# Re: starship-design: Required microwave-antenna size. 100-light-year trip.

```At 1:22 AM 10/24/96, DotarSojat@aol.com (Rex Finke)  wrote:
--------
>The range boundary between the "near" and "far" fields can be
>defined as the distance at which the focused image spot size is
>equal to the size of the beam-forming aperture, and at that range
>the spot size is that given by Fraunhofer diffraction (with a
>factor of 2 to go from radius to diameter), so--
>     spot diameter = De = range * 2 * 1.22 * lambda/De

???  Doesn't   De = range * 2 * 1.22 * lambda/De
Reduce to       1 = range * 2 * 1.22 * lambda

>If we set the Fraunhofer-diffraction angular width equal to the
>angle subtended by the sail diameter (Ds) at the range R, we can
>get an expression for the diameter of the emitting antenna (De)
>that is required to put "84 percent" of the emitted power within
>the area of the sail:
>     De = 2.44 * lambda * R/Ds   .
>
>For microwaves with lambda = 1 cm and a sail diameter of 100 km,
>say, the required diameter of the emitting antenna grows 2.31
>million km for each light-year of distance to the sail, to keep
>the main lobe just within the sail diameter.  This is for an
>antenna whose figure (shape) is correct to a fraction of a wave-
>length.
>
>For an emitting-antenna diameter of 2.31 million km (and wave-
>length of 1 cm) for a 1-lt-yr distance to the sail, the boundary
>between near and far fields is at a range of about 23 thousand
>lt-yr, far enough away to say we're operating in the near field.
>[Note: at 1 lt-yr distance, the spot size is
>(1 lt-yr/23,000 lt-yr) * 2.31 x 10^6 km = 100 km, the diameter of
>the sail, as desired.]
>
>Are we prepared to build an expanding antenna this large?  It
>looks as if the M(aser)ARS should be a L(aser)ARS.  For any wave-
>length, however, figure control is going to remain a headache.

This is much better than I would have guessed.  By the way when you say
that:  "This is for an antenna whose figure (shape) is correct to a
fraction of a wave-length."  Is this lateral, or for aft drift?  I'm of
course thinking of a synthetic appiture phased array antena made out of
syncronised free floating, solar powered, orbital power platforms.  If you
assume the platforms are in earths orbit around the sun thats a 306 million
kilometer ring around the sun.  Thou computing their position accuratly
enough to phase lock their output to the desired precision will be a pain!
Also you couldn't focus the beam to the ships exact sail size since you
couldn't know where exactly the ship is.  So you'ld need to focus to a
wider beam area (say ten times wider) and give the ship some ara to drift
around in.

Questions:
How much range deviation can you tolerate?  Since the beam is being aimed
at a ship you can't see in real time.  You'ld have to expect it would drift
ahead or behind the exact focus spot.  How much slack is allowed?

What is the lateral deviation of the beam?  I.E. whats the power per m^2 in
the center vs the edge of the focused spot?  The differences would distort
the sail and alter the ships course and acceleration.

As mentioned above, how precicely can we measure the possition of an object
floating in space?  Assuming each microwave emmiter platform has laser
ranging info to each/some of the others.  Can you get the nessisary
possitional accuracy?  (Within a couple MM?)  Note you don't need to
control the position that accurately, just know what it is so you can
compensate for it.

Kelly

----------------------------------------------------------------------
Kelly Starks                    Phone: (219) 429-7066    Fax: (219) 429-6859
Sr. Systems Engineer                                     Mail Stop: 10-39
Hughes defense Communications
1010 Production Road, Fort Wayne, IN 46808-4106
Email:  kgstar@most.fw.hac.com
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