# RE: The Math

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From: L. Parker
To: Brian Mansur
Cc: David; hous0042; KellySt; rddesign; Steve VanDevender;
T.L.G.vanderLinden
Subject: The Math
Date: Wednesday, March 06, 1996 10:46PM

Hi Lee

>Lee
>In regards to your request for the math on using a solar sail for more than
>just accelerating outward from the sun, I am sorry to say no. I was going
to
>attempt it, but after typing in just a few of the basic equations I
realized
>that it was an enormous task which I can't spare the time for.

Brian
I don't remember requesting that, but thanks for considering it.  Knowing it
isn't going to be easy just to calculate a few seemingly simple acceleration
problems for a solar sail just adds to this sinking feeling I've got about
my Argosy design.

>Lee
>Basically, you can do anything with a solar sail that you can with a normal
>watercraft sail. You can run, reach, tack, back up, and even perform
>"station keeping." In fact, a solar sail almost makes a better in system
>drive than it does an interstellar drive. Its best performance regime is
>when it is close to a star, not far away.

Brian
I have an idea.  Lets put this thing on the ocean, atach a surfboard and
have some wild fun.  (just kidding).  What would "station keeping" be like?

>Parker
>Sorry, it's not that I don't want to go into the math, it is more a matter
>of not wanting to type three pages on the basic physics of solar sailing
>just to get to the point where I can present deceleration (1 page) radial
>acceleration (1 page) and tangential acceleration (1 1/2 pages) adequately.
>Instead I am going to recommend you to an excellent primer that covers all
>of these topics:

Brian
Understandable.

>Parker
>You are quite right in your deduction that you are actually decelerating
>against orbital motion and thereby falling in toward the star on a
parabolic
>orbit.

Brian
Now I know that you've got me confused with someone else.  David I think is
who you are talking to.  But the attention you are giving to using our
interstellar sail for insystem flight is something I'll review when I take a
shot at writing up my Argosy summary this break.

>Parker
>A more efficient manuever would be to accelerate out from the sun (or
>other star) toward a gas giant, furl your sail and then perform a gravity
>assist manuever back towards the star on a HYPERBOLIC orbit. This >combined
with a powered perihelion manuever using a ramjet or equal) >around the star
will allow you to achieve the greatest possible amount of boost >from the
solar sail design.

Brian
I don't know if the sail could get a very fast acceleration for very long
unless it began near TC.  Given that the star's gravity will be greatest
where we get the most light pressure, I'm wonder if we wouldn't be better
off leaving the sail wrapped up while we use an ion drive to hope around
town.

>Parker
>Utilizing a maximum acceleration of 14 G

Brian
14 G!!!!  I know I can't take that.

>Parker
>this will produce a final velocity
>after boost phase of 0.003 c. for a 10,000 ton Explorer Class vehicle.

Brian
What do you mean by Explorer class?  10,000 tons does not account for
Kelly's 100,000+ ton design.  And where is your shielding mass?  Sorry, I
seem to be beating you up for a number that was probably just picked out for
convinence.  But be careful to remember that we presently don't have any
clue on how to make a decent sized ship that can protect a human crew
without a lot of heavy shielding.  Of course there is still that discussion

>Parker
>This
>would put it at Alpha Centauri in about 1200 years. Higher accelerations
(as
>much as 400 G) are possible but not for manned vehicles. The limiting
factor
>is of course the tensile strength of the sail and cables.

Brian
To Discusion group.  The strength of the cables and sails has, of late,
become a concern to me.  See my Problems mail about these concerns

>Parker
>A Pathfinder type
>vehicle could make the same trip in about 350 years. This all assumes no
>further acceleration from the sail beyond boost phase. (Its practically
>useless beyond a certain distance unless you are going to use a LOT of
>lasers or something.)

>There are additional considerations such as skin temperature at perihelion
>to consider, but most of these values were worked out in the late 80's and
>pronounced feasible.
>
>Rather than the wire mesh design I keep hearing here, I would suggest a
thin
>film metalloid connected in a "parachute" arrangement for a manned mission.

Brian
I've noticed it may be more efficient to do just you're suggesting.  Got to
go.

>Parker
>Such a sail can be made in space using vacuum deposition techniques and
>theoretically provides the highest possible thrust to weight ratio as well
>as being easy to manufacture. The materials for 100 sq km of such a sail
>would fit in one space shuttle payload bay. You would probably want to be
>able to manufacture several such sails during the course of the mission in
>case of damage.

Brian
Since they are going to be relatively unprotected during high %c travel, I
wonder if even one good strike from a dust partcle won't cause a nuke
explosion and rip a really big hole.  Definitely handy to have spare sheets.

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