship should not just follow the
beam, but more precisely it should follow the focussing point.

I also thought of the following: How bright can we make our laser/maser
array? How many Watts per square meter is realistic? Does this also limit
the minimal size?

>4. Pointing compensations
>   a. Direction: to ship or to destination
>
>I believe Timothy has made the case for pointing the beam at the
>destination star quite well.  Let the sail/ship steer to stay in
>the beam (see below).

the beaming station could make things easier for the ship by focussing on an
as straight possible track. Of course it can not sense where the ship is,
but it should just focus along a predestined path.
The ship would still needs to take care of staying just in front of the
focuspoint of the beam.
To make this possible there should be a small overcapacity in the system, so
that when the ship would drift off, there would be enough power to get back
on track. And thus when it was at the focuspoint, it would not use all the
power available.

>5. Sail/ship guidance
>
>The sail/ship can have outriggers beyond the edge of the sail to
>sense the edge of the beam and provide steering-correction inputs
>to adjust the tilt of the sail to stay at the radial center of the
>beam.
>
>The acceleration of the sail/ship will depend on its distance from
>the focus.  (Operating in the near field has some advantages).  A
>computer simulation of the sail/ship's motion based on a power
>level reduced by a safety factor from that at the focus can be
>made to provide a projected safe position of the sail/ship at any
>time.

Yes, every radial deviation from the center will push the ship further away
from the center. The pressure on one side of the sail will become less than
on the other side, this means the sail (and the ship) will turn/tilt.
Unfortunately the way in which the sail will be tilted, will make things
even worse.

>If the focus is placed behind the projected safe position of the
>sail/ship during the actual flight, any lag in acceleration of the
>sail below the "safe" level will drop it back closer to the focus
>where the power is greater.  The higher power there will drive it
>forward again toward the safe position, in a stable control
>condition at a power level between full (at the focus) and "safe."

To bad we can't make the sides of the beam more intense than the center,
that would create a minimum, which would automatically keep the ship in the
beam.

>(I think I might have described this better if I had first written
>the control equation and observed its effects in a simulation.)
>
>6. Effects of reduced wavelength (some already covered by Timothy/
>Kelly/Kevin)
>
>While reducing the wavelength of the radiation in the beam to that
>of blue-green light allows the required aperture to be reduced
>to "only" 385 km, the "antenna" becomes a mirror.  A mirror has
>the problem (among others) of maintaining its reflectivity over
>long periods in the presence of hazards of the space environment
>such as micrometeoroid erosion.

True, therefore it would be interesting to know how much micrometeoroids
would exist in interstellar space.
However, since we have a smaller mirror it may be easier to shield it on the
back side(=the non reflecting side, pointing to TC).

Tim

```