RE: starship-design: Deceleration scheme

["L. Parker" <lparker@cacaphony.net>]

Timothy,

> No, but by then it is neglectable:

Agreed

> Neat formula, but how did you get from "as" to "V@"?
> And where did this "l" come from?

I skipped a lot of ASCII math, I TOLD you I don't like doing math on this forum :-P

> I haven't seen any relation between the sail size and the sail mass. That
> relation is the most important one when you are talking about sails.
> This alone makes your formula quite doubtful.
 
Umm, sorry, again, I skipped a lot.

> True, if you can make it light enough per square mile, then you indeed can
> reach relativistic velocities. But I think there aren't materials that work
> under the circumstances we need.

Although true if possible, I don't think we can get light enough for a manned
ship. I am quite certain it can be done for unmanned probes.

> In the rest of your letter where you show that for a sail WITH ship it
> indeed isn't possible to slow down from relativistic velocities.

Actually, what I said was that we can't accelerate a manned ship up to relativistic 
velocities without additional thrust besides the sun. And if we do use additional 
thrust, you can't slow it down in time because that extra thrust will not be present 
at the other end. All other things being equal, if acceleration out from the sun = A 
then deceleration at the other end must also be equal to or greater than A. Unless you 
are planning on purposefully not using some available acceleration at this end, in 
which case, what is the point?

> This isn't true either (ASSUMING you can make a sail without a ship that can
> slow down from relativistic speeds).
> You simply would need to make the sail larger so that the "total mass" per
> "area of sail" would go down to similar numbers as for a sail without ship.

True to a point. As you pointed out there is a point at which Ps approaches zero
close enough that it can be neglected. If you are working within realistic limits
for maximum acceleration, then there is a corresponding maximum sail size that will
produce that acceleration while close to the sun. The equations I used had already 
been optimized (sail size) to max at 14g for a very brief time during the initial 
acceleration.

Although you could increase sail area somewhat as you moved farther out to compensate 
for the steadily decreasing thrust, no matter what you do your limits (areal density, acceleration per unit of sail area, inverse square) are going to rapidly converge 
to where you won't get any thrust no matter how much bigger you make the sail.

I am not going to work through the math. I don't like doing ASCII math and you've 
reached my limit!

Lee Parker

                                                          (o o)
------------------------------------------------------oOO--(_)--OOo---------
"Thomas Godfrey, a self-taught mathematician, great in his way . . . knew 
little out of his way, and was not a pleasing companion; as, like most 
great mathematicians I have met with, he expected universal precision in 
everything said, or was forever denying or distinguishing upon trifles, to 
the disturbance of all conversation." 


-- Benjamin Franklin (1706-1790), Autobiography